Particle-in-Cell Simulations of Particle Acceleration. E. A. Startsev and C. J. McKinstrie. Laboratory for Laser Energetics, U.

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1 Particle-in-Cell Simulations of Particle Acceleration E. A. Startsev and C. J. McKinstrie Laboratory for Laser Energetics, U. of Rochester Previous analytical calculations suggest that a preaccelerated test particle can be ponderomotively accelerated to energies in excess of 1 MeV by an intense electromagnetic pulse propagating in a underdense plasma. 1 To check these predictions we have developed a relativistic, two-dimensional particle-in-cell code. Test simulations that validate the code will be described in detail. Preliminary simulations of the interaction of a preaccelerated electron bunch with an electromagnetic pulse in a plasma will be presented. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC3-92SF1946, the University of Rochester, and the New York State Energy Research and Development Authority. 1.C.J.McKinstrieandE.A.Startsev,Phys.Rev.E54, R17 (1996); 56, 213 (1997).

2 Particle-in-Cell Simulations of Particle Acceleration E. A. STARTSEV and C. J. McKINSTRIE University of Rochester Laboratory for Laser Energetics

3 Abstract Previous analytical calculations suggest that a preaccelerated test particle can be ponderomotively accelerated to energies in excess of 1 MeV by an intense electromagnetic pulse propagating in an underdense pasma. 1 To check these predictions we have developed a relativistic, two-dimensional particle-in-cell code. Test simulations that validate the code will be described in detail. Preliminary simulations of the interaction of a preaccelerated electron bunch with an electromagnetic pulse in a plasma will be presented. 1. C. J. McKinstrie and E. A. Startsev. Phys. Rev. E 54, R17 (1996); 56, 213 (1997)

4 An intense laser pulse in a plasma repels the particle In vacuum the pulse displaces the particle but leaves it at rest. A A In a plasma the pulse repels the particle if intensity exceeds a threshold V B = V p ( ) 2 1 a2 B = 2 γ p γ A u p u A where a B = e A m e c 2. V p V C V A P1984 Here, γ g = 1 1 v g 2 ( ) 1 2 and u p = γ 2 ( p 1 ) 1 2.

5 The particle can be effectively accelerated The energy gain δγ = 2 u2 ( p γ A γ p u p u A ). Threshold and gain γ p = Energy gain Repelling threshold Injection energy ( m e c 2 ) With energy measured in units of the particle rest mass, if the injection energy γ A = 7., the repelling threshold a2 B = 8.3 and the energy gain δγ = 12. P1985

6 1-D simulations show good agreement with theory 1, 2 1-D propagation of an intense circularly polarized laser pulse in a plasma is described by the equations u x = [ v g ( 1+ φ) ψ] 1 v 2 ( g ), φ = 2π [ ], ( ) 2 1 v g ( 1+ φ) ψ ( ) 1 v 2 ( g ) ( 1+ a 2 ) [ ] 1 2, ψ = 1+ φ 2 where φ = eϕ/mc 2 is electrostatic potential, v g is pulse group speed, and a = ea/mc 2. The fluid and PIC results were compared for a = 5 sin(πx/9), ω p /ω =.1. U x X/λ ee x mcω X/λ P29 2. P. K. Kaw, A. Sen and T. Katsouleas, Phys. Rev. Lett. 68, 3172 (1992).

7 Forward SRS was observed The 1-D simulation with a =.8, ω /ω p = 1, l = 2 λ, λ = 1 µm, and linear polarization. At t = 1 λ RFS grows at the head of the pulse from anomalously large noise source provided by RBS. At t = 16 λ the nonlinear state of the beam evolution leads to spectral cascading 3. 3C. D. Decker, W. B. Mori, and T. Katsouleas, Phys. Rev. E, 5, R3338 (1994). eez/mωc eez/mωc eex/mωc t = 1 λ 1 4 t = 16 λ k/k p k/k p x/λ x/λ P241

