177 research outputs found
Limitations of stationary Vlasov-Poisson solvers in probe theory
Physical and numerical limitations of stationary Vlasov-Poisson solvers based on backward Liouville methods are investigated with five solvers that combine different meshes, numerical integrators, and electric field interpolation schemes. Since some of the limitations arise when moving from an integrable to a non-integrable configuration, an elliptical Langmuir probe immersed in a Maxwellian plasma was considered and the eccentricity (ep) of its cross-section used as integrability-breaking parameter. In the cylindrical case, ep=0, the energy and angular momentum are both conserved. The trajectories of the charged particles are regular and the boundaries that separate trapped from non-trapped particles in phase space are smooth curves. However, their computation has to be done carefully because, albeit small, the intrinsic numerical errors of some solvers break these conservation laws. It is shown that an optimum exists for the number of loops around the probe that the solvers need to classify a particle trajectory as trapped. For ep≠0, the angular momentum is not conserved and particle dynamics in phase space is a mix of regular and chaotic orbits. The distribution function is filamented and the boundaries that separate trapped from non-trapped particles in phase space have a fractal geometry. The results were used to make a list of recommendations for the practical implementation of stationary Vlasov-Poisson solvers in a wide range of physical scenarios.This work was supported by the European Union's Horizon 2020 Research and Innovation Programme under grant agreement No 828902 (E.T.PACK project). GSA work is supported by the Ministerio de Ciencia, Innovación of Spain under the Grant RYC-2014-15357. The authors thank the Reviewers for their valuable comments and suggestions about the use of energy-conserving numerical integrators
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
Accuracy of the Explicit Energy-Conserving Particle-in-Cell Method for Under-resolved Simulations of Capacitively Coupled Plasma Discharges
The traditional explicit electrostatic momentum-conserving Particle-in-cell
algorithm requires strict resolution of the electron Debye length to deliver
numerical accuracy. The explicit electrostatic energy-conserving
Particle-in-Cell algorithm alleviates this constraint with minimal modification
to the traditional algorithm, retaining its simplicity and ease of
parallelization and acceleration on modern supercomputing architectures. In
this article we apply the algorithm to model a one-dimensional radio-frequency
capacitively coupled plasma discharge relevant to industrial applications. The
energy-conserving approach closely matches the results from the
momentum-conserving algorithm and retains accuracy even for cell sizes up to 8x
the electron Debye length. For even larger cells the algorithm loses accuracy
due to poor resolution of steep gradients in the radio-frequency sheath. This
can be amended by introducing a non-uniform grid, which allows for accurate
simulations with 9.4x fewer cells than the fully resolved case, an improvement
that will be compounded in higher-dimensional simulations. We therefore
consider the explicit energy-conserving algorithm as a promising approach to
significantly reduce the computational cost of full-scale device simulations
and a pathway to delivering kinetic simulation capabilities of use to industry
Modeling of very high frequency large-electrode capacitively coupled plasmas with a fully electromagnetic particle-in-cell code
Phenomena taking place in capacitively coupled plasmas with large electrodes
and driven at very high frequencies are studied numerically utilizing a novel
energy- and charge-conserving implicit fully electromagnetic particle-in-cell /
Monte Carlo code ECCOPIC2M. The code shows a good agreement with different
cases having various collisionality and absorbed power. Although some aspects
of the underlying physics were demonstrated in the previous literature with
other models, the particle-in-cell method is advantageous for the predictive
modeling due to a complex interplay between the surface mode excitations and
the nonlocal physics of the corresponding type of plasma discharges operated at
low pressures, which is hard to reproduce in other models realistically
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