Problems In Plasma Physics Research Articles

Role of transverse magnetic field in the capacitive discharge

The influence of magnetic field on the plasma which is one of the oldest problems in plasma physics and remains of great interest in plasma fusion studies, recently has been an important problem in many plasma discharge used in processing semiconductor materials, because the application of a magnetic field results in enhancement of some desirable features of specific plasma sources. In this paper, the transverse magnetic field effects on the radio frequency capacitive discharge of low and intermediate gas pressure (1.33 Pa∼40.00 Pa) are reviewed to clarify the role of the magnetic field in the capacitive discharge. Lots of physical phenomena induced by transverse magnetic field, such as power dissipation mode transition, low energy electron heating/cooling, axial variation of electron density and temperature and E × B drift are presented and analyzed. This article is expected to provide qualitative insight to understand the role of magnetic field in the capacitive discharges.

A Particle-in-cell Method with Adaptive Phase-space Remapping for Kinetic Plasmas

We present a new accurate and efficient particle-in-cell (PIC) method for computing the dynamics of one-dimensional kinetic plasmas. The method overcomes the numerical noise inherent in particle-based methods by periodically remapping the distribution function on a hierarchy of locally refined grids in phase space. Remapping on phase-space grids also provides an opportunity to integrate a collisional model and an associated grid-based solver. The positivity of the distribution function is enforced by redistributing excess phase-space density in a local neighborhood. We demonstrate the method on a number of standard plasma physics problems. It is shown that remapping significantly reduces the numerical noise and results in a more consistent second-order method than the standard PIC method. An error analysis is presented which is based on prior results of Cottet and Raviart's work [SIAM J. Numer. Anal., 21 (1984), pp. 52–76].

A Hamiltonian approach for a plasma physics problem

A Hamiltonian approach is applied to a plasma physics problem. A conservative oscillator admits a Hamiltonian invariant, which can be used to determine the approximate solution. The solution procedure is of deceptive simplicity and the insightful solutions obtained are of high accuracy.

Mode-impedance technique for modeling of electromagnetic wave propagation in plasmas

The impedance technique, also known as a particular case of the invariant embedding approach, is generalized for modeling electromagnetic wave propagation in anisotropic and gyrotropic media with spatial dispersion such as hot magnetized plasmas. That provides a new way for analytical and numerical studies of ‘full-wave’ problems in plasma physics that require exact solutions of Maxwell equations. Several examples of such a treatment are considered to demonstrate the flexibility and computational robustness of the proposed technique.

Integral and Lagrangian simulations of particle and radiation transport in plasma

Accurate integral and Lagrangian models of transport in plasmas, in which the models reflect the actual physical behaviour as closely as possible, are presented. These methods are applied to the behaviour of particles and photons in plasmas. First, to show how these types of models arise in a wide range of plasma physics applications, an application to radiation transport in a lighting discharge is given. The radiation transport is solved self-consistently with a model of the discharge to provide what are believed to be very accurate 1D simulations of fluorescent lamps. To extend these integral methods to higher dimensions is computationally very costly. The wide utility of ‘treecodes’ in solving massive integral problems in plasma physics is discussed, and illustrated in modelling vortex formation in a Penning trap, where a remarkably detailed simulation of vortex formation in the trap is obtained. Extension of treecode methods to other integral problems such as radiation transport is under consideration.

A numerical method for solving the Vlasov–Poisson equation based on the conservative IDO scheme

We have applied the conservative form of the Interpolated Differential Operator (IDO-CF) scheme in order to solve the Vlasov–Poisson equation, which is one of the multi-moment schemes. Through numerical tests of the nonlinear Landau damping and two-stream instability, we compared the present scheme with other schemes such as the Spline and CIP ones. We mainly investigated the conservation property of the L1-norm, energy, entropy and phase space area for each scheme, and demonstrated that the IDO-CF scheme is capable of performing stable long time scale simulation while maintaining high accuracy. The scheme is based on an Eulerian approach, and it can thus be directly used for Fokker–Planck, high dimensional Vlasov–Poisson and also guiding-center drift simulations, aiming at particular problems of plasma physics. The benchmark tests for such simulations have shown that the IDO-CF scheme is superior in keeping the conservation properties without causing serious phase error.

