Electron Acceleration in Laser Plasma

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1 Electron Acceleration in Laser Plasma Vojt ech Horn y IPP AV CR 4th December 2014, Praha Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 1 / 34

2 List of Contents 1 Motivation 2 Physics of electron acceleration in laser plasma 3 Particle-in-cell 4 Own simulation Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 2 / 34

Conventional way of electron acceleration Classical electron accelerators betatrons (pioneers, 1940, up to 300 MeV) synchrotrons (GeV+), rather for X-ray radiation generation de/dz E 4 /(m 4 R 2 )

3 Conventional way of electron acceleration Classical electron accelerators betatrons (pioneers, 1940, up to 300 MeV) synchrotrons (GeV+), rather for X-ray radiation generation de/dz E 4 /(m 4 R 2 ) Linacs (SLAC, 3.2 km, 90 GeV electrons) Limit accelerating eld < 100 MV/m Example Diamond Synchrotron Lenght: Electron energy: Costs: 150 m 33 GeV 13 GK c Operating since Located in Oxfordshire, England. Image from ianvisits.co.uk Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 3 / 34

4 Advantages and disadvantages of classical accelerators Advantages quasimonoenergetical resulting electron energy distribution understood, proven and estabilished technology high resulting electron energies relatively simple principle Disadvantages huge facilities including several buildings high acquisition costs high running costs Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 4 / 34

5 Advantages and disadvantages of classical accelerators Advantages quasimonoenergetical resulting electron energy distribution understood, proven and estabilished technology high resulting electron energies relatively simple principle Disadvantages huge facilities including several buildings high acquisition costs high running costs Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 4 / 34

6 Alternative possibility: Electron acceleration in laser plasma Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 5 / 34

7 Electron acceleration in laser plasma Prehistory Breakthrough article (1979, before CPA discovered). Based on simulations, Dawson was a pioneer in PIC computing. Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 6 / 34

Laser Plasma Accelerators New possibillities Laser Plasma Accelerators have electric eld 100 GV/m, i.e. 1,000 higher than conventional accelerators Implies tens meter's to centimeters reduction in

8 Laser Plasma Accelerators New possibillities Laser Plasma Accelerators have electric eld 100 GV/m, i.e. 1,000 higher than conventional accelerators Implies tens meter's to centimeters reduction in size for same electron energy - attractive To date have always produced broad range of energies which severely limited application Quasimonoenergetic electrons up to GeVs already produced Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 7 / 34

9 Ponderomotive force, Hora (1969) ( ) F p = e2 a 4m e ω 2 E2 = m e c (1) non-linear associated with the intensity gradients in the pulse pushes electron and ions out of high-intensity region ions are slow, i.e. relativistic plasma wave is formed in underdense plasma its eld can accelerate electrons Ponderomotive force Ponderomotive force drives wakeelds in laser plasma acceleration. breaks the quasineutrality of plasma generates longitudinal plasma wave compromises Lawson-Woodward theorem (EMW does not accelerate charged particle in vaccuum) Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 8 / 34

10 Electron acceleration in laser plasma Conditions and expectations Longitudinal accelerating electric eld generated by the ponderomotive force of an ultrashort and ultraintense laser. Parameter overview electron densities cm 3 laser intensities higher than W/cm 2 electric eld amplitude up to several hundred GV/m size of plasma in order if milimeters electron energies 10 MeV several GeV energy spread 5-10% charge in the electron bunch in order of hundreds of picocoulombs Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 9 / 34

11 Generation of the wake waves General idea Electron oscillation is exited by a force traveling in the plasma at the force front. The phase velocity of the wake wave is to the velocity of the force perturbation. Simulation by Jean-Luc Vay and Cameron Geddes, Berkeley Lab. newscenter.lbl.gov Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 10 / 34

12 Generation of the wake waves E x = m eω p u 0 sin(ω p τ)θ(τ) (2) e u 0 n e n 0 = n 0 cos(ω p τ)θ(τ) (3) v f From Macchi, A. A Superintense Laser-Plasma Interaction Theory Primer. (2013). Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 11 / 34

13 Generation of the wake waves Wake wave in my own simulation Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 12 / 34

