DongSheng Cai

Kinetic equilibria of plasma shear layers

The analysis of plasma beam and shear problems in magnetic fields is usually based on a hydromagnetic fluid model. In a low‐density collisionless plasma, however, the kinetic effects of the plasma, such as finite Larmor radius effects, are not yet clearly understood. In this paper, the kinetic equilibria of plasma shears in a uniform and fixed magnetic field, with full ion motion, are discussed by solving the Vlasov equation with a given electric field and drift velocity. In this model, the ion density profile through the plasma shear layer is quite different from the one predicted by a hydromagnetic model. As a result of a complicated ion gyromotion through the shear layer, single‐ and double‐humped ion density profiles are obtained. The dependence on the temperature and the strength of the shear will be discussed. The results show a significant difference between positive and negative shears.

Implementation of parallel plasma particle-in-cell codes on PC cluster

Plasma particle-in-cell (PIC) codes model the interaction of charged particles with the surrounding fields, and they have been implemented on many advanced parallel computers. Recently, many PC clusters which consist of inexpensive PCs have been developed to do parallel computing, and we also build such a PC cluster. In this paper, we present the implementation of a parallel plasma PIC code on our PC cluster using MPI, PGHPF and JavaMPI.

Formation and stability of polarization sheaths of a cross‐field beam

A layer of plasma (such as that comoving with the space shuttle) can travel across a magnetic field if it is flanked by ‘‘polarization sheaths’’ that create the E field necessary for E×B drift. Both the spontaneous evolution and the stability of these positive and negative sheaths can be studied by their analogy with the charge configuration in magnetron‐type electron devices. That is, conservation of canonical momentum results in ‘‘Brillouin flow,’’ i.e., shear flows in a pure ion sheath on one side and a pure electron sheath on the other side of the neutral plasma beam. The equilibrium parameters of this flow were obtained and the stability of the equilibria was analyzed. Both the ion and electron sheaths were found to be one‐dimensionally stable and two‐dimensionally unstable in a mode variously known as ‘‘magnetron,’’ ‘‘slipping stream,’’ or ‘‘diocotron.’’ This mode connects up with the Kelvin–Helmholtz instability in neutral matter. The analytical results were confirmed both qualitatively and quantit...

The eigenvalue problem for infinite complex symmetric tridiagonal matrices with application

Abstract We consider an infinite complex symmetric (not necessarily Hermitian) tridiagonal matrix T whose diagonal elements diverge to ∞ in modulus and whose off-diagonal elements are bounded. We regard T as a linear operator mapping a maximal domain in the Hilbert space l2 into l2. Assuming the existence of T−1 we consider the problem of approximating a given simple eigenvalue λ of T by an eigenvalue λn of Tn, and nth order principal submatrix of T. Let x = [x(1),x(2),…]T be an eigenvector corresponding to λ. Assuming xTx ≠ 0 and f n+1 x (n+1) x (n) → 0 as n → ∞, we show that there exists a sequence {λn} of Tn such that λ − λ n = f n + 1 x (n+1) [1 + o(1)] (x T x) → 0 , where fn+1 represents the (n, n + 1) element of T. Application to the following problems is included: (a) solve Jv(z) = 0 for v, given z ≠ 0, and (b) compute the eigenvalues of the Mathieu equation. Fortunately, the existence of T−1 need not be verified for these examples since we may show that T + αI with α taken appropriately has an inverse.

Particle simulation of the kinetic Kelvin–Helmholtz instability in a magnetoplasma

The kinetic Kelvin–Helmholtz instability in a collisionless magnetoplasma is simulated numerically in cases where the ion gyroradius is comparable with or larger than the spatial scale of the cross‐field shear. The approach consists of starting the simulation from a state close to equilibrium, then observing the linear growth of instabilities and their ultimate saturation. The initial quasiequilibrium state is set up by a newly developed particle loading method; the instabilities are excited by numerical noise. The simulation is performed in two dimensions, in the plane perpendicular to the magnetic field, using an electrostatic particle code. The results for the kinetic Kelvin–Helmholtz instability are similar to those predicted by a hydromagnetic model, except that they depend slightly on the sign of the shear. Other instabilities are observed also: when the ion gyroradius is small on the scale of the shear, there is an unidentified short‐wavelength instability characterized by ku2009Δx≥1, where k is the wa...

Parallel PIC code using Java on PC cluster

The Java language has emerged as a dominant language that could eventually replace C++, due to it being object-oriented, architecture neutral, multi-threaded etc. and its support for applets. But Java is believed to be too slow for scientific computing. Many high-performance PCs such as those based on the Pentium II have been introduced, and these have great potential for high-performance computing. We are currently building a dual PentiumPro PC cluster. In this report, using a test skeleton-PIC-code developed by Prof. V.K. Decyk of UCLA for benchmarking purposes, we have measured the performance of the Java language in serial and parallel on our PC cluster compared with the Fortran language which is the main language for scientific computing. In our benchmarking, we use JavaMPI as an interface to MPI for message passing between PCs through a 100Base-TX/10Base-T Ethernet switch. The benchmark results indicate that Java is a good candidate for scientific computing.

Error analysis for the computation of zeros of regular Coulomb wave function and its first derivative

In 1975 one of the coauthors, Ikebe, showed that the problem of computing the zeros of the regular Coulomb wave functions and their derivatives may be reformulated as the eigenvalue problem for infinite matrices. Approximation by truncation is justified but no error estimates are given there. The class of eigenvalue problems studied there turns out to be subsumed in a more general problem studied by Ikebe et al. in 1993, where an extremely accurate asymptotic error estimate is shown. In this paper, we apply this error formula to the former case to obtain error formulas in a closed, explicit form.

Fractal dimension and convergence property of recursively generated symplectic integrators

Abstract Recursive constructions of symplectic integrators for the Hamiltonian dynamical system are discussed in a general form. Moreover, using the fractal dimensions, we introduce the classification procedure of the symplectic integrators. We also show that the obtained fractal dimensions are related to the convergence and stability of the symplectic integrators.

Three-Dimensional Electromagnetic Particle-in-Cell Code Using High Performance Fortran on PC Cluster

A three-dimensional full electromagnetic particle-in-cell (PIC) code, TRISTAN (Tridimensional Stanford) code, has been parallelized using High Performance Fortran (HPF) as a RPM (Real Parallel Machine). In the simulation, the simulation domains are decomposed in one-dimension, and both the particle and field data located in each domain that we call the sub-domain are distributed on each processors. Both the particle and field data on a sub-domain is needed by the neighbor sub-domains and thus communications between the sub-domains are inevitable. Our simulation results using HPF exhibits the promising applicability of the HPF communications to a large scale scientific computing such as 3D particle simulations.

E-Learning Experiment over Satellite Between Asian Universities Toward the Development of Wideband InterNetworking Engineering Test and Demonstration Satellite (WINDS)

KDDI has been involved in the E-learning Experiment over satellite between Asian Universities, in cooperation with Japan Aerospace Exploration Agency (JAXA), and University of Tsukuba. This pilot experiment is positioned as one of preparation works towards the launch of the Wideband InterNetworking engineering test and Demonstration Satellite (WINDS) planned in early 2008. The development of WINDS is a part of the Research and Development (R&D) program named i-Space to build the most advanced information networks based on e-Japan Priority Policy Program ** announced by Japanese Government. Those activities are promoted by JAXA and other national R&D organizations. This paper describes the outline and the outcome of the above pilot experiment since 2002.