Comment on "Dynamics of a Potential Barrier Formed on the Tail of a Moving Double Layer in a Collisionless Plasma"

1994

Contrib. Plasma Phys.

The dynamical behavior of a bounded plasma system (BPS) is, by definition, characterized by the simultaneous and self-consistent interaction of the plasma itself, its material boundaries, and whatever external circuit(s) there may be. A full theoretical description of these systems, which are of relevance in a variety of fields (e.g., plasma technology), must involve (microscopic or macroscopic) evolution equations for the plasma, Maxwell's equations for the fields, boundary conditions for the plasma and the fields, and the external-circuit equation(s). By "BPS simulation" we mean obtaining theoretical (including numerical) results from models accounting, at least conceptually, for all the basic features mentioned above.This paper is exclusively concerned with microscopic (i.e., kinetic and particle) BPS simulation. A very general system of basic equations for kinetic BPS simulation is proposed. With the PD ("plasma device") codes from U.C. Berkeley [BIRDSALL, C. K., IEEE Trans. Plasma Sci. 19 (1991) 651, particle simulations of (14 3 4 BPS's can now be routinely performed by everybody. Particular emphasis is laid on an alternative method called "trajectory simulation", which has shown great potential for kinetic BPS simulation with high accuracy and resolution. From the point of view of nonlinear dynamics, BPS's are rather complex dissipative systems exhibiting, in particular, regular and chaotic attractor states. For their proper interpretation, an advisable (if not indispensable) first step is to carefully study relatively simple, but still representative "archetypal" BPS's, such as the Pierce diode [GODFREY, B. B., Phys. Fluids 30 (1987) I5531 and the single-emitter plasma diode or "KDSI" [CRYSTAL. T. L., et al., Phys. Fluids B 3 (1991) 2441. These systems and representative results obtained therewith are surveyed, and both recent developments and future perspectives of BPS physics are addressed.

The Physics of Bounded Plasma Systems (BPS's): Simulation and Interpretation

1994

Contrib. Plasma Phys.

Linear longitudinal oscillations in collisionless plasma diodes with thin sheaths. Part I. Method

1984

The Physics of Fluids

A method is proposed for treating linear longitudinal perturbations in one-dimensional collisionless plasma diodes with a uniform plasma region and thin electrode sheaths. The method is comprehensive in that it allows for very general equilibrium, initial, boundary, and external-circuit conditions. Upon Laplace-transforming the Vlasov and Poisson equations in both space and time, appropriate evaluation of all pertinent relations leads to a set of 2+2nσ(nσ is the number of particle species) coupled integral equations in x and v for the following quantities (which are the time Laplace transforms of the respective physical perturbations): j̃e(ω) (external-circuit current density), Ẽ(x,ω) (electrostatic field), f̃σl(v>0,ω), and f̃σr(v<0,ω) (velocity distribution functions of the plasma-bound particles at the left- and right-hand plasma boundaries, respectively), where σ is the species index. The formal solution of these integral equations and the inverse Laplace transformation (ω→t) are discussed in general terms. In particular, it is shown that the intrinsic eigenfrequencies are given by the zeros of the coefficient determinant of the integral equations. A comparison with previous treatments is given, and it is concluded that extensions of the method proposed to more general systems should be feasible.

Linear longitudinal oscillations in collisionless plasma diodes with thin sheaths. Part II. Application to an extended Pierce-type problem

1984

The Physics of Fluids

The integral-equation method developed in Part I is applied to a Pierce-type diode [J. Appl. Phys. 15, 721 (1944)] whose external circuit involves a resistor, an inductor, and a signal generator. The general linear perturbational problem is solved analytically for the small-amplitude quantities j̃e(t) (external-circuit current density) and Ẽ(x, t) (electrostatic field). Each of these quantities can be constructed from a ‘‘spatial’’ Green’s function (accounting for initial perturbations of the plasma), a ‘‘temporal’’ Green’s function (accounting for external-generator signals), and two functions associated with the initial state of the external circuit. The solutions generally exhibit an initial transient and an asymptotic part, the latter being a superposition of eigenmodes only. Systematic numerical results for eigenfrequencies and eigenmode profiles in some typical parameter regions demonstrate that the linear response and stability behavior of the diode system may substantially depend on the properties of the external circuit.