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Laser Envelope Model In Laser Envelope model in Maison de la Simulation Francesco– March 2019 Massimo Francesco Massimo Outline I. Motivations II. Modeling Laser Wakefield Acceleration with a laser envelope III. Case study: Laser Wakefield Acceleration with external injection IV. Perspectives and future developments Laser Wakefield Acceleration (LWFA): Characteristic Scales 1.5 Laser Beam Duration: 28 fs Transverse 1.2 Electric Field Ponderomotive (A.U.) Force: 0.9 F= - ILaser 0.6 Electrons Immobile Ions Mi >>me 0.003 Plasma density: 3.1018 cm-3 0.002 Electron Charge Density Plasma 0.001 (A.U.) wavelength: ~20 μm 0.000 Laser Wakefield Acceleration (LWFA): Characteristic Scales E > 100 GV/m 0.04 Longitudinal Electric Field Electrons 0.00 (A.U.) injected here on propagation axis are accelerated -0.04 0.003 Laser wavelength: Electron ~1 μm 0.002 Charge Laser duration ~ Density Plasma wavelength: 0.001 (A.U.) ~20 μm 0.000 0.000 LWFA PIC simulations are cumbersome X. Davoine, Physics of Plasmas 15, 113102 (2008) 2D cartesian simulations are not accurate enough for LWFA! 3D LWFA simulations: 1 mm plasma ~ 320 kcpu-heures ~ 10.2 k€ Laser Envelopes need less sampling points Spatial variation scales: Laser Envelope Laser length ~ Plasma wavelength (10-100 μm) Laser wavelength Laser “Standard” (~1 μm) Points sampling Laser “Standard” = 10 Points sampling Laser Envelope Larger Δx and Δt can be used! Structure of a PIC code with Laser Envelope Standard PIC Envelope (/Ponderomotive) PIC ~ E, B field E,B field Envelope A (laser) (plasma fields+laser fields) (plasma fields) Lorentz Lorentz Force Ponderomotive Force Force Plasma Current Current Density J Density J Susceptibility Particles Particles The Laser Envelope evolution: wave equation D. Terzani and P. Londrillo, submitted (2018) Laser Envelope Laser “Standard” Hypothesis: D’Alembert Equation: ^ Laser Complex Envelope Envelope Equation: Plasma Susceptibility Ponderomotive Equations of motion Ponderomotive force acts as a radiation 2 pressure on charged particles : it expels |A|~ the electrons from high-intensity zones Fponderomotive Motion Equations for the macroparticles (here electrons): B. Quesnel and P. Mora, Physics Review E 58, 3719 (1998) Ponderomotive Lorentz Force Force (plasma fields) (laser envelope) Standard Particle in Cell loop Update of EM fields: Maxwell’s Equations Current density projection Interpolation of force of each particle on grid acting on the each particle Δt UpdateUpdate Update particles particles Positions Momenta C.K. Birdsall, A.B. Langdon, Plasma Physics Via Computer Simulation (1985) Envelope (/Ponderomotive) Particle in Cell loop Update of EM fields: Maxwell’s Equations Current density projection Interpolation of force of each particle on grid acting on the each particle Projection Δt of susceptibility on grid Update Update particles particles Positions Momenta Update laser envelope: D. Terzani and P. Londrillo, Envelope Equation submitted (2018) Envelope (/Ponderomotive) Particle in Cell loop Update of EM fields: Maxwell’s Equations Interpolation of envelope Current density projection Interpolation of force of each particle on grid acting on the each particle Projection Δt of susceptibility on grid Interpolation Update Update of updated particles particles envelope Positions Momenta Update laser envelope: D. Terzani and P. Londrillo, Envelope Equation submitted (2018) Define a Laser Envelope in Smilei 3D cylindrically symmetric gaussian beam in : Env_A_abs = |A|~ a0 t = 0 fwhm x center Validation test: Nonlinear LWFA, Electron density 18 -3 a0 = 5 , n0 = 3∙10 cm , 8 ppc, Δy = Δz = 3 c/ω0 w0 = 12 μm, LFWHM = 28 fs Standard Laser simulation Envelope Simulation Δx = 0.125 c/ω0 Δt = 0.124 c/ω0 Envelope simulation Δx = 0.75 c/ω0 Δt = 0.675 c/ω0 TStandard Laser Standard Laser Simulation = 20 TEnvelope Propagation direction @1 mm