1Vay - Compass 09
QuickTime™ and a decompressor
are needed to see this picture.SciDAC-IICompass
SciDAC-IICompass
Boosted frame e-cloud simulations
J.-L. Vay
Lawrence Berkeley National Laboratory
Compass 2009 all hands meeting - Beam Dynamics session Tech-X, Boulder, CO - Oct 5-6, 2009
QuickTime™ and a decompressor
are needed to see this picture.
SciDAC-IICompass
SciDAC-IICompass
2Vay - Compass 09
QuickTime™ and a decompressor
are needed to see this picture.SciDAC-IICompass
SciDAC-IICompass
Toward fully self-consistent e-cloud simulations
• To date, electron cloud distributions have been predicted using ‘build-up’ simulations (using Posinst, Ecloud, Cloudland, Warp,…) and provided as inputs to codes calculating their interaction with the beam.
• This mode of operation is dictated by the widely separate time scales associated with the beam and electrons dynamics: the quasistatic or the boosted frame* methods are used to bridge the time scales in codes like Headtail, QuickPIC, Pehts, CMAD, Warp,…. electron
streamlinesbeam
*J.-L. Vay, Phys. Rev. Lett. 98, 130405 (2007)
quasistatic boosted frame
build-up
3Vay - Compass 09
QuickTime™ and a decompressor
are needed to see this picture.SciDAC-IICompass
SciDAC-IICompass
• This model is appropriate for single bunch instability but fails to capture memory effects for multibunch instabilities.
• Toward integrating the build-up and interaction phases, we have modified routines related to electron build-up in Warp to accommodate calculations in a boosted frame:
– calculation of velocity and angle of particles impacting surfaces,– generation of secondary electrons, – background gas ionization.
Toward fully self-consistent e-cloud simulations
bunch nbunch n+1
4Vay - Compass 09
QuickTime™ and a decompressor
are needed to see this picture.SciDAC-IICompass
SciDAC-IICompass
Modified routines successfully benchmarked on SPS toy problem
• The build-up of electrons was simulated in a fully self-consistent simulation in a boosted frame (=27).• Electrons generated from gas ionization and secondary emission at walls.• Assumed continuous focusing.• One bunch was simulated, the bunch train being emulated by periodic BC.
Excellent agreement with simulations:• in the laboratory frame,• from the LBNL build-up code Posinst (M. Furman), • Warp running in build-up mode.
5Vay - Compass 09
QuickTime™ and a decompressor
are needed to see this picture.SciDAC-IICompass
SciDAC-IICompass
Fully self-consistent simulation of e-cloud driven instability
If not properly resolving the betatron frequency, the choice of the parameter = time step/betatron frequency is critical.
• The background gas pressure was x10, to trigger a strong instability.
• At these high electron densities, the electron space charge is large, which may explains observed differences between build-up and full 3D calculations. This is under investigation.
6Vay - Compass 09
QuickTime™ and a decompressor
are needed to see this picture.SciDAC-IICompass
SciDAC-IICompass
Plans
• Implement calls to gas ionization and secondary electrons generation in Warp’s quasistatic class,
• Compare fully self-consistent (build-up+beam tracking) simulations between full PIC in a Lorentz boosted frame and quasistatic, cross-benchmarking and assessing the pros and cons of each approach.
• Replace continuous focusing by FODO lattice and redo above.
• Modify photo-electron generation class to accommodate boosted frame calculations.
• Add Monte-Carlo generation of photons radiated by beam, and the generation of photo-electrons at wall.
• Pursue benchmarking with other ecloud codes (to complement extensive benchmarking done with Headtail and Posinst to date).