Computational Plasmadynamics applied to parametric studies

A Three-Dimensional Finite Volume Arbitrary Lagrangian-Eulerian simulation code was developed to study different plasma physics problems in 3D+t. The code is based on a complex multi-component species program with transport and radiation terms written and applied to plasma and fusion physics problems. The integration domain is represented with a structured irregular mesh, with fixed connectivity made of hexahedral cells. Coordinates and velocities are assigned to cell vertices. After each calculation cycle, mesh vertices are moved arbitrary over the fluid. The adaptive method consists of shifting mesh vertices over the fluid in order to keep a reasonable mesh structure and increase the spatial resolution where the physical solution demands. The code was a valuable tool for parametric study of different physical problems, mainly optimization of Plasma Focus Machine, detonation and propagation of thermonuclear reactions, and Kelvin-Helmholtz instabilities in the boundary layer of the terrestrial magnetopause.

Nonlinear theoretical tools for fusion-related microturbulence: Historical evolution, and recent applications to stochastic magnetic fields, zonal-flow dynamics, and intermittency

Fusion physics poses an extremely challenging, practically complex problem that does not yield readily to simple paradigms. Nevertheless, various of the theoretical tools and conceptual advances emphasized at the KaufmanFest 2007 have motivated and/or found application to the development of fusion-related plasma turbulence theory. A brief historical commentary is given on some aspects of that specialty, with emphasis on the role (and limitations) of Hamiltonian/symplectic approaches, variational methods, oscillation-center theory, and nonlinear dynamics. It is shown how to extract a renormalized ponderomotive force from the statistical equations of plasma turbulence, and the possibility of a renormalized K–χ theorem is discussed. An unusual application of quasilinear theory to the problem of plasma equilibria in the presence of stochastic magnetic fields is described. The modern problem of zonal-flow dynamics illustrates a confluence of several techniques, including (i) the application of nonlinear-dynamics methods, especially center-manifold theory, to the problem of the transition to plasma turbulence in the face of self-generated zonal flows; and (ii) the use of Hamiltonian formalism to determine the appropriate (Casimir) invariant to be used in a novel wave-kinetic analysis of systems of interacting zonal flows and drift waves. Recent progress in the theory of intermittent chaotic statistics and the generation of coherent structures from turbulence is mentioned, and an appeal is made for some new tools to cope with these interesting and difficult problems in nonlinear plasma physics. Finally, the important influence of the intellectually stimulating research environment fostered by Prof. Allan Kaufman on the author's thinking and teaching methodology is described.

A route to explosive large-scale magnetic reconnection in a super-ion-scale current sheet

Abstract. How to trigger magnetic reconnection is one of the most interesting and important problems in space plasma physics. Recently, electron temperature anisotropy (αeo=Te⊥/Te||) at the center of a current sheet and non-local effect of the lower-hybrid drift instability (LHDI) that develops at the current sheet edges have attracted attention in this context. In addition to these effects, here we also study the effects of ion temperature anisotropy (αio=Ti⊥/Ti||). Electron anisotropy effects are known to be helpless in a current sheet whose thickness is of ion-scale. In this range of current sheet thickness, the LHDI effects are shown to weaken substantially with a small increase in thickness and the obtained saturation level is too low for a large-scale reconnection to be achieved. Then we investigate whether introduction of electron and ion temperature anisotropies in the initial stage would couple with the LHDI effects to revive quick triggering of large-scale reconnection in a super-ion-scale current sheet. The results are as follows. (1) The initial electron temperature anisotropy is consumed very quickly when a number of minuscule magnetic islands (each lateral length is 1.5~3 times the ion inertial length) form. These minuscule islands do not coalesce into a large-scale island to enable large-scale reconnection. (2) The subsequent LHDI effects disturb the current sheet filled with the small islands. This makes the triggering time scale to be accelerated substantially but does not enhance the saturation level of reconnected flux. (3) When the ion temperature anisotropy is added, it survives through the small island formation stage and makes even quicker triggering to happen when the LHDI effects set-in. Furthermore the saturation level is seen to be elevated by a factor of ~2 and large-scale reconnection is achieved only in this case. Comparison with two-dimensional simulations that exclude the LHDI effects confirms that the saturation level enhancement is due to the ion anisotropy effects, while the LHDI effects shorten the overall time scale significantly. The results imply that the ion temperature anisotropy is one of the key properties that enable large-scale magnetic reconnection to develop in a super-ion-scale current sheet.

