No Arabic abstract
In continuation of previous work, numerical results are presented, concerning relativistically counter-streaming plasmas. Here, the relativistic mixed mode instability evolves through, and beyond, the linear saturation -- well into the nonlinear regime. Besides confirming earlier findings, that wave power initially peaks on the mixed mode branch, it is observed that, during late time evolution wave power is transferred to other wave numbers. It is argued that the isotropization of power in wavenumber space may be a consequence of weak turbulence. Further, some modifications to the ideal weak turbulence limit is observed. Development of almost isotropic predominantly electrostatic -- partially electromagnetic -- turbulent spectra holds relevance when considering the spectral emission signatures of the plasma, namely bremsstrahlung, respectively magneto-bremsstrahlung (synchrotron radiation and jitter radiation) from relativistic shocks in astrophysical jets and shocks from gamma-ray bursts and active galactic nuclei.
In recent years, a strong reduction of plasma turbulence in the presence of energetic particles has been reported in a number of magnetic confinement experiments and corresponding gyrokinetic simulations. While highly relevant to performance predictions for burning plasmas, an explanation for this primarily nonlinear effect has remained elusive so far. A thorough analysis finds that linearly marginally stable energetic particle driven modes are excited nonlinearly, depleting the energy content of the turbulence and acting as an additional catalyst for energy transfer to zonal modes (the dominant turbulence saturation channel). Respective signatures are found in a number of simulations for different JET and ASDEX Upgrade discharges with reduced transport levels attributed to energetic ion effects.
Trapped electron mode turbulence is studied by gyrokinetic simulations with the GYRO code and an analytical model including the effect of a poloidally varying electrostatic potential. Its impact on radial transport of high-Z trace impurities close to the core is thoroughly investigated and the dependence of the zero-flux impurity density gradient (peaking factor) on local plasma parameters is presented. Parameters such as ion-to-electron temperature ratio, electron temperature gradient and main species density gradient mainly affect the impurity peaking through their impact on mode characteristics. The poloidal asymmetry, the safety factor and magnetic shear have the strongest effect on impurity peaking, and it is shown that under certain scenarios where trapped electron modes are dominant, core accumulation of high-Z impurities can be avoided. We demonstrate that accounting for the momentum conservation property of the impurity-impurity collision operator can be important for an accurate evaluation of the impurity peaking factor.
The turbulent transport of main ion and trace impurities in a tokamak device in the presence of steep electron density gradients has been studied. The parameters are chosen for trapped electron (TE) mode turbulence, driven primarily by steep electron density gradients relevant to H-mode physics, but with a transition to temperature gradient driven turbulence as the density gradient flattens. Results obtained through non-linear (NL) and quasilinear (QL) gyrokinetic simulations using the GENE code are compared with results obtained from a fluid model. Main ion and impurity transport is studied by examining the balance of convective and diffusive transport, as quantified by the density gradient corresponding to zero particle flux (peaking factor). Scalings are obtained for the impurity peaking with the background electron density gradient and the impurity charge number. It is shown that the impurity peaking factor is weakly dependent on impurity charge and significantly smaller than the driving electron density gradient.
We have extended our study of the competition between the drive and stabilization of plasma microinstabilities by sheared flow to include electromagnetic effects at low plasma $beta$ (the ratio of plasma to magnetic pressure). The extended system of characteristic equations is formulated, for a dissipative fluid model developed from the gyrokinetic equation, using a twisting mode representation in sheared slab geometry and focusing on the ion temperature gradient mode. Perpendicular flow shear convects perturbations along the field at the speed we denote as $Mc_s$ (where $c_s$ is the sound speed). $M > 1/ sqrt{beta}$ is required to make the system characteristics unidirectional and inhibit eigenmode formation, leaving only transitory perturbations in the system. This typically represents a much larger flow shear than in the electrostatic case, which only needs $M>1$. Numerical investigation of the region $M < 1/sqrt{beta}$ shows the driving terms can conflict, as in the electrostatic case, giving low growth rates over a range of parameters. Also, at modest drive strengths and low $beta$ values typical of experiments, including electromagnetic effects does not significantly alter the growth rates. For stronger flow shear and higher $beta$, geometry characteristic of the spherical tokamak mitigates the effect of an instability of the shear Alfv{e}n wave, driven by the parallel flow shear.
Ion sound instabilities driven by the ion flow in a system of a finite length are considered by analytical and numerical methods. The ion sound waves are modified by the presence of stationary ion flow resulting in negative and positive energy modes. The instability develops due to coupling of negative and positive energy modes mediated by reflections from the boundary. It is shown that the wave dispersion due to deviation from quasineutrality is crucial for the stability. In finite length system, the dispersion is characterized by the length of the system measured in units of the Debye length. The instability is studied analytically and the results are compared with direct, initial value numerical simulations.