New improved formulas for magnetron characteristic curves

Improved analytic formulas for the magnetron characteristic curves (V/sub 0/ versus I/sub 0/ and P/sub RF/ versus I/sub 0/ for fixed B) are derived using the authors guiding-center fluid model. It is shown that if the anode voltage V/sub 0/, the Hartree voltage V/spl circ//sub s/, and the RF voltage V/sub 1/ satisfy the inequality |V/sub 0/-V/spl circ//sub s/|/spl les/V/sub 1/ then the anode current is directly proportional to the RF voltage. Under these (typical) conditions, explicit expressions for the V-I and P-I relations may be obtained. The new equation for V versus I, which differs significantly from the classical relation of J. Hull predicts that current is drawn to the anode for voltages both above and below the Hartree voltage, in direct contradiction with the traditional view of magnetron operation; this result is closely related to the fact that the gain in a crossed-field amplifier (CFA) is an even function of the difference between the phase velocity of the wave and the drift velocity of the electrons, when space-charge effects are small. A new expression is given for the Hartree voltage that includes the effect of the space charge in the spoke. It is also shown that the best quantitative agreement between the new formula and experimental measurements of magnetron V-I curves is obtained when the hub density is taken to be about 1/2 of Brillouin density.