Download - 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
14.04.2005 Collimation for the Linear Collider, Daresbury. 2
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
14.04.2005 Collimation for the Linear Collider, Daresbury. 3
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
14.04.2005 Collimation for the Linear Collider, Daresbury. 4
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
14.04.2005 Collimation for the Linear Collider, Daresbury. 5
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
14.04.2005 Collimation for the Linear Collider, Daresbury. 6
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
14.04.2005 Collimation for the Linear Collider, Daresbury. 7
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
14.04.2005 Collimation for the Linear Collider, Daresbury. 8
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
14.04.2005 Collimation for the Linear Collider, Daresbury. 9
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!
14.04.2005 Collimation for the Linear Collider, Daresbury. 10
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.
14.04.2005 Collimation for the Linear Collider, Daresbury. 11
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)
14.04.2005 Collimation for the Linear Collider, Daresbury. 12
SLAC Experimental results
• From SLAC report 2004
14.04.2005 Collimation for the Linear Collider, Daresbury. 13
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)
14.04.2005 Collimation for the Linear Collider, Daresbury. 14
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
14.04.2005 Collimation for the Linear Collider, Daresbury. 15
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