high-beta cavity design - cernaccelconf.web.cern.ch/accelconf/srf2009/contents/... ·...

1

High-beta Cavity Design

1 SW Operation with SRF RF Cavity2 Pill Box Cavity3 Figure of merits of SRF Cavity Design 4 Criteria for Multi-Cell Structures5 Example of SRF High-beta Cavities

KSaitoHigh Energy Accelerator Research Organization (KEK)

Accelerator Lab

KSaito SRF09 Tutorial on 17 Sept 2009

AcknowledgementIn this lecture I used many slides by Dr JSektuwitz DESY which he made nice lecture in China I would like to thank for him very much

2

1 Sanding Wave (SW) Operation and Standing Wave in SRF Cavity

3

6 Multi-cell Structures and Weakly Coupled Structures Cavities

Synchronic acceleration and max of (RQ)accharr lactive =Nlcell= Ncszlig(2f) and the injection takes place at an optimum phase φopt which ensures that particles will arrive at the mid-plane of the first cell when Eacc reaches its maximum (+q passing to the right) or minimum (-q passing to the right)

Ez(r=0z)

lcell

lactive

v = szligc

s

-

+

-

+

-

π-phase advancecell-to-cell

SW Scheme in SRF Cavity Operation

Standing wave (CW) is used in SRF cavity acceleration

ΤΜ010π-mode

for electron β=1 proton β lt 1β=vc

2cellcLf

β λ λsdot= =

4

Transit Time Factor Due to SW Operation

d=λ2

v=c

0 0t z= =

z c t= sdot

6 6Tt z λ

= = 4 4Tt z λ

= =5 5 12 12Tt z λ

= = 2 2Tt z λ

= =

0 0 00 0 0

0

sin2( 0 ) ( 0 )

2 Transit time factor

2 0637 (for Pill Box Cavity)

z zi id d di t c cz z

dcV E r z e dz E r z e dz E e dz E d E d Td

cT

T

VEacc E Td

ω ωω

ω

ω

π

⎛ ⎞⎜ ⎟⎝ ⎠= = = = = = = sdot

= =

equiv =

int int int

Acceleration efficiency is automatically reduced by ~ 40 in the SW scheme

Ze-e- e- e- e- e-

5

2 Pill Box Cavity

6

LC Equivalent Circuit of Cavity

I = minusdQdt

Q = CV V = LdIdt

+ RI

d2Vdt

+RL

⎛ ⎝ ⎜

⎞ ⎠ ⎟

dVdt

+1

LC⎛ ⎝ ⎜

⎞ ⎠ ⎟ = 0 V(t ) = VO exp(minusα + iω )t

(minusα + iω )2 + (minusα + iω )RL

⎛ ⎝ ⎜

⎞ ⎠ ⎟ +

1LC

⎛ ⎝ ⎜

⎞ ⎠ ⎟ = 0

α =R2L

ω2 =1

LCminus

R2

4L2

R ltlt L ω O2 =

1LC

rArr f =1

2π LC

Q-value of the circuit

Q proportional to 1R

Stored Energy ( )Powerlosssec ( )

=2

P t LQdP t dt R

ω ω ω

ωα

equiv sdot = sdot = sdot

7

Electro-magnetic field in a waveguideMaxwell equations in a waveguide

22

2

=0 =0 =0 =0

0

( ) ( )exp( ) wavevector( ) ( )exp( )

i ic c

cx y z t x y ikz i t kx y x t x y ikz i t

ω ωμε ρ

ωμε

ωω

nablatimes = nablasdot nablatimes = minus nablasdot

⎛ ⎞⎧ ⎫nabla + =⎨ ⎬⎜ ⎟⎩ ⎭⎝ ⎠

= plusmn minus= plusmn minus

E B B B E E j

EB

E EB B

2 22 2 2 2

2 2

22

2

22

2

( 0 =

1

1

t t z z t z z t

zt t z t z

zt t z t z

k E Bc z

B i Ez c

kc

E i Bz c

kc

ωεμ

ωεμωεμ

ωωεμ

⎡ ⎤ part⎧ ⎫nabla + minus = nabla equiv nabla minus = + +⎨ ⎬⎢ ⎥ part⎩ ⎭⎣ ⎦⎡ part ⎤⎛ ⎞= nabla + timesnabla⎜ ⎟⎢ ⎥part⎛ ⎞ ⎝ ⎠⎣ ⎦minus⎜ ⎟

⎝ ⎠⎡ part ⎤⎛ ⎞= nabla minus timesnabla⎜ ⎟⎢ ⎥part⎛ ⎞ ⎝ ⎠⎣ ⎦minus⎜ ⎟

⎝ ⎠

Ε E e E B e BB

B e

E e

Homework ILead this formula

mode 0 0mode 0 = 0

z z

z z

TM B ETE B E

= nene

8

TM- Modes TM-mode

Bz = 0 Ez ne 0 Can accelerate beam Beam

Solve the eigenvalue problemget k and Ez

[ ]22

2

22

2

22 2

2

1

( ) 0

t z t z

zt t

t z z

ic E

kc

Ez

kc

E k Ec

ωεμ

ωεμ

ωεμ

ωεμ

= timesnabla⎛ ⎞

minus⎜ ⎟⎝ ⎠

part⎛ ⎞= nabla ⎜ ⎟part⎛ ⎞ ⎝ ⎠minus⎜ ⎟⎝ ⎠

⎡ ⎤nabla + minus =⎢ ⎥

⎣ ⎦

B e

E

Boundary condition E z S = 0 ( Q on the surface of perfect conductoBzn S = 0 ( on the surface

but automatically satisfied by the TM- mode condition)

0times =n E

0sdot =n BQ

Similar for TE modes which kicks beamhelliphellip

9

Eigen-value problemψ(x y ) = Ez(x y ) for TM- mode or Bz(x y) for TE- mode

From the boundary condition

γ2 = γ λ

2 ψ = ψ λ (λ = 1 2L) kλ2 = εμ

ω 2

c 2 minus γ λ2

If then is an imaginal number

The wave is dampedtrapped in the waveguide if surface resistance largesmall

cutoff frequency

When wave number is a real number then the

c k

c

k

λλ

λλ

λ λ

γω

εμ

γω

εμω ω

lt

=

ge

L

wave can propagate into the waveguide

( )2 2

22 2

2

0 0 (for TM-Modes) or 0 (for TE-Modes)

0

t S Sn

kc

γ ψ ψ ψ

ωγ εμ

partnabla + = = =

part

= sdot minus ge

r

10

0 0

mnp

02

mode

cos( ) ( )exp( ) 0

( )cos( ) exp( ) cos( ) ( )exp( )

cos( ) ( )exp(

m n p

m nz o m z

m n p m nmr r m

m n p

m nm

m n p

TM

E E kz J r im Ba

E miE p JpE z im B kz J r imd a

E mp pE z J r id adcθ

ρθ

εμω ρπ ρπ θ θγ ρ γ

ρπ πγ

minus

= minus =

part= minus = minus minus

part

= minus 0

2 2 2

2 2

( )) cos( )exp( )

resonace frequency

m n p m

m n p

m nm n p m n p

iE Jm B kz im

c

c pfa d

θ

εμω ρθ θ

γ ρ

ρ πωεμ

part= minus

part

rArr = +

TEmnp Modes

)sin()sin(02 d

zpmra

JErm

kiE mn

mrπθρωε

⎟⎠⎞

⎜⎝⎛=

)sin()cos(02 d

zpmra

JEak

iE mnm

mn πθρρωεθ ⎟

⎠⎞

⎜⎝⎛=

0=zE

)cos()cos(102 d

zpmra

JEdp

kH mn

mrπθρπ

⎟⎠⎞

⎜⎝⎛=

)cos()sin(102 d

zpmra

JErm

dp

kH mn

mπθρπ

θ ⎟⎠⎞

⎜⎝⎛minus=

)sin()cos(0 d

zpmra

JEH mnmz

πθρ⎟⎠⎞

⎜⎝⎛=

2222

002

2

⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=rArr⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

dp

acf

dp

amnmn πρ

ππρμεωResonance frequency

11

TMmnp Modes

d

2a

Ez

ｒ=a

J0(ρ01) J0(ρ02) J1(ρ11)

Acceleration Modes

12

TEmnp Modes

Z

Kick Modes

13

4 Figure of merits of Cavity Design

Figure of Merits of The RF Cavity DesignItems Notation

1) Surface resistance RS [Ω]2) RF dissipation Ploss[W]3) Acceleration gradient V[V]3) Unloaded Q QO

4) Geometrical factor Γ[Ω]5) Shunt Impedance Rsh[Ω]6) R over Q (RQ) [Ω]7) Acceleration gradient Eacc[Vm]

8) Ratio of the surface peak electric field vs Eacc EpEacc [Oe(MVm)

9) Ratio of the surface magnetic field vs Eacc HpEacc

10) HOM loss factor11) Field flatness factor aff

12) Cell to cell coupling kCC

κ κperp

15

Surface Resistance

Surface Impedance

ts s

t Surface

EZ R iXH k

μωequiv + equiv =

Rs =μω2σ

=1σ

μσω2

=1

σδ2

S Sloss1P R H2 S

dS= sdot int

Homework IILead the formula of Rs for good electric conductor

Rs Surface resistance

HB = 0 E + 0tED = 0 H E 0t

J = E (Ohms Law)

μ

ε σ

σ

partnabla sdot nablatimes =

partpart

nabla sdot nablatimes minus minus =part

rr r

rr r r

r rt t

2 2 t

t

1H (xt) = [k E (xt)]

E (xt)[ k ( ) ] = 0

H (xt)i

μω

εμω μωσ

times

⎧ ⎫⎪ ⎪minus + ⎨ ⎬⎪ ⎪⎩ ⎭

rr r r

r r

r r

t

t

E(xt) = E (xt) + E (xt)