7Vay - Compass 09
QuickTime™ and a decompressor
are needed to see this picture.SciDAC-IICompass
SciDAC-IICompass
Backup
Vay - Compass 09 8
Benchmarking of Warp vs Headtail-1
• LHC =479.6
– Np=1.11011
– continuous focusing x,y=66.0,71.54
x,y=64.28,59.31
– longitudinal motion OFF
– ne=1012-1014
– Nb ecloud station/turn=10-100
– dipole magnetic field effect: frozen x-motion of electrons
– same initial distribution of macro-protons with initial offset of 0.1y
No dipole fieldNo dipole field
e- motion frozen in xe- motion frozen in x
Vay - Compass 09 9
Benchmarking of Warp vs Headtail-2
• LHC =479.6
– Np=1.11011
– continuous focusing x,y=66.0,71.54
x,y=64.28,59.31
– longitudinal motion ON
– ne=1012-1014
– Nb ecloud station/turn=10-100
– No dipole magnetic
– same initial distribution of macro-protons with initial offset of 0.1y
Vay - Compass 09 10
Benchmarking of Warp vs Headtail-3 • LHC
=479.6
– Np=1.11011
– continuous focusing x,y = 66.0, 71.54
x,y,z = 64.28, 59.31, 0.0059
= 3.4710-4
p/p = 4.6810-4
• chromx,y = 2., 2.
– ne=1011-1014
– Nb ecloud station/turn=10-100
– dipole magnetic field effect: frozen x-motion of electrons
– same initial distribution of macro-protons with initial offset of 0.1y
– threshold 2-particle model for TMCI
ne=1014m-3
ne=1014m-3
ne=1013m-3
ne=1013m-3
ne=1012m-3
ne=1012m-3
ne=1011m-3
ne=1011m-3
≈ 6.431011
11Vay - Compass 09
QuickTime™ and a decompressor
are needed to see this picture.SciDAC-IICompass
SciDAC-IICompass
E-cloud: benchmarking against quasistatic model for LHC scenario
The “quasistatic” approximation uses the separation of time scales for pushing beam and e-cloud macro-particles with different “time steps”: used in QuickPIC (USC/UCLA), Headtail (CERN), PEHTS (KEK), CMAD (SLAC), Warp (LBNL), …
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and a decompressor
are needed to see this picture.
Excellent agreement on emittance growth between boosted frame full PIC and “quasistatic” for e-cloud driven transverse instability in continuous focusing model of LHC:
The 2 runs have similar computational cost, thus how to choose one method other another? – boosted frame method offers less approximation to the physics, which may matter in some cases,
– parallelization of quasistatic codes more complicated due to pipelining in the longitudinal direction.
12Vay - Compass 09
QuickTime™ and a decompressor
are needed to see this picture.SciDAC-IICompass
SciDAC-IICompass
Other possible complication: inputs/outputs
QuickTime™ and a decompressor
are needed to see this picture.
z’,t’=LT(z,t)
frozen active
QuickTime™ and a decompressor
are needed to see this picture.
• Often, initial conditions known and output desired in laboratory frame
– relativity of simultaneity => inject/collect at plane(s) to direction of boost.
• Injection through a moving plane in boosted frame (fix in lab frame)
– fields include frozen particles,– same for laser in EM calculations.
• Diagnostics: collect data at a collection of planes
– fixed in lab fr., moving in boosted fr.,– interpolation in space and/or time,– already done routinely with Warp for comparison with experimental data, often known at given stations in lab.
13Vay - Compass 09
QuickTime™ and a decompressor
are needed to see this picture.SciDAC-IICompass
SciDAC-IICompass
space+time
x/t= (L/l, T/t)*
0
0
0
0
0
*J.-L. Vay, Phys. Rev. Lett. 98, 130405 (2007)
Range of space and time scales spanned by two identical beams crossing each
otherspace
F0-center of mass frame
x
y
x
y
FB-rest frame of “B”
• is not invariant under the Lorentz transformation: x/t .• There exists an “optimum” frame which minimizes it.• Result is general and applies to light beams too.
14Vay - Compass 09
QuickTime™ and a decompressor
are needed to see this picture.SciDAC-IICompass
SciDAC-IICompass
boosted frame
10km
10cm
10km/10cm=100,000.
10m
10m/1nm=10,000,000,000.
1nm
3cm
3cm/1m=30,000.
1m
compaction x103
450m
4.5m
frame ≈ 22
450m/4.5m=100.
