On very short and intense laser–plasma interactions

Abstract

We briefly report on some results regarding the impact of very short and intense laser pulses on a cold, low-density plasma initially at rest, and the consequent acceleration of plasma electrons to relativistic energies. Locally and for short times the pulse can be described by a transverse plane electromagnetic travelling-wave and the motion of the electrons by a purely Magneto-Fluido-Dynamical (MFD) model with a very simple dependence on the transverse electromagnetic potential, while the ions can be regarded as at rest; the Lorentz-Maxwell and continuity equations are reduced to the Hamilton equations of a Hamiltonian system with 1 degree of freedom, in the case of a plasma with constant initial density, or a collection of such systems otherwise. We can thus describe both the well-known wakefield behind the pulse and the recently predicted slingshot effect, i.e. the backward expulsion of high energy electrons just after the laser pulse has hit the surface of the plasma.

On cold diluted plasmas hit by short laser pulses

“…If ⊥ is slowly modulated (i.e. | | |k | on [0, l]) then α ⊥ (ξ) (ξ) ⊥ o (ξ + π/2k); hence α ⊥ (ξ), u ⊥ (ξ) 0 if ξ > l. Since |f | |kf | holds also for f =ŝ e , ∂ẑ e /∂Z, (17) yields ∆x ⊥ e −e ⊥ /k 2 mc 2ŝ e , and using (19) one can easily estimate rhs (13), so as to check the condition R |∆x ⊥ eM | and the approximation A ⊥ α ⊥ .…”

“…In section II we discuss the motion of electrons when R = ∞ (χ R ≡ 1) using an improved plane hydrodynamical model [11,12] (for shorter presentations see [13]) that allows to reduce the system of Lorentz-Maxwell and continuity partial differential equations (PDEs) into ordinary differential equations (ODEs), more precisely into a family of decoupled systems of arXiv:1803.02915v2 [physics.plasm-ph] 25 Mar 2018 non-autonomous Hamilton Equations in dim 1 in rational form. In the model we alternatively adopt the light-like coordinate ξ = ct−z or time t to parametrize the electron motion, the transverse and the light-like components p ⊥ e , p 0 e −cp z e ≡ mc 2 s e (instead of the longitudinal one p z e ) of the electron 4-momentum as unknowns, neglect pump depletion, control how long this is valid, how long the hydrodynamical picture holds, when and where it fails (by wave-breaking [4]).…”

Simple model of the slingshot effect

“…On the contrary, in the relevant space-time region a MHD description of the impact is self-consistent, simple and predictive (collisions are negligible, and recourse to kinetic theory is not needed). Here we develop and improve the 2-fluid MHD approach introduced in [13,14] and apply it to determine a broad range of conditions enabling the effect, as well as detailed quantitative predictions about it (a brief summary is given in [15,16]). In section II we study the plane problem (R = ∞) and show that for sufficiently low density and small times (after the impact) we can neglect the radiative corrections [backreaction of the plasma on the electromagnetic (EM) field (3)] and determine the motion of the surface electrons in the bulk by (numerically) solving a single system of two coupled first order ordinary differential equations of Hamiltonian form, if the initial density n 0 is step-shaped, or a collection of such systems, otherwise; the role of 'time' is played by the light-like coordinate ξ = ct − z.…”

Travelling waves and light-front approach in relativistic electrodynamics

“…Case E s = E z s k, B s = 0 Left: the motion(28) induced by a linearly polarized modulated EM wave(4) with wavelength λ = 2π/k = 0.8µm, gaussian enveloping amplitude (ξ) = E ⊥ M exp[−ξ 2 /2σ] with σ = 20µm 2 and |q|E ⊥ M /kmc 2 = 6.6, trivial initial conditions, B s = 0, E s = kE z M , where E zM q 37GeV/m (with such a wave this yields the maximum energy gain, E f 1.5). Right: the corresponding trajectory in the zx plane within an hypothetical acceleration device based on a laser pulse and metallic gratings G, P at potentialsV = 0, V p , with qV p /z p 37GeV/m.Then the solution (24) reduces to 4ŝ (ξ) = 1−κ ξ, (x + iŷ)(ξ) =…”

“…the backward acceleration and expulsion from the plasma of some surface electrons (those with smallest Z and closest to the z-axis) with remarkable energy. For reviews see also [27,28]. On the other hand, if R is smaller the LE may close the rear part of c t and make it into a ion bubble (completely deprived of electrons), before any electron gets out of the bulk.…”