Issues in the Formation and Dissipation of the Electron Cloud Miguel A. Furman, LBNL

M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 1

Issues in the Formation and Dissipationof the Electron Cloud

Miguel A. Furman, [email protected]

13th ICFA Beam Dynamics Mini Workshop“Beam-Induced Pressure Rise in Rings”

BNL, Dec. 8–12, 2003

Lawrence Berkeley National Laboratory

My gratitude to:

A. Adelmann, G. Arduini, M. Blaskiewicz, O. Brüning, Y. H. Cai, R. Cimino, I. Collins, O. Gröbner, K. Harkay, S. Heifets, N. Hilleret, J. M. Jiménez, R. Kirby,G. Lambertson, R. Macek, K. Ohmi, M. Pivi, G. Rumolo, F. Zimmermann.


Summary• Motivation: better understand electron cloud (EC) dynamics

– in particular: effect of secondary electron process

• Tools:– simulations (mostly code POSINST – Furman and Pivi); other codes by Ohmi, Zimmermann,

Rumolo, Blaskiewicz, Adelmann,... also take SE into account

– electron detectors (APS, SPS, PSR, RHIC – Harkay, Jiménez, Macek, Browman, Zhang,...)

• EC formation– primary processes: photoelectrons, residual gas ionization, beam-particle losses

– secondary electron emission (SEY): may lead to beam-induced multipatcing (BIM)

– examples:

• sensitivity to secondary emission yield (E0) (E0=incident electron energy)

• secondary emission spectrum d/dE (E=emitted electron energy)

• EC dissipation– focus: mostly PSR, also APS and SPS: role of (0)

• Scrubbing effect and conclusions



Tools• Simulation

– detailed model for and d/dE– input data: measurements by R. Kirby, N. Hilleret, R. Cimino, I. Collins and

others• St. St., Cu, Al, TiN

– electron cloud is dynamical– beam is a prescribed function of time, space

• Electron detectors– RFA (Harkay and Rosenberg, NIMPR A453, 507 (2000); PRSTAB 6, 034402)

• installed at APS, PSR, BEPC, ANL IPNS RCS

• measure Iew and d/dE at chamber wall (“prompt” electrons)

– “sweeping detector” at PSR (Browman, Macek)• installed at PSR• measure EC density in the bulk (“swept” electrons)

– strip detector at SPS, COLDEX, PUs• (Jiménez et al., PAC03)• strip detector in an adjustable B field


(ROAB003; ROPA007)

(ROAB003)

(TOPC003; TPPB054)

PAC03 refs. in blue


EC formation: basics

• Electron charge conservation in a given chamber section– assuming no antechamber, no net end-losses

– assumes 3 primary processes: • photoelectrons

• residual gas ionization

• beam-particle losses

Assume: =beam line density Z=beam particle chargep=chamber x-section perimeter

Iew=e– flux at wall [A/m2]

=primary production rate [m–1]

per beam particleLawrence Berkeley National Laboratory

(M. Blaskiewicz)


EC formation: primary e– rate of creation


vb = beam speed

Yeff = eff. quantum efficiency (e– yield per )

i = ioniz. cross-section per beam particle

pvac = vac. pressure

T = temperature

eff = eff. e– yield per (beam particle)-wall collision

n'bpl = beam particle loss rate per unit length per beam particle

• Electron production rate per beam particle per unit length of beam trajectory:


Secondary e– emission

Simulation (Furman-Pivi, PRSTAB 5, 124404):– event=one electron-wall collision– instantaneous generation of n secondaries (or absorption)– include E0 and 0 dependence– detailed phenomenological model for and d/dE

Three main components of emitted electrons:

elastics:

rediffused:

true secondaries:

NB: d/dE is different for e, r and ts!!!



Two sample measurements of the SEY

2.0

1.5

1.0

0.5

0.010009008007006005004003002001000

E0 [eV]

measured data (R. Kirby) model fit (Furman-Pivi)

E0ts=0E0tspk=310dtspk=1.22powts=1.813P1epk=0.5P1einf=0.07E0epk=0powe=0.9E0w=100P1rinf=0.74Ecr=40qr=1

Stainless steel sample (data R. Kirby) 2.0

1.5

1.0

0.5

0.010009008007006005004003002001000

E0 [eV]

fit (Furman-Pivi) measured data

E0tspk=276.812dtspk=1.8848powts=1.54033E0ts=0P1epk=0.496229P1einf=0.02E0epk=0powe=1E0w=60.8614P1rinf=0.2Ecr=0.0409225qr=0.104045

Copper sample (Hilleret data)


Cu St. steel

• caveat: samples not fully conditioned!

