simulation of experiments on transverse rms-emittance growth along an alvarez dtl

L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL

L. Groening, W. Barth, W. Bayer, G. Clemente, L. Dahl, P. Forck, P. Gerhard, I. Hofmann, G. Riehl, S. Yaramyshev,

GSI, Germany

D. Jeon, ORNL, U.S.A.

D. Uriot, CEA/Saclay, France

R. Tiede, University of Frankfurt, Germany

Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL

• Introduction and set-up

• Data reduction

• Reconstruction of initial distribution

• Results of experiment and simulations

• Emittance growth reduction by rms-matching

• Summary & outlook

We acknowledge the support of the European Community – Research Infrastructure Activity under the FP6 "Structuring the European Research Area" program (CARE, contract number RII3-CT-2003-506395).


UNILAC at GSI: Overview

MEVVA

MUCIS

PIGRFQ IH1 IH2

Alvarez DTL

HLI: (ECR,RFQ,IH)

Transfer toSynchrotron

2.2 keV/uβ = 0.0022

120 keV/uβ = 0.016

11.4 MeV/uβ = 0.16

RFQ, IH1, IH2 Alvarez DTL

Gas Stripper

1.4 MeV/uβ = 0.054

1 ≤ A/q ≤ 9.5

1 ≤ A/q ≤ 65


The UNILAC Alvarez DTL

E [MeV/u]

:

Tank :

A1 A2a A3 A4A2b

1.4

3.6

4.8

5.9

8.6

11.4

• 5 independent rf-tanks

• 108 MHz, 192 rf-cells

• DTL based on F-D-D-F focusing

• DC-quads grouped to 13 families

• Inter-tank focusing : F-D-F

• Synchr. rf-phases -(30°,30°,30°,25°,25°)

54 m


Section in Front of DTL

36 MHz 108 MHz

Gas Stripper


Experimental Set-up & Procedure

• set beam current to 7.1 mA of 40Ar10+ (equiv. to FAIR design of 15 mA of 238U28+)

• measure hor., ver., emittance and long. rms-bunch length at DTL entrance

• set DTL transverse phase advance to values from 35° to 90°

• tune depression varied from 21% (90°) to 43% (35°)

• measure transmission, hor., and ver. rms-emittance at DTL exit

rms-bunch length measurement


Data Reduction

Measurement

• projection of 6-dim to 2-dim plane

• matrix of pixels

• pixel size 0.8 mm / 0.5 mrad

• evaluation based on pixel contents

Simulations

• full 6-dim information available

to compare measurement and simulation adequately, the evaluation procedures must be identical


Data Reduction

• particle coordinates from simulations are projected onto virtual meas. device

• projection is evaluated as a measurement


Definition of Fractional rms-Emittance

rms-emittance from a fraction of p% of the total intensity

• calculate sum ∑100 of all pixel contents

• sort pixels from top by their contents

• sum them up until the fraction p from ∑100 is reached

• use the pixels included in this sum for rms-emittance evaluation

benchmarking used p = 95% of the intensity


horizontal

vertical

→ (α, β, ε)xy

rms-tracking backwards

meas. (α, β, ε)xy

guessed (α, β, ε)l

bunch length measurement

check (βε)l

Re-Construction of initial rms-Parameters for Simulations

1. Selfconsistent backtracking finding (α,β,ε)l that fit to measured bunch length

2. Varification wether applied machine settings would give full DTL transmission

DTLBuncher 108 MHz

Buncher 36 MHz

Start of Simulations


0.00

0.05

0.10

0.15

0.20

0.25

0 10 20 30 40 50 60 70 80 90 100

Number of Particles [%]

No

rm. F

ract

ion

al H

or.

rm

s-E

mit

tan

ce [

mm

mra

d]

hor., Exp.

hor., Gauss_2s

hor., Gauss_4s

hor., Input for Sim.

