Takayuki Umeda

A new charge conservation method in electromagnetic particle-in-cell simulations

Abstract We developed a fast algorithm for solving the current density satisfying the continuity equation of charge in electromagnetic particle-in-cell (PIC) simulations. In PIC simulations of the charge conservation, a particle trajectory over one time step is conventionally assumed to be a straight line. In the present new scheme we assume that a particle trajectory is a zigzag line. Compared with the Villasenor–Buneman method and Esirkepovs method, the present scheme has an advantage in computation speed without any substantial distortion of physics.

An improved masking method for absorbing boundaries in electromagnetic particle simulations

We have developed a new scheme to mask electromagnetic fields for absorbing boundaries used in electromagnetic particle codes. The conventional masking method can suppress reflection of various plasma waves by assigning large damping regions for absorbing boundaries. It requires substantial computer memory and processing time. We introduce two new parameters to control absorption of outgoing electromagnetic waves. The first parameter is a damping parameter to change the effective length of damping regions. The second parameter is a retarding parameter to change phase velocities of electromagnetic waves in the damping regions. As a new masking method, we apply both damping and retarding factors. We also found that the best absorption of outgoing waves is realized with a combination of a smaller damping factor and a larger retarding factor. The new method allows us to reduce the size of damping regions substantially.

A conservative and non-oscillatory scheme for Vlasov code simulations

A new numerical positive interpolation technique for conservation laws and its application to Vlasov code simulations are presented. In recent Vlasov simulation codes, the Vlasov equation is solved based on the numerical interpolation method because of its simplicity of algorithm and its ease of programming. However, a large number of grid points are needed in both configuration and velocity spaces to suppress numerical diffusion. In this paper we propose a new high-order interpolation scheme for Vlasov simulations. The current scheme is non-oscillatory and conservative and is well-designed for Vlasov simulations. This is compared with the latest interpolation schemes by performing one-dimensional electrostatic Vlasov simulations.

Harmonic Langmuir waves. I. Nonlinear dispersion relation

Generation of electrostatic multiple harmonic Langmuir modes during beam–plasma interaction process has been observed in laboratory and spaceborne active experiments, as well as in computer simulation experiments. Despite earlier efforts, such a phenomenon has not been completely characterized both theoretically and in terms of numerical simulations. This paper is a first in a series of three papers in which analytic expressions for harmonic Langmuir mode dispersion relations are derived and compared against the numerical simulation result.

ELECTRON ACCELERATION AT A LOW MACH NUMBER PERPENDICULAR COLLISIONLESS SHOCK

A full particle simulation study is carried out on the electron acceleration at a collisionless, relatively low Alfven Mach number (MA = 5), perpendicular shock. Recent self-consistent hybrid shock simulations have demonstrated that the shock front of perpendicular shocks has a dynamic rippled character along the shock surface of low Mach number perpendicular shocks. In this paper, the effect of the rippling of perpendicular shocks on the electron acceleration is examined by means of large-scale (ion-scale) two-dimensional full particle simulations. It has been shown that a large-amplitude electric field is excited at the shock front in association with the ion-scale rippling, and that reflected ions are accelerated upstream at a localized region where the shock-normal electric field of the rippled structure is polarized upstream. The current-driven instability caused by the highly accelerated reflected ions has a high growth rate of up to large-amplitude electrostatic waves. Energetic electrons are then generated by the large-amplitude electrostatic waves via electron surfing acceleration at the leading edge of the shock-transition region. The present result suggests that the electron surfing acceleration is also a common feature at low Mach number perpendicular collisionless shocks.

