26 research outputs found
Wavebreaking and Particle Trapping in Collisionless Plasmas: Final Report
The final report describing accomplishments in understanding phase-space processes involved in particle trapping and in developing advance numerical models of laser-plasma interactions
Variational Formulation of Macro-Particle Models for Electromagnetic Plasma Simulations
A variational method is used to derive a self-consistent macro-particle model
for relativistic electromagnetic kinetic plasma simulations. Extending earlier
work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp.
376-398, 2013], the discretization of the electromagnetic Low Lagrangian is
performed via a reduction of the phase-space distribution function onto a
collection of finite-sized macro-particles of arbitrary shape and
discretization of field quantities onto a spatial grid. This approach may be
used with both lab frame coordinates or moving window coordinates; the latter
can greatly improve computational efficiency for studying some types of
laser-plasma interactions. The primary advantage of the variational approach is
the preservation of Lagrangian symmetries, which in our case leads to energy
conservation and thus avoids difficulties with grid heating. Additionally, this
approach decouples particle size from grid spacing and relaxes restrictions on
particle shape, leading to low numerical noise. The variational approach also
guarantees consistent approximations in the equations of motion and is amenable
to higher order methods in both space and time. We restrict our attention to
the 1-1/2 dimensional case (one coordinate and two momenta). Simulations are
performed with the new models and demonstrate energy conservation and low
noise.Comment: IEEE Transaction on Plasma Science (TPS) Special Issue: Plenary and
Invited Papers of the Pulsed Power and Plasma Science Conference (PPPS 2013
Metriplectic Integrators for the Landau Collision Operator
We present a novel framework for addressing the nonlinear Landau collision
integral in terms of finite element and other subspace projection methods. We
employ the underlying metriplectic structure of the Landau collision integral
and, using a Galerkin discretization for the velocity space, we transform the
infinite-dimensional system into a finite-dimensional, time-continuous
metriplectic system. Temporal discretization is accomplished using the concept
of discrete gradients. The conservation of energy, momentum, and particle
densities, as well as the production of entropy is demonstrated algebraically
for the fully discrete system. Due to the generality of our approach, the
conservation properties and the monotonic behavior of entropy are guaranteed
for finite element discretizations in general, independently of the mesh
configuration.Comment: 24 pages. Comments welcom
Hamiltonian reductions of the one-dimensional Vlasov equation using phase-space moments
We consider Hamiltonian closures of the Vlasov equation using the phase-space
moments of the distribution function. We provide some conditions on the
closures imposed by the Jacobi identity. We completely solve some families of
examples. As a result, we show that imposing that the resulting reduced system
preserves the Hamiltonian character of the parent model shapes its phase space
by creating a set of Casimir invariants as a direct consequence of the Jacobi
identity