Effective Cavity Length of Gyrotrons

Megawatt-class gyrotron oscillators for electron cyclotron heating and non-inductive current drive (ECH&CD) in magnetically confined thermonuclear fusion plasmas have relatively low cavity quality factors in the range of 1000 to 2000. The effective length of their cavities cannot be simply deduced from the cavity electric field profile, since this has by far not a Gaussian shape. The present paper presents a novel method to estimate the effective length of a gyrotron cavity just from the eigenvalue of the operating TE_m,n mode, the cavity radius and the exact oscillation frequency which may be numerically computed or precisely measured. This effective cavity length then can be taken to calculate the Fresnel parameter in order to confirm that the cavity is not too short so that the transverse structure of any mode in the cavity is the same as that of the corresponding mode in a long circular waveguide with the same diameter.