Charge particle dynamics in the field of two monochromatic waves in a magnetized plasma

We study the dynamics of charged particles in the presence of two electrostatic waves propagating obliquely to an ambient magnetic field. The presence of a second wave makes the problem a two dimensional and time dependent one with a complicated phase space behavior. We derive a set of difference equations (maps) for the nonrelativistic particle motion limit and numerically study them to elucidate the various aspects of the phase space dynamics. For the general case of oblique propagation, we observe synergistic effects leading to the lowering of the stochasticity threshold and the concomitant reduction in electric field amplitudes for particle heating applications. These results can be understood in terms of the resonance structures associated with the two waves and we obtain approximate analytic expressions for the thresholds. For the degenerate case of ω1 = nΩ, ω2 = mΩ (where ω1, ω2 axe the frequencies of the two waves, Ω is the cyclotron frequency and n, m axe integers) and strictly perpendicular propagation, the problem simplifies to a one and half dimensional one. We observe the presence of stochastic webs in this situation