simulation of halo collimation in bds

14.04.2005 Collimation for the Linear Collider, Daresbury. 1

Adam Mercer, German Kurevlev, Roger Barlow

Simulation of Halo Collimation in BDS


Halo Collimation

• What is Halo– ~ 104 of bunch particles at the BDS entry (TESLA)

• Standard Goals of Halo Collimation– High Luminosity

– Machine protection from direct hit etc. and detector protection for acceptable backgrounds

• Two tasks for investigation– Transverse wake fields in small collimation apertures

– Backgrounds and material damage analysis


Wake Fields• Lattice element excitation when beam bunch passing through

it that can hit: – the bunch itself (short-range wake) – energy loss or transverse kick

– or the next bunches (long-range) – instabilities

• Wake Fields Classification– Longitudinal (energy loss)

– Transverse (center mass offset results in kick in transverse angle)• Geometric (on discontinuities)

• Resistive wall (finit conductivity)

• Surface roughness

• Transverse geometric and resistive wall effects are the most critical types for steep and tapered collimators


General Wake Fields Theory• Usual approach is to get integrated forces and apply charge

distribution moments (m=0 – monopole, m=1 – dipole, etc )

• For a bunch particle e:

• Impedances:

For example, for a round steep spoiler monopole and dipole components:

mrzWIce

dsFc

zrwce

p

mmrmrzWIce

dsFc

zrwce

p

mmm

L

Lzzz

mmm

L

L

cos)(1

),(

)sinˆcosˆ()(1

),(

2/

2/

12/

2/

)()()()()()(22

sswssdcNe

spsswssdcNe

sp t

s

z

s

z

)(2

)()(21

)(

)()()()(

//

//

Zedi

sWZedsW

sWecds

iZsWecds

Z

csim

lm

csim

mcsi

mcsil

m

)(2

)()(ln2

)(2

)(ln)( 20

10

0200 s

acZ

sWsabcZ

sWacZ

ZabZ

Z tl


Collimators Wake Fields Theory-Geometric

Below: α – taper angle, σ – bunch length, b – aperture radius or half width, h – horizontal half width)

• Round pipe (Yokoya)– Diffractive– Inductive

• Rectangular (Stupakov)– Diffractive– Intermediate– Inductive

kyNr

y e

'

1/1

2 bb

k

hbbb

k //138

3

hbbbh

k //2 2

1/2

2 bb

k

1/

b

bk


Collimators Wake Fields Theory-Resistive

• Piwinski (according to Onoprienko)– Small offset (L – collimator length, σz – bunch length, σz – bunch

length, σ – conductivity)• No taper

• Tapered

– Offset ~ half gap

flatFroundFc

bL

Fk GGz

G 8

12

)25.0( 3

33

zG

cb

Fk 23

1

2

)25.0(

byvvbvvcLNr

Fyz

eG /

)2/(cossin

2

)25.0(' 223


Wake Fields Simulation

• Different type of codes

– Full dimension in frequency or time domain to test analytical wake functions or get table data

• MAFIA, ECHO, …

– Optical codes with phenomenological wake fields to get the effect on beam transport through the BDS

• Merlin – Written by Nick Walker (DESY) and Andre Wolski (LBL)

– Set of C++ class libraries

– Originally for linear collider, now does storage rings


Wake Fields in Merlin

Merlin had a process for handling wake fields

Now inserted Wake Functions (thanks to Frank Jackson)

Bunch slices for wakes integration prepared and integration already implemented

Momentum change on slice i)()(

)()()(

1

2

1

2

sswssdpcNe

psp

sswssdpcNe

pp

t

nbins

il

nbins

i

z


Merlin ExampleParticles feel integrated force from those in front "banana bunch"

Off-axis bunch after collimator, no wakefields. Looking down (from above) at the bunch.

Exaggerated!


Merlin ExampleParticles feel integrated force from those in front "banana bunch"

Exaggerated!

Off-axis bunch after collimator, with wakefields. Looking down (from above) at the bunch.


Comparison of MERLIN results with SLAC experiment

• Beam parameters used in experiment and simulation:

• Beam (bunch) charge Q_total = 2e+10 e - number of electrons in the bunch - Ne = 2e+10Beam energy p0 = 1.19 GeVLattice horizontal betta function betta_x = 3 mHorizontal emittance emit_x = 0.36 mm, emit_y = 0.16 mm ,Lattice vertical betta function betta_y = 10 m (we used these ones to have minimal emittance grow - there are no exact values from experiment)Longitudinal bunch size sigma_z = 0.65 mmSquared aperture of the spoiler with the side width 38 mm (half width to use in wake formulas b1 = 1.9 mm)


SLAC Experimental results

• From SLAC report 2004


Merlin simulation result• Vertical offset Y of the beam centroid is in mm as in experiment, mean Yp kick is in 10s

mkrad units so our constant is close to the correct one. We used diffraction limit formula for transverse wake function. As a result in our case in Merlin we don't have effect of near wall wake fields as in ECHO code so it should be almost strait line.

• The table confirms also the following formula for rms kick: Krms=Kt/sqrt(3)


Backgrounds and material damage simulations

• Standard approach is to use industrial standard Finite Element Analysis or Finite Element Method code linked with beam transport code– SCRAPER-RTS&T + ANSYS

– MAFIA + interface code + ANSYS

– SUPERFISH + linking codes + ANSYS and other FEA codes

– FronTier + ANSYS

• Plan to use available ANSYS code


Future project plan

• Wake fields for tapered collimators in Merlin• Wake fields with higher order modes as in ECHO code

for near wall wakes simulation in Merlin• Tracking of all the spoilers until the IP• Backgrounds and material damage simulations with

Merlin and ANSYS plus probably some linking code

simulation of halo collimation in bds

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