H(xt) = H (xt) + H (xt)l

l

r r rr r r

r r rr r r

t t

For the transvers

Plane wave E (xt) = E (0) exp( k x - t)i ωsdot sdotrr rr r

Maxwell Equations

16

U equiv stored energy PlossSurface RF Heating

Unloaded QO

For acceleration mode (TM010) the higher Qo is better

2 2

2

1 12 2

12

V V

loss S SS

Oloss

U E dV H dV

P R H dS

UQP

ε μ

ω

= sdot = sdot

= sdot

equiv

int int

int

Charismatic RF Parameter of Cavity

Shunt Impedance2

[ ]shloss

VRP

Ω equiv

Acceleration Voltage0

[V] on the beam axiseffLV Edz= int

This means the efficiency of the acceleration

17

3 RF Parameters Cavities

(RQ)2

( ) ( )sh OVR Q R Q

Uωequiv =

This means how much energy is concentrated on beam axisThis does not depend on material but only cavity shapeThis means the goodness of the cavity shape

Geometrical factor

2

2[ ]

12

VO S

SS

H dVQ R

H dS

ωΓ Ω equiv sdot = int

intWhen you know the Γ using a computer code you can calculate the surface resistance RS from the measured QO value

Γ is about 270Ω for β=1 cavities with elliptical or spherical shape

Charismatic RF Parameter of Cavity continued

18

Con

tour

plo

t of

E

Con

tour

plo

t of

B

lactive

acc

peak

EE

acc

peak

EB

Smaller value is preferred againstelectron emission phenomenon

Ratio shows the limit in Eacc due tothe break-down of superconduc-tivity (Nb ~2000 Oe )

( )acc loss O loss O

eff

R QE P Q Z P Q

L= sdot sdot = sdot sdotGradient


19

When ultra relativistic point charge q passes empty cavity

Longitudinal and Transverse Loss Factors

Er ~1r

Cone ~1γro

HOM modes are excited in the cavityIf those are damped fast enough the following beam feel them and can be kicked Thus the beam can be degradated

20

HOM nth (RQ)n a ldquomeasurerdquo of the energy exchange between point charge and mode n

mode n ωn En Hn Trajectory of the point charge qassumed here to be a straight line

Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv

3 RF Parameters Cavities(RQ)n of n-th HOM

21

The amount of energy lost by charge q to the cavity isΔUq = kmiddotq2 for monopole modes (max on axis)ΔUq = kmiddotq2 for non monopole modes (off axis)

where k and k(r) are loss factors for the monopole and transverse modes respectively

The induced E-H field (wake) is a superposition of cavity eigenmodes(monopoles and others) having the En(rφz) field along the trajectory

4)QR(k nn

n||sdot

=ωp

For individual mode n and point-like charge

Similar for other loss factorshelliphellip

3 RF Parameters CavitiesLongitudinal and Transverse Loss Factors JSekutwitzrsquos Slide

These harmful HOM power should be take out from the cavityDr Noguchi will make a lecture about the HOM coupler design

22

This is an empirical correction based on intuition

szligkNacc

2

ff sdot=

Field flatness factor for elliptical cavities with arbitrary szlig=vc

1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2

The same error partx causes bigger partf

when a cell is thinner

Cells which geometric szlig lt1 are more sensitive to shape errors

Field Flatness Factor affJSekutwitzrsquos Slide

ffA fa

A fΔ Δ

= sdot

23

The last parameter relevant for multi-cell accelerating structures is the coupling kcc

between cells for the accelerating mode pass-band (Fundamental Mode pass-band)

2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -

no Er (in general transverse E field) component at the symmetry plane

The normalized difference between these frequencies is a measure of the Poynting vector (energy flow via the coupling region)

no Hφ (in general transverse H field) component at the symmetry plane

ωπωo

Cell to cell coupling kCC

24

SphericalElliptical Shape in SRF cavity design

Choose spherical shape to reduce multipacting

Multipacting

Design of SRF cavity is usually done with spherical or Elliptical shapes

R Parodi (1979) presented first spherical C-band cavity with much less multipactingbarrier than other cavities at that timeP Kneisel (early 80rsquos) proposed for the DESY experiment the elliptical shape of 1 GHzcavity preserving good performance of the spherical one and stiffer mechanically

The RF cavity design tool will be given by Dr U van Rienen In this tutorial

25

5 Geometry and Criteria for Cavity Design Cavities

RF parameters summary

FM (RQ) G EpeakEacc BpeakEacc kcc

HOM k k

There are 7 parameters we want to optimize for a inner cell

iris ellipsis half-axis hr hz

iris radius ri

equator ellipsis half-axis hr hz

Geometry

We begin with inner cells design because these cells ldquodominaterdquo parameters of a multi-cell superconducting accelerating structure

There is some kind of conflict 7 parameters and only 5 variables to ldquotunerdquo

Optimization of Cell Shape

JSekutwitzrsquos Slide

26A Mosnier E Haebel SRF Workshop 1991

Examplef = 15 GHz

5 Geometry and Criteria for Cavity Design Cavities Effect of Cavity Aperture on RF Parameters

27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)

(RQ) = 86 Ω Bpeak Eacc = 46 mT(MVm)Epeak Eacc = 32


Aperture Effects on κ and κᅩ)JSekutwitzrsquos Slide

28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)

Aperture Effect on Cell to Cell Coupling (κCC)JSekutwitzrsquos Slide

29

Criteria RF-parameter Improves when Cavity examples

Operation at high gradient

Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV

Low cryogenic losses (RQ) Γri

Equator shape

LL CEBAF-12 GeV

LL- ILC cavity

High Ibeam harrLow HOM impedance

k k riB-Factory

RHIC cooling

5 Geometry and Criteria for Cavity Design Cavities General Trends of Cavity Optimization on RF Geometrical Parameters


iris radius ri


30

What about accelerating mode frequency of a superconducting cavity

fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f

Choice of the RF Frequency


31

Frequency Choice of the SRF Cavity

2 21 ( ) exp( )2loss s S acc SS

B

AP R H dS E R BCS fT k T

Δ= prop = sdot sdot minusint

Cryogenic power

Cavity fabrication cost

f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)

Cost + Existing RF source

L-band cavity is preferred and it is operated at 2K to reduce the cryogenic power

32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198

BpeakEacc [mT(MVm)] 415

RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840

The inner cell geometry was optimize with respect to low EpeakEacc and coupling kcc

At that time (1992) the field emission phenomenon and field flatness were of concern no onewas thinking about reaching the magnetic limit

Inner cell Contour of E field

TESLA Cavity Inner Cell Shape

33

High Gradient Shapes

Cavity shape designs with low HpEacc

TTF TESLA shapeReentrant (RE) Cornell Univ Low Loss(LL) JLABDESYIchiroｰSingle(IS) KEK

from JSekutowicz lecture Note

TESLA LL RE IS

Diameter [mm] 70 60 66 61

EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03

High pressuer water rinsing

(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07

2nd Breakthrough1st Breakthrough

35

4 Criteria for Multi-cell StructuresSingle-cell is attractive from the RF-point of view

Easier to manage HOM dampingNo field flatness problemInput coupler transfers less powerEasy for cleaning and preparationBut it is expensive to base even a smalllinear accelerator on the single cell We doit only for very high beam current machines

A multi-cell structure is less expensive and offers higher real-estate gradient but

Field flatness (stored energy) in cells becomessensitive to frequency errors of individual cellsOther problems arise HOM trappinghellip

How to decide the number of cells

36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot

Field flatness factor

Beam pipe has no acceleration beamBP reduce the efficiency

Multi-cell is more efficient

HOM RF

2

ffcc

Nak

=

Parameters considered with N

HOM trapped mode

Input handling power

More serious within creasing N

NINPUTP prop

Handling Easy to bend Difficult to preparation hellip

37

Many years of experience with heat treatment chemical treatment handling and assembly allowsone to preserve tuning of cavities even for those with bigger N and weaker kcc

For the TESLA cavities field flatness is better than 95

OriginalCornellN = 5

HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N

6 Multi-cell Structures and Weakly Coupled Structures Cavities Effect of N on Field Flatness Sensitivity FactorJSekutwitzrsquos Slide

38

No fields at HOM couplers positions which are always placed at end beam tubes

e-m fields at HOM couplers positions

N = 17

N = 13

N = 9

N = 5

HOM trapping vs NJSekutwitzrsquos Slide

Cure for the trapped mode Make the bore radius largerBreak mirror symmetry

39

HOM couplers limit RF-performance of sc cavities when they are placed on cells no E-H fields at HOM couplers positions which

are always placed at end beam tubes

The HOM trapping mechanism is similar to the FM field profile unflatness mechanism

weak coupling HOM cell-to-cell kccHOM

difference in HOM frequency of end-cell and inner-cell

f = 2385 MHz

That is why they hardly resonate

togetherf = 2415 MHz

12 Trapping of Modes within Cavities HOM HOM Issue with Multi-Cell StructureJSekutwitzrsquos Slide

40

6 Multi-cell Structures and Weakly Coupled Structures Cavities Adjustment of End-Cells

The geometry of end-cells differs from the geometry of inner cells due to the attached beam tubes

Their function is multi-folded and their geometry must fulfill three requirements

field flatness and frequency of the accelerating modefield strength of the accelerating mode at FPC location enabling operation with matched Qextfields strength of dangerous HOMs ensuring their required damping by means of HOM couplers orand beam line absorbers

All three make design of the end-cells more difficult than inner cells

+ +


41

Power capability of fundamental power couplers vs N

When Ibeam and Eacc are specified and a superconducting multi-cell structure does not operate in the energy recovery mode

PINPUT ~ N

6 Multi-cell Structures and Weakly Coupled Structures Cavities Capable Input Power on N

Coupler handling power limits the small N in the intensity frontier machine like KEK B(N=1)

KEKB Acceleration beam current gt 1 A

42

2 TESLA Cavities and Auxiliaries as ILC Baseline Design

TTF 9-cells Contour of E field

7 identical inner cellsEnd-cell 1 End-cell 2

f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271

Active length [mm] 1038

The cavity was designed in 1992 (A Mosnier D Proch and JS )

