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Register a new userHow large can the electron to proton mass ratio be in Particle-In-Cell simulations of unstable systems?
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Particle-in-cell (PIC) simulations are widely used as a tool to investigate instabilities that develop between a collisionless plasma and beams of charged particles. However, even on contemporary supercomputers, it is not always possible to resolve the ion dynamics in more than one spatial dimension with such simulations. The ion mass is thus reduced below 1836 electron masses, which can affect the plasma dynamics during the initial exponential growth phase of the instability and during the subsequent nonlinear saturation. The goal of this article is to assess how far the electron to ion mass ratio can be increased, without changing qualitatively the physics. It is first demonstrated that there can be no exact similarity law, which balances a change of the mass ratio with that of another plasma parameter, leaving the physics unchanged. Restricting then the analysis to the linear phase, a criterion allowing to define a maximum ratio is explicated in terms of the hierarchy of the linear unstable modes. The criterion is applied to the case of a relativistic electron beam crossing an unmagnetized electron-ion plasma.
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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.
Results of the first validation of large guide field, $B_g / delta B_0 gg 1$, gyrokinetic simulations of magnetic reconnection at a fusion and solar corona relevant $beta_i = 0.01$ and solar wind relevant $beta_i = 1$ are presented, where $delta B_0$ is the reconnecting field. Particle-in-cell (PIC) simulations scan a wide range of guide magnetic field strength to test for convergence to the gyrokinetic limit. The gyrokinetic simulations display a high degree of morphological symmetry, to which the PIC simulations converge when $beta_i B_g / delta B_0 gtrsim 1$ and $B_g / delta B_0 gg 1$. In the regime of convergence, the reconnection rate, relative energy conversion, and overall magnitudes are found to match well between the PIC and gyrokinetic simulations, implying that gyrokinetics is capable of making accurate predictions well outside its regime of formal applicability. These results imply that in the large guide field limit many quantities resulting from the nonlinear evolution of reconnection scale linearly with the guide field.
Large-scale two-dimensional (2D) full particle-in-cell simulations are carried out for studying the relationship between the dynamics of a perpendicular shock and microinstabilities generated at the shock foot. The structure and dynamics of collisionless shocks are generally determined by Alfven Mach number and plasma beta, while microinstabilities at the shock foot are controlled by the ratio of the upstream bulk velocity to the electron thermal velocity and the ratio of the plasma-to-cyclotron frequency. With a fixed Alfven Mach number and plasma beta, the ratio of the upstream bulk velocity to the electron thermal velocity is given as a function of the ion-to-electron mass ratio. The present 2D full PIC simulations with a relatively low Alfven Mach number (M_A ~ 6) show that the modified two-stream instability is dominant with higher ion-to-electron mass ratios. It is also confirmed that waves propagating downstream are more enhanced at the shock foot near the shock ramp as the mass ratio becomes higher. The result suggests that these waves play a role in the modification of the dynamics of collisionless shocks through the interaction with shock front ripples.
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.
The propagation of intense laser pulses and the generation of high energy electrons from the underdense plasmas are investigated using two dimensional particle-in-cell simulations. When the ratio of the laser power and a critical power of relativistic self-focusing is the optimal value, it propagates stably and electrons have maximum energies.
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