RELATIVISTIC HARMONIC CONTENT OF NONLINEAR ELECTROMAGNETIC-WAVES IN UNDERDENSE PLASMAS

The relativistic harmonic content of large amplitude electromagnetic w aves propagating in underdense plasmas is investigated. The steady sta te harmonic content of nonlinear linearly polarized waves is calculate d for both the very underdense (w(p)/w(o)) much less than 1 and critic al density (w(p)/w(o)) congruent-to 1 limits. For weak nonlinearities, eE(o)/mcomega(o) < 1, the nonlinear source term for the third harmoni c is derived for arbitrary w(p)/w(o). Arguments are given for extendin g these results for arbitrary wave amplitudes. We also show that the u se of the variable x - ct and the quasi-static approximation leads to errors in both magnitude and sign when calculating the third harmonic. In the absence of damping or density gradients the third harmonic's a mplitude is found to oscillate between zero and twice the steady state value. Preliminary PIC simulation results are presented. The simulati on results are in basic agreement with the uniform plasma predictions for the third harmonic amplitude. However, the higher harmonics are or ders of magnitude larger than expected and the presence of density ram ps significantly modifies the results.