515 research outputs found
A particle method for the homogeneous Landau equation
We propose a novel deterministic particle method to numerically approximate
the Landau equation for plasmas. Based on a new variational formulation in
terms of gradient flows of the Landau equation, we regularize the collision
operator to make sense of the particle solutions. These particle solutions
solve a large coupled ODE system that retains all the important properties of
the Landau operator, namely the conservation of mass, momentum and energy, and
the decay of entropy. We illustrate our new method by showing its performance
in several test cases including the physically relevant case of the Coulomb
interaction. The comparison to the exact solution and the spectral method is
strikingly good maintaining 2nd order accuracy. Moreover, an efficient
implementation of the method via the treecode is explored. This gives a proof
of concept for the practical use of our method when coupled with the classical
PIC method for the Vlasov equation.Comment: 27 pages, 14 figures, debloated some figures, improved explanations
in sections 2, 3, and
On the relativistic large-angle electron collision operator for runaway avalanches in plasmas
Large-angle Coulomb collisions lead to an avalanching generation of runaway
electrons in a plasma. We present the first fully conservative large-angle
collision operator, derived from the relativistic Boltzmann operator. The
relation to previous models for large-angle collisions is investigated, and
their validity assessed. We present a form of the generalized collision
operator which is suitable for implementation in a numerical kinetic-equation
solver, and demonstrate the effect on the runaway-electron growth rate. Finally
we consider the reverse avalanche effect, where runaways are slowed down by
large-angle collisions, and show that the choice of operator is important if
the electric field is close to the avalanche threshold.Comment: 18 pages, 6 figure
- …