TESLAILC Baseline Cavity

43

CEBAFOriginalCornell

szlig=1

CEBAF -12High

Gradientszlig=1

CEBAF -12LowLossszlig=1

TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085

new new newnewExamples of Inner cells

Overview of CavitiesJSekutwitzrsquos Slide

β vs RF parameters β smallerEpEacc largerHpEacc larger(RQ) smaller

44

5 Example of SRF High-beta Cavities

45

Type No of cavities Pbeamcavity[kW]

PHOM cavity[kW]

x 8Single-cell with max

Ibeam

Ibeam= 134 A1389 bunches

cw350 16

x 16

Multi-cell with max

Ibeam

Ibeam le 40 mA180 bunches

cw60 013

x 1 Multi-cell with max Eacc

Eacc= 35 MVm13mspulse 1Hz

PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz

Cavities operating with highest Ibeam or Eacc

6 Multi-cell Structures and Weakly Coupled Structures Cavities JSekutwitzrsquos Slide

46

Type No cavities Pbeamcavity[kW]

PHOM cavity[kW]

x 33 Multi-cell with max

Ibeam

Ibeam=38 (59 ) mA13mspulseDF = 6

240 (366) 006 peak

x 48 482 006 peak

x 8Multi-cell with max

Eacc


PRF146 lt 002gt

Cavities which will operate with high Ibeam in the near future

SNS szlig= 061 0805 GHz

SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5


Electro-magnetic field in a waveguide

TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13

Figure of Merits of The RF Cavity Design

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

2

1 Sanding Wave (SW) Operation and Standing Wave in SRF Cavity

3



Ez(r=0z)

lcell

lactive

v = szligc

s

-

+

-

+

-




ΤΜ010π-mode


2cellcLf

β λ λsdot= =

4


d=λ2

v=c

0 0t z= =

z c t= sdot

6 6Tt z λ

= = 4 4Tt z λ

= =5 5 12 12Tt z λ

= = 2 2Tt z λ

= =

0 0 00 0 0

0

sin2( 0 ) ( 0 )





cT

T

VEacc E Td

ω ωω

ω

ω

π

⎛ ⎞⎜ ⎟⎝ ⎠= = = = = = = sdot

= =

equiv =

int int int


Ze-e- e- e- e- e-

5

2 Pill Box Cavity

6


I = minusdQdt

Q = CV V = LdIdt

+ RI

d2Vdt

+RL

⎛ ⎝ ⎜

⎞ ⎠ ⎟

dVdt

+1

LC⎛ ⎝ ⎜



⎛ ⎝ ⎜

⎞ ⎠ ⎟ +

1LC

⎛ ⎝ ⎜

⎞ ⎠ ⎟ = 0

α =R2L

ω2 =1

LCminus

R2

4L2

R ltlt L ω O2 =

1LC

rArr f =1

2π LC




=2

P t LQdP t dt R

ω ω ω

ωα


7


22

2

=0 =0 =0 =0

0


i ic c


ω ωμε ρ

ωμε

ωω


⎛ ⎞⎧ ⎫nabla + =⎨ ⎬⎜ ⎟⎩ ⎭⎝ ⎠


E B B B E E j

EB

E EB B

2 22 2 2 2

2 2

22

2

22

2

( 0 =

1

1

t t z z t z z t

zt t z t z

zt t z t z

k E Bc z

B i Ez c

kc

E i Bz c

kc

ωεμ

ωεμωεμ

ωωεμ



⎝ ⎠

Ε E e E B e BB

B e

E e


mode 0 0mode 0 = 0

z z

z z

TM B ETE B E

= nene

8

TM- Modes TM-mode



[ ]22

2

22

2

22 2

2

1

( ) 0

t z t z

zt t

t z z

ic E

kc

Ez

kc

E k Ec

ωεμ

ωεμ

ωεμ

ωεμ

= timesnabla⎛ ⎞

minus⎜ ⎟⎝ ⎠



⎣ ⎦

B e

E



0times =n E

0sdot =n BQ


9



γ2 = γ λ

2 ψ = ψ λ (λ = 1 2L) kλ2 = εμ

ω 2

c 2 minus γ λ2



cutoff frequency


c k

c

k

λλ

λλ

λ λ

γω

εμ

γω

εμω ω

lt

=

ge

L


( )2 2

22 2

2


0

t S Sn

kc

γ ψ ψ ψ

ωγ εμ

partnabla + = = =

part

= sdot minus ge

r

10

0 0

mnp

02

mode

cos( ) ( )exp( ) 0

( )cos( ) exp( ) cos( ) ( )exp( )

cos( ) ( )exp(

m n p

m nz o m z

m n p m nmr r m

m n p

m nm

m n p

TM

E E kz J r im Ba



ρθ


ρπ πγ

minus

= minus =


part

= minus 0

2 2 2

2 2

( )) cos( )exp( )

resonace frequency

m n p m

m n p

m nm n p m n p

iE Jm B kz im

c

c pfa d

θ

εμω ρθ θ

γ ρ

ρ πωεμ

part= minus

part

rArr = +

TEmnp Modes

)sin()sin(02 d

zpmra

JErm

kiE mn

mrπθρωε

⎟⎠⎞

⎜⎝⎛=

)sin()cos(02 d

zpmra

JEak

iE mnm


⎠⎞

⎜⎝⎛=

0=zE

)cos()cos(102 d

zpmra

JEdp

kH mn

mrπθρπ

⎟⎠⎞

⎜⎝⎛=

)cos()sin(102 d

zpmra

JErm

dp

kH mn

mπθρπ

θ ⎟⎠⎞

⎜⎝⎛minus=

)sin()cos(0 d

zpmra

JEH mnmz

πθρ⎟⎠⎞

⎜⎝⎛=

2222

002

2

⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=rArr⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

dp

acf

dp

amnmn πρ


11

TMmnp Modes

d

2a

Ez

ｒ=a

J0(ρ01) J0(ρ02) J1(ρ11)

Acceleration Modes

12

TEmnp Modes

Z

Kick Modes

13









κ κperp

15

Surface Resistance

Surface Impedance

ts s

t Surface

EZ R iXH k

μωequiv + equiv =

Rs =μω2σ

=1σ

μσω2

=1

σδ2

S Sloss1P R H2 S

dS= sdot int



HB = 0 E + 0tED = 0 H E 0t

J = E (Ohms Law)

μ

ε σ

σ


partpart


rr r

rr r r

r rt t

2 2 t

t

1H (xt) = [k E (xt)]

E (xt)[ k ( ) ] = 0

H (xt)i

μω

εμω μωσ

times

⎧ ⎫⎪ ⎪minus + ⎨ ⎬⎪ ⎪⎩ ⎭

rr r r

r r

r r

t

t

E(xt) = E (xt) + E (xt)


l

r r rr r r

r r rr r r

t t

For the transvers


Maxwell Equations

16


Unloaded QO


2 2

2

1 12 2

12

V V

loss S SS

Oloss

U E dV H dV

P R H dS

UQP

ε μ

ω

= sdot = sdot

= sdot

equiv

int int

int


Shunt Impedance2

[ ]shloss

VRP

Ω equiv




17


(RQ)2

( ) ( )sh OVR Q R Q

Uωequiv =


Geometrical factor

2

2[ ]

12

VO S

SS

H dVQ R

H dS





18

Con

tour

plo

t of

E

Con

tour

plo

t of

B

lactive

acc

peak

EE

acc

peak

EB




eff

R QE P Q Z P Q



19



Er ~1r

Cone ~1γro


20



Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv


21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

3



Ez(r=0z)

lcell

lactive

v = szligc

s

-

+

-

+

-




ΤΜ010π-mode


2cellcLf

β λ λsdot= =

4


d=λ2

v=c

0 0t z= =

z c t= sdot

6 6Tt z λ

= = 4 4Tt z λ

= =5 5 12 12Tt z λ

= = 2 2Tt z λ

= =

0 0 00 0 0

0

sin2( 0 ) ( 0 )





cT

T

VEacc E Td

ω ωω

ω

ω

π

⎛ ⎞⎜ ⎟⎝ ⎠= = = = = = = sdot

= =

equiv =

int int int


Ze-e- e- e- e- e-

5

2 Pill Box Cavity

6


I = minusdQdt

Q = CV V = LdIdt

+ RI

d2Vdt

+RL

⎛ ⎝ ⎜

⎞ ⎠ ⎟

dVdt

+1

LC⎛ ⎝ ⎜



⎛ ⎝ ⎜

⎞ ⎠ ⎟ +

1LC

⎛ ⎝ ⎜

⎞ ⎠ ⎟ = 0

α =R2L

ω2 =1

LCminus

R2

4L2

R ltlt L ω O2 =

1LC

rArr f =1

2π LC




=2

P t LQdP t dt R

ω ω ω

ωα


7


22

2

=0 =0 =0 =0

0


i ic c


ω ωμε ρ

ωμε

ωω


⎛ ⎞⎧ ⎫nabla + =⎨ ⎬⎜ ⎟⎩ ⎭⎝ ⎠


E B B B E E j

EB

E EB B

2 22 2 2 2

2 2

22

2

22

2

( 0 =

1

1

t t z z t z z t

zt t z t z

zt t z t z

k E Bc z

B i Ez c

kc

E i Bz c

kc

ωεμ

ωεμωεμ

ωωεμ



⎝ ⎠

Ε E e E B e BB

B e

E e


mode 0 0mode 0 = 0

z z

z z

TM B ETE B E

= nene

8

TM- Modes TM-mode



[ ]22

2

22

2

22 2

2

1

( ) 0

t z t z

zt t

t z z

ic E

kc

Ez

kc

E k Ec

ωεμ

ωεμ

ωεμ

ωεμ

= timesnabla⎛ ⎞

minus⎜ ⎟⎝ ⎠



⎣ ⎦

B e

E



0times =n E

0sdot =n BQ


9



γ2 = γ λ

2 ψ = ψ λ (λ = 1 2L) kλ2 = εμ

ω 2

c 2 minus γ λ2



cutoff frequency


c k

c

k

λλ

λλ

λ λ

γω

εμ

γω

εμω ω

lt

=

ge

L


( )2 2

22 2

2


0

t S Sn

kc

γ ψ ψ ψ

ωγ εμ

partnabla + = = =

part

= sdot minus ge

r

10

0 0

mnp

02

mode

cos( ) ( )exp( ) 0

( )cos( ) exp( ) cos( ) ( )exp( )