14 Wave-breaking Electron in wakeeld E x = E 0 cos(k p x ω p t) (4) If electron velocity v v p, dens maximum diverges, i. e. wave-breaking. Non-relativistic wave-breaking limit E 0 = m eω p v p e (5) Relativistic wave-breaking limit E 0 = m eω p c 2 γp 1, (6) e where γ p refers to phase velocity of wake wave (Gibbon, 2004). Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 13 / 34

Various electron acceleration regimes 1 Laser wakeeld accelerator 2 Plasma beat wave accelerator 3 Multiple laser pulses 4 Self-modulated laser wakeeld accelerator 5

15 Various electron acceleration regimes 1 Laser wakeeld accelerator 2 Plasma beat wave accelerator 3 Multiple laser pulses 4 Self-modulated laser wakeeld accelerator 5 Blow-out regime 6 Other "pseudo-resonance" "forced" laser wakeeld regimes Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 14 / 34

16 Laser wakeeld electron acceleration Acceleration by short intense laser pulse cτ = λ p ( = tens fs). Ti:sapphire laser appropriate Accelerating distance ( ) ω 3 (7) on order of milimeters. L acc = λ π ω p Example Required electron energy: 100MeV ω/ω p = 10 n e = cm 3 λ = 1 µm L acc = 300 µm Similar to my own experiences gained by PIC simulations. Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 15 / 34

17 Bubble regime (cavitated wakeeld regime) Ponderomotive force generated by intense laser pulse expels electrons and creates ion cavity. Condition for bubble generation k p w 0 = 2 a 0 a cτ λ p /2 b a 0 > 2 a a 0 = I[10 18 W/cm 2 ] λ 2 L [µm] b λ p[µm] = / n e[cm 3 ] Corde, S. et al. Femtosecond x rays from laser-plasma accelerators. Rev. Mod. Phys. 85, 148 (2013). Size of the bubble Size of bubble from the balance between ponderomotive expulsion and Coulomb repulsion R = w 0. Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 16 / 34

Bubble regime (cavitated wakeeld regime) Electric eld In the rear part of the bubble electrons accelerated. In the front part of the bubble electrons decelerated.

18 Bubble regime (cavitated wakeeld regime) Electric eld In the rear part of the bubble electrons accelerated. In the front part of the bubble electrons decelerated. Observation There is an optimum plasma width depending on plasma and pulse parameters. Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 17 / 34

Laser wakeeld electron acceleration From www.vacet.

19 Laser wakeeld electron acceleration From Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 18 / 34

20 Useful scaling laws overview According to Esarey, RMP, 2009 dephasing length L d λ3 p 2λ 2 pump depletion length L pd λ3 p λ 2 energy gain if limited by dephasing W d (MeV) 630I(W/cm2 ) n(cm 3 ) { 1 for a ( 2/π)a 0 /N p for a { 2/a 2 0 for a ( 2/π)a 0 for a { 1 for a (2/π)/N p for a energy gain if limited by depletion { W pd (MeV) 21 /[λ 2 (µm)n(cm 3 )] for a I(W/cm 2 )/n(cm 3 ) for a Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 19 / 34

Plasma beat-wave acceleration (PBWA) Principle

to plasma frequency Resonance condition ω 1 ω 2 =

21 Plasma beat-wave acceleration (PBWA) Principle two longer pulses dierent frequency beat equals to plasma frequency Resonance condition ω 1 ω 2 = ω p From Wiki From Malka et al., Nature Physics, Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 20 / 34

Injection of electrons into the bubble Plasma wave only accelerates

bubble electron buch has to be preaccelerated to achieve from plasma

ionisation by optical eld inside the bubble using second pulse change

22 Injection of electrons into the bubble Plasma wave only accelerates electrons; electrons have to be delivered into a bubble to be accelerated. Injection mechanisms 1 external injection of electron bunch into bubble electron buch has to be preaccelerated to achieve from plasma wave e ective acceleration 2 self-injection of plasma electrons ionisation by optical eld inside the bubble using second pulse change of plasma density by bubble shape development Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 21 / 34

23 Particle-in-cell Overview PIC method enables to simulate the development of relatively large amount of physical particles using a smart trick. Macroparticles representing up to million physical particles are introduced. Advantages of grid and gridless computing connected. Particle-in-cell cycle Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 22 / 34

