Topic/Type: 2.2 Kinetic methods, Particle-In-Cell and Vlasov, Oral

Progress in mesh-free plasma simulation with parallel tree codes

P. Gibbon1, 4, L. Arnold1, B. Berberich1, 3, A. Karmakar1, 4, M. Masek1, 2, R. Speck1

1 Institute for Advanced Simulation, JSC, Forschungszentrum Julich GmbH
2 Institute of Physics, Academy of Sciences of the Czech Repulic, Prague, Czech Republic
3 Institute for Energy Research (IEF-4), Plasma Physics, Forschungszentrum Julich GmbH
4 ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt, Germany

Nearly all kinetic plasma modelling over the past four decades has relied on a spatial mesh to
mediate the interplay between plasma particles and their associated electric and magnetic
fields. While these models have proved highly successful, the presence of a grid ultimately
places restrictions on the spatial resolution or geometry which can be handled ? especially in
three dimensions. Recently a versatile, mesh-free plasma simulation paradigm has been
introduced which overcomes some of these limitations. Inspired by the N-body tree
algorithms designed to speed up gravitational problems in astrophysics, this approach reverts
to first principles by computing forces on individual particles directly, following their
trajectories in a Lagrangian, \'molecular dynamics\' fashion. Following the first application of
this technique to strongly coupled plasmas [1], tree codes have since been used to model
atomic clusters [2], 2D bounded plasmas [3] and 1D electrostatic sheaths in tokamaks [4].
Despite their physical simplicity compared to fully electromagnetic particle-in-cell codes,
mesh-free tree codes already offer completely new possibilities in plasma simulation,
particularly where collisions are important; for modelling complex geometries including
strong density gradients; or for mass-limited systems in which artificial boundaries would
normally compromise the simulation\'s validity (for example atomic clusters). At JSC we
have further developed and applied this technique to study 3D phenomena in laser and
particle beam interactions with resistive, mass-limited and porous targets [5]. Exploiting this
algorithm on modern parallel computer architectures is a significant challenge in
computational science: our current electrostatic version (PEPC-E) is capable of performing
dynamic simulations with 256 million particles on 8192 cores of the new JSC BlueGene/P
system [6,7].
Some recent examples of mesh-free ion acceleration and electron transport simulation will be
presented, together with new applications in magnetic fusion [8]. Prospects for future
magnetoinductive, radiation free simulations including slowly varying electric and magnetic
fields will also be addressed.

[1] S. Pfalzner, P. Gibbon, Phys. Rev. E 57, 4698 (1998).

[2] U. Saalmann & J. M. Rost, Phys. Rev. Lett. 91, 223401 (2003).

[3] A. J. Christlieb et al., IEEE Trans. Plasma Sci. 34, 149 (2006).

[4] K. Matyash, R. Schneider, R. Sydora, F. Taccogna, Contrib. Plasma Phys. 48, 116 (2008).

[5] P. Gibbon, Phys. Rev. E 72, 026411 (2005); P. Gibbon et al., Phys. Plasmas 11, 4032 (2004); A. P. L. Robinson, P. Gibbon, Phys. Rev. E 74, 015401 (2007); P. Gibbon, O. Rosmej, Plasma Phys. Contr. Fus. 49, 1873 (2007).

[6] R. Speck, P. Gibbon, M. Hoffmann, Efficiency and scalability of the parallel Barnes-Hut code PEPC, Proc. ParCo\'09.

[7] A public version of PEPC is available from

[8] B. Berberich, D. Reiter, P. Gibbon, Proc. DPG Spring Meeting (March, 2009)