Positron Source Relocation Damping Ring @ 10Hz S. Guiducci (INFN-LNF)
Electron cloud build up studies for the CLIC positron damping ring
description
Transcript of Electron cloud build up studies for the CLIC positron damping ring
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Electron cloud build up studies for the CLIC positron damping ring
G. Iadarola, G. Rumolo, H. Bartosik
Thanks to:F. Antoniou, E. Koukovini-Platia, Y. Papaphilippou
CLIC Workshop 2014
CERN, 5 February 2014
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Outline
• Introduction
o CLIC Damping Ring machine elements and beam scenarios
• e-cloud buildup simulation with PyECLOUD
o Peculiarities of simulations for low emittance rings
• Features of the e-cloud buildup in the CLIC DR machine elements
o Wigglers
o Dipoles
o Quadrupoles
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Outline
• Introduction
o CLIC Damping Ring machine elements and beam scenarios
• e-cloud buildup simulation with PyECLOUD
o Peculiarities of simulations for low emittance rings
• Features of the e-cloud buildup in the CLIC DR machine elements
o Wigglers
o Dipoles
o Quadrupoles
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Introduction
When the an accelerator is operated with close bunch spacing an Electron Cloud
(EC) can develop in the beam chamber due to the Secondary Emission from the
chamber’s wall.
0 200 400 600 800 10000.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Primary e- energy [eV]
Seco
ndar
y El
ectro
n Yi
eld
[SEY
]
SEYmax
Secondary Electron Yield (SEY) of the
chamber’s surface:
• ratio between emitted and impacting
electrons
• function of the energy of the primary
electron
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Introduction
When the an accelerator is operated with close bunch spacing an Electron Cloud
(EC) can develop in the beam chamber due to the Secondary Emission from the
chamber’s wall.
• Strong impact on beam quality (EC
induced instabilities, particle losses,
emittance growth)
• Dynamic pressure rise
• Heat load (on cryogenic sections)
LHC Dipole chamber @ 7TeV
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Injected(εx, εy) = (63 μm, 1.5 μm)
Extracted(εx, εy) = (500 nm, 5 nm)
CLIC e+ damping ring
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CLIC e+ damping ring
C = 427.5 m
Wigglera=40mm, b=6mm
Ltot = 104 m
Dipole a=40mm, b=9mm
Ltot = 58 m
Quadrupolea=9mm, b=9mm
Ltot = 86 m
e-cloud formation has been investigated in three families of devices
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CLIC e+ damping ring
Studies performed with parameters of beam before extraction:
• Beam energy: 2.86 GeV• Bunch population: 4x109 e+
• Transverse emittances (εx, εy): (500 nm, 5 nm)
• Two bunch patterns:
0.5 ns bunch spacing – b.l. = 6.4 mm
156 b. 556 empty buckets 156 b. 556 empty buckets
312b. 2538 empty buckets
1.0 ns bunch spacing – b.l. = 7.2 mm
Trev = 1.425 μs
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Outline
• Introduction
o CLIC Damping Ring machine elements and beam scenarios
• e-cloud buildup simulation with PyECLOUD
o Peculiarities of simulations for low emittance rings
• Features of the e-cloud buildup in the CLIC DR machine elements
o Wigglers
o Dipoles
o Quadrupoles
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t=t+Δt
Evaluate the electric field of beam at each MP location
Generate seed e-
Compute MP motion (t->t+Δt)
Detect impacts and generate secondaries
PyECLOUD simulation recipe
Evaluate the e- space charge electric field
PyECLOUD is a 2D macroparticle (MP) code for
the simulation of the electron cloud build-up with:
• Arbitrary shaped chamber
• Ultra-relativistic beam
• Arbitrary magnet configuration
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t=t+Δt
Evaluate the electric field of beam at each MP location
Generate seed e-
Compute MP motion (t->t+Δt)
Detect impacts and generate secondaries
Evaluate the e- space charge electric field
Evaluate the number of seed e- generated
during the current time step and generate
the corresponding MP:
• Residual gas ionization and
photoemission are implemented
PyECLOUD simulation recipe
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x [mm]
y [m
m]
E log(normalizad magnitude) - with image charges
-60 -40 -20 0 20 40 60
-20-10
01020
-4
-3
-2
-1
t=t+Δt
Evaluate the electric field of beam at each MP location
Generate seed e-
Compute MP motion (t->t+Δt)
Detect impacts and generate secondaries
Evaluate the e- space charge electric field
• The field map for the relevant chamber
geometry and beam shape is pre-computed
on a suitable rectangular grid or loaded
from file in the initialization stage
PyECLOUD simulation recipe
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t=t+Δt
Evaluate the electric field of beam at each MP location
Generate seed e-
Compute MP motion (t->t+Δt)
Detect impacts and generate secondaries
Evaluate the e- space charge electric field
Classical Particle In Cell (PIC) algorithm:
• Electron charge density distribution ρ(x,y)
computed on a rectangular grid
• Poisson equation solved using finite
difference (FD) method
• Field at MP location evaluated through
