Efficient Particle-In-Cell modeling of laser-plasma accelerators - PowerPoint PPT Presentation

Efficient Particle-In-Cell modeling of laser-plasma accelerators J.-L. Vay Lawrence Berkeley National Laboratory Johns Adams Institute, Oxford, United Kingdom June 12, 2014

In collaboration with • the LOASIS program – Lawrence Berkeley National Laboratory Program head – Wim Leemans Deputy – Eric Esarey • B. Godfrey, I. Haber – U. of Maryland • D. Grote – Lawrence Livermore National Laboratory • T. Drummond, A. Koniges – Lawrence Berkeley National Laboratory

Laser plasma acceleration (LPA) offers path to shorter, cheaper particle accelerators surfer boat water wake plasma e- beam laser Strong electric fields ~1,000x that of conventional accelerators 3

Primary method for simulations of beams and plasmas is the Particle-In-Cell (PIC) method Based in first principles Charged particles Push particles time Newton-Lorentz EM fields Particle-In-Cell (PIC) Deposit current Gather forces Clouds of Usually ‘Yee’ staggered mesh particles E x E x Filtering Filtering E y E y E y currents fields Field solve E x E x Maxwell E y E y E y + filtering (currents and/or fields). E x E x - first principles  includes nonlinear, 3D, kinetic effects, - particle push and EM solver locals  scales well to >100ks CPUs. 4

Field interpolation options (B z – not shown – at cell centers) “Energy - Conserving” “Momentum - Conserving” “Uniform” (a.k.a. “ Galerkin ”) • interpolates from staggered grid • interpolates from staggered grid • first interpolate at grid nodes • one order down in // direction • same order in all directions • same order in all directions E x E x E x E x E x,y E x E x,y E x E x,y E y E y E y E y E y E y E y E y E y E x E x E x E x E x,y E x E x,y E x E x,y E x E x E y E y E y E y E y E y E y E y E y E x E x E x E x E x,y E x E x,y E x E x,y E x E x E x E x E x,y E x,y E x,y E y E y E y E y E y E y E x E x E x E x E x,y E x,y E x,y E y E y E y E y E y E y E y E y E x E x E x E x E x,y E x,y E x,y

Example: 3-D simulation of a new concept for injection of very low emittance beams Two-color laser-ionization injection*: e- bunch projections Y vs X Py/mc vs Y 2 50 20 50 0.1 1 40 40 Py/mc 30 30 0 0.0 Y 20 20 10 −1 10 −0.1 10 E z (V/m) −2 0 0 −2 −1 −2 −1 0 1 2 0 1 2 pump X Y 0 laser Px/mc vs X pulse 1.5 200 0.1 10 +5 -10 150 Px/mc 1.0 0.0 100 0.5 50 −0.1 0 0.0 −2 −1 0 1 2 1.5 2.0 2.5 3.0 3.5 energy 10 +6 X Emittance [mm.mrad] injection laser pulse 0.03 0.02 trapped 0.01 electron bunch 0 200 400 600 800 Z [microns] Low emittance enables focusability Warp-3D to tight spot. Simulations confirm that new scheme enables the production of very high quality beams. Emittance < 0.03 mm-mrad for HEP and light sources *L.-L. Yu, E. Esarey, C. B. Schroeder, J.-L. Vay, C. Benedetti, C. G. R. Geddes, M. Chen, and W. P. Leemans, Phys. Rev. Lett. 112, 125001 (2014)

Laser plasma acceleration is especially challenging  Numerical limitations • discretization errors (finite cell size, finite time step, staggering of quantities)  high resolution, small time steps • sampling errors (noise)  many macroparticles and/or smoothing/filtering  Large space and time scale disparities • short wavelength laser propagates into long plasma channel Lab (full) Lab (w/ moving window) Warp-3D Warp-3D even with moving window, many time steps needed for first principles simulations (tens of millions of time steps for 10 GeV stage) 7

Dealing with large spatial/time scale disparities Many techniques available:  downscaled parameters • e.g. LPA: 100 MeV/10 19 cm -3 stage proxy for 10 GeV/10 17 cm -3 stage  reduced dimensionality: 1D, 2D, 2D-RZ, 2D-RZ-multimodes, fluid  large spatial disparities • parallelization • moving window • mesh refinement  large time scale disparities • envelope/ponderomotive – averages over shortest time scale • quasistatic – separates slow macro- & fast micro-evolutions  large spatial & time scale disparities • Lorentz boosted frame – reduces scale disparities 8

Dealing with large spatial/time scale disparities Many techniques available:  downscaled parameters • e.g. LPA: 100 MeV/10 19 cm -3 stage proxy for 10 GeV/10 17 cm -3 stage  reduced dimensionality: 1D, 2D, 2D-RZ, 2D-RZ-multimodes, fluid  large spatial disparities • parallelization • moving window • mesh refinement  large time scale disparities • envelope/ponderomotive – averages over shortest time scale • quasistatic – separates slow macro- & fast micro-evolutions  large spatial & time scale disparities • Lorentz boosted frame – reduces spatial/time scale disparities 9