A THREE-DIMENSIONAL TIME DOMAIN ELECTROMAGNETIC PARTICLE-IN-CELL CODE ON UNSTRUCTURED GRIDS

AbstractAccurate charged particle beam simulations are desired for modelling plasma physics problems or for designing microwave/accelarator technology devices. In complicated geometries, it might be preferable to use unstructured grids, for example, to be able to select between several issues in the design of high-power microwave devices. In this framework, we have proposed a numerical method for solving the three-dimensional time-dependent Vlasov—Maxwell equations on unstructured grids, based on a continuous Galerkin approximation. In this paper, we present numerical results obtained on characteristic three-dimensional applications: an open electromagnetic problem without any particle coupling and a microwave device example.

A Three-Dimensional Time Domain Electromagnetic Particle-In-Cell Codeon Unstructured Grids

Accurate charged particle beam simulations are desired for modelling plasma physics problems or for designing microwave/accelarator technology devices. In complicated geometries, it might be preferable to use unstructured grids, for example, to be able to select between several issues in the design of high-power microwave devices. In this framework, we have proposed a numerical method for solving the three-dimensional time-dependent Vlasov—Maxwell equations on unstructured grids, based on a continuous Galerkin approximation. In this paper, we present numerical results obtained on characteristic three-dimensional applications: an open electromagnetic problem without any particle coupling and a microwave device example.

Deterministic and Stochastic Methods for Nonlinear Landau-Fokker-Planck Kinetic Equations with Applications to Plasma Physics

A short review of deterministic and stochastic methods for nonlinear, spatially uniform Landau-Fokker-Planck equations is given in the Introduction. Then we describe in more detail completely conservative difference schemes (obtained by the authors) for the Landau-Fokker-Planck equations and various applications of these schemes to problems of plasma physics. We also present some asymptotic solutions and compare them with numerical results. A new Direct Simulation Monte Carlo (DSMC) method is also presented and tested by comparison with numerical results based on completely conservative schemes.

Problems of bound states in plasmas—physical and chemical picture revisited

We discuss several problems of plasma physics which were in the center of interest of the Rostock group and the research activities of Gerd Ropke who was appointed a docent in 1977 by Rostock University. In particular we will consider the problem of bound states and several approaches to treat bound states in dense systems.

Modeling of Plasma Probe Interactions With a PIC Code Using an Unstructured Mesh

A new Spacecraft Plasma Interaction Software has been developed in the frame of the Spacecraft Plasma Interaction Network (SPINE). This software is designed to simulate the kinetic processes of ions and electrons, taking into account their space charge and their interaction with spacecraft surfaces. It is freely available worldwide in open source. While the development and the qualification of the software functionalities were under the responsibility of a consortium led by ONERA under contract with the European Space Agency, the test and validation of the applicability of the code for solving problems in plasma physics remained under SPINE responsibility. The validation program includes step-by-step applications of the software to sheath modeling in simple geometry, artificial plasma injection, and spacecraft charging. We report here on the progress along this program, including Langmuir probe tests with spherical and cylindrical geometry and comparison with other numerical methods.

Regularized solution of the solar Bremsstrahlung inverse problem: model dependence and implementation issues

We address an important inverse problem in solar plasma physics by means of an ‘ad hoc’ implementation of the Tikhonov regularization method. Our approach is validated in the case of different modifications of the mathematical model of the problem based on physical motivations, and for data sets obtained with synthetic experiments. Finally, an application to a real observation recorded by the NASA mission ‘Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI)’ is considered.

The Conjugate Variable Method in Hamilton-Lie Perturbation Theory - Applications to Plasma Physics -

The conjugate variable method, an essential ingredient in the path-integral formalism of classical statistical dynamics, is used to apply the Hamilton-Lie perturbation theory to a system of ordinary differential equations that does not have the Hamiltonian dynamic structure. The method endows the system with this structure by doubling the unknown variables; hence, the canonical Hamilton-Lie perturbation theory becomes applicable to the system. The method is applied to two classical problems of plasma physics to demonstrate its effectiveness and study its properties: a non-linear oscillator that can explode and the guiding center motion of a charged particle in a magnetic field.

