**Topic/Type**:
2.5 Adaptative & multi-scale methods, Poster

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Development of a relativistic adaptive mesh refinement particle-in-cell (AMR-PIC) code

**
N. Elkina, H. Ruhl
**

*
Ludwig-Maximilians Universit?t M?nchen, Germany*

The acceleration of a plasma particles to relativistic velocities

represents one of the central issues of modern plasma physics and astrophysics. In the ultrarelativistic regime, the accumulated effect from radiation damping can severely limit individual particle

acceleration. Taking into account radiative losses effects introduces additional time scales, which have to be resolved for

accurate representation of plasma processes. The numerical simulation of collective phenomena in high energy astrophysics and laser plasmas requires methods of accurate solution for the relativistic Vlasov-Maxwell equations (possibly with source terms).

However, the simulations based on the conventional uniform grid Particle-In-Cell (PIC) method, have difficulty in supplying a usefully precise description of the particle acceleration process.

To overcome this the Adaptive Mesh Refinement (AMR) method and adaptive particle management algorithm can help to resolve multiscale processes and to reduce a computational time. In order to develop AMR-PIC method, three issues have to be addressed.

First, one have to develop criteria for grid adaptation/coarsening.

These criteria can be defined using physical as well mathematical properties of solution. We discuss a variety of possible criteria for adaptation and coarsening of grid in order to resolve all relevant scales of problem of interest. Second issue is related to development of accurate Maxwell solver for non-uniform grid.

In order to avoid sporadic reflections of waves at coarse/fine grid interface particular attention should be paid to possible changes of numerical dispersion on non-uniform grid.

Finally, the most important part of AMR-PIC approach is development of macro-particle management algorithm for flexible re-sampling of phase space, in order to adjust the distribution function to new computation grid. The algorithm has to conserve the moments of distribution function, like mass, momentum, energy. In order to show our way to deal with outlined problems, we present a new electromagnetic relativistic AMR PIC code which also incorporates

the radiation reaction force into the equations of motion

We also discuss a possible application of new code to model an particle acceleration in relativistic laser and astrophysics plasma.