The momentum transfer and velocity diffusion of electrons periodically interacting with a coherent longitudinal wavepacket is considered. Applying the resonance overlap criterion, we -establish the threshold for intrinsic stochasticity and the width of the stochastic region AVstoch in velocity space.Direct numerical integration of the singleparticle dynamics and an approximate discrete mapping are used to corroborate the resonance overlap results and to find the short-and long-term momentum transfer and diffusion in the field. After the onset of stochasticity, we find a net induced current j ~Av stoch and in the weakfield regime (autocorrelation time< i bounce time) an initial rate of change of the variance <6 v>/2t equal to the quasilinear-theory diffusion coefficient.In the strong-field regime momentum transfer and stochasticity persist owing to non-adiabatic transitions between trapped and untrapped states as the electron traverses the wavepacket. The diffusion coefficient substantially deviates from the quasilinear (~LE ) as well as from resonance broadening (~E3 /2) scaling, while the scattering in velolocity space tends to lose the local, diffusive, nature characteristic of weak fields. 1.2.

The launching of RF waves from a two- and four-waveguide array is studied. From Brambilla's grill theory, analytic expressions for the reflection coefficients, the power spectrum and the fields in the slab model of a cold inhomogeneous plasma are derived. As a first approximation to the coupling problem, only the fundamental mode in the waveguides is considered, the fast wave in the plasma is neglected and the density profile near the plasma edge is assumed to be linear. It is shown that for a fourwaveguide array with alternate 0, π phases, optimum coupling is obtained when the inside waveguides carry about four times the power of the outside ones. This reduces and equalizes the waveguide reflection coefficients and avoids excessive shifts of the penetrated power spectrum to low values of the wavenumber parallel to the magnetic field.