2D PIC simulations of collisional transport of relativistic electrons in dense plasma

Abstract

We report results of a series of simulations about electron transport in plasma close to solid density performed with a collisional 2D3V PIC code and compare the results to published ones obtained using hybrid codes. We show that the dispersion of energetic particles remains similar to the one observed in the collisionless case and discuss and compare our results in the light of hybrid codes. The transport of fast electrons in dense cold plasmas remains a challenging problem in many situations of interest. The main tool for the study of kinetic effects in the laser-plasma interaction, i.e. PIC code, is at pain in this regime. First it must be extended in the collisional regime, which has proven to be doable but add a significant burden in term of computing time. Second the stability of the model imposes - a priori - severe constraints on the mesh size and the time step usable. In order to alleviate these constraints several kinds of reduced aiming at the replacement of brute force by physical insight have been proposed and used. The basic physical assumption of all these models is that for a given temperature of the background plasma, above some value of the density, collisional damping prevails and suppresses collective modes of the plasma (1). The use of this assumption has given rise to various flavours of codes. So-called hybrid models ignore the laser/plasma interaction and merely describe the transport of energetic particles in a background plasma assuming quasi-neutrality. The energetic particles are described by PIC particles, while the background plasma is handled by fluid equations. The electric field is obtained by Ohm law applied to the thermal plasma and the Faraday law then gives the magnetic field. One of the difficulties with this kind of model is the initialization of the high energy electrons, whose distribution function is by essence arbitrary. Several studies showed that the results are dependent on the injection used. Attempts have been made to alleviate these constraints, either by coupling this kind of model with a PIC code (2) or by building directly a PIC code presenting an adequate behaviour for dense plasmas. Two of these codes have been recently published. In one of them (3) the collective behaviour is progressively ignored as the density becomes larger than some critical value ndamp , while in the other one (4) Maxwell equations are replaced by MHD equations-as in an hybrid code- above some critical value ndamp. The study of the published literature shows that the validation of such models is limited to peculiar cases, that a lot of caution has to be exercised in their use and in particular that the hypothesis about collisional damping must remain valid during all the simulation including after heating of the background plasma by energetic particles. Finally the same study of literature shows that similar problems handled with different hybrid codes give different results (2, 5). In the present paper we report results based on a series of reference PIC simulations, in the sense that all standard conditions for stability have been fulfilled. The use of high order spline interpolation combined with fourth order smoothing has allowed us to increase the mesh up to values large as compared to the Debye length (20d) but this point in itself has been validated by comparing