(N. Hilleret; R. Kirby)


PSR simulation: sensitivity to max


• stainless steel chamber, field-free region, • dominant primary process: proton losses:

beam signal(arb. units)

0.1

1

10

100

1000

line density [nC/m]

2.0x10-6

1.81.61.41.21.00.80.60.40.20.0

runtime [s]

beam line density EC line density (deltamax=1.5) EC line density (deltamax=1.7)

PSR simulation, field-free regionnsteps=1000 or 2000, macrop=500, nkicks=1001prot. loss rate=4.44e-8, yield=100

aver. beam neutralization

max=1.5, (0)=0.36

max=1.7, (0) = 0.4

aver. electron line density vs. time

(see also RPPB035)




beam signal(arb. units)

e– flux at the wall vs. time

101

2

3

4

5

6

789102

2

3

4

5

6

789103

2

3

4

5

6

789104

electron wall current [micro-A/cm**2]

2.0x10-6

1.81.61.41.21.00.80.60.40.20.0

tsm [s]

electron-wall current (dpk=1.5) electron-wall current (dpk=1.7) beam signal (arb. units)


max=1.7, (0) = 0.4

max=1.5, (0)=0.36



300

250

200

150

100

50

0

electron energy at wall [eV]

2.0x10-6

1.81.61.41.21.00.80.60.40.20.0

tsm [s]

Ek0_sm15 (dpk=1.5) Ek0_sm17 (dpk=1.7) beam signal (arb. units)



electron-wall collision energy vs. time


PSR simulation-contd.

8000

6000

4000

2000

0

beam potential [V]

2.0x10-6

1.81.61.41.21.00.80.60.40.20.0

timekick [s]



beam potential well vs. time


Sample spectrum: d/dE

• Depends on material and state of conditioning – St. St. sample, E0=300 eV, normal incidence, (Kirby-King, NIMPR A469, 1 (2001))

0.08

0.06

0.04

0.02

0.00300250200150100500

Secondary electron energy [eV]

Secondary energy spectrum St. St., E0=300 eV, normal incidence

true secondaries(area[0,50]=1.17)

backscattered(area[295,305]=0.12)

rediffused(area[50,295]=0.75)


st. steel sample= 2.04e = 6%r = 37%ts =57%

e+r =43%

– Hilleret’s group CERN: Baglin et al, CERN-LHC-PR 472. – Other measurements: Cimino and Collins, 2003)

Cu sample= 2.05e = 1%r = 9%ts =90%

e+r =10%


Sensitivity to relative ratios of e, r and ts: LHC


• LHC simulation max fixed at 2.05;

• dominated by photoelectrons; electron line density vs. time (LHC arc dipole)

7

6

5

4

3

2

1

0

aver. electron line density [nC/m]

1.4x10-61.21.00.80.60.40.20.0

timeW [s]

aver. beam neutralization level

beam signal (arb. units) Copper, true sec. only Copper Stainless st.

LHC arc dipole simulation average line density

photoelectrons: outer edge only

n'e() =6.3 -4 / ,e e m max=2.05

e+r = 43%

e+r = 10%

e+r = 0

(Furman-PiviEPAC02)

max=2.05

(see also: TPPB054)



2000

1500

1000

500

0

electron-wall collision energy [eV]

1.4x10-61.21.00.80.60.40.20.0

time_sm [s]

beam signal (arb. units) Copper Stainless st. Copper, true sec. only

LHC arc dipole simulation electron-wall collision energy


n'e() =6.3 -4 / ,e e m max=2.05


e–-wall collision energy vs. time (LHC arc dipole)

e+r = 43%

e+r = 10%

e+r = 0



2.0

1.5

1.0

0.5

0.0

effective SEY

1.4x10-61.21.00.80.60.40.20.0

time_sm [s]

beam signal (arb. units) Copper Stainless Copper, true sec. only

LHC arc dipole simulation effective SEY


n'e() =6.3 -4 / ,e e m max=2.05


effective SEY vs. time (LHC arc dipole)

e+r = 43%

e+r = 10%

e+r = 0


800

600

400

200

0

aver. power deposition [W/m]

1.4x10-6

1.21.00.80.60.40.20.0

time_sm [s]

