Magnetron injection gun (MIG) design for gyrotron applications

First-order magnetron injection gun (MIG) design trade-off equations are given for use in obtaining an adequate starting point for gun simulations on the computer. These equations are based on conservation of angular momentum and adiabatic electron flow and they contain relativistic corrections for high voltage design. The equations provide considerable insight into the basic physical processes by which gyro-cyclotron beams are formed and controlled. They have also proven very useful in design feasibility studies of high power MIGs. Two examples of MIG designs are given in which these equations were utilized.