D.L. Bruhwiler,1 G.I. Bell,1 A.V. Sobol,1

V. Litvinenko,2 E. Pozdeyev,2

A. Fedotov,2 I. Ben-Zvi,2

Y. Zhang,3 S. Derbenev3 & B. Terzic3

Parallel Simulation of Electron Cooling Physics for Relativistic Ion Beams – Status & Plans

1. Tech-X Corporation2. Brookhaven National Lab3. Thomas Jefferson National Lab

ComPASS All-Hands MeetingTech-X, October 6, 2009

Supported by DOE Office of Science, Office of Nuclear Physics

Outline

• Motivation• Brief review of what has been done

– “conventional” electron cooling for relativistic ion beams simulating dynamical friction with VORPAL

– coherent electron cooling (CEC) simulating a CEC modulator with VORPAL

• Overview of recent DOE/NP SBIR awards• Future Plans

Motivation

Long-term motivation for electron cooling of relativistic hadron beams:the Electron-Ion Collider (EIC) concept

C. Aidala et al. (The EIC Working Group), “A High Luminosity, High EnergyElectron-Ion-Collider; A New Experimental Quest to Study the Gluethat Binds Us All,” White Paper prepared for the NSAC LRP (2007). http://www.phenix.bnl.gov/WWW/publish/abhay/Home_of_EIC/NSAC2007/070424_EIC.pdf

High luminosity relativistic ion beams require electron cooling

• EIC requires orders-of-magnitude higher ion luminosity– can only be achieved by reducing phase space volume of

beams ions have no natural mechanism for phase space

damping– hence, external cooling techniques are required

in some cases, stochastic cooling can be used; however… 8.9 GeV antiprotons in Fermilab accumulator ring require e-

cooling 250 GeV polarized protons will require e- cooling

• Two EIC concepts are being considered in the US– eRHIC (add energy recovery linac to the RHIC complex)– ELIC (add e- and ion rings to Jefferson Lab complex)

electron cooling is included in all present designs

ERL-based Layout for eRHIC

Image taken from 2007 eRHIC position paper

ELIC Schematic (Electron – Light Ion Collider)

p. 7

30-225 GeV protons15-100 GeV/n ions

3-9 GeV electrons3-9 GeV positronsGreen-field design of ion

complex directly aimed at full exploitation of science program.

Parallel simulation of electron cooling physics…

Previous Work – Simulating Dynamical Friction

Dynamical friction is the key physical process for e- cooling

• Case of isotropic plasma, with no external fields, was first explained 65 years ago– S. Chandrasekhar, Principles of Stellar Dynamics

(U. Chicago Press, 1942).– B.A. Trubnikov, Rev. Plasma Physics 1 (1965), p.

105.

– Physics can be understood in two different ways Binary collisions (integrate over ensemble of e-/ion

collisions) Dielectric plasma response (ion scatters off of plasma

waves)

e-

e-

e-

e-

• Culmination of years of work, beginning in 2002

VORPAL simulations support decision to use conventional wiggler for e- cooling of 100 GeV/n Au+79

A.V. Fedotov, D.L. Bruhwiler, A. Sidorin, D. Abell, I. Ben-Zvi, R. Busby, J.R. Cary, and V.N. Litvinenko, "Numerical study of the magnetized friction force," Phys. Rev. ST Accel. Beams 9, 074401 (2006).

A.V. Fedotov, I. Ben-Zvi, D.L. Bruhwiler, V.N. Litvinenko and A.O. Sidorin, "High-energy electron cooling in a collider," New J. Phys. 8 (2006), p. 283.

G.I. Bell, D.L. Bruhwiler, A. Fedotov, A.V. Sobol, R. Busby, P. Stoltz, D.T. Abell, P. Messmer, I. Ben-Zvi and V.N. Litvinenko, “Simulating the dynamical friction force on ions due to a briefly co-propagating electron beam”, J. Comp. Phys. 227 (2008), p. 8714.

• Conventional wiggler could replace expensive solenoid– friction force is reduced

only logarithmically

Full e- cooling sim’s are distinct from simulating micro-physics of a single pass

• BETACOOL code is used to model many turns A.O. Sidorin et al., Nucl. Instrum. Methods A 558, 325 (2006). A.V. Fedotov, I Ben-Zvi, D.L. Bruhwiler, V.N. Litvinenko, A.O. Sidorin,

New J. Physics 8, 283 (2006).

– a variety of electron cooling algorithms are available i.e. simple models for dynamical friction and diffusion

– various models for “heating” are included intra-beam scattering (IBS), beam-beam collisions, etc.

Fedotov et al. (2006) Fedotov et al. (2006)

Dynamical Friction Simulations for e- Cooling shed light on fundamental Plasma Physics

• Ad hoc limits on rimpact removed from Coulomb logarithm – logarithmic singularities result from approximations

Infinite time for collisions to occur; weak scattering approximation

A.V. Sobol, D.L. Bruhwiler, G.I. Bell, A. Fedotov and V. Litvinenko, "Numerical calculation of dynamical friction in future electron cooling systems, including magnetic field perturbations and finite time effects," submitted to New J. Physics.

