Numerical Experiments With Single Mode Gyrotron Equations

Abstract

Gyrotrons are microwave sources whose operation is based on the stimulated cyclotron radiation of electrons oscillating in a static magnetic field. This process is described by the system of two complex differential equations: nonlinear first order ordinary differential equation with parameter (averaged equation of electron motion) and second order partial differential equation for high frequency field (RF field) in resonator (Schrödinger type equation for the wave amplitude). The stationary problem of the single mode gyrotron equation in short time interval with real initial conditions was numerically examined in our earlier work. In this paper we consider the stationary and nonstationary problems in large time interval with complex oscillating initial conditions. We use the implicit finite difference schemes and the method of lines realized with MATLAB. Two versions of gyrotron equation are investigated. We consider different methods for modelling new and old versions of the gyrotron equations. The main physical result is the possibility to determine the maximal value of the wave amplitude and the electron efficiency coefficient.

The Gyrotron Startup Scenario in the Single Mode Time Dependent Approach

“…In this paper we have implemented the equation system presented in [1]. This model is often described in the literature as an "old" equation system [13], because it does not take into account two physical effects:…”

“…To solve the Schrodinger type linear partial differential field equation, the second order differential equation solver has to be used. In paper [13], the method of lines [8] with the "ode15s" solver was proposed. However, Matlab offers the "pdepe" function, which implements the second order algorithm that we have employed to find the solution.…”

On the numerical scheme employed in gyrotron interaction simulations

“…In [14] it was suggested that, for gyrotron time-dependent simulations, the BTCS may be preferable to the C-N on the grounds that C-N could be numerically unstable over long simulated time intervals. A discussion on this topic is beyond the scope of this paper.…”