LHC arc dipole simulation: electron-cloud power deposition


n'e() =6.3 -4 / ,e e m max=2.05

( . )beam signal arb unitsCopper Stainless steel , .Copper true sec only

. 0.5< <1.2Aver power deposition in t μs

:11 /copper W m. .:152 /st st W m

, :2.1 / .copper TS only W m



power deposition vs. time (LHC arc dipole)

e+r = 10%

800

600

400

200

01.060x10

-61.0501.0401.0301.020

time_sm [s]

e+r = 0

e+r = 43%


EC formation: beam-induced multipacting (BIM)


• train of short bunches, each of charge Q=NZe, separated by sb

• t = e– chamber traversal time

• b = chamber radius (or half-height if rectangular)

The parameter defines 3 regimes:

If G = 1 and eff > 1, EC can grow dramatically (O. Gröbner, ISR; 1977)

e−

e−

e−

e−

+ + + + + +

γ or p

(also for solenoidal fieldif T/2=sb/c: WOAA004)


BIM in the APS

120

100

80

60

40

20

0

aver. electron-wall current [nA/cm

2]

35302520151050

bunch spacing sB [RF buckets]

measured simulated

APS, positron beam

Detector Current vs. Bunch Spacing

(10 bunches, 2 mA/bunch in all cases; measurements courtesy K. Harkay, ANL)

region of BIM

sB=d2/(reN), b<d<a


(Furman, Pivi, Harkay, Rosenberg, PAC01)

time-averaged e– flux at wall vs. bunch spacing

measuredsimulated

• e+ beam, 10-bunch train, field-free region

(see also: RPPG002)


BIM for long bunches: case of PSR• bunch length >> t

– a portion the EC phase space is in resonance with the “bounce frequency”

– “trailing edge multipacting” (Macek; Blaskiewicz, Danilov, Alexandrov,…)


ED42Y electron detector signal 8μC/pulse beam

435 μA/cm2

(simulation input)

electron signal

measured (R. Macek) simulated (M. Pivi)

(max=2.05)

(ROAB003; RPPB035)


BIM for long bunches: case of PSR-contd.

head

truncated bunch(nominal charge)

nominalbunch

tail

L=150 ns

• simulated “experiment” in trailing edge multipacting: — truncate bunch tail at fixed bunch charge


• suppresses the resonance • hard to put into practice! (M. Pivi)

bunch profile

aver. e– line density

(RPPG024)


EC dissipation - simplest analysis


N

N’2b

If not monoenergetic and not along a straight line, then

• beam has been extracted, or gap between bunches• field-free region, or constant B field • assume monoenergetic blob of electrons• neglect space-charge forces

where K=f(angles)≈1.1–1.2

simulations show that this formulaworks to within ~20%

and = dissipation time


EC dissipation in PSR after beam extraction

• “Sweeping e– detector”– measures electrons in the bulk ≈ 200 ns eff ≈ 0.5 if E = 2–4 eV

– since eff ≈ (0), you infer (0)

– well supported by simulations (see next slide)

(Macek and Browman)


(RPPB035)

M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 23Lawrence Berkeley National Laboratory

EC dissipation after beam extraction: PSR simulation

0.01

0.1

1

10

100

1000

line density [nC/m]

2.0x10-61.81.61.41.21.00.80.60.40.20.0

time [s]

EC line density beam line density

exponential decay(slope=2e-07 s)

PSRdissip3

aver. neutralization level

PSR simulationfield-free section, N=5e13

p loss rate=4e-6/m, yield=100 e/pNB: primary e– rateis 100 x nominal

input SEY:

max = 1.7 (0) = 0.4

EC line density vs. time (field-free region)

slope = 200 ns


EC dissipation after beam extraction: PSR simulation

0.1

1

10

100

1000

electron energy [eV]

2.0x10-6

1.81.61.41.21.00.80.60.40.20.0

tsm [s]

collision energy per electron absorbed energy per electron beam signal (arb. units)

PSR simulationfield-free section, N=5e13

p loss rate=4e-6/m, yield=100 e/p

PSRdissip3

e–-wall collision energy vs. time (field-free region)



EC dissipation after beam extraction: SPS simulation

0.01

0.1

1

10

line density [nC/m]

2.4x10-62.22.01.81.61.41.21.00.80.60.40.20.0

time [s]

EC line density beam line density

exponential decayslope=1.7e-07 [s]