cos( ) ( )exp(

m n p

m nz o m z

m n p m nmr r m

m n p

m nm

m n p

TM

E E kz J r im Ba



ρθ


ρπ πγ

minus

= minus =


part

= minus 0

2 2 2

2 2

( )) cos( )exp( )

resonace frequency

m n p m

m n p

m nm n p m n p

iE Jm B kz im

c

c pfa d

θ

εμω ρθ θ

γ ρ

ρ πωεμ

part= minus

part

rArr = +

TEmnp Modes

)sin()sin(02 d

zpmra

JErm

kiE mn

mrπθρωε

⎟⎠⎞

⎜⎝⎛=

)sin()cos(02 d

zpmra

JEak

iE mnm


⎠⎞

⎜⎝⎛=

0=zE

)cos()cos(102 d

zpmra

JEdp

kH mn

mrπθρπ

⎟⎠⎞

⎜⎝⎛=

)cos()sin(102 d

zpmra

JErm

dp

kH mn

mπθρπ

θ ⎟⎠⎞

⎜⎝⎛minus=

)sin()cos(0 d

zpmra

JEH mnmz

πθρ⎟⎠⎞

⎜⎝⎛=

2222

002

2

⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=rArr⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

dp

acf

dp

amnmn πρ


11

TMmnp Modes

d

2a

Ez

ｒ=a

J0(ρ01) J0(ρ02) J1(ρ11)

Acceleration Modes

12

TEmnp Modes

Z

Kick Modes

13









κ κperp

15

Surface Resistance

Surface Impedance

ts s

t Surface

EZ R iXH k

μωequiv + equiv =

Rs =μω2σ

=1σ

μσω2

=1

σδ2

S Sloss1P R H2 S

dS= sdot int



HB = 0 E + 0tED = 0 H E 0t

J = E (Ohms Law)

μ

ε σ

σ


partpart


rr r

rr r r

r rt t

2 2 t

t

1H (xt) = [k E (xt)]

E (xt)[ k ( ) ] = 0

H (xt)i

μω

εμω μωσ

times

⎧ ⎫⎪ ⎪minus + ⎨ ⎬⎪ ⎪⎩ ⎭

rr r r

r r

r r

t

t

E(xt) = E (xt) + E (xt)


l

r r rr r r

r r rr r r

t t

For the transvers


Maxwell Equations

16


Unloaded QO


2 2

2

1 12 2

12

V V

loss S SS

Oloss

U E dV H dV

P R H dS

UQP

ε μ

ω

= sdot = sdot

= sdot

equiv

int int

int


Shunt Impedance2

[ ]shloss

VRP

Ω equiv




17


(RQ)2

( ) ( )sh OVR Q R Q

Uωequiv =


Geometrical factor

2

2[ ]

12

VO S

SS

H dVQ R

H dS





18

Con

tour

plo

t of

E

Con

tour

plo

t of

B

lactive

acc

peak

EE

acc

peak

EB




eff

R QE P Q Z P Q



19



Er ~1r

Cone ~1γro


20



Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv


21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

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Slide Number 33

Slide Number 34

Slide Number 35

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Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

4


d=λ2

v=c

0 0t z= =

z c t= sdot

6 6Tt z λ

= = 4 4Tt z λ

= =5 5 12 12Tt z λ

= = 2 2Tt z λ

= =

0 0 00 0 0

0

sin2( 0 ) ( 0 )





cT

T

VEacc E Td

ω ωω

ω

ω

π

⎛ ⎞⎜ ⎟⎝ ⎠= = = = = = = sdot

= =

equiv =

int int int


Ze-e- e- e- e- e-

5

2 Pill Box Cavity

6


I = minusdQdt

Q = CV V = LdIdt

+ RI

d2Vdt

+RL

⎛ ⎝ ⎜

⎞ ⎠ ⎟

dVdt

+1

LC⎛ ⎝ ⎜



⎛ ⎝ ⎜

⎞ ⎠ ⎟ +

1LC

⎛ ⎝ ⎜

⎞ ⎠ ⎟ = 0

α =R2L

ω2 =1

LCminus

R2

4L2

R ltlt L ω O2 =

1LC

rArr f =1

2π LC




=2

P t LQdP t dt R

ω ω ω

ωα


7


22

2

=0 =0 =0 =0

0


i ic c


ω ωμε ρ

ωμε

ωω


⎛ ⎞⎧ ⎫nabla + =⎨ ⎬⎜ ⎟⎩ ⎭⎝ ⎠


E B B B E E j

EB

E EB B

2 22 2 2 2

2 2

22

2

22

2

( 0 =

1

1

t t z z t z z t

zt t z t z

zt t z t z

k E Bc z

B i Ez c

kc

E i Bz c

kc

ωεμ

ωεμωεμ

ωωεμ



⎝ ⎠

Ε E e E B e BB

B e

E e


mode 0 0mode 0 = 0

z z

z z

TM B ETE B E

= nene

8

TM- Modes TM-mode



[ ]22

2

22

2

22 2

2

1

( ) 0

t z t z

zt t

t z z

ic E

kc

Ez

kc

E k Ec

ωεμ

ωεμ

ωεμ

ωεμ

= timesnabla⎛ ⎞

minus⎜ ⎟⎝ ⎠



⎣ ⎦

B e

E



0times =n E

0sdot =n BQ


9



γ2 = γ λ

2 ψ = ψ λ (λ = 1 2L) kλ2 = εμ

ω 2

c 2 minus γ λ2



cutoff frequency


c k

c

k

λλ

λλ

λ λ

γω

εμ

γω

εμω ω

lt

=

ge

L


( )2 2

22 2

2


0

t S Sn

kc

γ ψ ψ ψ

ωγ εμ

partnabla + = = =

part

= sdot minus ge

r

10

0 0

mnp

02

mode

cos( ) ( )exp( ) 0

( )cos( ) exp( ) cos( ) ( )exp( )

cos( ) ( )exp(

m n p

m nz o m z

m n p m nmr r m

m n p

m nm

m n p

TM

E E kz J r im Ba



ρθ


ρπ πγ

minus

= minus =


part

= minus 0

2 2 2

2 2

( )) cos( )exp( )

resonace frequency

m n p m

m n p

m nm n p m n p

iE Jm B kz im

c

c pfa d

θ

εμω ρθ θ

γ ρ

ρ πωεμ

part= minus

part

rArr = +

TEmnp Modes

)sin()sin(02 d

zpmra

JErm

kiE mn

mrπθρωε

⎟⎠⎞

⎜⎝⎛=

)sin()cos(02 d

zpmra

JEak

iE mnm


⎠⎞

⎜⎝⎛=

0=zE

)cos()cos(102 d

zpmra

JEdp

kH mn

mrπθρπ

⎟⎠⎞

⎜⎝⎛=

)cos()sin(102 d

zpmra

JErm

dp

kH mn

mπθρπ

θ ⎟⎠⎞

⎜⎝⎛minus=

)sin()cos(0 d

zpmra

JEH mnmz

πθρ⎟⎠⎞

⎜⎝⎛=

2222

002

2

⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=rArr⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

dp

acf

dp

amnmn πρ


11

TMmnp Modes

d

2a

Ez

ｒ=a

J0(ρ01) J0(ρ02) J1(ρ11)

Acceleration Modes

12

TEmnp Modes

Z

Kick Modes

13









κ κperp

15

Surface Resistance

Surface Impedance

ts s

t Surface

EZ R iXH k

μωequiv + equiv =

Rs =μω2σ

=1σ

μσω2

=1

σδ2

S Sloss1P R H2 S

dS= sdot int



HB = 0 E + 0tED = 0 H E 0t

J = E (Ohms Law)

μ

ε σ

σ


partpart


rr r

rr r r

r rt t

2 2 t

t

1H (xt) = [k E (xt)]

E (xt)[ k ( ) ] = 0

H (xt)i

μω

εμω μωσ

times

⎧ ⎫⎪ ⎪minus + ⎨ ⎬⎪ ⎪⎩ ⎭

rr r r

r r

r r

t

t

E(xt) = E (xt) + E (xt)


l

r r rr r r

r r rr r r

t t

For the transvers


Maxwell Equations

16


Unloaded QO


2 2

2

1 12 2

12

V V

loss S SS

Oloss

U E dV H dV

P R H dS

UQP

ε μ

ω

= sdot = sdot

= sdot

equiv

int int

int


Shunt Impedance2

[ ]shloss

VRP

Ω equiv




17


(RQ)2

( ) ( )sh OVR Q R Q

Uωequiv =


Geometrical factor

2

2[ ]

