Fast time-scale computation of gyrotrons using time-domain modal analysis

In this work, we present the development of a fast time-scale analysis for gyrotron simulation, which is believed to be as rigorous as the PIC codes approach, but which is more efficient especially in the case of an azimuthally non-homogeneous electromagnetic field. An accurate representation of the electromagnetic field is obtained by expanding the field components in terms of the solenoidal and the irrotational eigenfunctions of the equivalent completely closed cavity. The use of the modal expansion method reduces the boundary value problem for the field components to solving a linear system of ordinary differential equations (ODE) for the expansion coefficients. A convolution method together with analytic expressions in time-domain of the characteristic impedances of the waveguide modes at the apertures of the cavity are applied to formulate accurately the time-dependent boundary condition at the apertures.