TEnvelope= 16 kh-cpu Case Study: Multistage LWFA experiments Gas jet, ~ mm 1st Plasma Stage 1st Laser Injected Electrons Pulse ~ 50-100 MeV Magnetic Beam Transport Case study 2ème Étage Laser Plasma 2ème plasma channel, ~ 10 cm Accelerated Laser Electrons Pulse ~ 10 GeV External injection of an electron beam in a laser wakefield Comparison @15 mm of propagation Longitudinal Electron density electric field Propagation Direction TStandard Laser = 20 TEnvelope Grand challenge Grand Equipement National de Calcul Intensif http://www.genci.fr/fr F. Massimo et al. (2019), ICAP 2018 Proceedings http://icap2018.vrws.de/papers/mopag02.pdf Perspectives and future developments ▪ Dispersion-free envelope solver ▪ Absorbing boundary conditions for envelope ▪ Laser envelope model in cylindrical symmetry ▪ Tunnel ionisation with envelope model ▪ Laser envelope + plasma hybrid kinetic fluid model Thanks to Davide Terzani, Stefano Sinigardi and Alberto Marocchino for the help and discussions during the development of the envelope model. This work used computational resources of TGCC, CINES, through the allocation of resources 2018- A0010510062 granted by GENCI (Grand Equipement National de Calcul Intensif) and Grand Challenge "Irene" 2018 project gch0313 made by GENCI. F. Massimo was funded by P2IO LabEx (ANR-10-LABX-0038) in the Framework "Investissements d'Avenir" (ANR-11-IDEX-0003-01) managed by Agence Nationale de la Recherche (ANR, France) Additional slides Standard PIC vs Envelope PIC Standard PIC Envelope (/Ponderomotive) PIC Averaged E, B (plasma fields) Main E, B (laser+plasma fields) + particles averaged x, p quantities + particles x, p + ~A (laser field envelope) Plasma EM fields Maxwell’s equations Maxwell’s equations for E,B for averaged E,B evolution Laser Maxwell’s equations Envelope equation EM fields for E,B for A~ evolution Motions equations Motions equations Particles for x, p, for averaged x,p, dynamics Source terms: Source terms: E, B Averaged E, B, A~ Particles effects J in Maxwell’s χ in envelope on laser evolution equations equation Validation test: Relativistic Self-Focusing 18 -3 a0 = 5 , n0 = 3∙10 cm , 8 ppc, Δy = Δz = 3 c/ω0 w0 = 12 μm, LFWHM = 28 fs Standard Laser simulation Δx = 0.125 c/ω0 Δt = 0.124 c/ω0 Envelope simulation Δx = 0.75 c/ω0 Δt = 0.675 c/ω0 TStandard Laser = 20 TEnvelope Validation test: Nonlinear LWFA, beam loading 18 -3 a0 = 5 , n0 = 3∙10 cm , 8 ppc, Δy = Δz = 3 c/ω0 w0 = 12 μm, LFWHM = 28 fs Standard Laser simulation Δx = 0.125 c/ω0 Δt = 0.124 c/ω0 Envelope simulation Propagation direction Δx = 0.75 c/ω0 Δt = 0.675 c/ω0 TStandard Laser = 20 TEnvelope Centre Interdisciplinaire de la Lumière Extrême (CILEX) Initialisation of Electromagnetic Fields Immobiles Species: Poisson’s Equation Relativistic Species: “Relativistic” Poisson’s Equation Hypothesis: Negligible energy spread If non-negligible energy spread: Repeat for each energy “slice” J.-L. Vay, Physics of Plasmas 15, 056701 (2008) P. Londrillo, C. Gatti and M. Ferrario, Nucl. Instr. and Meth. A 740, 236-241 (2014) F. Massimo, A. Marocchino and A. R. Rossi, Nucl. Instr. and Meth. A 829, 378-382 (2016) Electromagnetic field initialization: Relativistic electron γ0 = 1 γ0 = 200 (immobile electron) (~100 MeV) B = 0 E B ≠ 0 E v = 0 v ~ c e- e- Electromagnetic field initialization: Relativistic electron beam γ0 = 1 Ex γ0 = 200 Ex (immobile beam) (meω0c/e) (~100 MeV) (meω0c/e) 80 0.008 6e-7 Propagation Direction 40 0.004 3e-7 0 0.000 0.0 y (μm) -3e-7 -40 -0.004 -6e-7 -0.008 -80 -80 -40 0 40 80 -80 x (μm) -40 x 0(μm) 40 80 x (μm) x (μm) Electromagnetic field initialization: Relativistic electron beam γ0 = 1 Ey γ0 = 200 Ey (immobile beam) (meω0c/e) (~100 MeV) (meω0c/e) 80 0.008 Propagation Direction 0.012 40 0.008 0.004 0.004 0 0.000 0.000 y (μm) -0.004 -0.004 -40 -0.008 -0.012 -0.008 -80 -80 -40 0 40 80 -80 -40 0 40 80 x (μm) x (μm).
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