1nm
compaction x3.107
2.5mm
4m
2.5mm/4m=625.
frame ≈ 4000
compaction x560
1.6mm
30m
1.6mm/30m=53.
frame ≈ 19
Lorentz transformation => large level of compaction of scales range
HEP accelerators (e-cloud)
Laser-plasma acceleration
Hendrik Lorentz
Free electron lasers
15Vay - Compass 09
QuickTime™ and a decompressor
are needed to see this picture.SciDAC-IICompass
SciDAC-IICompass
# of computational steps grows with the full range of space and time scales involved
Choosing optimum frame of reference to minimize range can lead to dramatic speed-up for relativistic matter-matter or light-matter
interactions.
Consequence for computer simulations
Calculation of e-cloud induced instability of a proton bunch*
• Proton energy: =500 in Lab
• L=5 km, continuous focusing
Code: Warp (Particle-In-Cell)
electron streamlinesbeam
(from Warp movie)
proton bunch radius vs. z
CPU time (2 quad-core procs):• lab frame: >2 weeks• frame with 2=512: <30 min
Speedup x1000
*J.-L. Vay, Phys. Rev. Lett. 98, 130405 (2007)
16Vay - Compass 09
QuickTime™ and a decompressor
are needed to see this picture.SciDAC-IICompass
SciDAC-IICompass
Seems simple but ! . Algorithms which work in one frame may break in another. Example: the Boris particle pusher.
• Boris pusher ubiquitous
– In first attempt of e-cloud calculation using the Boris pusher, the beam was lost in a few betatron periods!– Position push: Xn+1/2 = Xn-1/2 + Vn t -- no issue
– Velocity push: n+1Vn+1 = nVn + (En+1/2 + Bn+1/2)
issue: E+vB=0 implies E=B=0 => large errors when E+vB0 (e.g. relativistic beams).
• Solution
– Velocity push: n+1Vn+1 = nVn + (En+1/2 + Bn+1/2)
• Not used before because of implicitness. We solved it analytically*q tm
n+1Vn+1 + nVn
2 n+1/2
*J.-L. Vay, Phys. Plasmas 15, 056701 (2008)
(with , , ,
q tm
Vn+1 + Vn
2
, , , ).
Vay - Compass 09LARP CM12, Napa, Apr. 8-10, 2009
ec feedback simulations - JL Vay, et al. 17
QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.QuickTime™ and a
TIFF (Uncompressed) decompressorare needed to see this picture.
Simulations of e-cloud instability in SPScomparison Warp-Headtail
SPS
– Np=1.11011
– ne=1.1012m-3 (uniform)
– :continuous focusing• x,y= 33.85, 71.87
• x,y= 26.13, 26.185
• chrom.x,y=0.1,0.1
– // : z= 0.00323
• Warp/HT (isyn=1): continuous focusing
• HT (isyn=4): focusing more localized
– 10 stations/turns– 512 turns
Eb=26 GeV
(at injection)
Eb=120 GeV
Good agreement between Warp and Headtail on emittance growth and tune shift using continuous focusing models at 26GeV and 120GeV.
Vay - Compass 09LARP CM12, Napa, Apr. 8-10, 2009
ec feedback simulations - JL Vay, et al. 18
QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.QuickTime™ and a
TIFF (Uncompressed) decompressorare needed to see this picture.
Simulations of e-cloud instability in SPScloser look at tune shift
Eb=26 GeV Eb=120 GeV
Warp
Headtail (isyn=1)
Headtail (isyn=4)
tail headtail head
Vay - Compass 09LARP CM12, Napa, Apr. 8-10, 2009
ec feedback simulations - JL Vay, et al. 19
QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.QuickTime™ and a
TIFF (Uncompressed) decompressorare needed to see this picture.
Simulations of e-cloud instability in SPSat injection - higher electron density
SPS at injection (Eb=26 GeV)
– Np=1.11011
– ne=31012m-3 (uniform)
– continuous focusing• x,y= 33.85, 71.87
• x,y= 26.12, 26.185
• chrom.x,y=0.,0.
• z= 0.0059
Warp
Headtail
Fractional emittance growth
horizontal vertical
tail head
tail head