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

### Darwin (magnetoinductive) model for laser plasma

M. Ma?ek1, P. Gibbon2

1 Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, Czech Republic
2 J?lich Supercomputing Centre, Institute for Advanced Simulation, Forschungszentrum J?lich GmbH, D-53435 J?lich, Germany

A new type of mesh-free plasma simulation model was recently introduced
by the authors. The model is implemented within the code
PEPC (Pretty Efficient Parallel Coulomb-solver), which uses an O$\small (N\
\log\ N)$
Barnes-Hut tree algorithm to speed up self-consistent
force calculation. The efficient scaling properties of the algorithm
permits multi-million particle simulation on up to 8192
CPUs of the newly installed 223-Teraflop BlueGene/P machine JuGene at the Research Centre J?lich. The model incorporates slowly varying magnetic fields within the so-called Darwin or magnetoinductive approximation, which neglects the transversal part of displacement current in the Amp?re?s law. It corresponds to omitting radiation, but it keeps the lowest order relativistic correction O$\small (v^2/c^2)$. Since high frequency wave
modes disappear and action-at-a-distance nature of forces is
introduced to the model, the integration step is no longer limited
by Courant condition taking into account finite speed of information spread.
On the other hand, numerical difficulties connected
to this approximation have already been reported by previous authors, who implemented the Darwin model within PIC or Vlasov codes. The standard scheme known from the fully electromagnetic codes used for the calculation of time derivative of the vector potential causes a violent numerical instability destroying the whole run in a few time-steps. One of the possible solutions to this problem is to express the quantities in terms of Hamiltonian generalized variables, which avoids the time derivative of the vector potential in the the equation of motion.

The paper will present the magnetoinductive model of the
self-consistently evolving N-body system employing a multipole
expansion of Darwin field equation computed within a
standard tree algorithm. A numerical algorithm overcoming the
numerical difficulty mentioned above will be presented and discussed
and the ability of the model to give a first-principles description of magnetized plasma evolution will be demonstrated by the results of
preliminary tests.