Diffusion limit of the Vlasov equation in the weak turbulent regime

@article{Bardos2021DiffusionLO,
  title={Diffusion limit of the Vlasov equation in the weak turbulent regime},
  author={Claude W. Bardos and Nicolas Besse},
  journal={Journal of Mathematical Physics},
  year={2021}
}
  • C. Bardos, N. Besse
  • Published 12 October 2021
  • Mathematics, Physics
  • Journal of Mathematical Physics
In this paper we study the Hamiltonian dynamics of charged particles subject to a non-selfconsistent stochastic electric field, when the plasma is in the so-called weak turbulent regime. We show that the asymptotic limit of the Vlasov equation is a diffusion equation in the velocity space, but homogeneous in the physical space. We obtain a diffusion matrix, quadratic with respect to the electric field, which can be related to the diffusion matrix of the resonance broadening theory and of the… 
1 Citations
About the derivation of the quasilinear approximation in plasma physics.
This contribution, built on the companion paper [1], is focused on the different mathematical approaches available for the analysis of the quasilinear approximation in plasma physics.

References

SHOWING 1-10 OF 78 REFERENCES
Proof of quasilinear equations in the strongly nonlinear regime of the weak warm beam instability
Quasilinear (QL) theory was developed in 1962 to describe the saturation of the weak warm beam-plasma instability, which involves the development of a Langmuir turbulence and the formation of a
On Landau damping
Going beyond the linearized study has been a longstanding problem in the theory of Landau damping. In this paper we establish exponential Landau damping in analytic regularity. The damping phenomenon
A Perturbation Theory for Strong Plasma Turbulence
A new perturbation theory for solving the Vlasov equation is derived. The theory is especially designed to cope with time secularities and nonanalyticity in the expansion parameter (the field
Revisiting the validity of quasilinear theory
The weak turbulence theory of Langmuir waves in a one‐dimensional, one‐species plasma is discussed. Analytic calculations using the theory of two‐point correlations show that in the weak turbulence
Validity of quasilinear theory: refutations and new numerical confirmation
The validity of quasilinear (QL) theory describing the weak warm beam-plasma instability has been a controversial topic for several decades. This issue is tackled anew, both analytically and by
Enhancement of the velocity diffusion in longitudinal plasma turbulence
Velocity diffusion has been observed to be significantly above that given by quasilinear theory in both test‐particle and self‐consistent simulations of the dynamics of turbulent electrostatic
Proof of quasilinear equations in the chaotic regime of the weak warm beam instability
The diffusion coefficient is proved rigorously to take on the quasilinear value for the chaotic motion of an electron in a prescribed set of strongly overlapping Langmuir waves with random phases.
Weak turbulence theory of Langmuir waves: a reconsideration of the validity of quasilinear theory
The weak turbulence theory of Langmuir waves in a one-dimensional, one-species plasma is discussed. Analytical calculations using the theory of two-point correlation show that in the weak turbulence
Nonlinear wave-particle interaction and conditions for the applicability of quasilinear theory
Abstract In this paper it is shown that the usual conditions of the broad wave packet and overlapping of the trapping intervals of neighboring harmonics are not sufficient for the applicability of
Formulation of a Statistical Theory of Strong Plasma Turbulence
A new formulation of methods introduced by Dupree, and Orszag and Kraichnan, for solving the Vlasov equation for turbulent plasmas based on. algebraic use of an averaging operator is described.
...
1
2
3
4
5
...