linear (4 points) interpolation
PyECLOUD simulation recipe
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t=t+Δt
Evaluate the electric field of beam at each MP location
Generate seed e-
Compute MP motion (t->t+Δt)
Detect impacts and generate secondaries
Evaluate the e- space charge electric field
The dynamics equation is integrated in order
to update MP position and momentum:
PyECLOUD simulation recipe
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t=t+Δt
Evaluate the electric field of beam at each MP location
Generate seed e-
Compute MP motion (t->t+Δt)
Detect impacts and generate secondaries
Evaluate the e- space charge electric field
• When a MP hits the wall
theoretical/empirical models are
employed to generate charge, energy
and angle of the emitted charge
PyECLOUD simulation recipe
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t=t+Δt
Evaluate the electric field of beam at each MP location
Generate seed e-
Compute MP motion (t->t+Δt)
Detect impacts and generate secondaries
Evaluate the e- space charge electric field
PyECLOUD simulation recipe
Simulations for the CLIC e+ Damping Ring
Bunch length ~20 ps
Δt = 0.5 ps necessary to resolve the e-pinch
~3x109 steps for a full turn (~36 h CPU time)
Beam and electron distributions at the limit of
present capabilities of the code
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Beam field
x [mm]
y [m
m]
E log(normalizad magnitude) - with image charges
-60 -40 -20 0 20 40 60
-20-10
01020
-4
-3
-2
-1LHC: Aperture = 100 x σbeam
CLIC-DR: Aperture = 10000 x σbeam
Finite Difference calculation unaffordable resorted to analytical expression for Gaussian beam in elliptical chamber:
2
20 0
2( , ) ( , )x yi zE x y iE x y e w wS S S
2 22 x yS y x
x yx i y
x y
x yi
Bassetti-Erskine formula
where:
Image terms (effect of bundary)2
. . . .1
4 ( 1) sinh(2 )( , ) ( , )cosh(2 ) sinh( )
cnn
i c x i c yn c
e nqE x y iE x yg n q
2 2g a b logca ba b
with: a b
where: q i cosh cosx g sinh siny g
+For the CLIC wiggler chamber (a/b=6.6)
150 terms needed for convergence
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e-cloud space charge field
• In the cases of wigglers and dipoles e-
accumulate in a narrow stripe close to the
beam
• Fine grid needed for Finite Difference
Poisson solver (Δh = 50 um, 1e5 nodes),
run many times during the simulation
• LU factorization of the FD (sparse) matrix
pre-calculated in the initialization stage to
speed-up the calculation*
*As proposed in: O. Haas, “Electron Cloud Modeling and Coupling to Tracking Codes”, joined CERN/TU Darmstadt e-cloud meeting (16/12/2013)
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During the bunch passage electric field due
to the e- is completely negligible
• In the cases of wigglers and dipoles e-
accumulate in a narrow stripe close to the
beam
• Fine grid needed for Finite Difference
Poisson solver (Δh = 50 um, 1e5 nodes),
run many times during the simulation
• LU factorization of the FD (sparse) matrix
pre-calculated in the initialization stage to
speed-up the calculation*
• e- field map re-evaluated only every
Δtsc=0.02ns (≈b.l.)
Cut on chamber’s positive semiaxis
*As proposed in: O. Haas, “Electron Cloud Modeling and Coupling to Tracking Codes”, joined CERN/TU Darmstadt e-cloud meeting (16/12/2013)
e-cloud space charge field
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Outline
• Introduction
o CLIC Damping Ring machine elements and beam scenarios
• e-cloud buildup simulation with PyECLOUD
o Peculiarities of simulations for low emittance rings
• Features of the e-cloud buildup in the CLIC DR machine elements
o Wigglers
o Dipoles
o Quadrupoles
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e-cloud in the wiggler magnets
• Threshold lower for 0.5 ns (mainly due to faster risetime)
1 1.2 1.4 1.6 1.810-3
10-2
10-1
100
101
102
SEY
Hea
t loa
d [W
/m]
wiggler_0p5ns_heatload_vs_SEY_nomint
1.0 ns0.5 ns
0 0.5 1
106
108
1010
Time [us]
Num
ber
of e
- per
uni
t len
gth
[m-1
]
SEY = 1.8
1.0 ns0.5 ns
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1 1.2 1.4 1.6 1.810-3
10-2
10-1
100
101
102
SEY
Hea
t loa
d [W
/m]
wiggler_0p5ns_heatload_vs_SEY_nomint
1.0 ns0.5 ns
• Threshold lower for 0.5 ns (mainly due to faster risetime)
• Large e- densities (>1e13) at the beam location (severe effects on beam quality/stability)
• e- horizontally confined in a narrow region around the beam (local low SEY coating or
clearing electrode for full e-cloud suppression)
e-cloud in the wiggler magnets
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1 1.2 1.4 1.6 1.810-3
10-2
10-1
100
101
SEY
Hea
t loa
d [W
/m]
dipoles_0p5ns_heatload_vs_SEY_nomint
1.0 ns0.5 ns
• Threshold lower for 0.5 ns (mainly due to faster risetime)
• Large e- densities (>1e13) at the beam location (severe effects on beam quality/stability)
• e- horizontally confined in a narrow region around the beam (local low SEY coating or
clearing electrode for full e-cloud suppression)
e-cloud in the dipole magnets
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0 0.5 1106
107
108
109
1010
1011
Time [us]
Num
ber
of e
- per
uni
t len
gth
[m-1
]
0.5 ns - SEY = 1.8
312b.