8 Multistage ponderomotive acceleration is possible in a plasma with a density gradient V p i n( x) n V A i+ 1 V A i V p = n( x) n cr V p i+ 1 V A i+ 2 V A i+ 1 i+1 On each stage γ A = γ i γ i p A γ i, where i A denotes quantities before acceleration and i + 1 denotes quantities after acceleration. Also, the threshold for each stage is P a i 2 2 = 1 γ i p 2 i γ A + γ A i γ p i If, on each stage, γ p i. 2 γ A i = α = const, then a i th = const. and the final energy after N stages is γ A final = α 2N γa. If the density profile is chosen as n(x) = n /(1 + x/l) 2, then γ p i+1 γp i = α 2 and γ p i+ 1 i+ 1 γ = γ i p = α = const. A γ i A On the distance L, these will be N = 1 2 l n ( 1+ L l) l n γ p γ ( A ) number of stages; here, γ p = ω ω p. If L/l = 1, γ A = 5, ω /ω p = 1, then N = 5 and γ A final = 5 m e c i = 2.5 GeV!

9 Accelerated particles were observed A bunch of electrons was preinjected ahead of the pulse in the direction of the pulse propagation with initial energies γ = 7. ee x /mω c t = 1 λ ee x /mω c t = 3 λ Pulse intensity a = 1 and plasma density γ p = ω /ω p = 3, l = 3 λ. Pulse was circularly polarized. At the time t ~ γ 2 p l ~ 3 λ, preinjected particles have completed their acceleration and are moving ahead of the pulse. Energy gain δγ = (γ p /γ ) 2 γ ~ 13 was observed. ee z /mω c P z 8 9 x/λ P x 14 ee z /mω c 2 9 x/λ 1 P z 8 2 x/λ 2 P x P x P x/λ o 9 P x

10 Relativistic self-focusing was observed for a pulse with P > P c e E.25 z /mω c e E z /mω c The 2-D simulations were made with the parameters (a) a =.75, 21.5 b) a =.35, ω /ω p = 5, l = 4 λ, r = 7 λ, λ = 1 µm y/λ y/λ k y /k p. 5 t = 3 λ a =.75 a =.35 ee x /mω c 1 1 X/λ X/λ ee z /mω c ee x /mω c ee z /mω c For these parameters L R = π r 2 /λ = 15 λ, (a) P/P c = 2, (b) P/P c =.5. In the case of P/P c = 2 beam stays focused for two Rayleigh lengths. Substantial Raman sidescatter (RSS) was present. RSS has only a downshifted Stokes component because the anti-stokes cannot be simultaneously resonant. P k x /k p k x /k p In comparison, for (b) P/P c =.5, no self focusing was observed.

11 Electrostatic field does not prevent particle acceleration y/λ y/λ y/λ t = 1 λ t = 4 λ 8 e E z /mω c e E z /mω c ee x /mω c ee x /mω c n/n 15 n/n 4 2-D simulation of the particle acceleration was conducted with parameters a = 1, ω /ω p = 1, r /λ = 1, l/λ = 3. L R /λ = π (r /λ ) 2 3. The power of the pulse is being quickly depleted by the wake generation. Though the electrostatic field is significant, it is negligible ahead of the pulse where particles are accelerated x/λ x/λ The initial particle energy was γ = 5. The energy gain δγ = 25 was observed. P244 P x P x x/λ 7 x/λ 9 Particles are spread in transverse direction by the ponderomotive force in the angle θ = p max =.1 γ max

12 Summary/Conclusion A simple 1-D acceleration scheme was suggested that uses the PM force to accelerate preinjected electrons to energies as high as 1 MeV. The model of the multistage pondermotive acceleration in a plasma with a density profile predicts energy gains of δγ. 2 GeV on a distance of several centimeters. This scheme relies on the fact that the group speed of the laser pulse is less than c. A 2-D particle-in-cell code was developed to check this prediction. Test simulations that validate the code were presented. Simulations of the interaction of a preaccelerated electron bunch with an electromagnetic pulse in a plasma show evidence of electron acceleration. P199