24 Particle-in-cell method Principle PIC solves Vlasov equation: f s t + v f s x + q se f s m s v = 0. (8) Probability density function of particle of spicies s is sum throught macroparticles f s (x, v, t) = f p (x, v, t). (9) p Basic idea is to express f p as a certain function with a few free parameters f p (x, v, t) = N p S x (x x p (t))s v (v v p (t)), (10) where shape of functions S i is simple (δ, saw, Bessel,... ). Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 23 / 34

25 Particle-in-cell: Equations of motion solver 1 Converting s Vlasov equations into p s equations for every macroparticle f p t + v f p x + q se f p m s v 2 Solution should satisfy also several moments of (11) = 0. (11) dn p dt dx p dt dv p dt = 0, (12) = v p, (13) = q s m s E p. (14) 3 Boris scheme or scheme leap-frog used after discretisation. Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 24 / 34

26 Particle-in-cell: Maxwell's equations solver Set of Maxwell's equations on the discrete grid is usually solved using E = ρ ε 0 (15) E = B (16) t B = 0 (17) E B = µ 0 j + µ 0 ε 0 (18) t nite dierence method (advanced schemes) spectral methods. nite elements method Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 25 / 34

27 Particle-in-cell: Interpolations Macroparticles can be found anywhere in space. Macroscopic quantities reprezented only in the grid points. Interpolation functions are used, e.g. W (x i x p ) = Charge of the particle (in gray) is distributed among the surrounding nodes. Charge contributed to each node is based on the proximity of the particle to that node. From ( ) x xi dx S x (x x p ) b 0. (19) x Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 26 / 34

28 Example of own simulation 2D PIC simulation for Ti:sapphire system at PALS Physical parameters Gaussian beam E = 500 mj λ = 800 nm τ = 40 fs w 0 = 7 µm n e = cm 3 100µm exponentional density ramp L = 3.2 mm Simulation Parameters 2D PIC code EPOCH used Size of domain 100 µm 80µm Number of particles per λ n x = 24 n y = 8 Technical Details 11 hours on 24 CPUs computed at MetaCentrum Video: density n Video: momentum p x Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 27 / 34

29 Example of own simulation: Electron density plot 2D PIC simulation for Ti:sapphire system at PALS Generation of the bubble Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 28 / 34

30 Example of own simulation: Electron density plot 2D PIC simulation for Ti:sapphire system at PALS Self-injection Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 29 / 34

31 Example of own simulation: Electron density plot 2D PIC simulation for Ti:sapphire system at PALS Divergence of accelerated beam in vacuum Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 30 / 34

32 Example of own simulation: Electron density plot 2D PIC simulation for Ti:sapphire system at PALS Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 31 / 34

33 Example of own simulation: Electron density plot 2D PIC simulation for Ti:sapphire system at PALS Electric eld E x during propagation Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 32 / 34

34 Conclusions Repetitio est mater studiorum 1 Laser-plasma interaction oers a new possibility to generate high energy electron beams cheaper and easier in comparison with conventional accelerators. 2 Electron can be accelerated as a consequence of laser-plasma interation up to tens or hunderds of MeV even in our Ti:sapphire laser system. 3 Bubble regime of acceleration seems to be the most promising way. 4 There is an ideal length of plasma accelerator, limited by dephasing or laser depletion. 5 Beam characteristics as monochromacity and beam divergence is questionable. 6 Particle-in-cell method (PIC) oers reasonable simulation insight into the topic. 7 Own simulations related to our Ti:sapphire laser system introduced. Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 33 / 34

35 Thanks for your attention Vojt ech Horn y UFP AV CR KFE FJFI CVUT v Praze horny@pals.cas.cz kfe.fjfi.cvut.cz/~horny Presentation available at kfe.fjfi.cvut.cz/~horny Vojt ech Horn y (IPP AV CR) Electron Acceleration in Laser Plasma 4th December 2014, Praha 34 / 34

Laser Plasma Wakefield Acceleration : Concepts, Tests and Premises

Laser Plasma Wakefield Acceleration : Concepts, Tests and Premises J. Faure, Y. Glinec, A. Lifschitz, A. Norlin, C. Réchatin, V.Malka Laboratoire d Optique Appliquée ENSTA-Ecole Polytechnique, CNRS 91761