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

Kühn, S.

doi:10.1063/1.864795

Cited by 17 publications

(4 citation statements)

References 24 publications

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“…We note that up to now we have only considered conditions inside the discharge gap, and that the important parameter Φ L (the wall potential) is still unspecified. To determine it we need an 'external-circuit condition', i.e., a condition on the potential at the wall and/or the total current (per unit area) in external circuit (Kuhn 1984).…”

Section: External-circuit Conditionmentioning

confidence: 99%

Extended Tonks–Langmuir-type model with non-Boltzmann-distributed electrons and cold ion sources

et al. 2012

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A general formalism for calculating the potential distribution Φ(z) in the quasineutral region of a new class of plane Tonks–Langmuir (TL)-type bounded-plasma-system (BPS) models differing from the well-known ‘classical’ TL model (Tonks, L. and Langmuir, I. 1929 A general theory of the plasma of an arc. Phys. Rev. 34, 876) by allowing for arbitrary (but still cold) ion sources and arbitrary electron distributions is developed. With individual particles usually undergoing microscopic collision/sink/source (CSS) events, extensive use is made here of the basic kinetic-theory concept of ‘CSS-free trajectories’ (i.e., the characteristics of the kinetic equation). Two types of electron populations, occupying the ‘type-t’ and ‘type-p’ domains of electron phase space, are distinguished. By definition, the type-t and type-p domains are made up of phase points lying on type-t (‘trapped’) CSS-free trajectories (not intersecting the walls and closing on themselves) and type-p (‘passing’) ones (starting at one of the walls and ending at the other). This work being the first step, it is assumed that ε ≡ λD/l → 0+ (where λD and l are a typical Debye length and a typical ionization length respectively) so that the system exhibits a finite quasineutral ‘plasma’ region and two infinitesimally thin ‘sheath’ regions associated with the ‘sheath-edge singularities’ | dΦ/dz|z→±zs → ∞. The potential in the plasma region is required to satisfy a plasma equation (quasineutrality condition) of the form ni {Φ} =ne (Φ), where the electron density ne (Φ) is given and the ion density ni {Φ} is expressed in terms of trajectory integrals of the ion kinetic equation, with the ions produced by electron-impact ionization of cold neutrals. While previous TL-type models were characterized by electrons diffusing under the influence of frequent collisions with the neutral background particles and approximated by Maxwellian (Riemann, K.-U. 2006 Plasma-sheath transition in the kinetic Tonks–Langmuir model. Phys. Plasmas 13, 063508) or bi-Maxwellian (Godyak, V. A. et al. 1995 Tonks–Langmuir problem for a bi-Maxwellian plasma. IEEE Trans. Plasma Sci. 23, 728) electron velocity distribution functions (VDFs), which satisfy the zero-CSS-term (Vlasov) kinetic equation and imply zero electron currents, we here propose a more general class of electron VDFs allowing, in an approximate manner, for non-zero CSS terms and finite electron currents inside the plasma region. The sheath-edge and floating-wall potentials are calculated by balancing the ion and electron current densities at sheath-edge singularities. In a first detailed application, the type-t and type-p electron VDFs are assumed to be ‘inner’ and ‘outer’ cut-off Maxwellians respectively, with different amplitudes and ‘formal’ temperatures, implying the perfectly CSS-free limit. For the special case of equal type-t and type-p electron VDF amplitudes and formal temperatures, the classical Boltzmann distribution for electrons is formally retrieved. Special cases with other amplitude and formal-temperature ratios show significant deviations from the classical case.

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Section: External-circuit Conditionmentioning

confidence: 99%

Extended Tonks–Langmuir-type model with non-Boltzmann-distributed electrons and cold ion sources

et al. 2012

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“…26,27 In our case ͑in the waveguide cavity, say͒ this capacitor term is absent, being discarded by the boundary condition E z (rϭR)ϭ0.…”

Section: ͑10ј͒mentioning

confidence: 99%

Nonresonant radiative Pierce instability and its saturation—Chaos

2000

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Instabilities of a nonrelativistic electron beam in a magnetized waveguide partially filled with semiconductorThe review of theoretical investigations of a nonresonance stimulated Pierce radiation by the relativistic electron beam ͑REB͒ in a waveguide is presented. REB is supposed to be stabilized by an infinitely strong longitudinal magnetic field. Using the analytical methods of linear theory, the conditions leading to the rise of radiative Pierce instabilities, their growth rates and the radiation spectrum are determined. By numerical modeling of the problem, the efficiency of beam energy transformation into electromagnetic field energy as a function of the beam current, its relativism, and geometry are calculated. The physical nature of the instability is clarified and its saturation mechanisms are discussed. In particular, in the saturated state the chaotic motion of beam particles and chaos in the radiation spectrum are observed.

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“…To cope with realistic plasma devices the model has to be extended in various directions to include ion dynamics, collisions with neutrals, and the influence of boundary sheaths. Much work in this area has already been done by Kuhn [10,11] who reported that Q-machine equilibria in the limiting case of thin electrode sheaths are Pierce-unstable in a very broad range of operating conditions. This is, however, in contradiction with experience where stable plasma states are often observed.…”

Section: Introductionmentioning

confidence: 99%

The Pierce diode as a model for the stability of thermionic gas discharges

Kolinsky

Greiner

Klinger

1997

J. Phys. D: Appl. Phys.

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In this work an attempt is made to understand theoretically the trigger mechanism of a Pierce-type hydrodynamic instability found experimentally in thermionic discharges at low pressure. Particle-in-cell simulations are used to obtain detailed information about plasma parameters such as phase space and potential distributions. In contrast to earlier studies, the simultaneous influence of the ion dynamics, collisions with neutrals, and the sheath capacitance is taken into account. This is done by adopting the Lagrangian description of a general Pierce diode model developed previously. The new results obtained are threefold. First, few ion - neutral collisions prevent the coupling between electron and ion dynamics on the electronic time-scale thus removing oscillatory growing Pierce - Buneman modes. Second, the classical Pierce-diode supplemented by an external capacitance to account for the damping effect of the sheath on the Pierce instability explains the existence of stable equilibria. It further reveals the nature of the bifurcation at the instability threshold, i.e. a Hopf bifurcation is the trigger mechanism of the non-linear relaxation oscillations observed in both simulation and experiment. Third, the transient behaviour prior to the instability onset is found to be qualitatively described within the hydrodynamic model.

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

Cited by 17 publications

References 24 publications

Extended Tonks–Langmuir-type model with non-Boltzmann-distributed electrons and cold ion sources

Extended Tonks–Langmuir-type model with non-Boltzmann-distributed electrons and cold ion sources

Nonresonant radiative Pierce instability and its saturation—Chaos

The Pierce diode as a model for the stability of thermionic gas discharges

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