Nonlinear Landau Damping of Resonantly Excited Fields in Nonuniform Plasmas.

This thesis considers the resonant excitation of a nonuniform plasma by two electromagnetic waves at closely spaced frequencies omega_1, omega_2 with omega_1 > omega_2. Each of the pump waves excites a Langmuir wave at the point in the density profile where plasma resonance is achieved. For profiles having scale lengths L large compared to the characteristic Airy scale length (i.e., k_{A}L gg 1) the linear Landau damping of the Langmuir waves is quite small close to their cutoff, hence the beat interaction with slow electrons plays an important role. The problem is formulated in terms of differential equations in configuration space for the waves at omega_1, omega_2, which are coupled to the idler field at omega_1 - omega_2. The idler is described kinetically by a differential equation in Fourier space. The interaction is governed by the parameter ~ omega_3 = (1 - omega _2/omega_1)k_{A}L and the scaled pump strength p = (k_{D }L)^2E_sp{0j}{2}/24 pi n_0(T_{e} + T_{i }), where k_{D} is the Debye wave-number and E_0 the external pump amplitude. For ~omega _3 << 1 the ponderomotive nonlinearity is recovered and a dissipative contribution is obtained. For ~omega_3 > 1 plasmon transfer from omega_1 to omega_2 causes strong depletion of the high frequency wave before significant ponderomotive profile changes set in. The fractional power absorbed through the idler is smaller than the power transferred to omega_2 by a factor of (1 - omega_2/omega_1). . Additionally, the thesis investigates the nonlinear Landau damping associated with two electromagnetic waves that do not undergo resonant absorption. The governing field equations and the corresponding conservation laws are obtained. The mechanism of dissipation is collisional damping. The photon decay rate for the system is found to be proportional to the collisional damping rate gamma_3 and the electromagnetic nonlinearity parameter | p_{j} = ( | k_{A}L)e^2E_sp {sj}{2}/m^2c^2omega _{p}^2, where | k_{A} is the electromagnetic Airy wave-number (| k_{A} = (omega_1L/c)^{2/3}L^ {-1}) and E_{sj} is the electromagnetic wave amplitude.