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Nonlinear interaction of a finite-amplitude electromagnetic wave with a uniform, unmagnetized plasma is considered, taking into account impurity-driven radiation losses. It is shown that this interaction is governed by the wave equation for electromagnetic sidebands, together with two coupled equations which are the electromagnetic radiation pressure-driven electron number density and temperature perturbations associated with plasma slow motions. The latter involve coupled radiative-Langmuir or ion-acoustic modes. Radiative thermal condensation instabilities are investigated in the absence of electromagnetic waves. The presence of an electromagnetic pump is shown to modify the spectra of radiative thermal condensation instabilities. This is demonstrated from the newly derived nonlinear dispersion relations. The relevance of our investigation to filamentary structures or jetting in laser-produced plasmas is pointed out.

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The oblate spheroidal shape is close to the commonly used elliptical rf cavity shape employed in accelerators. Here we solve the oblate spheroidal radial and angular wave functions to obtain the frequencies of the axisymmetric TM and TE modes. We develop a semianalytic formalism to calculate the characteristic parameters, such as shunt impedance, of higher order modes (HOMs). Our formulation is applied to calculate the HOM frequencies of the INDUS-2 and ILC cavities, and the agreement with three-dimensional finite element calculations is excellent. Using this formalism we investigate the effect of changing the oblate shape, and predict an optimized range of 0 (one of the key parameters to define the geometry), to reduce the number of significant HOMs.