This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON PLASMA SCIENCE 1 Snapshots From Particle-In-Cell Simulations of Superintense Laser–Plasma Interaction Tatiana V. Liseikina and Andrea Macchi Abstract—Particle-in-cell simulations are a very useful ap- proach for the study of laser–plasma interactions at ultrahigh intensities, such that the electron dynamics is relativistic. They are essential for the study of nonlinear laser–plasma dynamics and as a support tool for experiments and applications, including particle acceleration, ultrashort radiation sources, and nuclear fusion. We present a few images taken from investigations of ion acceleration in high-density plasmas and of coherent electromagnetic-structure generation in low-density plasmas. These images, as a common feature, are reminiscent of trees. Index Terms—Coherent structures generation, particle acceler- ation, PIC simulations. I T IS NOWADAYS possible to study laser–plasma interac- tions at laser-pulse intensities exceeding 10 21 W · cm −2 . In such a regime, the electrons oscillate in the laser field with relativistic momentum, and the optical properties of the plasma are strongly nonlinear. The ultrashort pulse duration may cause the excitation of high-amplitude plasma waves and oscillations, which in turn may break and lead to particle acceleration. The ultrastrong radiation pressure dominates the hydrodynamic motion of the plasma, leading to self-consistent modifications of the density profiles. These combined effects give rise to a very rich variety of phenomena, including the generation of coherent electromagnetic structures and long-lived ultrahigh fields, as well as the basis for advanced applications, such as novel laser–plasma accelerators of electrons and ions, ultrashort sources of hard X-rays, or the fast-ignition approach to inertial confinement fusion [1]. In the next future, it is expected that the building of novel laser facilities (such as the ELI and HiPER projects in the European Union [2], [3]) will allow to obtain even higher intensities, approaching the frontier of 10 26 W · cm −2 , and will further boost basic research and appli- cations development in this wide field, whose related definitions include “Relativistic Optics,” “High-Field Science,” “Extreme Light,” and so on. Numerical simulations are an essential tool to unfold the complex laser–plasma dynamics, which is dominated by col- Manuscript received April 6, 2008; revised April 8, 2008. This work was supported in part by the Italian Ministry for University and Research under a PRIN Project, by CNR under an RSTL Grant, and by CNR–INFM and CINECA (Italy) under the supercomputing initiative. T. V. Liseikina is with the Dipartimento di Fisica “Enrico Fermi,” Univer- sità di Pisa, 56127 Pisa, Italy, and also with the Institute of Computational Technologies, Siberian Division of Russian Academy of Science, Novosibirsk 630090, Russia (e-mail: t.liseikina@sns.it). A. Macchi is with polyLAB, CNR-INFM, 56127 Pisa, Italy, and also with Dipartimento di Fisica “Enrico Fermi,” Università di Pisa, 56127 Pisa, Italy. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPS.2008.924618 lective and kinetic effects, as well as to model experiments. To this aim, the Particle-In-Cell (PIC) method presently represents the most used and powerful approach. In its essence, the PIC method consists in a discrete Lagrangian representation of the distribution function in the Vlasov equation, leading to equations of motion for a set of computational particles which are formally identical to those of plasma electrons and ions. Electromagnetic fields are computed self-consistently on a spatial grid (i.e., in “cells”) using the charge and current densities calculated from a proper spatial average over the particles. Already in two spatial dimensions (2-D), PIC simulations typically require the use of parallel supercomputers to tackle spatio-temporal scales which are of experimental interest. “Fully realistic” simulations in 3-D and having the “same” parameters as experiments are almost always much beyond present-day supercomputing power. Despite these unavoidable limitations, PIC simulations in 2-D already provide precious insight on the plasma dynamics and support experimental observations. The images reported here were obtained from 2-D massively parallel PIC simulations performed on up to 100 processors on a Linux cluster at the CINECA supercom- puting facility in Bologna, Italy. The first image (Fig. 1) is from simulations performed to show the effect of laser-pulse polarization (linear versus cir- cular) on ion acceleration from a high-density plasma [4], [5]. The size of computational box was 50 × 50λ 2 L with a mesh of 100 cells per laser wavelength λ L . The total number of particles was 8 × 10 8 . The high spatio-temporal resolution was required to ensure convergence of the results, because the interaction causes a strong steepening of the plasma-density profile. The laser pulse is normally incident, and the ions are accelerated in the forward direction, crossing the target, and exiting in vacuum from the rear side. The figures show the contour levels of the ion distribution in logarithmic scale versus energy and the angle of emission with respect to the target normal. For circular polarization (CP), ion acceleration is dominated by the effect of the radiation pressure [4]. The “Xmas Tree” distribution obtained for CP shows a high degree of collimation of the ion beam, with the peak energy being a decreasing function of the angle. For linear polarization (LP), a more structured “tree” is observed, indicating a broader distribution with several beamlets. This effect, which is under current investigation, may be ascribed to the much stronger role of electron heating for LP or to the stronger rippling of the laser–plasma interface observed in the latter case [5]. The second image (Fig. 2) is from simulations of laser-pulse propagation in a low-density plasma. The size of computational 0093-3813/$25.00 © 2008 IEEE