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.
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 2
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
Lawrence Berkeley National Laboratory
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 3
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
Lawrence Berkeley National Laboratory
(ROAB003; ROPA007)
(ROAB003)
(TOPC003; TPPB054)
PAC03 refs. in blue
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 4
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)
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 5
EC formation: primary e– rate of creation
Lawrence Berkeley National Laboratory
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:
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 6
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!!!
Lawrence Berkeley National Laboratory
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 7
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)
Lawrence Berkeley National Laboratory
Cu St. steel
• caveat: samples not fully conditioned!
(N. Hilleret; R. Kirby)
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 8
PSR simulation: sensitivity to max
Lawrence Berkeley National Laboratory
• 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)
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 9
PSR simulation: sensitivity to max
Lawrence Berkeley National Laboratory
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)
PSR simulation, field-free regionnsteps=1000 or 2000, macrop=500, nkicks=1001prot. loss rate=4.44e-8, yield=100
max=1.7, (0) = 0.4
max=1.5, (0)=0.36
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 10
PSR simulation: sensitivity to max
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)
PSR simulation, field-free regionnsteps=1000 or 2000, macrop=500, nkicks=1001prot. loss rate=4.44e-8, yield=100
Lawrence Berkeley National Laboratory
electron-wall collision energy vs. time
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 11
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]
PSR simulation, field-free regionnsteps=1000 or 2000, macrop=500, nkicks=1001prot. loss rate=4.44e-8, yield=100
Lawrence Berkeley National Laboratory
beam potential well vs. time
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 12
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)
Lawrence Berkeley National Laboratory
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%
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 13
Sensitivity to relative ratios of e, r and ts: LHC
Lawrence Berkeley National Laboratory
• 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)
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 14
Sensitivity to relative ratios of e, r and ts: LHC
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
photoelectrons: outer edge only
n'e() =6.3 -4 / ,e e m max=2.05
Lawrence Berkeley National Laboratory
e–-wall collision energy vs. time (LHC arc dipole)
e+r = 43%
e+r = 10%
e+r = 0
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 15
Sensitivity to relative ratios of e, r and ts: LHC
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
photoelectrons: outer edge only
n'e() =6.3 -4 / ,e e m max=2.05
Lawrence Berkeley National Laboratory
effective SEY vs. time (LHC arc dipole)
e+r = 43%
e+r = 10%
e+r = 0
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 16
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
photoelectrons: outer edge only
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
Sensitivity to relative ratios of e, r and ts: LHC
Lawrence Berkeley National Laboratory
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%
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 17
EC formation: beam-induced multipacting (BIM)
Lawrence Berkeley National Laboratory
• 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)
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 18
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
Lawrence Berkeley National Laboratory
(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)
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 19
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,…)
Lawrence Berkeley National Laboratory
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)
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 20
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
Lawrence Berkeley National Laboratory
• suppresses the resonance • hard to put into practice! (M. Pivi)
bunch profile
aver. e– line density
(RPPG024)
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 21
EC dissipation - simplest analysis
Lawrence Berkeley National Laboratory
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
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 22
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)
Lawrence Berkeley National Laboratory
(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
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 24
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)
Lawrence Berkeley National Laboratory
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 25Lawrence Berkeley National Laboratory
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
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 26Lawrence Berkeley National Laboratory
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)
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 27
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
Lawrence Berkeley National Laboratory
(see also: MOPA001; TPPB054)
(TOPC003)
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 28
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
Lawrence Berkeley National Laboratory
(ROAB003; RPPB035)
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 29
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
Lawrence Berkeley National Laboratory
(R. Cimino and I. Collins, proc. ASTEC2003, Daresbury Jan. 03)
Copper SEY (CERN)
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 30
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
Lawrence Berkeley National Laboratory
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 31
Additional material
Lawrence Berkeley National Laboratory
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 32
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 33
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 34Lawrence Berkeley National Laboratory
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
E0ts=0E0tspk=310dtspk=1.22powts=1.813P1epk=0.5P1einf=0.07E0epk=0powe=0.9E0w=100P1rinf=0.74Ecr=40qr=1
SEY for stainless steel, normal incidence(data courtesy R. Kirby, SLAC standard 304 rolled sheet,chemically etched and passivated but not conditioned)
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 35
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=1.8848powts=1.54033E0ts=0P1epk=0.496229P1einf=0.02E0epk=0powe=1E0w=60.8614P1rinf=0.2Ecr=0.0409225qr=0.104045
SEY for Cu, normal incidence (Data courtesy N. Hilleret for chemically cleaned but not in-situ vacuum baked samples) (macro hilleret_fit_mauro)
Lawrence Berkeley National Laboratory
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 36
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)
Lawrence Berkeley National Laboratory
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 37
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)
Lawrence Berkeley National Laboratory
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 38Lawrence Berkeley National Laboratory
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)
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 39
NOTE: rediffused+backscattered~5%(assuming low-energy cutoff=50 eV)
Lawrence Berkeley National Laboratory
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 40Lawrence Berkeley National Laboratory
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 41Lawrence Berkeley National Laboratory
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 42Lawrence Berkeley National Laboratory
Current parameter values from fits to data
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 43
Q: is the electron emitted spectrum Maxwellian? A: only approximately.
Fits to data, however, imply pn~1.8–5, depending on n and material
Lawrence Berkeley National Laboratory
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
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 44
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)
Lawrence Berkeley National Laboratory
backscattered and rediffused electronsartificially suppressed (true secondaries only)
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 45
BIM for long bunches: case of PSR
• bunch length >> t
Lawrence Berkeley National Laboratory
ED02X electron detector signal 8μC/pulse beam
ED42Y electron detector signal 8μC/pulse beam
145 μA/cm2 435 μA/cm2
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 46Lawrence Berkeley National Laboratory
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
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 47Lawrence Berkeley National Laboratory
Effect of bunch shortening (PSR simulation; M. Pivi) – contd.
L=254 ns (nom..)
L=200 ns
L=180 ns
L=150 ns
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 48
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
Lawrence Berkeley National Laboratory
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 49
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)
Lawrence Berkeley National Laboratory
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 50
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
Lawrence Berkeley National Laboratory
(detailed view for copper only)
M. A. Furman, BNL, Dec. 8-12, 2003, “Electron Cloud ...” p. 51Lawrence Berkeley National Laboratory
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