NUMERICAL SIMULATION OF INTERACTION.DYNAMICS OF SHOCK WAVES IN COLLISIONLESS PLASMA

V.A. Vshivkoy, G.I. Dudnikova
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.1. С. 66.

      The problems of formation and interaction between collisionless shock waves in plasma are important for the outer space processes such as Sun flashes, Supernova fragments dragging by inter-Galaxy medium sun wind flow-over Earth magnetic sphere etc.
      Numerical simulation method was used to study the interaction dynamics bf shock waves resulting from the dragging of dense plasma clouds expanding from one space point with a time delay. The 2-D axisymmetric hybrid plasma model is based on the kinetic description of plasma component and hydrodynamic approximation for electrons. The numerical implementation was accomplished using the particle-in-cell method for the calculation of kinetic Vlasov equation and finite-difference splitting schemes for Maxwell equations. The shock amplitude dependence on initial energy of plasma clouds, parameters of magnetized background delay time is obtained. The conditions are found when the second plasma cloud can expand without perturbation generation in plasma.
      The work was carried out under the auspice of Russian Fundamental Research Foundation (project N 94-01- 00112).

      The propagation of strong laser pulses through plasma is the source of multiple problems in nonlinear optics that represent a great interest in the general physics sense and for various applications. Currently extensive studies are underway for the interaction of super short pulses with plasma in connection with new methods for charged particle acceleration.
      The paper presents the numerical simulation results for the wake acceleration of particles based oh 3-D relativistic kinetic code. The source computational model includes Vlasov equations for ion and electron plasma components and the complete system of Maxwell equations. The kinetic equations are solved with the particle-in-cell method the finite-difference method is used for electromagnetic field equations.
      The results presented show that the pulses shorter than the plasma wavelength excite a regular wake wave in plasma with the electric field accelerated by electrons. In addition, the interaction of relativistically strong laser pulses with rarefied plasma demonstrates various nonlinear process types: fast absorption of the pulse energy, energy transformation and other wave types, variations in electromagnetic radiation frequency, shock wave formation.

      The particle-in-cell method (PIC) is commonly used for the calculations in collisionless plasma physics where a great importance is given to the interaction through electromagnetic fields.
      The PIC method represents plasma as a set of model particles with the motion trajectories being the characteristics of Vlasov equation.
      Since the evaluation of new velocities and coordinates of the particle does not directly depend on the other particles the problem is well suited to parallelization. However depending on the technique for data distribution (particles, and field values at the grid nodes) among the processors we deal either with nonuniform loading of processing elements (PEs) or high communications overhead. These problems appear in the case of nonuniform distribution of particles in the modeling space. Thus the parallel code textually depends on the law of particles distribution in the modeling space. In addition, the decision about the data and computation distribution among the processing elements depends on the pattern of particle expansion, their amount, grid size, the difference between sequential algorithms and of course on the computer system architecture, particularly on PE memory size.
      The work presents the development results, for the programming system intended for the implementation of various PIC method versions. The work is performed within the ASSY project (ASsembly SYstems). The project is oriented to the development of the metasystem supporting the development of problem-oriented programming systems. PIC method is one of the problems used to verify actual capabilities of ASSY technology.
      The work was carried out under the auspice of Russian Fundamental Research Foundation (project N 95-01- 01358) and the Commission of the European Communities (grant ITDC-203-822165).