SciDAC-II Compass SciDAC-II Compass 1 Vay - Compass 09 Boosted frame e-cloud simulations J.-L. Vay Lawrence Berkeley National Laboratory Compass 2009 all

1Vay - Compass 09

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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


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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

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• 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

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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.

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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.

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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).

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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


– No dipole magnetic


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


– dipole magnetic field effect: frozen x-motion of electrons


– 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

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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), …

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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.

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Other possible complication: inputs/outputs



z’,t’=LT(z,t)

frozen active



• 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.

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space+time

x/t= (L/l, T/t)*

0

0

0

0

0


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.

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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

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# 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


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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

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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.





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





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

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SciDAC-II Compass SciDAC-II Compass 1 Vay - Compass 09 Boosted frame e-cloud simulations J.-L. Vay Lawrence Berkeley National Laboratory Compass 2009 all