A. Ghizzo

Trapped-ion driven turbulence in tokamak plasmas

Ion turbulence is expected to play an important role in anomalous transport. Thus an original approach is proposed here to study trapped-ion instability. A Vlasov code is used to determine the behaviour of the instability near the threshold and compared with analytical solutions of the Vlasov equation. Some interesting features which appear in the nonlinear regime are discussed.

Persistent subplasma-frequency kinetic electrostatic electron nonlinear waves

Driving a one-dimensional collisionless Maxwellian (Vlasov) plasma with a sufficiently strong longitudinal ponderomotive driver for a sufficiently long time results in a self-sustaining nonsinusoidal wave train with well-trapped electrons even for frequencies well below the plasma frequency, i.e., in the plasma wave spectral gap. Typical phase velocities of these waves are somewhat above the electron thermal velocity. This new nonlinear wave is being termed a kinetic electrostatic electron nonlinear (KEEN) wave. The drive duration must exceed the bounce period τB of the trapped electrons subject to the drive, as calculated from the drive force and the linear plasma response to the drive. For a given wavenumber a wide range of KEEN wave frequencies can be readily excited. The basic KEEN structure is essentially kinetic, with the trapped electron density variation being almost completely shielded by the free electrons, leaving just enough net charge to support the wave.

Saturation process induced by vortex-merging in numerical Vlasov-Maxwell experiments of stimulated Raman backscattering

The influence of low-frequency nonlinear Bernstein-Greene-Kruskal (BGK)-type waves induced by trapped electrons in backward stimulated Raman scattering is investigated in optical mixing. Semi-Lagrangian Vlasov-Maxwell simulations show two nonlinear behaviors. First, there is a Morales-O’Neil plasma wave frequency downshift retuned by a small wavenumber shift which maintains the Stimulated Raman Scattering (SRS) resonance. The saturation of Raman backscattering begins with phase space vortex merging followed by a transition to lower wavenumbers following the (nonlinear) dispersion relation, resembling weak turbulence.

Shear flow instabilities induced by trapped ion modes in collisionless temperature gradient turbulence

One important issue in turbulence self-organization is the interplay between the Kelvin–Helmholtz (KH) instability and streamers and/or zonal flows. This question has been debated for a long time. The effects of the KH instability and its position in the sequence of events between streamers, turbulence, and zonal flows have been investigated with a reduced gyro-bounce averaged kinetic code devoted to study the primary ion temperature gradient (ITG) instability linked to trapped ion modes (TIM). In toroidal geometry, the specific dynamics of TIM linked to trapped particles becomes important when the frequency of ITG modes falls below the ion bounce frequency, allowing one to average on both the cyclotron and bounce motion fast time scales. This reduction of the number of degrees of freedom leads to a strong reduction of computer resources (memory and computation time). Bounce-averaged gyrokinetic code can be considered as a toy model able to describe basic structures of turbulent transport in tokamak devic...

A multi-stream Vlasov modeling unifying relativistic Weibel-type instabilities

We present a multi-stream model obtained from the Vlasov-Maxwell system of equations based on the invariance of the canonical momentum in the perpendicular direction in a 1D-2V phase space. The model is conceived for the study of the Weibel and current filamentation instability in the relativistic regime, but turns out to be of more general importance. It can be used numerically for the study of the non-linear, kinetic dynamics with a drastic reduction of the computational cost with respect to the integration of the corresponding Vlasov-Maxwell system.

Shear-flow trapped-ion-mode interaction revisited. II. Intermittent transport associated with low-frequency zonal flow dynamics

We address the mechanisms underlying low-frequency zonal flow generation in turbulent system and the associated intermittent regime of ion-temperature-gradient (ITG) turbulence. This model is in connection with the recent observation of quasi periodic zonal flow oscillation at a frequency close to 2 kHz, at the low-high transition, observed in the ASDEX Upgrade [Conway et al., Phys. Rev. Lett. 106, 065001 (2011)] and EAST tokamak [Xu et al., Phys. Rev. Lett 107, 125001 (2011)]. Turbulent bursts caused by the coupling of Kelvin-Helmholtz (KH) driven shear flows with trapped ion modes (TIMs) were investigated by means of reduced gyrokinetic simulations. It was found that ITG turbulence can be regulated by low-frequency meso-scale zonal flows driven by resonant collisionless trapped ion modes (CTIMs), through parametric-type scattering, a process in competition with the usual KH instability.

Multi-stream Vlasov model for the study of relativistic Weibel-type instabilities

We discuss and apply a recently proposed model (Inglebert et al 2011 Euro. Phys. Lett. 95 45002) using a Hamiltonian formalism for the study of Weibel-type instabilities in the relativistic limit. Taking advantage of the invariance of the generalized canonical momentum, we represent the plasma as a sum of N particle bunches invariant under the dynamics. This approach allows for a drastic reduction in the computational time when compared with the full Vlasov–Maxwell system of equations. Analytically, the model is exact and we recover the standard fluid dispersion relations in the case of the Weibel and filamentation instabilities. By initially selecting a specific class of particle bunches, we are able to give a fine description of the phase space dynamics interactions even in the saturation regime.

Fluid description of Weibel-type instabilities via full pressure tensor dynamics

We discuss a fluid model for the description of Weibel-type instabilties based on the inclusion of the full pressure tensor dynamics. The linear analysis first performed by Basu B., Phys. Plasmas , 9 , (2002) 5131, for the strong anisotropy limit of Weibels instability is extended to include the coupling between pure Weibels and current filamentation instability, and the potential of this fluid approach is further developed. It is shown to allow an easier interpretation of some physical features of these coupled modes, notably the role played by thermal effects. It can be used to identify the role of different closure conditions in pressure-driven instabilities which can be numerically investigated at a remarkably lower computational cost than with kinetic simulations.

Shear-flow trapped-ion-mode interaction revisited. I. Influence of low-frequency zonal flow on ion-temperature-gradient driven turbulence

Collisionless trapped ion modes (CTIMs) turbulence exhibits a rich variety of zonal flow physics. The coupling of CTIMs with shear flow driven by the Kelvin-Helmholtz (KH) instability has been investigated. The work explores the parametric excitation of zonal flow modified by wave-particle interactions leading to a new type of resonant low-frequency zonal flow. The KH-CTIM interaction on zonal flow growth and its feedback on turbulence is investigated using semi-Lagrangian gyrokinetic Vlasov simulations based on a Hamiltonian reduction technique, where both fast scales (cyclotron plus bounce motions) are gyro-averaged.

Electron temperature anisotropy instabilities represented by superposition of streams

The generation of magnetic field, together with the electrostatic activity met in the saturation regime of the Weibel instability (WI), is investigated by means of an analytical multi-stream model in a Hamiltonian framework. Taking advantage from the invariance of the generalized canonical momentum, the model allows to reduce the full kinetic 1D2V Vlasov equation into several 1D1V equations while keeping its kinetic character. The multi-stream model provides a more complete and accurate picture of the Weibel instability, because it is possible to separate the specific contribution of each stream during the development of the Weibel instability. An interesting result for the multi-stream mode is a lower cost in the perpendicular treatment of the py momentum component since no differential operator associated with some approximate numerical scheme has to be carried out on this variable. Indeed, a small number of streams or particle classes are sufficient to correctly describe the magnetic field generation a...