A comparison of weak-turbulence and PIC simulations of weak electron-beam plasma interaction

摘要

Quasilinear theory has long been used to treat the problem of a weak electronbeam interacting with plasma and generating Langmuir waves. Its extension toweak-turbulence theory treats resonant interactions of these Langmuir waveswith other plasma wave modes, in particular ion-sound waves. These are stronglydamped in plasma of equal ion and electron temperatures, as sometimes seen in,for example, the solar corona and wind. Weak turbulence theory is derived inthe weak damping limit, with a term describing ion-sound wave damping thenadded. In this paper we use the EPOCH particle-in-cell code to numerically testweak turbulence theory for a range of electron-ion temperature ratios. We findthat in the cold ion limit the results agree well, but increasing iontemperature the three-wave resonance becomes broadened in proportion to theion-sound wave damping rate. This may be important in, for example, the theoryof solar radio bursts, where the spectrum of Langmuir waves is critical.Additionally we establish lower limits on the number of simulation particlesneeded to accurately reproduce the electron and wave distributions in theirsaturated states, and to reproduce their intermediate states and timeevolution.