Propagation of space-charge waves in diodes and drift spaces

It has generally been found that propagation of space-charge waves may be described 1) in space-charge-limited gaps by Gauss´ hypergeometric functions, 2) in gaps with no space charge but with an accelerating homogeneous field by Bessel functions with real argument; and 3) in spaces free of dc fields by simple trigonometric functions. The equations derived become simpler through the selection of the dc velocity u, rather than the time t, as the independent variable.