Topic/Type: 1.3 High intensity Laser Plasma Interaction, Poster

### Ergodic particle method for the simulation of the dynamics of nonneutral plasmas in the presence of electron-neutral collisions

G. Coppa1, A. D ' Angola2, R. Mulas1

1 Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino - Italy
2 Universit? della Basilicata, via dell'Ateneo Lucano 10, 85100 Potenza - Italy

In a previous work [1], some of the Authors contributed to develop a new method to study the dynamics of the expansion of spherical nanoplasmas. The method was based on the assumption that, instead of following exactly the electron motion, one can use the time average of the trajectories, which are approximated by using a suitable ergodic distribution for each computational particle (a discussion on the validity of the method is reported in [2]). Although the assumption represents a simplification (in spherical symmetry the angular momentum is conserved and the correct density distribution for each particle contains a factor $\small \delta(|\mathbf{x}\times\mathbf{p}|-L)$), the method provides accurate results in terms of energy spectrum and space density distribution.
The present work proposes to use a similar technique for studying the dynamics of an electron plasma in the presence of collisions with neutral atoms. To show the effectiveness of the method, a simple 2D situation is considered, in which the electrostatic potential due to the electrodes is given by $\small \phi(x,y) =a\cdot(y^{2}-x^{2})$ and the self-consistent field is negligible. In addiction, a constant magnetic field $\small \mathbf{B}=B_{0}\mathbf{e}_{y}$ is present. In this case, the canonical momentum $\small p_{z}=m(v_{z}-\omega_{c}x)$ is a constant of the motion and in $\small (x,y)$ domain the particles move according to the effective potential $\small U(x,y)=q\phi(x,y)+\frac{1}{2m}(m\omega_{c}x+p_{z})^{2}$; in this case, each electron can be given a space distribution depending on three parameters $\small \{p_{z},\epsilon_{x},\epsilon_{y}\}$, where $\small \epsilon_{x}$ and $\small \epsilon_{y}$ represent the energies along $\small x$ and $\small y$ directions (in fact, the motion is a simple composition of two harmonic oscillations along $\small x$ and $\small y$). Alternatively, a simplified ergodic model can be used, in which each computational particle is associated the distribution $\small \delta(\frac{m}{2}(v_{x}^{2}+v_{y}^{2})+U(x,y;p_{z})-\epsilon)$, being $\small \epsilon$ the total energy, to which corresponds a constant space distribution in the region $\small \{U(x,y;p_{z})\leq\epsilon\}$ . This assumption is rigorously correct in the presence of a perturbation of the potential, otherwise it represents a simplified description of the physical system. In the presentation, results obtained with the two different approaches will be compared and discussed.

[1] F. Peano, F. Peinetti, R. Mulas, G. Coppa, and L. O. Silva, Phys. Rev. Lett. 96, 175002 (2006).

[2] F. Peano, G. Coppa, F. Peinetti, R. Mulas, and L. O. Silva, Phys. Rev. E 75, 066403 (2007).