SPS_P1e_4_nb72a.dir

av. beam neutralization level

SPS simulationP=1e-4 Torr, B=0.2 T, N=8e10,

rect. chamber (a,b)=(7.7,2.25) cm

NB: pvac is>> nominal

• stainless steel chamber, dipole magnet, B = 0.2 T, • dominant primary process: residual gas ionization;

slope = 170 ns

input SEY:

max = 1.9 (0) = 0.5


EC dissipation after beam extraction: SPS simulation

0.1

1

10

100

1000

electron energy [eV]

2.4x10-6

2.22.01.81.61.41.21.00.80.60.40.20.0

tsm [s]

collision energy per electron absorbed energy per electron

SPS simulationP=1e-4 Torr, B=0.2 T, N=8e10,

rect. chamber (a,b)=(7.7,2.25) cm SPS_P1e_4_nb72a.dir

e–-wall collision energy vs. time (B-field region)


Conditioning effects: beam scrubbing

• Decrease of SEY by e– bombardment– self-conditioning effect for a storage ring: “beam scrubbing”

• SPS ECE studies (M. Jiménez; F. Zimmermann):– 3+ years of dedicated EC studies with dedicated instrumentation

– scrubbing very efficient; favorable effects seen in:• vacuum pressure

• in-situ SEY measurements

• electron flux at wall

– e– energy distribution in good agreement with simulations above 30 eV

– TiZrV coating fully suppresses multipacting after activation


(see also: MOPA001; TPPB054)

(TOPC003)


Conditioning effects: beam scrubbing

• PSR “prompt” e– signal (BIM) is subject to conditioning: (R. Macek)– signal is stronger for st.st. than for TiN

– sensitive to location and N

– signal does not saturate as N increases up to ~8x1013

– conditioning: down by factor ~5 in sector 4 after few weeks (low current)

• PSR “swept” e– signal is not:– signal saturates beyond N~5x1013

– ≈ 200 ns, independent of:

• N

• location

• conditioning state

• st. st. or TiN

• Tentative conclusion: beam scrubbing conditions max but leaves (0) unchanged


(ROAB003; RPPB035)


Conditioning effects–contd.

• consistent with bench results for Cu found at CERN!

– the result (0)≈1 seems unconventional

– if validated, it could have a significant unfavorable effect on the EC power deposition in the LHC

• because electrons survive longer in between bunches


(R. Cimino and I. Collins, proc. ASTEC2003, Daresbury Jan. 03)

Copper SEY (CERN)


Conclusions

• A consistent picture of the ECE is emerging for– low-energy machines (long bunch, intense beam)

– high-energy machines (short, well separated bunches)

– methodical measurements and simulation benchmarks at APS, PSR and SPS are paying off

– some interesting surprises along the way

• Quantitative predictions are becoming more reliable– we are growing older but wiser



Additional material





2.5

2.0

1.5

1.0

0.5

0.010009008007006005004003002001000

E0 [eV]

delta_SS (Kirby data) delta_e delta_r delta_ts delta_er (=delta_e+delta_r) delta_tot delta_tsp


SEY for stainless steel, normal incidence(data courtesy R. Kirby, SLAC standard 304 rolled sheet,chemically etched and passivated but not conditioned)


2.5

2.0

1.5

1.0

0.5

0.010009008007006005004003002001000

E0 [eV]

delta_e delta_r delta_ts delta_er (=delta_e+delta_r) delta_tot delta_tsp deltaCuhilleret


SEY for Cu, normal incidence (Data courtesy N. Hilleret for chemically cleaned but not in-situ vacuum baked samples) (macro hilleret_fit_mauro)



2.0

1.5

1.0

0.5

0.010009008007006005004003002001000

E0 [eV]

fit (Furman-Pivi) measured data


Copper sample (Hilleret data)



2.0

1.5

1.0

0.5

0.010009008007006005004003002001000

E0 [eV]

measured data (R. Kirby) model fit (Furman-Pivi)


Stainless steel sample (data R. Kirby)



