AbstractA systematic theory to interpret discharge phenomena generated in E x B structural discharge devices (magnetron type, PIG type, concentric quasi‐spherical type, and so forth) is developed by applying the classical magnetron theory to E x B structural systems. The transforming efficiency h, γ) from the electrostatic energy of a charged particle (mass m) in an electrode system (voltage between the electrodes VCA) to the discharge energy and the coefficient ε(η, r)/(JQVCA/r2) of the energy ε per unit time in unit volume of the discharge bulk are obtained where a device constant k = e (r2 B)2 gives the dimensionless quantity h = √m/k; γ(<1) is a ratio of the electrodes' radii, JQ is the current density at the inner electrode γr2, r2 is the outer‐electrode radius, the potential U2 is U2 = VCA/(1 ‐ r2), and B is the magnetic flux density.The discharge occurs under the condition h2 + r2 < 1. Because 1 ‐ η is consumed for heating electrodes (raising the temperature of a device), one may select the optimum condition of h and γ for η → 1 if possible. The coefficient of ε is advantageous for γ +1, but care must be taken because it has a maximum value with the parameter h. The energy ε is related to the density and the temperature of discharge products, and the purposes of the device use.As for experimental examples of the forementioned types of devices, considerations and comparisons with calculated results of h, γ η and ε are given.The theory presented in this paper is useful for designing such devices as ion sources for ion beam technology, and fundamental researches on cosmic plasmas and nuclear fusion plasmas and for interpreting discharge phenomena generated in these types of devices.