12

VO S

SS

H dVQ R

H dS





18

Con

tour

plo

t of

E

Con

tour

plo

t of

B

lactive

acc

peak

EE

acc

peak

EB




eff

R QE P Q Z P Q



19



Er ~1r

Cone ~1γro


20



Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv


21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

5

2 Pill Box Cavity

6


I = minusdQdt

Q = CV V = LdIdt

+ RI

d2Vdt

+RL

⎛ ⎝ ⎜

⎞ ⎠ ⎟

dVdt

+1

LC⎛ ⎝ ⎜



⎛ ⎝ ⎜

⎞ ⎠ ⎟ +

1LC

⎛ ⎝ ⎜

⎞ ⎠ ⎟ = 0

α =R2L

ω2 =1

LCminus

R2

4L2

R ltlt L ω O2 =

1LC

rArr f =1

2π LC




=2

P t LQdP t dt R

ω ω ω

ωα


7


22

2

=0 =0 =0 =0

0


i ic c


ω ωμε ρ

ωμε

ωω


⎛ ⎞⎧ ⎫nabla + =⎨ ⎬⎜ ⎟⎩ ⎭⎝ ⎠


E B B B E E j

EB

E EB B

2 22 2 2 2

2 2

22

2

22

2

( 0 =

1

1

t t z z t z z t

zt t z t z

zt t z t z

k E Bc z

B i Ez c

kc

E i Bz c

kc

ωεμ

ωεμωεμ

ωωεμ



⎝ ⎠

Ε E e E B e BB

B e

E e


mode 0 0mode 0 = 0

z z

z z

TM B ETE B E

= nene

8

TM- Modes TM-mode



[ ]22

2

22

2

22 2

2

1

( ) 0

t z t z

zt t

t z z

ic E

kc

Ez

kc

E k Ec

ωεμ

ωεμ

ωεμ

ωεμ

= timesnabla⎛ ⎞

minus⎜ ⎟⎝ ⎠



⎣ ⎦

B e

E



0times =n E

0sdot =n BQ


9



γ2 = γ λ

2 ψ = ψ λ (λ = 1 2L) kλ2 = εμ

ω 2

c 2 minus γ λ2



cutoff frequency


c k

c

k

λλ

λλ

λ λ

γω

εμ

γω

εμω ω

lt

=

ge

L


( )2 2

22 2

2


0

t S Sn

kc

γ ψ ψ ψ

ωγ εμ

partnabla + = = =

part

= sdot minus ge

r

10

0 0

mnp

02

mode

cos( ) ( )exp( ) 0

( )cos( ) exp( ) cos( ) ( )exp( )

cos( ) ( )exp(

m n p

m nz o m z

m n p m nmr r m

m n p

m nm

m n p

TM

E E kz J r im Ba



ρθ


ρπ πγ

minus

= minus =


part

= minus 0

2 2 2

2 2

( )) cos( )exp( )

resonace frequency

m n p m

m n p

m nm n p m n p

iE Jm B kz im

c

c pfa d

θ

εμω ρθ θ

γ ρ

ρ πωεμ

part= minus

part

rArr = +

TEmnp Modes

)sin()sin(02 d

zpmra

JErm

kiE mn

mrπθρωε

⎟⎠⎞

⎜⎝⎛=

)sin()cos(02 d

zpmra

JEak

iE mnm


⎠⎞

⎜⎝⎛=

0=zE

)cos()cos(102 d

zpmra

JEdp

kH mn

mrπθρπ

⎟⎠⎞

⎜⎝⎛=

)cos()sin(102 d

zpmra

JErm

dp

kH mn

mπθρπ

θ ⎟⎠⎞

⎜⎝⎛minus=

)sin()cos(0 d

zpmra

JEH mnmz

πθρ⎟⎠⎞

⎜⎝⎛=

2222

002

2

⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=rArr⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

dp

acf

dp

amnmn πρ


11

TMmnp Modes

d

2a

Ez

ｒ=a

J0(ρ01) J0(ρ02) J1(ρ11)

Acceleration Modes

12

TEmnp Modes

Z

Kick Modes

13









κ κperp

15

Surface Resistance

Surface Impedance

ts s

t Surface

EZ R iXH k

μωequiv + equiv =

Rs =μω2σ

=1σ

μσω2

=1

σδ2

S Sloss1P R H2 S

dS= sdot int



HB = 0 E + 0tED = 0 H E 0t

J = E (Ohms Law)

μ

ε σ

σ


partpart


rr r

rr r r

r rt t

2 2 t

t

1H (xt) = [k E (xt)]

E (xt)[ k ( ) ] = 0

H (xt)i

μω

εμω μωσ

times

⎧ ⎫⎪ ⎪minus + ⎨ ⎬⎪ ⎪⎩ ⎭

rr r r

r r

r r

t

t

E(xt) = E (xt) + E (xt)


l

r r rr r r

r r rr r r

t t

For the transvers


Maxwell Equations

16


Unloaded QO


2 2

2

1 12 2

12

V V

loss S SS

Oloss

U E dV H dV

P R H dS

UQP

ε μ

ω

= sdot = sdot

= sdot

equiv

int int

int


Shunt Impedance2

[ ]shloss

VRP

Ω equiv




17


(RQ)2

( ) ( )sh OVR Q R Q

Uωequiv =


Geometrical factor

2

2[ ]

12

VO S

SS

H dVQ R

H dS





18

Con

tour

plo

t of

E

Con

tour

plo

t of

B

lactive

acc

peak

EE

acc

peak

EB




eff

R QE P Q Z P Q



19



Er ~1r

Cone ~1γro


20



Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv


21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

6


I = minusdQdt

Q = CV V = LdIdt

+ RI

d2Vdt

+RL

⎛ ⎝ ⎜

⎞ ⎠ ⎟

dVdt

+1

LC⎛ ⎝ ⎜



⎛ ⎝ ⎜

⎞ ⎠ ⎟ +

1LC

⎛ ⎝ ⎜

⎞ ⎠ ⎟ = 0

α =R2L

ω2 =1

LCminus

R2

4L2

R ltlt L ω O2 =

1LC

rArr f =1

2π LC




=2

P t LQdP t dt R

ω ω ω

ωα


7


22

2

=0 =0 =0 =0

0


i ic c


ω ωμε ρ

ωμε

ωω


⎛ ⎞⎧ ⎫nabla + =⎨ ⎬⎜ ⎟⎩ ⎭⎝ ⎠


E B B B E E j

EB

E EB B

2 22 2 2 2

2 2

22

2

22

2

( 0 =

1

1

t t z z t z z t

zt t z t z

zt t z t z

k E Bc z

B i Ez c

kc

E i Bz c

kc

ωεμ

ωεμωεμ

ωωεμ



⎝ ⎠

Ε E e E B e BB

B e

E e


mode 0 0mode 0 = 0

z z

z z

TM B ETE B E

= nene

8

TM- Modes TM-mode



[ ]22

2

22

2

22 2

2

1

( ) 0

t z t z

zt t

t z z

ic E

kc

Ez

kc

E k Ec

ωεμ

ωεμ

ωεμ

ωεμ

= timesnabla⎛ ⎞

minus⎜ ⎟⎝ ⎠



⎣ ⎦

B e

E



0times =n E

0sdot =n BQ


9



γ2 = γ λ

2 ψ = ψ λ (λ = 1 2L) kλ2 = εμ

ω 2

c 2 minus γ λ2



cutoff frequency


c k

c

k

λλ

λλ

λ λ

γω

εμ

γω

εμω ω

lt

=

ge

L


( )2 2

22 2

2


0

t S Sn

kc

γ ψ ψ ψ

ωγ εμ

partnabla + = = =

part

= sdot minus ge

r

10

0 0

mnp

02

mode

cos( ) ( )exp( ) 0

( )cos( ) exp( ) cos( ) ( )exp( )

cos( ) ( )exp(

m n p

m nz o m z

m n p m nmr r m

m n p

m nm

m n p

TM

E E kz J r im Ba



ρθ


ρπ πγ

minus

= minus =


part

= minus 0

2 2 2

2 2

( )) cos( )exp( )

resonace frequency

m n p m

m n p

m nm n p m n p

iE Jm B kz im

c

c pfa d

θ

εμω ρθ θ

γ ρ

ρ πωεμ

part= minus

part

rArr = +

TEmnp Modes

)sin()sin(02 d

zpmra

JErm

kiE mn

mrπθρωε

⎟⎠⎞

⎜⎝⎛=

)sin()cos(02 d

zpmra

JEak

iE mnm


⎠⎞

⎜⎝⎛=

0=zE

)cos()cos(102 d

zpmra

JEdp

kH mn

mrπθρπ

⎟⎠⎞

⎜⎝⎛=

)cos()sin(102 d

zpmra

JErm

dp

kH mn

mπθρπ

θ ⎟⎠⎞

⎜⎝⎛minus=

)sin()cos(0 d

zpmra

JEH mnmz

πθρ⎟⎠⎞

⎜⎝⎛=

2222

002

2

⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=rArr⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

dp

acf

dp

amnmn πρ


11

TMmnp Modes

d

2a

Ez

ｒ=a

J0(ρ01) J0(ρ02) J1(ρ11)

Acceleration Modes

12

TEmnp Modes

Z

Kick Modes

13









κ κperp

15

Surface Resistance

Surface Impedance

ts s

t Surface

EZ R iXH k

μωequiv + equiv =

Rs =μω2σ

=1σ

μσω2

=1

σδ2

S Sloss1P R H2 S

dS= sdot int



HB = 0 E + 0tED = 0 H E 0t

J = E (Ohms Law)

μ

ε σ

σ


partpart


rr r

rr r r

r rt t

2 2 t

t

1H (xt) = [k E (xt)]

E (xt)[ k ( ) ] = 0

H (xt)i

μω

εμω μωσ

times

⎧ ⎫⎪ ⎪minus + ⎨ ⎬⎪ ⎪⎩ ⎭

rr r r

r r

r r

t

t

E(xt) = E (xt) + E (xt)


l

r r rr r r

r r rr r r

t t

For the transvers


Maxwell Equations

16


Unloaded QO


2 2

2

1 12 2

12

V V

loss S SS

Oloss

U E dV H dV

P R H dS

UQP

ε μ

ω

= sdot = sdot

= sdot

equiv

int int

int


Shunt Impedance2

[ ]shloss

VRP

Ω equiv




17


(RQ)2

( ) ( )sh OVR Q R Q

Uωequiv =


Geometrical factor

2

2[ ]

