13 research outputs found
A dynamical adaptive tensor method for the Vlasov-Poisson system
A numerical method is proposed to solve the full-Eulerian time-dependent
Vlasov-Poisson system in high dimension. The algorithm relies on the
construction of a tensor decomposition of the solution whose rank is adapted at
each time step. This decomposition is obtained through the use of an efficient
modified Progressive Generalized Decomposition (PGD) method, whose convergence
is proved. We suggest in addition a symplectic time-discretization splitting
scheme that preserves the Hamiltonian properties of the system. This scheme is
naturally obtained by considering the tensor structure of the approximation.
The efficiency of our approach is illustrated through time-dependent 2D-2D
numerical examples
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
Electron dynamics in planar radio frequency magnetron plasmas: II. Heating and energization mechanisms studied via a 2d3v particle-in-cell/Monte Carlo code
The present work investigates electron transport and heating mechanisms using
an (r, z) particle-in-cell (PIC) simulation of a typical rf-driven axisymmetric
magnetron discharge with a conducting target. It is shown that for the
considered magnetic field topology the electron current flows through different
channels in the (r, z) plane: a ``transverse'' one, which involves current flow
through the electrons' magnetic confinement region (EMCR) above the racetrack,
and two ''longitudinal'' ones. Electrons gain energy from the electric field
along these channels following various mechanisms, which are rather distinct
from those sustaining dc-powered magnetrons. The longitudinal power absorption
involves mirror-effect heating (MEH), nonlinear electron resonance heating
(NERH), magnetized bounce heating (MBH), and the heating by the ambipolar field
at the sheath-presheath interface. The MEH and MBH represent two new mechanisms
missing from the previous literature. The MEH is caused by a reversed electric
field needed to overcome the mirror force generated in a nonuniform magnetic
field to ensure sufficient flux of electrons to the powered electrode, and the
MBH is related to a possibility for an electron to undergo multiple reflections
from the expanding sheath in the longitudinal channels connected by the
arc-like magnetic field. The electron heating in the transverse channel is
caused mostly by the essentially collisionless Hall heating in the EMCR above
the racetrack, generating a strong ExB azimuthal drift velocity. The latter
mechanism results in an efficient electron energization, i.e., energy transfer
from the electric field to electrons in the inelastic range. Since the main
electron population energized by this mechanism remains confined within the
discharge for a long time, its contribution to the ionization processes is
dominant
A methodology for the rigorous verification of Particle-in-Cell simulations
A methodology to perform a rigorous verification of Particle-in-Cell (PIC) simulations is presented, both for assessing the correct implementation of the model equations (code verification), and evaluating the numerical uncertainty affecting the simulation results (solution verification). The proposed code verification methodology is a generalization of the procedure developed for plasma simulation codes based on finite difference schemes that was described by Riva et al. [Phys. Plasmas 21, 062301 (2014)] and consists of an order-of-accuracy test using the method of manufactured solutions. The generalization of the methodology for PIC codes consists of accounting for numerical schemes intrinsically affected by statistical noise and providing a suitable measure of the distance between continuous, analytical distribution functions and finite samples of computational particles. The solution verification consists of quantifying both the statistical and discretization uncertainties. The statistical uncertainty is estimated by repeating the simulation with different pseudorandom number generator seeds. For the discretization uncertainty, the Richardson extrapolation is used to provide an approximation of the analytical solution and the grid convergence index is used as an estimate of the relative discretization uncertainty. The code verification methodology is successfully applied to a PIC code that numerically solves the one-dimensional, electrostatic, collisionless Vlasov-Poisson system. The solution verification methodology is applied to quantify the numerical uncertainty affecting the two-stream instability growth rate, which is numerically evaluated thanks to a PIC simulation