Analytic formulas for magnetron characteristic curves

Summary form only only given, as follows. A closed non-linear set of equations is obtained based on the guiding center fluid model to describe steady-state magnetron operation. Spoke charge effects are included self-consistently, by introducing a mean-field approximation so that the effective AC potential preserves the geometric similarity with the vacuum solutions. The characteristic equations, relating the anode current I and the RF power P to the applied DC voltage V at given RF frequency, are obtained. The dynamic impedance R, the electronic efficiency /spl eta/ and the constant /spl beta/ are computed at synchronism V=V/sub s/, where V/sub s/ is the Buneman-Hartree voltage. Operation in that range is characterized by the maximum achievable spoke current (saturation) at given AC voltage. Outside that range the departure from synchronism limits the current that reaches the anode. The two current cut-off voltages well above and below V/sub s/ are also obtained. Previously obtained V-I equations disagree with experiments in that (a) anode current and RF power go to zero when the resonance condition V=V/sub s/, is met, (b) the operation voltage V is a double-valued function of the current I; there exist two nearly symmetric operation points around V/sub s/ at the same current I. Yet magnetrons, and the related crossed-field amplifiers, are known to exhibit stable operation with single valued V-I characteristics well below V/sub s/. Although zero gain at Synchronism applies to other microwave devices (TWTs, FELs), experimental results and particle simulations of crossed field devices suggest otherwise.