Transient Drift-Dominated Unipolar Conduction between Concentric Cylinders and Spheres

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Abstract
A new analysis analogous to recent work for parallel-plateelectrodes is presented using a unipolar ion-mobility conduction modelbetween concentric cylindrical or spherical electrodes. Exact solutionsare obtained for the transient behavior of the bulk electric-field andspace-charge density distributions and for the terminal current-voltage(I-V) time dependence. The analysis is generalized to handle any initialand boundary conditions for any terminal constraints or excitations.Using the method of characteristics, the governing first-orderchargeconservation quasi-linear partial differential equation is converted into aset of first-order ordinary differential equations. It is shown that forcurrent source excitations these equations can be easily integrated,while for voltage-source excitations the equations are in the correctform for the Runge-Kutta method of numerical integration. Thecoaxial cylindrical geometry is emphasized, treating the special cases ofthe charging transients to a step voltage or current from rest underspace-charge limited conditions and the discharging transients ofsystems which are in the dc steady state and instantaneously open- orshort-circuited. The solutions are computer drawn in three dimensionsusing a recently available graphics package.