The integro‐differential equations for time‐dependent space‐charge decay currents in media between radially symmetrical electrodes

<div class="line" id="line-9"> <span style="font-family: Lora, serif; font-size: 20px;"> Using a single&nbsp;charge&hyphen;carrier&nbsp;species with a field&hyphen;independent&nbsp;mobility&nbsp;model,&nbsp;dimensionless, nonlinear integro&hyphen;differential equations have been derived whose&nbsp;solutions&nbsp;would exactly predict the time&hyphen;dependent current produced by the drift and collection of space&hyphen;charge swarms in media between&nbsp;electrodes&nbsp;with cylindrical and spherical symmetries. The equations are the one&hyphen;dimensional&nbsp;solutions&nbsp;of the mathematical problems involving arbitrary initial space&hyphen;charge distributions whose initial currents may or may not be space&hyphen;charge limited. In principle, if the initial&nbsp;charge&nbsp;distributions were known, the&nbsp;solutions&nbsp;would reduce to first&hyphen;order,&nbsp;nonlinear differential equations&nbsp;which then could be numerically integrated. The general equations are applied to a specific example of a&nbsp;charge&hyphen;density&nbsp;distribution which is important in scientific and technological applications. </span></div>