Strongly nonlinear oscillations below the plasma frequency

The authors consider a one dimensional, one species (fixed homogeneous ion background), collisionless Vlasov plasma. The conditions under which strong nonlinear plasma oscillations are always associated with the presence of phase space holes moving with velocities +- VH and exhibiting a periodicity of wave number κ, the associated angular frequency being ω = κ VH. The creation of these vortices can be obtained by different ways. The easier is to start with a homogeneous plasma where a multistream instability is excited around a wavenumber κo and a frequency ωo. The holes build themselves around the velocity ωo/κo and subsequently sustain the frequency ωo. Experiences have been conducted also on a 3 bags plasma where arbitrary small frequencies have been excited. If the size of the plasma allows the development of two (or more) vortices of positive (or negative) velocities, a coalescence of these vortices of same velocity takes place exciting subharmonic wavenumbers on still lower frequencies. When a situation with one hole (plus another of inverse velocity) has been reached, the oscillation persists for a long time. It is also possible to start with a strong average velocity modulation