Re-construction of initial type of Distribution

0.00

0.05

0.10

0.15

0.20

0.25

0 10 20 30 40 50 60 70 80 90 100

Number of Particles [%]

No

rm. F

rac

tio

na

l Ve

r. r

ms

-Em

itta

nc

e [

mm

mra

d]

ver., Exp.

ver., Gauss_2s

ver., Gauss_4s

ver., Input for Sim.

measured in front of DTL

horizontal vertical

measured initial distribution inhabits different amount of halo horizontally and vertically



• Gauss, Lorentz, Waterbag distributions do not fit the measured amount of halo

• Several functions tried in order to fit halo in both planes

• function found as:

applying different powers for different planes the amount of halo can be reproduced


Initial Distribution and Codes

initial distribution

Gaussian cut at 4σ assumed

Simulations with four different codes as used by the participating labs:

DYNAMION (GSI)

PARMILA (SNS)

PARTRAN (CEA/Saclay)

LORASR (Univ. of Frankfurt)


Beam Transmission through DTL

All codes reproduce measured full transmission. LORASR is lower by few percent

91.0

92.0

93.0

94.0

95.0

96.0

97.0

98.0

99.0

100.0

101.0

30 40 50 60 70 80 90

Transverse Phase Advance (zero current) [deg]

DT

L T

ran

sm

iss

ion

[%

]

Exp.

DYNAMION

PARMILA

PARTRAN

LORASR


Shapes of Final Horizontal Distributions

σo = 35° σo = 60°

Exp

erim

en

t

σo = 90°

DY

NA

MIO

NP

AR

MIL

AP

AR

TR

AN

LO

RA

SR

• agreement for intermediate σo

• disagreement for low/high σo

• high σo: attached wings (islands)

Int / Int_max [%]

0 – 5

5 – 10

10 – 20

20 – 40

40 -100


σo = 35° σo = 60°

Exp

erim

en

t

σo = 90°

DY

NA

MIO

NP

AR

MIL

AP

AR

TR

AN

LO

RA

SR

Shapes of Final Vertical Distributions

• differences even at intermediate σo

• high σo: no attached wings

Int / Int_max [%]

0 – 5

5 – 10

10 – 20

20 – 40

40 -100


Evolution of Simulated rms-Emittances (100%)

• growth occurs mainly along first two tanks (agrees to previous measurements*)

• LORASR predicts strongest growth

• lowest growth at intermediate phase advances

*www-dapnia.cea.fr/Phocea/file.php?class=std&&file=Doc/Care/care-report-07-030.pdf


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

30 40 50 60 70 80 90


No

rm. H

or.

95

%-r

ms

-Em

itta

nc

e [

mm

mra

d]

hor., initial

hor., Exp.

hor., DYNAMIONhor., PARMILA

hor., PARTRAN

hor., LORASR

Final 95%-rms Emittances as Function of Phase Advance

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

30 40 50 60 70 80 90


No

rm. V

er.

95

%-r

ms

-Em

itta

nc

e [

mm

mra

d]

ver., initial

ver., Exp.

ver., DYNAMION

ver., PARMILA

ver., PARTRAN

ver., LORASR

horizontal vertical

• three codes underestimate growth

• LORASR predicts more growth

• codes predict peak at σo=70°

• three codes fit to meas. (except σo≤ 45°)

• LORASR predicts more growth

• codes predict peak at σo=70° (but LORASR)

results do not depend on initial long. emittance within 0.1∙εl,o and 2∙εl,o


Final 95%-rms Emittances as Function of Phase Advance

(horizontal + vertical) / 2

• codes and measurements reveal minimum growth at σo≈ 60°

• LORASR predicts strongest growth

• DYNAMION, PARMILA, PARTRAN fit well at σo≥ 60°, LORASR fits well at σo≤ 60°

• codes predict peak at σo=70° (but LORASR)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

30 40 50 60 70 80 90


No

rm. T

ran

sv

. 95

%-r

ms

-Em

itta

nc

e [

mm

mra

d]

initial

Exp.

DYNAMION

PARMILA

PARTRAN

LORASR


Mismatch to Periodic DTL Envelopes

rms-tracking algorithm for re-construction of initial distribution was used to estimate mismatch to DTL

0.0

0.2

0.4

0.6

0.8

1.0

30 40 50 60 70 80 90


Mis

ma

tch

at

DT

L E

ntr

an

ce

horizontal

vertical

longitudinal

T.P. Wangler, Rf Linear Accelerators, p. 217


Reduction of Mismatch

• algorithm used to rms-match (incl. space charge) the initial distribution to periodic DTL

• test of matching by re-measuring emittance growth (one year later)

0.0

0.2

0.4

0.6

0.8

1.0

30 40 50 60 70 80 90


Mis

mat

ch a

t D

TL

En

tran

ce

horizontal

vertical

longitudinal

0

100

200

300

30 40 50 60 70 80 90

Transverse Phase Advance (zero current) [deg]N

orm

. Tra

ns

v. 9

5%

-rm

s-E

mit

tan

ce

Gro

wth

[%

]

mismatched

re-matched

• significant reduction of emittance growth by rms-matching including space charge

