A generalized empirical equation for the transmission coefficient of electrons

Tabata, Tatsuo; Ito, Rinsuke

doi:10.1016/s0029-554x(75)80016-4

Cited by 54 publications

(22 citation statements)

References 9 publications

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“…For the known attenuation function τ(e, х) we used semiempirical formulae (Tabata & Ito, 1975) tested on different materials (atomic numbers Z from 4 to 82) and in a wide range of electron energies (from 8 keV to 30 MeV). The formulae ensured approximation of the experimental attenuation factor to an accuracy of no worse than 3%.…”

Section: Av Kozyrev Et Al 184mentioning

confidence: 99%

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Reconstruction of electron beam energy spectra for vacuum and gas diodes

et al. 2015

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In this paper, the spectra of electron beams produced in vacuum and gas diodes were analyzed to study the capabilities and limitations of their reconstruction from beam attenuation in foils of different thickness. The electron energy distributions were calculated using the Tikhonov regularization for Fredholm integral equations on minimum a priori assumptions. The spectra reconstructed in the study were those of electron beams, including a supershort avalanche electron beam, produced in experiments on a DUET plasma-cathode electron accelerator and SLEP-150M accelerator.

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Section: Av Kozyrev Et Al 184mentioning

confidence: 99%

“…Here, the dimensionless function S(e) (Tabata & Ito, 1975) and extrapolated path length R in mm (Weber 1964) for aluminum are calculated by the formulae:…”

Section: Av Kozyrev Et Al 184mentioning

confidence: 99%

Reconstruction of electron beam energy spectra for vacuum and gas diodes

et al. 2015

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“…The experimental data for these cross-sections are given in [13] for electron energies up to 1 keV. We extrapolate the dependence of the cross-sections to the high-energy region, using the asymptotic dependences [14]. The dependences of the cross section on the energy of the electron are shown in Fig.…”

Section: Results Of the Discharge Simulation In Nitrogenmentioning

confidence: 99%

Why do Electrons with “Anomalous Energies” appear in High-Pressure Gas Discharges?

Kozyrev

Kozhevnikov

Semeniuk

2018

EPJ Web of Conferences

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Abstract. Experimental studies connected with runaway electron beams generation convincingly shows the existence of electrons with energies above the maximum voltage applied to the discharge gap. Such electrons are also known as electrons with "anomalous energies". We explain the presence of runaway electrons having so-called "anomalous energies" according to physical kinetics principles, namely, we describe the total ensemble of electrons with the distribution function. Its evolution obeys Boltzmann kinetic equation. The dynamics of self-consistent electromagnetic field is taken into the account by adding complete Maxwell's equation set to the resulting system of equations. The electrodynamic mechanism of the interaction of electrons with a travelling-wave electric field is analyzed in details. It is responsible for the appearance of electrons with high energies in real discharges.

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“…As this function τ(ε, х), we used semiempirical dependences from a well-known work [11], which had been tested for a variety of substances (atomic numbers Z from 4 to 82) and a wide range of electron energies (from 8 keV to 30 MeV). For an electrum spectrum normalized with respect to unity f(ε) for the extinction coefficient g(x) (beam fraction of electrons that have passed through the material of thickness х), we have the following expression:…”

Section: Problem Formulationmentioning

confidence: 99%

“…The other spectra shown demonstrate a good efficiency of the method in spectral reconstruction only. They cannot be treated as reliable, since after passing the Al-filter the electron beam undergoes angular scattering, and its passage through the remaining foils does not any longer satisfy the condition of orthogonal incidence, which was assumed in [11] in calculating the coefficient τ(х, ε). Nonetheless, a relative decrease in the number of low-energy electrons and a noticeable shift of the peak in the high-energy electron spectrum towards the region of lower energies as the beam passes increasingly thicker foils provides a correct representation of the physics of this phenomenon.…”

Section: Electron Beam Spectrum Reconstructionmentioning

confidence: 99%

Spectrum reconstruction of a nanosecond electron beam from the data on its extinction in thin foils

et al. 2010

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A possibility of reconstructing the electron beam spectrum from the dependence of beam extinction on foil thickness is demonstrated. The electron energy distributions are calculated using Tikhonov's regularization of the Fredholm integral equation with the least number of a priori assumptions on the beam spectrum shape. The spectra experimentally obtained in a vacuum diode loaded by nanosecond voltage pulses are reconstructed and analyzed.

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A generalized empirical equation for the transmission coefficient of electrons

Cited by 54 publications

References 9 publications

Reconstruction of electron beam energy spectra for vacuum and gas diodes

Reconstruction of electron beam energy spectra for vacuum and gas diodes

Why do Electrons with “Anomalous Energies” appear in High-Pressure Gas Discharges?

Spectrum reconstruction of a nanosecond electron beam from the data on its extinction in thin foils

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