Seminar

Synopsis:

Synopsis:

This work develops the geometric theory of charge conservation in particle-in-cell (PIC) plasma simulations. We define a new class of Hamiltonian algorithms---gauge-compatible splitting methods---that exactly preserve a Hamiltonian system's momentum map---even after time-discretization. We apply this general technique to design a novel, explicit, structure-preserving PIC splitting method, whose momentum map yields an exact local charge conservation law. We further study the preservation of Poincaré symmetry as a gauge symmetry of discrete dynamical fields, with an eye toward constructing plasma simulations that exactly conserve all ten relativistic energy-momenta.

Synopsis:

The particle-in-cell (PIC) method has been widely used for half a century in the simulation of kinetic plasmas. The last decade has seen two new versions of the method that move toward overcoming long-standing challenges. First, the fully implicit, energy-conserving PIC scheme mitigates the so-called finite grid instability, allowing larger time-steps and, in many cases, coarser spatial resolution while retaining stability. Second, a sparse grid version of PIC was recently introduced that shows the potential to mitigate the curse of dimensionality, thereby dramatically reducing the number of simulated particles needed to achieve satisfactory statistical resolution. In this talk, we present a scheme that marries these two advances. We prove that the energy- and charge-conservation properties of implicit PIC can be carried over to sparse grids. Key here is the appropriate definition of the electrostatic potential. In so doing, we also generalize previous conservation results for implicit PIC to more general classes of field solvers and discuss potential applications of this generalization.  Theoretical results are confirmed via numerical examples using a 2D electrostatic PIC code.

 

This is joint work with Guangye Chen (LANL).

 

*Work performed under the auspices of the U.S. Department of Energy by LLNL and LANL under contracts DE-AC52-07NA27344 and DE-AC52-06NA25396 and supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration.

Synopsis:

Synopsis:

Laser fusion is intended to initiate the nuclear fusion reactions through compressing the thermonuclear target by powerful laser beams. These beams propagate through the surrounding plasma resulting in strongly nonlinear interactions. Perhaps the most important among these interactions is the stimulated Brillouin scattering (SBS) which couples the laser beam to the plasma density fluctuations and results in the numerous catastrophic collapse events during the laser beam propagation. The strong turbulence dominated by such nearly singular collapse event is considered. To suppress the number of such collapses, the expensive optical beams smoothing is used in the experimental laser fusion facilities which randomizes the phases of the laser beams. A statistical theory of SBS of such randomized laser beam propagation is developed. A collective regime of BSBS is found which has a much larger threshold than the classical threshold of a coherent beam in long-scale-length laser fusion plasma. The instability threshold is inside the typical parameter region of National Ignition Facility.