12

VO S

SS

H dVQ R

H dS





18

Con

tour

plo

t of

E

Con

tour

plo

t of

B

lactive

acc

peak

EE

acc

peak

EB




eff

R QE P Q Z P Q



19



Er ~1r

Cone ~1γro


20



Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv


21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

7


22

2

=0 =0 =0 =0

0


i ic c


ω ωμε ρ

ωμε

ωω


⎛ ⎞⎧ ⎫nabla + =⎨ ⎬⎜ ⎟⎩ ⎭⎝ ⎠


E B B B E E j

EB

E EB B

2 22 2 2 2

2 2

22

2

22

2

( 0 =

1

1

t t z z t z z t

zt t z t z

zt t z t z

k E Bc z

B i Ez c

kc

E i Bz c

kc

ωεμ

ωεμωεμ

ωωεμ



⎝ ⎠

Ε E e E B e BB

B e

E e


mode 0 0mode 0 = 0

z z

z z

TM B ETE B E

= nene

8

TM- Modes TM-mode



[ ]22

2

22

2

22 2

2

1

( ) 0

t z t z

zt t

t z z

ic E

kc

Ez

kc

E k Ec

ωεμ

ωεμ

ωεμ

ωεμ

= timesnabla⎛ ⎞

minus⎜ ⎟⎝ ⎠



⎣ ⎦

B e

E



0times =n E

0sdot =n BQ


9



γ2 = γ λ

2 ψ = ψ λ (λ = 1 2L) kλ2 = εμ

ω 2

c 2 minus γ λ2



cutoff frequency


c k

c

k

λλ

λλ

λ λ

γω

εμ

γω

εμω ω

lt

=

ge

L


( )2 2

22 2

2


0

t S Sn

kc

γ ψ ψ ψ

ωγ εμ

partnabla + = = =

part

= sdot minus ge

r

10

0 0

mnp

02

mode

cos( ) ( )exp( ) 0

( )cos( ) exp( ) cos( ) ( )exp( )

cos( ) ( )exp(

m n p

m nz o m z

m n p m nmr r m

m n p

m nm

m n p

TM

E E kz J r im Ba



ρθ


ρπ πγ

minus

= minus =


part

= minus 0

2 2 2

2 2

( )) cos( )exp( )

resonace frequency

m n p m

m n p

m nm n p m n p

iE Jm B kz im

c

c pfa d

θ

εμω ρθ θ

γ ρ

ρ πωεμ

part= minus

part

rArr = +

TEmnp Modes

)sin()sin(02 d

zpmra

JErm

kiE mn

mrπθρωε

⎟⎠⎞

⎜⎝⎛=

)sin()cos(02 d

zpmra

JEak

iE mnm


⎠⎞

⎜⎝⎛=

0=zE

)cos()cos(102 d

zpmra

JEdp

kH mn

mrπθρπ

⎟⎠⎞

⎜⎝⎛=

)cos()sin(102 d

zpmra

JErm

dp

kH mn

mπθρπ

θ ⎟⎠⎞

⎜⎝⎛minus=

)sin()cos(0 d

zpmra

JEH mnmz

πθρ⎟⎠⎞

⎜⎝⎛=

2222

002

2

⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=rArr⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

dp

acf

dp

amnmn πρ


11

TMmnp Modes

d

2a

Ez

ｒ=a

J0(ρ01) J0(ρ02) J1(ρ11)

Acceleration Modes

12

TEmnp Modes

Z

Kick Modes

13









κ κperp

15

Surface Resistance

Surface Impedance

ts s

t Surface

EZ R iXH k

μωequiv + equiv =

Rs =μω2σ

=1σ

μσω2

=1

σδ2

S Sloss1P R H2 S

dS= sdot int



HB = 0 E + 0tED = 0 H E 0t

J = E (Ohms Law)

μ

ε σ

σ


partpart


rr r

rr r r

r rt t

2 2 t

t

1H (xt) = [k E (xt)]

E (xt)[ k ( ) ] = 0

H (xt)i

μω

εμω μωσ

times

⎧ ⎫⎪ ⎪minus + ⎨ ⎬⎪ ⎪⎩ ⎭

rr r r

r r

r r

t

t

E(xt) = E (xt) + E (xt)


l

r r rr r r

r r rr r r

t t

For the transvers


Maxwell Equations

16


Unloaded QO


2 2

2

1 12 2

12

V V

loss S SS

Oloss

U E dV H dV

P R H dS

UQP

ε μ

ω

= sdot = sdot

= sdot

equiv

int int

int


Shunt Impedance2

[ ]shloss

VRP

Ω equiv




17


(RQ)2

( ) ( )sh OVR Q R Q

Uωequiv =


Geometrical factor

2

2[ ]

12

VO S

SS

H dVQ R

H dS





18

Con

tour

plo

t of

E

Con

tour

plo

t of

B

lactive

acc

peak

EE

acc

peak

EB




eff

R QE P Q Z P Q



19



Er ~1r

Cone ~1γro


20



Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv


21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

8

TM- Modes TM-mode



[ ]22

2

22

2

22 2

2

1

( ) 0

t z t z

zt t

t z z

ic E

kc

Ez

kc

E k Ec

ωεμ

ωεμ

ωεμ

ωεμ

= timesnabla⎛ ⎞

minus⎜ ⎟⎝ ⎠



⎣ ⎦

B e

E



0times =n E

0sdot =n BQ


9



γ2 = γ λ

2 ψ = ψ λ (λ = 1 2L) kλ2 = εμ

ω 2

c 2 minus γ λ2



cutoff frequency


c k

c

k

λλ

λλ

λ λ

γω

εμ

γω

εμω ω

lt

=

ge

L


( )2 2

22 2

2


0

t S Sn

kc

γ ψ ψ ψ

ωγ εμ

partnabla + = = =

part

= sdot minus ge

r

10

0 0

mnp

02

mode

cos( ) ( )exp( ) 0

( )cos( ) exp( ) cos( ) ( )exp( )

cos( ) ( )exp(

m n p

m nz o m z

m n p m nmr r m

m n p

m nm

m n p

TM

E E kz J r im Ba



ρθ


ρπ πγ

minus

= minus =


part

= minus 0

2 2 2

2 2

( )) cos( )exp( )

resonace frequency

m n p m

m n p

m nm n p m n p

iE Jm B kz im

c

c pfa d

θ

εμω ρθ θ

γ ρ

ρ πωεμ

part= minus

part

rArr = +

TEmnp Modes

)sin()sin(02 d

zpmra

JErm

kiE mn

mrπθρωε

⎟⎠⎞

⎜⎝⎛=

)sin()cos(02 d

zpmra

JEak

iE mnm


⎠⎞

⎜⎝⎛=

0=zE

)cos()cos(102 d

zpmra

JEdp

kH mn

mrπθρπ

⎟⎠⎞

⎜⎝⎛=

)cos()sin(102 d

zpmra

JErm

dp

kH mn

mπθρπ

θ ⎟⎠⎞

⎜⎝⎛minus=

)sin()cos(0 d

zpmra

JEH mnmz

πθρ⎟⎠⎞

⎜⎝⎛=

2222

002

2

⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=rArr⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

dp

acf

dp

amnmn πρ


11

TMmnp Modes

d

2a

Ez

ｒ=a

J0(ρ01) J0(ρ02) J1(ρ11)

Acceleration Modes

12

TEmnp Modes

Z

Kick Modes

13









κ κperp

15

Surface Resistance

Surface Impedance

ts s

t Surface

EZ R iXH k

μωequiv + equiv =

Rs =μω2σ

=1σ

μσω2

=1

σδ2

S Sloss1P R H2 S

dS= sdot int



HB = 0 E + 0tED = 0 H E 0t

J = E (Ohms Law)

μ

ε σ

σ


partpart


rr r

rr r r

r rt t

2 2 t

t

1H (xt) = [k E (xt)]

E (xt)[ k ( ) ] = 0

H (xt)i

μω

εμω μωσ

times

⎧ ⎫⎪ ⎪minus + ⎨ ⎬⎪ ⎪⎩ ⎭

rr r r

r r

r r

t

t

E(xt) = E (xt) + E (xt)


l

r r rr r r

r r rr r r

t t

For the transvers


Maxwell Equations

16


Unloaded QO


2 2

2

1 12 2

12

V V

loss S SS

Oloss

U E dV H dV

P R H dS

UQP

ε μ

ω

= sdot = sdot

= sdot

equiv

int int

int


Shunt Impedance2

[ ]shloss

VRP

Ω equiv




17


(RQ)2

( ) ( )sh OVR Q R Q

Uωequiv =


Geometrical factor

2

2[ ]

12

VO S

SS

H dVQ R

H dS





18

Con

tour

plo

t of

E

Con

tour

plo

t of

B

lactive

acc

peak

EE

acc

peak

EB




eff

R QE P Q Z P Q



19



Er ~1r

Cone ~1γro


20



Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv


21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

9



γ2 = γ λ

2 ψ = ψ λ (λ = 1 2L) kλ2 = εμ

ω 2

c 2 minus γ λ2



cutoff frequency


c k

c

k

λλ

λλ

λ λ

γω

εμ

γω

εμω ω

lt

=

ge

L


( )2 2

22 2

2


0

t S Sn

kc

γ ψ ψ ψ

ωγ εμ

partnabla + = = =

part

= sdot minus ge

r

10

0 0

mnp

02

mode

cos( ) ( )exp( ) 0

( )cos( ) exp( ) cos( ) ( )exp( )

cos( ) ( )exp(

m n p

m nz o m z

m n p m nmr r m

m n p

m nm

m n p

TM

E E kz J r im Ba



ρθ


ρπ πγ

minus

= minus =


part

= minus 0

2 2 2

2 2

( )) cos( )exp( )

resonace frequency

m n p m

m n p

m nm n p m n p

iE Jm B kz im

c

c pfa d

θ

εμω ρθ θ

γ ρ

ρ πωεμ

part= minus

part

rArr = +

TEmnp Modes

)sin()sin(02 d

zpmra

JErm

kiE mn

mrπθρωε

⎟⎠⎞

⎜⎝⎛=

)sin()cos(02 d

zpmra

JEak

iE mnm


⎠⎞

⎜⎝⎛=

0=zE

)cos()cos(102 d

zpmra

JEdp

kH mn

mrπθρπ

⎟⎠⎞

⎜⎝⎛=

)cos()sin(102 d

zpmra

JErm

dp

kH mn

mπθρπ

θ ⎟⎠⎞

⎜⎝⎛minus=

)sin()cos(0 d

zpmra

JEH mnmz

πθρ⎟⎠⎞

⎜⎝⎛=

2222

002

2

⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=rArr⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

dp

acf

dp

amnmn πρ


11

TMmnp Modes

d

2a

Ez

ｒ=a

J0(ρ01) J0(ρ02) J1(ρ11)