0.08

0.06

0.04

0.02

0.00350300250200150100500

Esec [eV]

dde_300_ss_abs (Kirby data, renormalized to delta(300)=2.04489) ddeRV_totp_bin

dele=0.0916988delr=0.739591delts=1.21947deltot=2.05076int_ddeRV_tot=2.06258int_ddeRV_totp=1.83298int_ddeRV_totp_bin=2.0676delout=2.05075delpout=1.81494delpbinout=2.05076deltsout=1.21947deltspout=0.983654

maxsec=10E0=300 eVpr=0.4sige=-1 eVsigee=1.88287

pnpar[1]=1.6pnpar[2]=2pnpar[3]=1.8pnpar[4]=4.7pnpar[5]=1.8pnpar[6]=2.4pnpar[7]=1.8pnpar[8]=1.8pnpar[9]=2.3pnpar[10]=1.8

enpar[1]=3.9enpar[2]=6.2enpar[3]=13enpar[4]=8.8enpar[5]=6.25enpar[6]=2.25enpar[7]=9.2enpar[8]=5.3enpar[9]=17.8enpar[10]=10

Emission energy spectrum, E0=300 eVstainless steel, normal incidence(data courtesy R. Kirby, SLAC standard 304 rolled sheet,chemically etched and passivated but not conditioned)

NOTE: rediffused+backscattered~50%(assuming low-energy cutoff=50 eV)


NOTE: rediffused+backscattered~5%(assuming low-energy cutoff=50 eV)





Current parameter values from fits to data


Q: is the electron emitted spectrum Maxwellian? A: only approximately.

Fits to data, however, imply pn~1.8–5, depending on n and material


definition of Maxwellian spectrum:

dN

d3p∝ exp−E kT( ), E =

p2

2me

⇒dNdE

∝ E1/2 exp−E kT( )≡Epn−1exp−E εn( )

⇒ pn =3 2


2.5

2.0

1.5

1.0

0.5

0.010009008007006005004003002001000

E0 [eV]

delta_e delta_r delta_ts delta_er (=delta_e+delta_r) delta_tot delta_tsp deltaCuhilleret

E0tspk=276.812dtspk=2.1powts=1.54033E0ts=0P1epk=0P1einf=0E0epk=0powe=1E0w=60.8614P1rinf=0Ecr=0.0409225qr=0.104045

SEY for Cu, normal incidence (data courtesy N. Hilleret)

true secondaries only

(macro hilleret_fit_mauro_TS_only)


backscattered and rediffused electronsartificially suppressed (true secondaries only)


BIM for long bunches: case of PSR

• bunch length >> t


ED02X electron detector signal 8μC/pulse beam

ED42Y electron detector signal 8μC/pulse beam

145 μA/cm2 435 μA/cm2


Effect of bunch shortening (PSR simulation; M. Pivi)• truncate the bunch tail to reduce trailing-edge multipacting

truncated bunch(nominal charge)

nominal bunch

head

tail


Effect of bunch shortening (PSR simulation; M. Pivi) – contd.

L=254 ns (nom..)

L=200 ns

L=180 ns

L=150 ns


100

80

60

40

20

0

W/m

350x10-9

300250200150100500

time_sm [s]

curr (beam current, arb. units) avPD_sm_Cu (Copper) avPD_sm_SS (Stainless) avPD_sm_Cu_ts (Copper, true sec. only)

LHC arc dipole simulation average power deposition

time-averaged power deposition:Copper: 0.59 W/mStainless: 5.7 W/mCopper, TS: 0.01 W/m



2.0

1.5

1.0

0.5

0.0

nC/m

350x10-9

300250200150100500

timeW [s]

curr (beam current, arb. units) avlineden_Cu (Copper) avlineden_SS (Stainless) avlineden_Cu_ts (Copper, true sec. only)

LHC arc dipole simulation average line density

(Y'=0.05; phels. produced at outer edge only)



2.0

1.5

1.0

0.5

0.0

W/m

350x10-9

300250200150100500

time_sm [s]

curr (beam current, arb. units) avPD_sm_Cu (Copper) avPD_sm_Cu_ts (Copper, true sec. only)

LHC arc dipole simulationpower deposition

(Y'=0.05; phels. produced at outer edge only)

time-averaged power deposition:Copper: 0.59 W/mCopper, TS: 0.01 W/m


(detailed view for copper only)


800

600

400

200

0

eV

350x10-9

300250200150100500

time_sm [s]

curr (beam current, arb. units) E0_sm_Cu (Copper) E0_sm_SS (Stainless) E0_sm_Cu_ts (Copper, true sec. only)

LHC arc dipole simulation electron-wall collision energy

Issues in the Formation and Dissipation of the Electron Cloud Miguel A. Furman, LBNL

Documents

beam speedyeff

beam particlem

beam particlepvac

beam particle chargep

beam particle loss rate

beam line densityz

beam potential wel

unit length of beam