New algorithm used to obtain field-free dynamical friction - fast, serial, C - finite-time, asymmetric - arbitrary velocities - assumes uniform density

modified Pareto distribution

Previous Work – Coherent Electron Cooling

Coherent e- Cooling (CeC) offers dramatically shorter cooling times

Modulator Kicker

Dispersion section ( for hadrons)

Electrons

Hadrons

l2l1 High gain FEL (for electrons)

Eh

E < Eh

E > Eh

Eh

E < Eh

E > Eh

• Coherent Electron Cooling concept– uses FEL to combine electron & stochastic cooling concepts

– a CEC system has three major subsystems modulator: the ions imprint a “density bump” on e- distribution amplifier: FEL interaction amplifes density bump by orders of magnitude kicker: the amplified & phase-shifted e- charge distribution is used to

correct the velocity offset of the ions

Litvinenko & Derbenev, “Coherent Electron Cooling,” Phys. Rev. Lett. 102, 114801 (2009).

Comparison of simulations with theory is underway, with good results

• Recent analytical results for e- density wake

− theory makes certain assumptions: single ion; arbitrary velocities uniform e- density; anisotropic temperature

o Lorentzian velocity distributiono now implemented in VORPAL

linear plasma response; fully 3D

• Dynamic response extends over many lD and 1/wpe

− thermal ptcl boundary conditions are important

G. Wang and M. Blaskiewicz, Phys Rev E 78, 026413 (2008).

˜ n r ,t

Znop3

2vxvyvz

sin 2 x - vhx /p

rDx

2

y - vhy /p

rDy

2

z - vhz /p

rDz

2

2

0

pt

d

Electrostatic PIC can be used to simulate the electron response in an idealized modulator, but

df PIC is faster, quieter & more accurate

df PICPIC

• Movies above show 2D slice through e- density of 3D simulations• R=1 (isotropic e- temperatures); T=Z=0 (stationary ion)

df PIC shows ~10% deviations from theory

• Movie shows 1D integral of e- density perturbation

• R=1 (isotropic e- temperatures)

• T=Z=0 (stationary ion)

• Total e- shielding is shown in figure below• peak response is seen after

½ of a plasma period

• ~5x faster than PIC, due to fewer particles per cell

New DOE/NP SBIR Funding for CEC Simulations

“High-Fidelity Modulator Simulations of CEC Systems”

(NP Phase I: DE-SC0000835; PI: D. Bruhwiler)

• Supporting proposed CEC proof-of-principle experiment at BNL• Need a different algorithm to benchmark CEC modulator

simulations– PIC is marginal; d-f PIC looks extremely promising– no theory available for inclusion of important complicating effects

• Crossing ion trajectories, space charge effects, beam edge effects (surface waves)

• Implementing 2D Vlasov-Poisson algorithm in VORPAL– x, vx, y, vy, which requires a 4D mesh

• Simulate e- wake due to single ion; idealized case & finite beam size– must be done in 2D– Vlasov and d-f results will be benchmarked

• Consider possibility of fully 3D Vlasov-Poisson (requires 6D mesh)– evaluate high-order algorithms to enable low resolution

• Collaborating with Electron Cooling group at BNL– V. Litvinenko, E. Pozdeyev, A. Fedotov, I. Ben-Zvi

“Designing a Coherent Electron Cooling System for High-Energy Hadron Colliders”

(NP Phase II: DE-FG02-08ER85182; PI: D. Bruhwiler)

• Supporting proposed CEC proof-of-principle experiment at BNL• Goal: Integrated Simulation of Coherent Electron Cooling

– VORPAL simulation of the modulator– GENESIS modeling of the free-electron-laser (FEL) amplifier– Map-based propagation of electrons and ions between components

• electrons are bent in and out of the ion beam• ions go through a chicane to create a variable longitudinal phase shift

– VORPAL simulation of the kicker

• Collaborating with Electron Cooling group at BNL– V. Litvinenko, E. Pozdeyev, A. Fedotov, I. Ben-Zvi

Future Plans

Binary Collision Algorithm for Simulating Dynamical Friction – Plans for Moving Beyond 96

processors

),,(0 zyxx

z

x

y

x

y

z

00 vx

)0,,( yx

• Eight ions, many electrons • close collisions more

expensive• 12 cores per ion 60%

efficiency• limited to 96 cores

• Moving to 100’s and 1000’s of ions• future use of 1,000 to 10,000

cores

• Full transverse slice of ion/e- bunches • Space charge

effects• Ions near beam

edge• Ion trajectory x’ing

Support of Massively Parallel Computing Effortsfor SBIR-funded CEC Simulations

• VORPAL simulations of the CEC modulator and kicker– d-f PIC simulations of full transverse beam slices

• small domain: ~1,000 cores for ~2 hours• 50x larger domain for full beam slice• aiming for >10,000 cores before end of

project• Use of Vlasov/Poisson for modulator simulations

– by end of Phase I SBIR project, the 4D mesh will likely support only 2D domain decomposition

– future efforts will (resources permitting) enable 4D domain decomposition

G. I. Bell, R. Busby, J.R. Cary, P. Messmer, A. Sobol

I. Ben-Zvi, V. Litvinenko, A. Fedotov, E. Pozdeyev

Acknowledgments

We thank T. Austin, O. Boine-Frankenheim, A. Burov, A. Jain, W. Mori, S. Nagaitsev, A. Sidorin, P. Stoltz, N. Xiang, G. Zwicknagel and members of the Physics group of the RHIC Electron Cooling Project for many useful discussions.

We acknowledge assistance from the VORPAL development team.

Work at Tech-X Corp. was supported by the US DOE Office of Science, Office of Nuclear Physics under grants DE-FC02-07ER41499 and DE-FG02-08ER85182.

We used computational resources of NERSC, BNL and Tech-X.