Reconnection onset in the magnetotail: Particle simulations with open boundary conditions

The mechanism of the onset of magnetic reconnection in collisionless plasmas in the tails of planetary magnetospheres and similar processes in the solar corona is one of the most fundamental and yet not fully solved problems of space plasma physics. Modeling the onset with particle codes requires either extremely large simulation boxes or open boundary conditions. In this Letter we report on simulations of reconnection in the magnetotail that incorporate open boundaries. In a simulation setup with the initial geometry similar to that of the GEM Reconnection Challenge bursts of spontaneous reconnection are detected in outflow regions that mimic magnetotails. They strongly resemble the ion tearing instability predicted by Schindler [1974] as a mechanism of magnetospheric substorms. Quenching the onset by replacing open boundary conditions for particles with their reintroduction reveals the key role of passing particles in the tearing destabilization.

A global model of cometary tail disconnection events triggered by solar wind magnetic variations

Presented in this paper are the results of a time‐dependent, fully three‐dimensional self‐consistent ideal magneto‐hydrodynamics (MHD) model of disconnection events (DEs) in the cometary plasma tail. Understanding the interaction of cometary plasma with the solar wind is a very important problem in space plasma physics. This study focuses on the detailed MHD processes which occur during DEs based on typical comets with ideal solar wind conditions, as well as different experiences of DEs triggered by different forms of heliospheric current sheet (HCS). The crossing process against a typical HCS, which is interpreted as various tangential discontinuities (TDs), is simulated. Tail rays and/or disconnected tails are formed in such simulations. With our line‐of‐sight integration results, we conclude that observers from different directions relative to the IMF plane will see two different types of DE image series. The magnetic reconnection that occurs in our results confirms previous publications from different models. With additional cases, our study also provides the limitation for such DEs to be triggered: the angle of magnetic field rotation across the TD should be within 90° to 270°. The effects of various intervals of multiple HCS crossings are explored to show that a 2‐h minimum interval is needed for consecutive multiple HCS to trigger a DE. In addition, such DEs caused by multiple HCS crossings have more tail rays and appear closer to observations than those resulted by single HCS crossings. In addition to presenting the first global DE time evolution with a well‐resolved contact‐surface, our results are compared morphologically with observational images. Quasi‐quantitative agreement with observational measurements is found by investigating the recession speed during the DE. Moreover, the importance of having a solar wind condition being able to trigger a frontside magnetic reconnection is found critical for such DEs to originate. The importance of a well‐resolved contact surface to this problem is discussed regarding to the mass loading effect. On the basis of our deductions and simulations, an empirical equation and data table to estimate the minimum upwind boundary distance is derived with respect to the shock distance, which is sensitive to the cometary production rate.

Relativistic dynamical bistability and adiabatic excitation of strong plasma waves

Adiabatic evolution of the nonlinear resonantly driven dynamical system generic to a variety of plasma physics problems, including generation of large-amplitude plasma waves in a plasma beat-wave accelerator, is studied. The properties of the resonant Hamiltonian and the dynamics of its phase space for adiabatically varying parameters are considered. It is shown that the system can exhibit bistability and the Hamiltonian of a bistable system always follows the same trajectory for the adiabatically varying driver regardless of whether the system is excited or left quiescent. Descriptions of the bistability, autoresonance, and their possible combination based on the properties of the resonant Hamiltonian are given.

Magnetically dominated jets inside collapsing stars as a model for gamma-ray bursts and supernova explosions

It has been suggested that magnetic fields play a dynamically important role in core-collapse explosions of massive stars. In particular, they may be important in the collapsar scenario for gamma-ray bursts (GRB), where the central engine is a hyperaccreting black hole or a millisecond magnetar. The present paper is focused on the magnetar scenario, with a specific emphasis on the interaction of the magnetar magnetosphere with the infalling stellar envelope. First, the “pulsar-in-a-cavity” problem is introduced as a paradigm for a magnetar inside a collapsing star. The basic setup of this fundamental plasma-physics problem is described, outlining its main features, and simple estimates are derived for the evolution of the magnetic field. In the context of a collapsing star, it is proposed that, at first, the ram pressure of the infalling plasma acts to confine the magnetosphere, enabling a gradual buildup of the magnetic pressure. At some point, the growing magnetic pressure overtakes the (decreasing) ram pressure of the gas, resulting in a magnetically driven explosion. The explosion should be highly anisotropic, as the hoop stress of the toroidal field, confined by the surrounding stellar matter, collimates the magnetically dominated outflow into two beamed magnetic-tower jets. This creates a clean narrow channel for the escape of energy from the central engine through the star, as required for GRBs. In addition, the delayed onset of the collimated-explosion phase can explain the production of large quantities of nickel-56, as suggested by the GRB-supernova connection. Finally, the prospects for numerical simulations of this scenario are discussed.