Paper: Third and Fourth Harmonics of Electromagnetic Emissions by a Weak Beam in a Solar Wind Plasma with Random Density Fluctuations
Authors: C. Krafft, P. Savoini
Figure caption: Homogeneous plasma: time variations of wave energies (black curves) and products between them (color curves). (a)–(g): logarithmic scale; (h): linear scale. (a) Time variations of ﹩{W}_{{{ \mathcal H }}_{2}},﹩                    ﹩{W}_{{{ \mathcal H }}_{3}}﹩, and ﹩{W}_{{{ \mathcal H }}_{4}}﹩ (black). (b) Time variations of ﹩{W}_{{ \mathcal L }},﹩                    ﹩{W}_{{{ \mathcal L }}^{{\prime} }},﹩ and ﹩{W}_{{ \mathcal L }^{\prime\prime} }﹩ (black), and of ﹩{W}_{{{ \mathcal H }}_{3}}{W}_{{{ \mathcal H }}_{4}}﹩ and ﹩{W}_{{{ \mathcal H }}_{2}}{W}_{{{ \mathcal H }}_{3}},﹩ labeled by H 3*H 4 (green) and H 2*H 3 (red). (c) Time variations of ﹩{W}_{{{ \mathcal L }}_{2}}﹩ and ﹩{W}_{{{ \mathcal L }}_{3}}﹩ (solid black), ﹩{W}_{{{ \mathcal L }}_{2}^{{\prime} }}﹩ and ﹩{W}_{{{ \mathcal L }}_{3}^{{\prime} }}﹩ (dotted black), and ﹩{W}_{{{ \mathcal H }}_{3}}{W}_{{ \mathcal L }}﹩ and ﹩{W}_{{{ \mathcal H }}_{4}}{W}_{{ \mathcal L }},﹩ labeled by H 3*L (green) and H 4*L (green). (d) Time variations of ﹩{W}_{{ \mathcal L }}﹩ and ﹩{W}_{{{ \mathcal L }}^{{\prime} }}﹩ (black), ﹩{W}_{{{ \mathcal H }}_{3}}{W}_{{{ \mathcal H }}_{4}},﹩ and ﹩{W}_{{{ \mathcal H }}_{2}}{W}_{{{ \mathcal H }}_{3}}﹩, labeled by H 3*H 4 (green) and H 2*H 3 (red). (e) Time variations of ﹩{W}_{{{ \mathcal H }}_{2}}﹩ (black), as well as ﹩{W}_{{{ \mathcal H }}_{3}}{W}_{{ \mathcal L }},﹩                    ﹩{W}_{{{ \mathcal H }}_{3}}{W}_{{{ \mathcal L }}^{{\prime} }}﹩, and ﹩{W}_{{{ \mathcal H }}_{3}}{W}_{{ \mathcal L }^{\prime\prime} }﹩, labeled by H 3*L (green), ﹩{H}_{3}* {L}^{{\prime} }﹩ (blue), and H 3*L″ (red); the blue curve is duplicated (i.e., multiplied by another coupling factor) to show the relation ﹩{W}_{{{ \mathcal H }}_{2}}\propto {W}_{{{ \mathcal H }}_{3}}{W}_{{{ \mathcal L }}^{{\prime} }}﹩ occurring at different times. (f) Time variations of ﹩{W}_{{{ \mathcal H }}_{3}}﹩ (black), as well as ﹩{W}_{{{ \mathcal H }}_{2}}{W}_{{ \mathcal L }},﹩                    ﹩{W}_{{{ \mathcal H }}_{2}}{W}_{{{ \mathcal L }}^{{\prime} }}﹩ and ﹩{W}_{{{ \mathcal H }}_{2}}{W}_{{ \mathcal L }^{\prime\prime} }﹩, labeled by H 2*L (green), ﹩{H}_{2}* {L}^{{\prime} }﹩ (blue), and H 2*L″ (red). (g) Time variations of ﹩{W}_{{{ \mathcal H }}_{3}}﹩ (black), as well as ﹩{W}_{{{ \mathcal H }}_{4}}{W}_{{ \mathcal L }},﹩                    ﹩{W}_{{{ \mathcal H }}_{4}}{W}_{{{ \mathcal L }}^{{\prime} }}﹩, ﹩{W}_{{{ \mathcal H }}_{4}}{W}_{{ \mathcal L }^{\prime\prime} }﹩ and ﹩{W}_{{{ \mathcal L }}_{2}^{{\prime} }}{W}_{{ \mathcal L }}﹩, labeled by H 4*L (green), ﹩{H}_{4}* {L}^{{\prime} }﹩ (blue), H 4*L″ (red) and ﹩{L}_{2}^{{\prime} }* L﹩ (orange); the red curve is duplicated (i.e., multiplied by another coupling factor) to show the relation ﹩{W}_{{{ \mathcal H }}_{3}}﹩                    ﹩\propto ﹩                    ﹩{W}_{{{ \mathcal H }}_{4}}﹩                    ﹩{W}_{{{ \mathcal L }}^{{\rm{{\prime} }}{\rm{{\prime} }}}}﹩ occurring at different times. (h) Time variations of ﹩{W}_{{{ \mathcal H }}_{4}}﹩ (black), ﹩{W}_{{{ \mathcal H }}_{3}}{W}_{{{ \mathcal L }}^{{\prime} }}﹩ and ﹩{W}_{{{ \mathcal L }}_{3}^{{\prime} }}{W}_{{ \mathcal L }}﹩, labeled by ﹩{H}_{3}* {L}^{{\prime} }﹩ (blue) and ﹩{L}_{3}^{{\prime} }* L﹩ (orange); the two latter curves are smoothed, due to oscillations. Energies are normalized by the initial beam kinetic energy.