A framework for microscopic/macroscopic simulations of magnetized plasmas (with some space-physics application)

Many problems in plasma physics require the solution of the Vlasov-Maxwell (VM) or Vlasov-Boltzmann equations. These equations are extremely hard to solve numerically because of their high dimensionality, nonlinearities and the huge disparity of spatial and temporal scales that have to be bridged between microscopic and system scales. While several reduced methods have been developed in certain limits, a comprehensive approach capable of obtaining accurate solutions in all parameters regimes remains elusive. From an application standpoint, this is a longstanding challenge for space weather research, which has so far prevented the development of an operational space-weather global model that includes microscopic physics. Thus, we are currently unable to predict conditions in the near-Earth environment that can lead to spacecraft damage/failure during geomagnetic storms and substorms.

In this talk, I will present a spectral method for the VM equations based on a decomposition of the plasma phase-space density in Hermite or Legendre modes. Its most important aspect is that, with a suitable spectral basis, the low-order moments are akin to the typical moments (mass, momentum, energy) of a fluid/macroscopic description of the plasma, while the kinetic/microscopic physics can be retained by adding more moments. The method features favorable numerical properties (such as spectral convergence and exact conservation laws in the limit of finite time step) and a comparison against the Particle-In-Cell (PIC) on standard electrostatic test problems shows that it can be orders of magnitude faster/more accurate than PIC. With the 'built-in' fluid/kinetic coupling, spectral methods might offer an optimal way to perform accurate simulations of macroscopic phenomena including microscopic physics.

Since the development of the method has been partially motivated by the needs of space-weather programs at Los Alamos, I will also discuss its application to study the coupling between an electron beam and a magnetized plasma, as relevant to our current effort to use compact relativistic electron beams for active space experiments to (1) study the physics of magnetosphere-ionosphere coupling or (2) excite waves that can be exploited via wave-particle interaction to reduce hazardous high fluxes of relativistic particles in the near-Earth environment to safer levels (i.e. radiation belt remediation).