Non-Maxwellian electron distributions and continuum X-ray emission in inverse Bremsstrahlung heated plasmas

Abstract

The heating of a completely ionized plasma by inverse Bremsstrahlung absorption (IB) is studied by numerically integrating the time varying kinetic equation for electrons, and the resulting distribution functions are used to calculate the continuum X-ray emission. The shape of the distribution functions is determined by the competition between IB and electron4ectron collisions, and, in all our uniform plasma simulations, we find that the distributions are well fitted by the formula Cwhere m is between 2 and 5 . We find the dependence of m on a = Z2u,,,/v:h, where Z is the atomic number, v,,, is the oscillation velocity in the laser field and vth is the thermal velocity: m(a) = 2 f 3/(1+ 1.66/a0 724). More importantly, in the realistic case of a space and time dependent kinetic simulation of a Be plasma heated by a Nd laser, including heat flow and ion motion, this fit remains valid for electron densities below O.75Nc (with constant m), although other effects come into play closer to the critical surface. Thus, these simple results can be used to determine the continuum X-ray spectrum due to Bremsstrahlung (BR) and to direct radiative recombination (DRR). The contributions of BR (valid for average and large atomic numbers) and DRR into each shell are given in a parametric form as functions of m and T,. The implications for the plasma diagnostics based on continuum X-ray emission are discussed.

A comparison of non-local electron transport models for laser-plasmas relevant to inertial confinement fusion

“…These are computed by the MHD model and assumed to heat the electrons while maintaining a thermal (i.e. Maxwellian) distribution: deviations from this assumption for ionization have been discussed by Robinson [7], and for P dV work by Matte [8]. We have found no deviation from a Maxwellian distribution when including the full electron-ion energy exchange terms (except in extreme conditions not relevant to this study).…”

Different Fokker–Planck approaches to simulate electron transport in plasmas

“…To determine the nonlocal kernel w, we solve numerically the FokkerPlanck equation with the modified collisions operator in a perturbation regime as in [2,5] to obtain a new set of nonlocal kernels for different Z, kλ e and for different values of the Langdon parameter α = Z(v osc /v th ) 2 [8], where Z is the ion charge state, v osc = |eE|/mω 0 is the velocity of oscillation of the electrons in the laser field E, v th = (k B T e /m e ) 1/2 is the electron thermal velocity, and ω 0 is the laser angular frequency. The parameter α is a direct indicator of the non-Maxwellian behavior of the distribution function due to the collisional laser heating: when α goes to 0 we have a Maxwellian distribution, and in the opposite case, the angle-averaged distribution function (f 0 (v)) tends to a super-Gaussian shape [14], and this in turn affects nonlocal heat flow [2]. The nonlocal propagator for parallel transport in Tokamak plasmas (Z = 1), corresponds to α = 0, because of the absence of inverse bremsstrahlung heating, and here, we approximate this value by running with α = 10 −3 .…”

Rate of radiated power loss with different statistical distributions

“…In addition to [8,[10][11][12] we wish to recall the works of Langdon [ 13 ] and of Whitney and Pulsifer [ 14] concerning the conditions under which nonMaxwellian distributions must be used when analyzing inverse bremsstrahlung and heated-electron, laser produced plasmas and high current discharges. Non-Maxwellian distribution are important also in the field of nuclear physics, where, on one side we have the proposal by Clayton [15] to use non-Maxwellian distributions in the solar plasma in order to explain the solar neutrino puzzle, and on the other side we have studies on non-Maxwellian distributions of nucleons in nuclear matter with momentum-dependent effective interaction [16].…”