Application of the Lie transform method to the linear analysis of gyrotrons

Summary form only given. The Lie transform method is used to compute the start oscillation current in gyrotrons. Although the start oscillation current for gyrotrons is well understood, the calculation is laborious when done by conventional techniques. The authors develop a compact formalism for the start oscillation current for a simple cavity and extend this formalism to handle complex cavities. The major advantages of the Lie transform method are the reduction of the amount of algebra in an analytical calculation and the amount of computer time in a numerical calculation. The start oscillation current can be expressed in terms of physically meaningful quantities. A compact expression for the start oscillation current for both TE and TM modes in a closed cylindrical cavity and relevant numerical results have been obtained. The Lie transform method was used to compute the start oscillation current for a complex cavity. Numerical results based on the Lie transform method for the complex cavity were compared with results based on conventional techniques