electron cloud build up studies for the clic positron damping ring

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

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

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

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

Injected(εx, εy) = (63 μm, 1.5 μm)

Extracted(εx, εy) = (500 nm, 5 nm)

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


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

Outline

• Introduction





o Wigglers

o Dipoles

o Quadrupoles

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

t=t+Δt


Generate seed e-




Evaluate the number of seed e- generated

during the current time step and generate

the corresponding MP:

• Residual gas ionization and

photoemission are implemented


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


Generate seed e-




• 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


t=t+Δt


Generate seed e-




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


t=t+Δt


Generate seed e-




The dynamics equation is integrated in order

to update MP position and momentum:


t=t+Δt


Generate seed e-




• When a MP hits the wall

theoretical/empirical models are

employed to generate charge, energy

and angle of the emitted charge


t=t+Δt


Generate seed e-





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

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

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)

http://indico.cern.ch/conferenceDisplay.py?confId=281279



During the bunch passage electric field due

to the e- is completely negligible


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




Outline

• Introduction





o Wigglers

o Dipoles

o Quadrupoles

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

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


• 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

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


• 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

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

• 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.


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


• 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)


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

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

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)

Thanks for your attention!

Dipole


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

electron cloud build up studies for the clic positron damping ring

Documents

t tevaluate

electric field of beam

beam chamber

electron cloud ec

beam energy

number of seed e

parameters of beam

cloud formation