• reduction demonstrates that algorithm to re-construct initial rms-values is valid


Summary

• rms-emittance growth along a 5-tank DTL measured for 12 phase advances from ..35° to 90°

• Measurements simulated using four codes (DYNAMION, PARMILA, PARTRAN, LORASR)

• Special emphasis put on re-construction of amount of halo within initial distribution

• Very good agreement found among DYNAMION, PARMILA, and PARTRAN

• LORASR predicts higher growth rates with respect to other three codes

• Codes describe well the behavior of measured sum of hor. and ver. emittances

• Considerable differences between meas. & sim. growth within single planes

• For low and high phase advances orientations and shapes of final distributions ..depend on the code

• Systematic reduction of rms-mismatch to DTL under space charge conditions

• rms-mismatch reduction resulted in considerable emittance growth reduction

(experimental reduction from 90% to 20% for space charge conditions equivalent to FAIR requirements)


Outlook

• Using improved rms-matching measurements to be extended towards σo≈ 130°

• Emittances to be measured after first DTL tank to avoid inter-tank-mismatch

• Simulations predict a space charge driven 4th order resonance (talk by D. Jeon)

• Attempt for experimental verfication at UNILAC scheduled for Dec. 2008

0.0

0.1

0.2

0.3

0.4

85 95 105 115 125


No

rm. 9

5%

-rm

s-E

mit

tan

ce

[m

m*m

rad

]

hor., initialver., initialhor., DYNAMIONver., DYNAMIONhor.,LORASRver., LORASR


Gesellschaft für SchwerIonenforschung GSI

UNILAC, p – U : 3 – 12 MeV/u

Synchrotron, Bδ = 18 Tm

p: 4 GeV

Ne: 2 GeV

U: 1 GeV

3 sources

ion species vary from pulse to pulse:

simultaneous experiments using different ions

Stor. Ring, Bδ = 10 Tm

Fragment Separator

High Energy Physics


Alvarez 1st

Tanktransv. emitt. meas.

"t"

Buncher 36 MHz Buncher 108 MHzQuadrupoles

bunch length meas. "l"

15° 15°

30°

starting point of simulations

"s"

Construction of initial rms-Parameters for Simulations

• DTL transmission is very sensitive to buncher settings, i.e. long. mismatch

• applied buncher settings resulted in full DTL transmission and minimized low energy tails

-> useful in re-constructing the long. input distribution for simulations

• transv. and long. emittance were measured at different locations, i.e. at "t" & "l"

• distances from "l" and "s" to point "A" differ by 0.4 m

• to merge transv. & long. measurements together some approximations were used

"A"

initial bunch length & transv. emittances measured at different locations !!


transv. emitt. meas. "t"

Buncher 36 MHz Buncher 108 MHzQuadrupoles

bunch length meas. "l"

15°15°

30°

Starting point of simulations "s"

Re-construction of initial rms-Parameters for Simulations

• to merge measurements together some approximations were used :

• "transport" from "l" to "s" approximated by drift of 0.4 m (with space charge)

• at "t": combine measured x&y-rms-Twiss parameters with guessed long. rms-Twiss ..parameters

• rms-tracking with space charge from "t" to "s-0.4m", using applied machine settings

• if bunch length at "s-0.4m" agrees reasonably with measured one at "l": -> ok

• if not: -> do different guess on long. Twiss parameters at "t"

• put "s"-rms-Twiss parameters (x,y,l) into rms-matching routine

• compare suggested buncher settings with those used during experiment

• agreement: -> ok, rms-parameters of distribution re-constructed

• no agreement: -> do different guess on long. Twiss parameters at "t"

"A"



• emittance growth is sensitive to type of initial distribution (i.e. amount of halo)

• amount of halo can be visualized by plotting the fractional emittance vs. fraction

fract

ional rm

s-em

itta

nce

fraction of particles [%]0 100

no halo (KV)

some halo

strong halo


Phase Advances


0.0

0.1

0.2

0.3

0.4

0.5

0 20 40 60 80 100 120

Init. Long. Emittance [100%, rms, deg mrad]

No

rm. r

ms

-Em

itta

nc

e [

mm

*mra

d]

hor., DYN ver., DYN

hor, exp ver, exp

hor., PARMILA ver., PARMILA

Dependence on Initial Long. rms-Emittance Value

(using Gaussians cut at 2σ in each plane)

simulation of experiments on transverse rms-emittance growth along an alvarez dtl

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