An extension of the method of characteristics for parabolic equations is proposed that allows the integration of the energy equation for a static, heated and radiating, heat-conducting, optically thin plasma in a magnetic field. The invariance of all physical quantities is assumed, throughout the work, to occur along an arbitrary curvilinear direction. Finally, an example is presented to illustrate how the algorithm actually works.

Experimental observations are reported on the interaction of 1-μm laser light with underdense plasmas (n ≤ 0·25 nc) from thin foil plastic targets. Nominal laser intensity on target was up to 3 × 1013 W/cm2 in a 3-ns pulse, but much higher intensity was reached due to spiky laser pulses. We studied forward-emitted second harmonic light as a diagnostic of the interaction and in particular of the occurrence of filamentation. Measurements included: energy monitoring of 2ω forward emission vs. target position and laser energy; time resolved (120-ps gate) imaging of the interaction region cross section. The second harmonic energy level was found to be sensitive to target position. In addition, the images obtained with the target in position of maximum second harmonic generation showed unstable structures whose scale length is comparable with the expected one for maximum filamentation growth. These results are shortly discussed in the framework of stationary filamentation theory and second harmonic generation in inhomogeneous media.

Experimental data are reported on second harmonic generation (SHG) during the interaction between a Nd laser beam (20 ns pulse-duration and peak intensity 1013 W/cm2) and a plasma of density 1019 cm−3 produced in helium. The behavior of self-focusing and the onset of steep plasma gradients under the same experimental conditions have been previously characterized by independent techniques as already reported. In the light of these former findings, the observed SH magnitude, emission pattern and time dependence are briefly discussed and compared with expectations.

Among MHD waves, Alfvén waves have been proved to be the best candidates to reach the solar corona and, eventually, to be responsible for the heating of this outer part of the solar atmosphere. The problem arises, however, about the mechanism able to transform the energy stored in the waves into heat.