Abstract <p>The steady states of a diode in which electrons and positrons come from opposite electrodes with relativistic velocities have been studied. Such a situation may occur, e.g., in the plasma of pulsar diodes. Both the mode when charged particles reach the opposite electrode and the mode when a portion of particles is reflected by the potential barriers within the inter-electrode gap are considered. It is established that with a fixed potential difference between the electrodes, the solutions are determined by only three dimensionless parameters: the inter-electrode distance <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11452_2025_3785_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\delta \)</EquationSource>  </InlineEquation>, the relativistic factor of the entering electrons <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11452_2025_3785_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\gamma }_{0}}\)</EquationSource>  </InlineEquation>, and the electric field strength at the left electrode <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11452_2025_3785_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\varepsilon }_{0}}\)</EquationSource>  </InlineEquation>. The whole variety of solutions is represented by a set of curves in <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11452_2025_3785_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\(\{ {{\varepsilon }_{0}},\delta \} \)</EquationSource>  </InlineEquation> plane. It turned out that these curves qualitatively coincide with the branches of the solutions in the non-relativistic case. The relativistic factor effect on structure of the solution branches has been analysed.</p>

Steady States of a Diode with Relativistic Electron and Positron Beams

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发表日期：

2025年3月1日

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V. I. Kuznetsov,
L. A. Bakaleinikov,
I. K. Morozov,
E. Yu. Flegontova

摘要

Abstract

The steady states of a diode in which electrons and positrons come from opposite electrodes with relativistic velocities have been studied. Such a situation may occur, e.g., in the plasma of pulsar diodes. Both the mode when charged particles reach the opposite electrode and the mode when a portion of particles is reflected by the potential barriers within the inter-electrode gap are considered. It is established that with a fixed potential difference between the electrodes, the solutions are determined by only three dimensionless parameters: the inter-electrode distance \(\delta \) , the relativistic factor of the entering electrons \({{\gamma }_{0}}\) , and the electric field strength at the left electrode \({{\varepsilon }_{0}}\) . The whole variety of solutions is represented by a set of curves in \(\{ {{\varepsilon }_{0}},\delta \} \) plane. It turned out that these curves qualitatively coincide with the branches of the solutions in the non-relativistic case. The relativistic factor effect on structure of the solution branches has been analysed.