Current drive in tokamak plasmas by a beat wave is considered in two-dimensional (2-D) geometry. The beat wave is excited by the non-linear interaction of two intense microwave pulses (free electron lasers) in the plasma. The three-wave non-linear interaction equations in steady state are solved numerically. The 2-D toroidal effect and the effect of finite spatial width of the pump microwave pulses are taken into account for the excitation of the beat mode. To illustrate the principle, two types of tokamak are considered: one is small, such as, typically, the Microwave Tokamak Experiment (MTX), and the other one is larger, such as the Joint European Torus (JET). In both cases, it is found that good beat wave coupling exists for a Langmuir beat wave with a phase velocity of around 2.0 to 4.0 times the thermal velocity of the electrons. The fraction of total input power of the right circularly polarized pump waves deposited in the beat mode can be as high as 29% in JET and 32% in MTX. In these cases, there is almost complete pump depletion of the higher frequency pump microwave. It is also found that, for the same input parameters, left circularly polarized pump waves are less efficient than right circularly polarized pump waves for depositing power in the beat mode.
Theory of waveguide antennas for plasma heating and current drive