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

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.