Acceleration Modes

12

TEmnp Modes

Z

Kick Modes

13









κ κperp

15

Surface Resistance

Surface Impedance

ts s

t Surface

EZ R iXH k

μωequiv + equiv =

Rs =μω2σ

=1σ

μσω2

=1

σδ2

S Sloss1P R H2 S

dS= sdot int



HB = 0 E + 0tED = 0 H E 0t

J = E (Ohms Law)

μ

ε σ

σ


partpart


rr r

rr r r

r rt t

2 2 t

t

1H (xt) = [k E (xt)]

E (xt)[ k ( ) ] = 0

H (xt)i

μω

εμω μωσ

times

⎧ ⎫⎪ ⎪minus + ⎨ ⎬⎪ ⎪⎩ ⎭

rr r r

r r

r r

t

t

E(xt) = E (xt) + E (xt)


l

r r rr r r

r r rr r r

t t

For the transvers


Maxwell Equations

16


Unloaded QO


2 2

2

1 12 2

12

V V

loss S SS

Oloss

U E dV H dV

P R H dS

UQP

ε μ

ω

= sdot = sdot

= sdot

equiv

int int

int


Shunt Impedance2

[ ]shloss

VRP

Ω equiv




17


(RQ)2

( ) ( )sh OVR Q R Q

Uωequiv =


Geometrical factor

2

2[ ]

12

VO S

SS

H dVQ R

H dS





18

Con

tour

plo

t of

E

Con

tour

plo

t of

B

lactive

acc

peak

EE

acc

peak

EB




eff

R QE P Q Z P Q



19



Er ~1r

Cone ~1γro


20



Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv


21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

10

0 0

mnp

02

mode

cos( ) ( )exp( ) 0

( )cos( ) exp( ) cos( ) ( )exp( )

cos( ) ( )exp(

m n p

m nz o m z

m n p m nmr r m

m n p

m nm

m n p

TM

E E kz J r im Ba



ρθ


ρπ πγ

minus

= minus =


part

= minus 0

2 2 2

2 2

( )) cos( )exp( )

resonace frequency

m n p m

m n p

m nm n p m n p

iE Jm B kz im

c

c pfa d

θ

εμω ρθ θ

γ ρ

ρ πωεμ

part= minus

part

rArr = +

TEmnp Modes

)sin()sin(02 d

zpmra

JErm

kiE mn

mrπθρωε

⎟⎠⎞

⎜⎝⎛=

)sin()cos(02 d

zpmra

JEak

iE mnm


⎠⎞

⎜⎝⎛=

0=zE

)cos()cos(102 d

zpmra

JEdp

kH mn

mrπθρπ

⎟⎠⎞

⎜⎝⎛=

)cos()sin(102 d

zpmra

JErm

dp

kH mn

mπθρπ

θ ⎟⎠⎞

⎜⎝⎛minus=

)sin()cos(0 d

zpmra

JEH mnmz

πθρ⎟⎠⎞

⎜⎝⎛=

2222

002

2

⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=rArr⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

dp

acf

dp

amnmn πρ


11

TMmnp Modes

d

2a

Ez

ｒ=a

J0(ρ01) J0(ρ02) J1(ρ11)

Acceleration Modes

12

TEmnp Modes

Z

Kick Modes

13









κ κperp

15

Surface Resistance

Surface Impedance

ts s

t Surface

EZ R iXH k

μωequiv + equiv =

Rs =μω2σ

=1σ

μσω2

=1

σδ2

S Sloss1P R H2 S

dS= sdot int



HB = 0 E + 0tED = 0 H E 0t

J = E (Ohms Law)

μ

ε σ

σ


partpart


rr r

rr r r

r rt t

2 2 t

t

1H (xt) = [k E (xt)]

E (xt)[ k ( ) ] = 0

H (xt)i

μω

εμω μωσ

times

⎧ ⎫⎪ ⎪minus + ⎨ ⎬⎪ ⎪⎩ ⎭

rr r r

r r

r r

t

t

E(xt) = E (xt) + E (xt)


l

r r rr r r

r r rr r r

t t

For the transvers


Maxwell Equations

16


Unloaded QO


2 2

2

1 12 2

12

V V

loss S SS

Oloss

U E dV H dV

P R H dS

UQP

ε μ

ω

= sdot = sdot

= sdot

equiv

int int

int


Shunt Impedance2

[ ]shloss

VRP

Ω equiv




17


(RQ)2

( ) ( )sh OVR Q R Q

Uωequiv =


Geometrical factor

2

2[ ]

12

VO S

SS

H dVQ R

H dS





18

Con

tour

plo

t of

E

Con

tour

plo

t of

B

lactive

acc

peak

EE

acc

peak

EB




eff

R QE P Q Z P Q



19



Er ~1r

Cone ~1γro


20



Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv


21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

11

TMmnp Modes

d

2a

Ez

ｒ=a

J0(ρ01) J0(ρ02) J1(ρ11)

Acceleration Modes

12

TEmnp Modes

Z

Kick Modes

13









κ κperp

15

Surface Resistance

Surface Impedance

ts s

t Surface

EZ R iXH k

μωequiv + equiv =

Rs =μω2σ

=1σ

μσω2

=1

σδ2

S Sloss1P R H2 S

dS= sdot int



HB = 0 E + 0tED = 0 H E 0t

J = E (Ohms Law)

μ

ε σ

σ


partpart


rr r

rr r r

r rt t

2 2 t

t

1H (xt) = [k E (xt)]

E (xt)[ k ( ) ] = 0

H (xt)i

μω

εμω μωσ

times

⎧ ⎫⎪ ⎪minus + ⎨ ⎬⎪ ⎪⎩ ⎭

rr r r

r r

r r

t

t

E(xt) = E (xt) + E (xt)


l

r r rr r r

r r rr r r

t t

For the transvers


Maxwell Equations

16


Unloaded QO


2 2

2

1 12 2

12

V V

loss S SS

Oloss

U E dV H dV

P R H dS

UQP

ε μ

ω

= sdot = sdot

= sdot

equiv

int int

int


Shunt Impedance2

[ ]shloss

VRP

Ω equiv




17


(RQ)2

( ) ( )sh OVR Q R Q

Uωequiv =


Geometrical factor

2

2[ ]

12

VO S

SS

H dVQ R

H dS





18

Con

tour

plo

t of

E

Con

tour

plo

t of

B

lactive

acc

peak

EE

acc

peak

EB




eff

R QE P Q Z P Q



19



Er ~1r

Cone ~1γro


20



Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv


21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

12

TEmnp Modes

Z

Kick Modes

13









κ κperp

15

Surface Resistance

Surface Impedance

ts s

t Surface

EZ R iXH k

μωequiv + equiv =

Rs =μω2σ

=1σ

μσω2

=1

σδ2

S Sloss1P R H2 S

dS= sdot int



HB = 0 E + 0tED = 0 H E 0t

J = E (Ohms Law)

μ

ε σ

σ


partpart


rr r

rr r r

r rt t

2 2 t

t

1H (xt) = [k E (xt)]

E (xt)[ k ( ) ] = 0

H (xt)i

μω

εμω μωσ

times

⎧ ⎫⎪ ⎪minus + ⎨ ⎬⎪ ⎪⎩ ⎭

rr r r

r r

r r

t

t

E(xt) = E (xt) + E (xt)


l

r r rr r r

r r rr r r

t t

For the transvers


Maxwell Equations

16


Unloaded QO


2 2

2

1 12 2

12

V V

loss S SS

Oloss

U E dV H dV

P R H dS

UQP

ε μ

ω

= sdot = sdot

= sdot

equiv

int int

int


Shunt Impedance2

[ ]shloss

VRP

Ω equiv




17


(RQ)2

( ) ( )sh OVR Q R Q

Uωequiv =


Geometrical factor

2

2[ ]

12

VO S

SS

H dVQ R

H dS





18

Con

tour

plo

t of

E

Con

tour

plo

t of

B

lactive

acc

peak

EE

acc

peak

EB




eff

R QE P Q Z P Q



19



Er ~1r

Cone ~1γro


20



Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv


21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

13









κ κperp

15

Surface Resistance

Surface Impedance

ts s

t Surface

EZ R iXH k

μωequiv + equiv =

Rs =μω2σ

=1σ

μσω2

=1

σδ2

S Sloss1P R H2 S

dS= sdot int



HB = 0 E + 0tED = 0 H E 0t

J = E (Ohms Law)

μ

ε σ

σ


partpart


rr r

rr r r

r rt t

2 2 t

t

1H (xt) = [k E (xt)]

E (xt)[ k ( ) ] = 0

H (xt)i

μω

εμω μωσ

times

⎧ ⎫⎪ ⎪minus + ⎨ ⎬⎪ ⎪⎩ ⎭

rr r r

r r

r r

t

t

E(xt) = E (xt) + E (xt)


l

r r rr r r

r r rr r r

t t

For the transvers


Maxwell Equations

16


Unloaded QO


2 2

2

1 12 2

12

V V

loss S SS

Oloss

U E dV H dV

P R H dS

UQP

ε μ

ω

= sdot = sdot

= sdot

equiv

int int

int


Shunt Impedance2

[ ]shloss

VRP

Ω equiv




17


(RQ)2

( ) ( )sh OVR Q R Q

Uωequiv =


Geometrical factor

2

2[ ]

