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Register a new userVolume-preserving particle integrator based on exact flow of velocity for nonrelativistic particle-in-cell simulations
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We construct a particle integrator for nonrelativistic particles by means of the splitting method based on the exact flow of the equation of motion of particles in the presence of constant electric and magnetic field. This integrator is volume-preserving similar to the standard Boris integrator and is suitable for long-term integrations in particle-in-cell simulations. Numerical tests reveal that it is significantly more accurate than previous volume-preserving integrators with second-order accuracy. For example, in the $E times B$ drift test, this integrator is more accurate than the Boris integrator and the integrator based on the exact solution of gyro motion by three and two orders of magnitude, respectively. In addition, we derive approximate integrators that incur low computational cost and high-precision integrators displaying fourth- to tenth-order accuracy with the aid of the composition method. These integrators are also volume-preserving. It is also demonstrated that the Boris integrator is equivalent to the simplest case of the approximate integrators derived in this study.
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The paper provides a tutorial to the conceptual layout of a self-consistently coupled Particle-In-Cell/Test-Particle model for the kinetic simulation of sputtering transport in capacitively coupled plasmas at low gas pressures. It explains when a kinetic approach is actually needed and which numerical concepts allow for the inherent nonequilibrium behavior of the charged and neutral particles. At the example of a generic sputtering discharge both the fundamentals of the applied Monte Carlo methods as well as the conceptual details in the context of the sputtering scenario are elaborated on. Finally, two in the context of sputtering transport simulations often exploited assumptions, namely on the energy distribution of impinging ions as well as on the test particle approach, are validated for the proposed example discharge.
In recent years, several gauge-symmetric particle-in-cell (PIC) methods have been developed whose simulations of particles and electromagnetic fields exactly conserve charge. While it is rightly observed that these methods gauge symmetry gives rise to their charge conservation, this causal relationship has generally been asserted via ad hoc derivations of the associated conservation laws. In this work, we develop a comprehensive theoretical grounding for charge conservation in gauge-symmetric Lagrangian and Hamiltonian PIC algorithms. For Lagrangian variational PIC methods, we apply Noethers second theorem to demonstrate that gauge symmetry gives rise to a local charge conservation law as an off-shell identity. For Hamiltonian splitting methods, we show that the momentum map establishes their charge conservation laws. We define a new class of algorithms -- gauge-compatible splitting methods -- that exactly preserve the momentum map associated with a Hamiltonian systems gauge symmetry -- even after time discretization. This class of algorithms affords splitting schemes a decided advantage over alternative Hamiltonian integrators. We apply this general technique to design a novel, explicit, symplectic, gauge-compatible splitting PIC method, whose momentum map yields an exact local charge conservation law. Our study clarifies the appropriate initial conditions for such schemes and examines their symplectic reduction.
We design and develop a new Particle-in-Cell (PIC) method for plasma simulations using Deep-Learning (DL) to calculate the electric field from the electron phase space. We train a Multilayer Perceptron (MLP) and a Convolutional Neural Network (CNN) to solve the two-stream instability test. We verify that the DL-based MLP PIC method produces the correct results using the two-stream instability: the DL-based PIC provides the expected growth rate of the two-stream instability. The DL-based PIC does not conserve the total energy and momentum. However, the DL-based PIC method is stable against the cold-beam instability, affecting traditional PIC methods. This work shows that integrating DL technologies into traditional computational methods is a viable approach for developing next-generation PIC algorithms.
This paper discusses temporally continuous and discrete forms of the speed-limited particle-in-cell (SLPIC) method first treated by Werner et al. [Phys. Plasmas 25, 123512 (2018)]. The dispersion relation for a 1D1V electrostatic plasma whose fast particles are speed-limited is derived and analyzed. By examining the normal modes of this dispersion relation, we show that the imposed speed-limiting substantially reduces the frequency of fast electron plasma oscillations while preserving the correct physics of lower-frequency plasma dynamics (e.g. ion acoustic wave dispersion and damping). We then demonstrate how the timestep constraints of conventional electrostatic particle-in-cell methods are relaxed by the speed-limiting approach, thus enabling larger timesteps and faster simulations. These results indicate that the SLPIC method is a fast, accurate, and powerful technique for modeling plasmas wherein electron kinetic behavior is nontrivial (such that a fluid/Boltzmann representation for electrons is inadequate) but evolution is on ion timescales.
Upon inclusion of collisions, the speed-limited particle-in-cell (SLPIC) simulation method successfully computed the Paschen curve for argon. The simulations modelled an electron cascade across an argon-filled capacitor, including electron-neutral ionization, electron-neutral elastic collisions, electron-neutral excitation, and ion-induced secondary-electron emission. In electrical breakdown, the timescale difference between ion and electron motion makes traditional particle-in-cell (PIC) methods computationally slow. To decrease this timescale difference and speed up computation, we used SLPIC, a time-domain algorithm that limits the speed of the fastest electrons in the simulation. The SLPIC algorithm facilitates a straightforward, fully-kinetic treatment of dynamics, secondary emission, and collisions. SLPIC was as accurate as PIC, but ran up to 200 times faster. SLPIC accurately computed the Paschen curve for argon over three orders of magnitude in pressure.
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