Non‐Markovian diffusion in plasma turbulence

Turbulence and Microprocesses in Inhomogeneous Solar Wind Plasmas

The random density fluctuations observed in the solar wind plasma crucially influence on the Langmuir wave turbulence generated by energetic electron beams ejected during solar bursts. Those are powerful phenomena consisting of a chain of successive processes leading ultimately to strong electromagnetic emissions. The small-scale processes governing the interactions between the waves, the beams and the inhomogeneous plasmas need to be studied to explain such macroscopic phenomena. Moreover, the complexity induced by the plasma irregularities requires to find new approaches and modelling. Therefore theoretical and numerical tools were built to describe the Langmuir wave turbulence and the beam’s dynamics in inhomogeneous plasmas, in the form of a self-consistent Hamiltonian model including a fluid description for the plasma and a kinetic approach for the beam. On this basis, numerical simulations were performed in order to shed light on the impact of the density fluctuations on the beam dynamics, the electromagnetic wave radiation, the generation of Langmuir wave turbulence, the waves’ coupling and decay phenomena involving Langmuir and low frequency waves, the acceleration of beam electrons, their diffusion mechanisms, the modulation of the Langmuir waveforms and the statistical properties of the radiated fields’ distributions. The paper presents the main results obtained in the form of a review.

Origin of hyperdiffusion in generalized Brownian motion

We study a minimal non-Markovian model of superdiffusion which originates from long-range velocity correlations within the generalized Langevin equation approach. The model allows for a three-dimensional Markovian embedding. The emergence of a transient hyperdiffusion, (Δx2(t))∝t(2+λ), with λ∼1-3 is detected in tilted washboard potentials before it ends up in a ballistic asymptotic regime. We relate this phenomenon to a transient heating of particles T(kin)(t)∝t(λ) from the thermal bath temperature T to some maximal kinetic temperature Tmax. This hyperdiffusive transient regime ceases when the particles arrive at the maximal kinetic temperature.

Kinetic theory for distribution functions of wave-particle interactions in plasmas

The evolution of a charged particle distribution function under the influence of coherent electromagnetic waves in a plasma is determined from kinetic theory. For coherent waves, the dynamical phase space of particles is an inhomogeneous mix of chaotic and regular orbits. The persistence of long time correlations between the particle motion and the phase of the waves invalidates any simplifying Markovian or statistical assumptions--the basis for usual quasilinear theories. The generalized formalism in this Letter leads to a hierarchy of evolution equations for the reduced distribution function. The evolution operators, in contrast to the quasilinear theories, are time dependent and nonsingular and include the rich phase space dynamics of particles interacting with coherent waves.