12

VO S

SS

H dVQ R

H dS





18

Con

tour

plo

t of

E

Con

tour

plo

t of

B

lactive

acc

peak

EE

acc

peak

EB




eff

R QE P Q Z P Q



19



Er ~1r

Cone ~1γro


20



Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv


21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46








κ κperp

15

Surface Resistance

Surface Impedance

ts s

t Surface

EZ R iXH k

μωequiv + equiv =

Rs =μω2σ

=1σ

μσω2

=1

σδ2

S Sloss1P R H2 S

dS= sdot int



HB = 0 E + 0tED = 0 H E 0t

J = E (Ohms Law)

μ

ε σ

σ


partpart


rr r

rr r r

r rt t

2 2 t

t

1H (xt) = [k E (xt)]

E (xt)[ k ( ) ] = 0

H (xt)i

μω

εμω μωσ

times

⎧ ⎫⎪ ⎪minus + ⎨ ⎬⎪ ⎪⎩ ⎭

rr r r

r r

r r

t

t

E(xt) = E (xt) + E (xt)


l

r r rr r r

r r rr r r

t t

For the transvers


Maxwell Equations

16


Unloaded QO


2 2

2

1 12 2

12

V V

loss S SS

Oloss

U E dV H dV

P R H dS

UQP

ε μ

ω

= sdot = sdot

= sdot

equiv

int int

int


Shunt Impedance2

[ ]shloss

VRP

Ω equiv




17


(RQ)2

( ) ( )sh OVR Q R Q

Uωequiv =


Geometrical factor

2

2[ ]

12

VO S

SS

H dVQ R

H dS





18

Con

tour

plo

t of

E

Con

tour

plo

t of

B

lactive

acc

peak

EE

acc

peak

EB




eff

R QE P Q Z P Q



19



Er ~1r

Cone ~1γro


20



Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv


21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

15

Surface Resistance

Surface Impedance

ts s

t Surface

EZ R iXH k

μωequiv + equiv =

Rs =μω2σ

=1σ

μσω2

=1

σδ2

S Sloss1P R H2 S

dS= sdot int



HB = 0 E + 0tED = 0 H E 0t

J = E (Ohms Law)

μ

ε σ

σ


partpart


rr r

rr r r

r rt t

2 2 t

t

1H (xt) = [k E (xt)]

E (xt)[ k ( ) ] = 0

H (xt)i

μω

εμω μωσ

times

⎧ ⎫⎪ ⎪minus + ⎨ ⎬⎪ ⎪⎩ ⎭

rr r r

r r

r r

t

t

E(xt) = E (xt) + E (xt)


l

r r rr r r

r r rr r r

t t

For the transvers


Maxwell Equations

16


Unloaded QO


2 2

2

1 12 2

12

V V

loss S SS

Oloss

U E dV H dV

P R H dS

UQP

ε μ

ω

= sdot = sdot

= sdot

equiv

int int

int


Shunt Impedance2

[ ]shloss

VRP

Ω equiv




17


(RQ)2

( ) ( )sh OVR Q R Q

Uωequiv =


Geometrical factor

2

2[ ]

12

VO S

SS

H dVQ R

H dS





18

Con

tour

plo

t of

E

Con

tour

plo

t of

B

lactive

acc

peak

EE

acc

peak

EB




eff

R QE P Q Z P Q



19



Er ~1r

Cone ~1γro


20



Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv


21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

16


Unloaded QO


2 2

2

1 12 2

12

V V

loss S SS

Oloss

U E dV H dV

P R H dS

UQP

ε μ

ω

= sdot = sdot

= sdot

equiv

int int

int


Shunt Impedance2

[ ]shloss

VRP

Ω equiv




17


(RQ)2

( ) ( )sh OVR Q R Q

Uωequiv =


Geometrical factor

2

2[ ]

12

VO S

SS

H dVQ R

H dS





18

Con

tour

plo

t of

E

Con

tour

plo

t of

B

lactive

acc

peak

EE

acc

peak

EB




eff

R QE P Q Z P Q



19



Er ~1r

Cone ~1γro


20



Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv


21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

17


(RQ)2

( ) ( )sh OVR Q R Q

Uωequiv =


Geometrical factor

2

2[ ]

12

VO S

SS

H dVQ R

H dS





18

Con

tour

plo

t of

E

Con

tour

plo

t of

B

lactive

acc

peak

EE

acc

peak

EB




eff

R QE P Q Z P Q



19



Er ~1r

Cone ~1γro


20



Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv


21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

18

Con

tour

plo

t of

E

Con

tour

plo

t of

B

lactive

acc

peak

EE

acc

peak

EB




eff

R QE P Q Z P Q



19



Er ~1r

Cone ~1γro


20



Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv


21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

19



Er ~1r

Cone ~1γro


20



Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv


21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

20



Wn

a b

2z

za

nzn

2z

za

nznn

b

a

b

a

dz))zz(c

cos(Edz))zz(c

sin(EV⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛minus= intint β

ωβω

nn

2n

n WV)QR(

ωequiv


21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

21




4)QR(k nn

n||sdot

=ωp





22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

22


szligkNacc

2

ff sdot=


1

2

2

1

szligxszligx

ff

sdotpartsdotpart

=partpart

szlig1 szlig2





ffA fa

A fΔ Δ

= sdot

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

23



2

k0

0cc ωω

ωωπ

π

+minus

=

+ + + -




ωπωo


24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

24



Multipacting




25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

25




HOM k k



iris radius ri


Geometry






Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46


Examplef = 15 GHz


27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

27

00

20

40

60

80

20 25 30 35 40 ri [mm]

k_m

on(r

)k_m

on(4

0)

k_di

pole

(r)k

_dip

ole(

40)




28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

28



00

02

04

06

08

10

20 25 30 35 40 ri [mm]

kcc(

r)k

cc(4

0)


29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

29



Epeak Eacc

Bpeak Eacc

ri

Iris Equator shape

TESLA

HG CEBAF-12 GeV


Equator shape

LL CEBAF-12 GeV

LL- ILC cavity


k k riB-Factory

RHIC cooling



iris radius ri


30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

30


fπ [MHz] 2600

RQ [Ω] 57

rq=(RQ)l [Ωm] 2000

G [Ω] 271

fπ [MHz] 1300

RQ [Ω] 57

rq=(RQ)l [Ωm] 1000

G [Ω] 271

x 2 =

rq=(RQ)l ~ f



31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

31



B



Cryogenic power


f

f

350MHz500MHz

(U-band)

13GHz

(L-band)

2896GHz

(S-band)



32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

32

f π [MHz] 13000

riris [mm] 35

kcc [] 19

EpeakEacc - 198


RQ [Ω] 1138

G [Ω] 271

RQG [ΩΩ] 30840





33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

33





TESLA LL RE IS


EpEacc 20 236 221 202

HpEacc [OeMVm] 426 361 376 356

RQ [W] 1138 1337 1268 138

G[W] 271 284 277 285

Eacc max 411 485 465 492

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

34

Eacc vs Year

10

20

30

40

50

60

70

Eac

cm

ax [M

Vm

]

Date [Year]91 0095 0593 97 03


(HPR)

Electropolshing(EP)

+ HPR + 120OC Bake

New Shape

Chemical Polishing

RE LL IS shape

99 07


35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

35






36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

36

2i i i

ffi i cc i

A f fNaA f k f

Δ Δ Δ= = sdot




HOM RF

2

ffcc

Nak

=


HOM trapped mode



NINPUTP prop


37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

37




HighGradient

N =7

LowLossN =7

TESLA

N=9

SNSszlig=061

N=6

SNSszlig=081

N=6

RIAszlig=047

N=6

RHIC

N=5

year 1982 2001 2002 1992 2000 2000 2003 2003

aff 1489 2592 3288 4091 3883 2924 5040 850

Field flatness vs N


38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

38



N = 17

N = 13

N = 9

N = 5



39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

39






f = 2385 MHz




40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

40






+ +


41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

41



PINPUT ~ N




42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

42




f π [MHz] 130000

f π-1 [MHz] 129924

RQ [Ω] 1012

G [Ω] 271




43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

43


szlig=1

CEBAF -12High

Gradientszlig=1


TESLA

szlig=1

SNS

szlig=061

SNS

szlig=081

RIA

szlig=047

RHICCoolerszlig=1

fo [MHz] 14483 14689 14751 12780 7928 7928 7930 6830

fπ [MHz] 14970 14970 14970 13000 8050 8050 8050 7037

kcc [] 329 189 149 19 152 152 152 294

EpeakEacc - 256 196 217 198 266 214 328 198

BpeakEacc [mT(MVm)] 456 415 374 415 544 458 651 578

RQ [Ω] 965 112 1288 1138 492 838 285 802

G [Ω] 2738 266 280 271 176 226 136 225

RQG [ΩΩ] 26421 29792 36064 30840 8659 18939 3876 18045

k (σz=1mm) [VpCcm2] 022 032 053 023 013 011 015 002

k (σz=1mm) [VpC] 136 153 171 146 125 127 119 085




44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

44


45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

45


PHOM cavity[kW]


Ibeam


cw350 16

x 16

Multi-cell with max

Ibeam


cw60 013



PRF

~100Almost no beam

loading0

HERA 05 GHz

KEK-B 05 GHz

TTF-I 13 GHz



46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

46


PHOM cavity[kW]


Ibeam


240 (366) 006 peak

x 48 482 006 peak


Eacc


PRF146 lt 002gt



SNS szlig= 0805 GHz

TTF-II ep 13 GHz



Slide Number 2

Slide Number 3

Slide Number 4

Slide Number 5



TM- Modes

Eigen-value problem

Slide Number 10

TMmnp　Modes

TEmnp Modes

Slide Number 13


Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

Slide Number 38

Slide Number 39

Slide Number 40

Slide Number 41

Slide Number 42

Slide Number 43

Slide Number 44

Slide Number 45

Slide Number 46

high-beta cavity design - cernaccelconf.web.cern.ch/accelconf/srf2009/contents/... ·...

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