Theory for low‐frequency modulated Langmuir wave packets

Langmuir wave packets with low frequency modulations (or beats) have been observed in the Jovian foreshock. Here it is argued that these modulations are direct evidence for the Langmuir wave decay L → L ′ + S . In this decay, ‘pump’ Langmuir waves L , driven by an electron beam, produce backscattered product Langmuir waves L ′ and ion sound waves S . The L and L ′ waves beat at the frequency and wavevector of the S waves, thereby modulating the wave packets. Electron beam speeds are deduced from the observed modulations, thereby providing testable predictions for the theory. Beam speeds calculated using the modulated Jovian wave packets (1) are reasonable, at 4 – 10 times the electron thermal speed, (2) are consistent with theoretical limits on the decay process, and (3) decrease with increasing foreshock depth, as expected theoretically. These results strongly support the theory. The modulation depth of some wave packets suggests saturation by the decay L → L ′ + S . Applications to modulated Langmuir packets in the Venusian and terrestrial foreshocks and in a type III radio source are proposed, and future tests are described.