Nonlinear boundary-value problem for cylindrical corona discharge

Closed-form (one-dimensional) solutions are derived for the electric field E(r) and potential V(r) in a positive ion discharge between a stressed wire anode at r=a and a coaxial cylinder cathode at r=b. It is shown that this system sustains two different corona discharge modes, namely with radially (i) decreasing (k<1) and (ii) increasing (k>1) electric field strength E(r), where k=E_I/E_a is the crucial discharge number. E_I = (I/2πμε₀)^1/2 [V/m] is given in terms of the discharge current I [A/m], whereas the electric field E_a [V/m] at the anode depends on current I and ion temperature T_i at the cathode. The physical properties of these discharge modes are discussed analytically.