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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 αe and ion αi, normalized potential minimum αm, and ratio of ion current density to electron current density q is shown to be given by Je=JCL[Γ(αe,αi,αm,q)]2 in the form of a definite integral, where the function Γ is independent of the gap voltage and gap spacing of the diode, and JCL 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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