# Effects of collision on the time-independent states of a non-neutral plasma diode

TL;DR: In this paper, the steady states of a planar plasma diode where static ions uniformly occupy the inter-electrode region were investigated with the help of Lagrangian description of fluid-Maxwell's equations, and time independent states were explored for arbitrary values of the neutralization parameter.

Abstract: A theoretical investigation is presented on the steady states of a planar plasma diode where static ions uniformly occupy the inter-electrode region. A cold and purely monochromatic electron beam is injected from the emitter plate, and the emitted electrons are carried to the collector plate through the uniform background of stationary ions. It is considered that the electrons suffer collisions with the other particles (with ions or neutral atoms) during its transportation through the inter-electrode gap. The effects of collisions are incorporated through a simplified one-dimensional model. With the help of Lagrangian description of fluid-Maxwell's equations, time-independent states are explored for arbitrary values of the neutralization parameter. Using the emitter electric field as a characteristic parameter, the steady-state solutions are categorized into “Bursian” and “Non-Bursian” branches in “emitter electric field vs diode gap” parametric space. The Non-Bursian solutions are found to be very sensitive to the dissipative term as they only exist for small, non-zero values of the normalized collision-frequency.

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TL;DR: In this article, a thermionic energy converter as the Pierce diode of which the interelectrode space is filled with a uniform background of immobile ions is considered, and the features of stability of its time-independent solutions are investigated under electron collisions with background gas.

Abstract: A thermionic energy converter as the Pierce diode of which the interelectrode space is filled with a uniform background of immobile ions is considered. The features of stability of its time-independent solutions are investigated under electron collisions with background gas. The solutions are obtained analytically by the Lagrange method. A dispersion equation is derived using a perturbative approach. The aperiodic solutions of this equation, as well as the oscillatory ones, are obtained and their properties are studied too. The regions of unstable aperiodic modes are determined. It is shown that all the oscillatory modes are stable.

3 citations

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TL;DR: In this article, the stationary states of the Pierce diode were found in the presence of reflection of electrons from the potential barrier when electron scattering by background particles is taken into account.

Abstract: The stationary states of the Pierce diode are found in the presence of reflection of electrons from the potential barrier when electron scattering by background particles is taken into account. Solutions are divided into two groups: Bursian and non-Bursian. It is shown that non-Bursian solutions disappear when the average collision frequency is of the order of 10% of the plasma frequency. The results can be used to optimize the characteristics of a thermionic energy converter operating in the regime with surface ionization.The stationary states of the Pierce diode are found in the presence of reflection of electrons from the potential barrier when electron scattering by background particles is taken into account. Solutions are divided into two groups: Bursian and non-Bursian. It is shown that non-Bursian solutions disappear when the average collision frequency is of the order of 10% of the plasma frequency. The results can be used to optimize the characteristics of a thermionic energy converter operating in the regime with surface ionization.

2 citations

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01 Nov 2019

TL;DR: In this paper, the stability features of the Pierce diode steady states were investigated in the presence of electron-background-particle collisions in the regime without electron reflection from the potential barriers.

Abstract: Stability features of the Pierce diode steady states are investigated in the presence of electron-background-particle collisions. The regime without electron reflection from the potential barriers is studied. Steady states are obtained analytically by means of the Lagrangian fluid description. Employing the first order perturbation theory, the relevant dispersion equation is derived. Both aperiodic and oscillatory solutions of this equation are found and their properties are studied.

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TL;DR: In this paper, the authors evaluated the limiting current for flow normal to parallel plane equipotentials and for flow filling a conducting tube and constrained to motion parallel to the axis, and showed that the limiting currents are roughly 6 times as great as in the absence of ions.

Abstract: In electron flow, the net electronic charge may be neutralized by positive ions. In this case, for a given geometry there is a limiting current beyond which homogeneous flow is unstable. This limiting current is evaluated for flow normal to parallel plane equipotentials and for flow filling a conducting tube and constrained to motion parallel to the axis. For parallel planes at a potential V0 volts and spaced a distance L cm apart, the limiting current density in amperes/cm2 isi0=104×10−6V032/L2. For a long conducting tube the limiting current is I0=160×10−6V032. These limiting currents are roughly 6 times as great as in the absence of ions.

206 citations

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TL;DR: In this article, the Q machine was used to generate a linear, highly ionized, low temperature cesium plasma by having the output of atomic beam ovens impinge on hot tungsten plates placed at both ends of a cylindrical vacuum chamber.

Abstract: A device for generating a linear, highly ionized, low temperature cesium plasma is described. The plasma is generated by having the output of cesium atomic beam ovens impinge on hot tungsten plates placed at both ends of a cylindrical vacuum chamber. The walls of the chamber are cooled so that neutral cesium condenses on them. The theory of the device, designated as the Q machine, is presented and some experimental results given. The maximum density achieved was 2×1012/cm3, with an estimated fractional ionization of 99%, and a confining field of 5900 gauss.

147 citations

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TL;DR: In this article, the stability properties of one-dimensional Pierce diode beam flow were investigated and the static equilibria, although nonlinear, were evaluated analytically and their stability properties derived.

Abstract: Uniform density electron beam flow in a one‐dimensional Pierce diode is alternately stable and unstable as the diode width is increased. Each stability transition corresponds to an equilibrium bifurcation involving either a static nonuniform equilibrium or a steady oscillatory configuration. The static equilibria, although nonlinear, are evaluated analytically and their stability properties derived. Details of the oscillatory solutions are determined numerically from integral equations relating the transit time of electrons in the diode to the electric field at the entrance plane. As the diode width is reduced, each oscillatory solution undergoes a sequence of subharmonic bifurcations, culminating in a chaotic strange attractor. The chaotic attractor itself terminates in a crisis after a further reduction of the diode width. Unlike other electron beam nonlinear oscillations (e.g., virtual cathodes), no particle reflections are required. This behavior has intrinsic interest as a possible model for beam turbulence in more complex geometries. In addition, it may find application in microwave generation.

95 citations

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TL;DR: In this article, an analytical study of the plasma states in nonneutral plasma diodes and of their stability is presented for an arbitrary neutralization parameter γ, including the Pierce ( γ = 1) and the Bursian (δ = 0) diode as special cases.

50 citations