0 0.5 1106
107
108
109
1010
1011
Time [us]
Num
ber
of e
- per
uni
t len
gth
[m-1
]
1.0 ns - SEY = 1.8
2x156b.
• In the case of the quadrupoles, we noticed that saturation was not achieved
within a single turn, but due to e- trapping it can be reached in a multiturn
regime (not investigated yet)
e-cloud in the quadrupole magnets
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• In the case of the quadrupoles, we noticed that saturation was not achieved
within a single turn, but due to e- trapping it can be reached in a multiturn
regime (not investigated yet)
• To get a first idea, we simulated an artificially longer train
0 0.5 1106
107
108
109
1010
1011
Time [us]
Num
ber
of e
- per
uni
t len
gth
[m-1
]
1.0 ns - SEY = 1.8
2x156b.500b.
0 0.5 1106
107
108
109
1010
1011
Time [us]
Num
ber
of e
- per
uni
t len
gth
[m-1
]
0.5 ns - SEY = 1.8
312b.700b.
e-cloud in the quadrupole magnets
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1 1.2 1.4 1.6 1.810-2
10-1
100
101
SEY
Hea
t loa
d [W
/m]
300 ns train
1.0 ns0.5 ns
• Threshold lower for 0.5 ns (mainly due to faster risetime)
• Large e- densities (>1e13) at the beam location
• e- move around the quadrupole field line. Multipacting concentrated around the magnet
pole regions (local low SEY coating or clearing electrode for full e-cloud suppression)
e-cloud in the quadrupole magnets
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Dependence on bunch population
1 1.2 1.4 1.6 1.8 20
5
10
15
20
25
30
35
SEY
Hea
t loa
d [W
/m]
dipoles_heatload_vs_SEY_lin
1 1.2 1.4 1.6 1.8 20
10
20
30
40
50
60
SEYH
eat l
oad
[W/m
]
dipoles_0p5ns_heatload_vs_SEY_lin
• In the framework of CLIC parameter optimization, different bunch
intensities have been also investigated
• The multipacting threshold shows a weak dependence on the bunch population
• Heat load significantly stronger for intensities larger than nominal
Dipole - 1 ns Dipole - 0.5 ns
1 1.5 2 2.5 310
-4
10-2
100
102
104
SEY
Scr
ubbi
ng d
ose
(20e
V) [
mA
/m]
wiggler_0p5ns_simulated_beam_scrubdose_vs_sey_log_legend
1e9 ppb2e9 ppb3e9 ppb4e9 ppb5e9 ppb6e9 ppb7e9 ppb8e9 ppb9e9 ppb10e9 ppb
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1 1.2 1.4 1.6 1.8 20
10
20
30
40
50
SEY
Hea
t loa
d [W
/m]
wiggler_heatload_vs_SEY_lin
1 1.2 1.4 1.6 1.8 20
20
40
60
80
100
120
140
SEY
Hea
t loa
d [W
/m]
wiggler_0p5ns_heatload_vs_SEY_lin
Dependence on bunch population
• In the framework of CLIC parameter optimization, different bunch
intensities have been also investigated
• The multipacting threshold shows a weak dependence on the bunch population
• Heat load significantly stronger for intensities larger than nominal
Wiggler - 1 ns Wiggler - 0.5 ns
1 1.5 2 2.5 310
-4
10-2
100
102
104
SEY
Scr
ubbi
ng d
ose
(20e
V) [
mA
/m]
wiggler_0p5ns_simulated_beam_scrubdose_vs_sey_log_legend
1e9 ppb2e9 ppb3e9 ppb4e9 ppb5e9 ppb6e9 ppb7e9 ppb8e9 ppb9e9 ppb10e9 ppb
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Summary and conclusions
• The e-cloud formation in the wigglers, dipoles and quadrupoles of the CLIC e+ damping ring
has been investigated with PyECLOUD simulations
• Quite challenging simulation scenario (very short bunches, extremely small beam size,
electron density concentrated in a small region of the beam pipe)
• Dipoles and wigglers show similar features:
o e- horizontally confined in a narrow region around the beam (local low SEY coating
or clearing electrode for full e-cloud suppression)
o Weak dependence of SEY multipacting threshold on bunch population
• In the quadrupoles e-cloud buildup is slower:
o most likely saturation is reached in more than one turn (still to be fully investigated)
o multipacting concentrated around the magnet pole regions
• large e- densities (>1e13) at the beam location (which can have serious impact on
beam quality see talk by H. Bartosik)
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Thanks for your attention!
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Dipole
• In the cases of wigglers and dipoles e-
accumulate….
0 0.5 1
106
108
1010
Time [us]
Num
ber
of e
- per
uni
t len
gth
[m-1
]
SEY = 1.8
1.0 ns0.5 ns