3.3.2 &spacetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3.3 &phasespace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
CONTENTS
i
Contents
1 Introduction
1
2 Receiving and Installing
3
2.1 Plain version . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Parallel version . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1.7 Parallel LPIC++ version (&parallel) . . . . . . . . . . . . . . . . 12
3.2 Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 User's Guide
5
3.1 Input for LPIC++ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.1.1 Laser pulses (&pulse front, &pulse rear) . . . . . . . . . . . . . 5
3.4 Running LPIC++ under PVM . . . . . . . . . . . . . . . . . . . . . . . . . 21
4 Examples
22
4.1 Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.2 Simulation time (&propagate) . . . . . . . . . . . . . . . . . . . 9
3.1.3 Simulation box, plasma shape and density (&box) . . . . . . . . 10
3.1.4 Particle species (&electrons, &ions) . . . . . . . . . . . . . . . . 10
6.3 Program Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
A Moving frame for oblique incidence
50
B Units
53
1
1 Introduction
Particle-In-Cell (PIC) codes are well established tools for kinetic simulations in plasma physics and astro physics. In recent years, the progress in producing intense (I > 1018Wcm;2) ultra-short (< 100fs) laser pulses 1] demanded more and more for kinetic descriptions of the interaction of such laser pulses with plasmas, since high intensities, short time scales and large density gradients occuring lead to the failure of conventional hydrodynamic approaches assuming nonrelativistic dynamics, local thermodynamic equilibrium, etc. New insight has meanwhile been obtained with the guidance of numerical kinetic treatments, mainly PIC simulations, in the eld of absorption of short laser pulses 2, 3, 4], the propagation of short pulses in underdense plasma, wake eld generation, fast electron production 5, 6, 13], magnetic eld generation 6], harmonic generation at overdense plasma surfaces 7, 8, 9, 10], and even in a new discipline of inertial con nement fusion (ICF), the fast ignitor concept 11, 12, 13]. The code LPIC++ presented here, is based on a one-dimensional, electromagnetic, relativistic PIC code that has originally been developed by one of the authors 14] during a PhD thesis at the Max-Planck-Institut fur Quantenoptik for kinetic simulations of high harmonic generation from overdense plasma surfaces 10]. The code uses essentially the algorithm of Birdsall and Langdon 15] and Villasenor and Bunemann 16]. It is written in C++ in order to be easily extendable and has been parallelized to be able to grow in power linearly with the size of accessable hardware, e.g. massively parallel machines like Cray T3E. The parallel LPIC++ version uses PVM for communication between processors. PVM is public domain software, can be downloaded from the world wide web 17]. The power of LPIC++ is mainly based on its clear program and data structure, which uses chained lists for the organization of grid cells and enables dynamic adjustment of spatial domain sizes in a very convenient way, and therefore easy balancing of processor loads. Also particles belonging to one cell are linked in a chained list and are immediately accessable from this cell. In addition to this convenient type of data organization in a PIC code, the code shows excellent performance in both its single processor and parallel version. It is planned to extend the code to three spatial dimensions.
4.6 More Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5 Algorithm
29
5.1 Maxwell Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Max-Planck-Institut fur Quantenoptik Hans-Kopfermann-Stra e 1 D-85748 Garching, Germany fax: +49-89-32905200
email: meyer-ter-vehn@mpq.mpg.de pfund@mpq.mpg.de
4.2 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.3 Re ection from Overdense Plasma . . . . . . . . . . . . . . . . . . . . . 22