Lorentz boosted frame reduces scale range by orders of magnitude 1 Boosted frame  = 100 Lab frame l≈ 1.  m l’ =200.  m Hendrik Lorentz L ≈ 1. m L’ =0.01 m compaction 1. m/1.  m=1,000,000. 0.01 m/200.  m=50. X20,000. LBF predicted speedup 1,2 : • > 10,000 for single 10 GeV (Bella) stage, • > 1,000,000 for single 1 TeV stage. 1 J.-L. Vay, P hys. Rev. Lett. 98 , 130405 (2007) 2 J.-L. Vay, et al., Phys. Plasmas 18 ,123103 (2011) 10

LBF method carefully validated in deeply depleted beam loaded stages -- Excellent agreement between runs at various  boost Warp-3D – a 0 =1, n 0 =10 19 cm -3 ( ~ 100 MeV) scaled to 10 17 cm -3 ( ~ 10 GeV) Wake early late energy X R.M.S. momentum spread e- beam * J.-L. Vay, et al., Phys. Plasmas 18 , 123103 (2011) 11

But two difficulties were identified at high  boost: • relative shortening of Rayleigh length complicates laser injection, • instability developing at entrance of plasma. 12

Laser injection through moving plane solves initialization issue in LBF Lab frame Boosted frame Shorter Rayleigh length L R /  boost Standard laser injection from left boundary or all at once prevents standard laser injection plasma plasma Solution: injection through a moving planar antenna in front of plasma* • Laser injected using macroparticles using Esirkepov current deposition ==> verifies Gauss’ Law. -v boost • For high  boost , backward radiation is blue shifted and unresolved. Method developed in Warp*, and implemented in other codes (e.g. Osiris and V-Sim). * J.-L. Vay, et al., Phys. Plasmas 18 , 123103 (2011) 13

Short wavelength instability observed at entrance of plasma for large  100) Longitudinal electric field plasma laser Warp 2D simulation 10 GeV LPA (n e =10 17 cc,  =130) Is it numerical Cherenkov instability? BTW, what is “numerical Cherenkov instability”? 14

Numerical Cherenkov discovered by B. Godfrey in 1974* Lagrangian plasma streaming through Eulerian grid at relativistic velocity Exact Standard PIC Numerical dispersion leads to crossing of EM field and plasma modes -> instability. *B. B. Godfrey, “Numerical Cherenkov instabilities in electromagnetic particle codes”, J. Comput. Phys. 15 (1974)

Non-Standard Finite-Difference solver offers tunability of numerical dispersion FD (Yee) NSFD (Karkkainen) NSFD 1,2 : weighted No dispersion along axes average of quantities transverse to FD ( ab ). -   - b b b - -  b  - a  - a - b  b - b b  - D x  NSFD=FD if a , b =  0. Pukhov algo 3 for 1 set of a,b, 1 J. B. Cole, IEEE Trans. Microw. Theory Tech. 45 (1997). 2 M. Karkkainen et al., Proc. ICAP, Chamonix, France (2006). J. B. Cole, IEEE Trans. Antennas Prop. 50 (2002). 3 A. Pukhov, J. Plasma Physics 61 (1999) 425 16

Comparing runs using Yee or NSFD (Karkkainen) solvers Surprise: Instability mostly insensitive to tuning of numerical dispersion… …but very sensitive to time step *! Sharp decrease of instability level Power spectrum (a.u.) around cδt = δz/√ 2 Used special time step to reduce instability but was not enough: wideband filtering? * J.-L. Vay, et al., J. Comput. Phys. 230 , 5908 (2011). 17

Does physics allow to use wideband filtering? Time history of laser spectrum (relative to laser l 0 in vacuum) Spectrum very different in lab and boosted frames Frame of wake (  =130) Dephasing time Lab frame spectrum spectrum 0 0 Content concentrated around l 0 Content concentrated at much larger l More filtering possible without altering physics*. *J.-L. Vay, et al., PoP Lett. 18 (2011). 18

Laser field Time Hyperbolic rotation … spatial oscillations from Lorentz into Transformation converts time beating laser… Lab frame Laser field Time Wake frame 19

Digital filtering of current density and/or fields -- commonly used for improving stability and accuracy Multiple pass of bilinear filter + compensation routinely used 1/4 1/2 1/4 Bilinear (B) 100% absorption at Nyquist freq. Bilinear (B) + compensation (C) Bilinear filter Wideband filtering difficult in parallel (footprint limited by size of local domains) or expensive 1×B + C 4×B + C Example: wideband filters using 20×B + C N repetitions of bilinear filter 50×B + C 80×B + C 20