Non-equilibrium thermionic electron emission for metals at high temperatures

Abstract

The stationary thermionic electron emission currents from heated metals are compared against an analytical expression derived using a non equilibrium quantum Kappa energy distribution for the electrons. This later depends on the temperature decreasing parameter κ(T ) which can be estimated from the raw experimental data and characterizes the departure of the electron energy spectrum from the equilibrium Fermi-Dirac statistics. The calculations accurately predict the measured thermionic emission currents for both high and moderate temperature ranges. The Richardson-Dushman law governs the electron emission for large values of Kappa or equivalently, for moderate metal temperatures. The high energy tail in the electron energy distribution function which develops at higher temperatures or lower Kappa parameters, increases the emission currents well over the predictions of the classical expression. This analysis also permits the quantitative estimation of the departure of the metal electrons from the equilibrium Fermi-Dirac statistics.

Lorentzian Entropies and Olbert's κ - Distribution

“…It does, in this form, not describe quantum systems consisting of many components-a conclusion we had drawn already from different reasoning. This conclusion may, however, be circumvented when large external potential fields are imposed, for instance, strong electric (cf., e.g., [21], who tried an application to high temperature non-ideal quantum systems) or gravitational potential fields (an example would be the region around the black hole horizon), in which case the difference U(β) − > 0 may become positive for − > κ/2β.…”

Olbertian Partition Function in Scalar Field Theory

“…They were also derived in plasma wave-wave interaction theory [11][12][13]. Physically, they represent quasi-stationary states far from equilibrium [14][15][16][17][18]. To some degree, they are related to Tsallis' thermostatistics [19].…”

Propagator integral method for plasma physics kinetic equations with practical applications

“…Many works have provided fluid models, as the those by T. Gyergyek et al [116,144] or kinetic descriptions, as the works by M. D.Campanell et al [89,145] or J. P.Sheehan et al [98,143], as well as many other authors [23,85,[146][147][148][149][150]. Moreover, different approaches to describe the emission of electrons as the works by J. L. Domenech-Garret et al [88,113] and references therein, can be found in the literature, but the description of the complete processes involved in the plasma-wall interaction are still an open topic of discussion because of the variety and peculiarities of each plasma device.…”

“…When plasmas are approximately described as evolving in a one-dimensional velocity space, this view comes from considering there is a dominant cause, usually a strong external electric field, that makes the flow of particles move in one privileged direction, leaving the others unaltered. In this case, the scattering of charged particles may be constrained, limiting the interaction to the privileged direction of interest and sometimes leading to non-Maxwellian distribution functions [86,88,113]. Here, an approach to describe this dynamics based on the full Fokker-Planck-Landau operator is taken…”

“…For example, in solar wind [86,87] Lorentzian or κ-like distributions commonly appear, characterised by higher velocity tails than the Maxwellian. Furthermore, when plasma-wall interaction is analysed, the interplay of emission and collection of charged particles may disrupt the ideal Maxwellian equilibrium [88,89].…”