Ion effects in relativistic diodes

Abstract

In relativistic diodes, ions are emitted from the anode plasma surface. The space charge of these ions enhances the electron emission. One−dimensional analysis and two−dimensional computer simulation are used to show the necessity of including this effect in any realistic diode theory.

Current Density Scaling Expressions for a Bipolar Space-Charge-Limited Cylindrical Diode

“…Early work in planar geometry derived scaling for the nonrelativistic single-species SCL electron current density [8], [9] and then the bipolar current density [10]. Later scaling for the relativistic single-species SCL electron current density [11], [12] was derived and then the bipolar current density for relativistic electrons was developed [13]. Recently, the results have been generalized to both relativistic electrons and ions [14].…”

“…For simplicity, the ions are also assumed to be singly ionized. In this case, the factor f bp is found to be f nr bp = 1.860 for eV a /m e c 2 1 [10] and f r bp = π 2 /4 = 2.437 for eV a /m e c 2 1 [13], [14]. Because some voltages of interest fall inside these bounds where f bp transitions, the expression derived in [15] for f bp in planar geometry will be applied to this cylindrical geometry problem.…”

“…Because some voltages of interest fall inside these bounds where f bp transitions, the expression derived in [15] for f bp in planar geometry will be applied to this cylindrical geometry problem. This function provides an accurate representation of the variation in f bp with voltage and is given by [15], is a more accurate calculation than the value of 1.860 (2.437) arrived at in [10] ( [13], [14]). Parameters C and D were chosen to minimize the relative error in the transition between these regimes.…”

“…It is assumed in the following that this expression for f bp carries over to cylindrical geometry. In addition, the ion current density can be found from [13] …”

Space-charge-limited bipolar flow in a nano-gap

“…Using nano-scale emitters, local current density higher than 10 8 A/cm 2 may be contained with voltages below 20 V at room temperature. 11 Compared to the classical 7 and relativistic models, [12][13][14] there are no studies of SCL bipolar flow in the regime of low voltage and small spacing, where quantum effects may become important. Recently, the 1D classical CL law has been extended to quantum regime, where quantum effects such as the electron tunneling and many electron exchange-correlation effects are included.…”