Space charge limited current for bipolar flow with uniform initial velocity

摘要

The characteristics of space charge limited (SCL) bipolar flow in a planar ion diode with uniform initial velocity are studied in terms of the potential distribution. As a negative potential minimum occurs, a general expression for the limiting current density as a function of the normalized initial kinetic energy of electron @@@ alpha e and ion @@@ alpha i, normalized potential minimum @@@ alpha m, and ratio of ion current density to electron current density q is shown to be given by @@@ J e = @@@ J @@@ C L @@@ [ @@@ Gamma @@@ ( @@@ alpha e , @@@ alpha i , @@@ alpha m , q ) ] 2 in the form of a definite integral, where the function @@@ Gamma is independent of the gap voltage and gap spacing of the diode, and @@@ J @@@ C L is the classical Child-Langmuir law. According to the expression, the SCL current density can be found by traversing all the values of the potential minimum. We also proposed a separation method to numerically obtain the spatial profile of the electrostatic potential as a negative potential minimum develops in a steady state. The theoretical and numerical results are compared with some special cases that have been derived previously and also verified by the extrapolation method in the presence of ions.

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