Full electromagnetic Vlasov code simulation of the Kelvin-Helmholtz instability

Recent advancement in numerical techniques for Vlasov simulations and their application to cross-scale coupling in the plasma universe are discussed. Magnetohydrodynamic (MHD) simulations are now widely used for numerical modeling of global and macroscopic phenomena. In the framework of the MHD approximation, however, diffusion coefficients such as resistivity and adiabatic index are given from empirical models. Thus there are recent attempts to understand first-principle kinetic processes in macroscopic phenomena, such as magnetic reconnection and the Kelvin–Helmholtz (KH) instability via full kinetic particle-in-cell and Vlasov codes. In the present study, a benchmark test for a new four-dimensional full electromagnetic Vlasov code is performed. First, the computational speed of the Vlasov code is measured and a linear performance scaling is obtained on a massively parallel supercomputer with more than 12 000 cores. Second, a first-principle Vlasov simulation of the KH instability is performed in order ...

Relativistic electron shock drift acceleration in low mach number galaxy cluster shocks

An extreme case of electron shock drift acceleration (SDA) in low Mach number collisionless shocks is investigated as a plausible mechanism for the initial acceleration of relativistic electrons in large-scale shocks in galaxy clusters, where the upstream plasma temperature is of the order of 10 keV and the degree of magnetization is not too small. One-dimensional electromagnetic full particle simulations reveal that, even when a shock is rather moderate, a part of the thermal incoming electrons are accelerated and reflected through relativistic SDA and form a local non-thermal population just upstream of the shock. The accelerated electrons can self-generate local coherent waves and further be back-scattered toward the shock by those waves. This may be a scenario for the first stage of the electron shock acceleration occurring at the large-scale shocks in galaxy clusters, such as CIZA J2242.8+5301, which have well-defined radio relics.

Harmonic Langmuir waves. II. Turbulence spectrum

The Langmuir wave turbulence generated by a beam–plasma interaction has been studied since the early days of plasma physics research. In particular, mechanisms which lead to the quasi-power-law spectrum for Langmuir waves have been investigated, since such a spectrum defines the turbulence characteristics. Meanwhile, the generation of harmonic Langmuir modes during the beam–plasma interaction has been known for quite some time, and yet has not been satisfactorily accounted for thus far. In paper I of this series, nonlinear dispersion relations for these harmonics have been derived. In this paper (paper II), generalized weak turbulence theory which includes multiharmonic Langmuir modes is formulated and the self-consistent particle and wave kinetic equations are solved. The result shows that harmonic Langmuir mode spectra can indeed exhibit a quasi-power-law feature, implying multiscale structure in both frequency and wave number space spanning several orders of magnitude.

Particle simulation of plasma response to an applied electric field parallel to magnetic field lines

[1] We study response of thermal plasmas to an induction electric field via one-dimensional particle simulations. The induction electric field is assumed to be uniform in space and constant in time. Because of acceleration of electrons and ions in the opposite directions, there arise counter streaming electrons and ions that cause the Buneman instability. Depending on the ratio of the ion temperature T i to the electron temperature T e , responses to the electric field are different. For a case with hot ions (T i >> T e ) the Buneman instability leads to formation of large isolated electrostatic potentials which trap some electrons to move with ions. For a case with colder ions (T i « T e ) the Buneman instability is taken over by excitation of ion acoustic waves, which diffuse the low-energy part of the accelerated electrons to stabilize the instability. However, a substantial part of the electrons are grouped together at the high-energy part, forming a distinct bump in the electron distribution. In the present simulations we have found that the induction electric field can form an electron beam along the magnetic field line. Since the electron beam leaves the region of the induction electric field and moves into an unperturbed plasma, the accelerated electrons can cause a bump-on-tail instability. This can lead to formation of electrostatic solitary waves as frequently observed by the GEOTAIL spacecraft in the plasma sheet boundary layer (PSBL). The persistent observation of the electrostatic solitary waves indicates their association with the induction electric field that results from meandering motion of the current sheet in the magnetotail.

Comparison of numerical interpolation schemes for one-dimensional electrostatic Vlasov code

We discuss numerical interpolation schemes used in Vlasov codes. An improved conservative semi-Lasrangian scheme is compared with the latest non-conservative and conservative schemes for a long run-time nonlinear problem of the beam-plasma interaction with respect to the mass and energy conservation.