Failure of Landau theory
The article "Particle Trapping: A key requisite of structure formation and stability of Vlasov-Poisson plasmas", Phys. Plasmas 22, 042301 (2015), shows the failure of Landau's linear wave theory in describing the formation of coherent structures and with it the onset of instability of realistic Vlasov-Poisson (VP) plasmas.
The reason of failure in two lines:
Coherent equilibria of VP plasmas necessarily imply trapping and hence exclude van Kampen modes, which on the other hand are a central issue for linear Landau solutions.
For more details see
- H.Schamel, Phys. Plasmas 22, 042301 (2015)
- H.Schamel, D.Mandal, D.Sharma, Phys. Plasmas 24, 032109 (2017)
- H.Schamel, N. Das, and P. Borah, Phys. Lett. A 382, 168
(2018)
- H.Schamel, Pattern formation in Vlasov-Poisson plasmas beyond Landau caused by the continuous spectrum of electron and ion holes, https://arxiv.org/pdf/2110.01433v2.pdf or ReviewSoElHo-Nov.pdf