A closed-form analytical solution is found for the nonlinear dynamics of isolated, near-threshold waves in the presence of strong scattering. The proposed solution can be useful in verifying codes across several disciplines, including Alfvénic instabilities and thermal plasma turbulence in fusion plasmas and studies of viscous shear flows in fluid dynamics, as well as a rapid means for predicting and analyzing experimental outcome.
I theoretically found eigenmodes and growth rates of relativistic current filamentation instability in collisional regimes, deriving a generalized dispersion relation from self-consistent beam-Maxwell equations. For symmetrically counterstreaming, fully relativistic electron currents, the collisional coupling between electrons and ions creates the unstable modes of growing oscillation and wave, which stand out for long-wavelength perturbations. In the stronger collisional regime, the growing oscillatory mode tends to be dominant for all wavelengths. In the collisionless limit, those modes vani…
Wave-Energy Partition Governs Weak Collisional Damping in Cold Plasmas
School of Nuclear Science and Technology, University of Science and Technology of China（中国科学技术大学核科学技术学院）；Theoretical Division, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室理论部）
The collisional drift wave instability is reexamined taking into account the ion response in the direction parallel to the magnetic field lines, which appears due to friction with electrons and which can not be omitted in view of the momentum conservation. A modified instability threshold is obtained. In plasmas with dominant electron collisions with neutrals, the instability threshold is shifted towards higher frequencies, compared to the case of dominant electron collisions with ions. The difference between the two cases vanishes when the ion sound response is negligible, i.e., when the inst…
Landau damping and Bernstein-Greene-Kruskal (BGK) modes are among the most fundamental concepts in plasma physics. While the former describes the surprising damping of linear plasma waves in a collisionless plasma, the latter describes exact undamped nonlinear solutions of the Vlasov equation. There does exist a relationship between the two: Landau damping can be described as the phase-mixing of undamped eigenmodes, the so-called Case-Van Kampen modes, which can be viewed as BGK modes in the linear limit. While these concepts have been around for a long time, unexpected new results are still b…
Alfven Eigenmodes (AE) can be destabilized during ITER discharges driven by neutral beam injection (NBI) energetic particles (EP) and alpha particles. The aim of the present study is to analyze the AE stability of different ITER operation scenarios considering multiple energetic particle species. We use the reduced magneto-hydrodynamic (MHD) equations to describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particles species including the effect of the…
The achievement of sustained nuclear fusion in magnetically confined plasma relies on efficient confinement of high-energy ions produced by the fusion reaction. Such particles can excite Alfven Eigenmodes (AEs), which significantly degrade their confinement and threatens the vacuum vessel of future reactors. To develop diagnostics and control schemes, a better understanding of linear and nonlinear features of resonant interactions between plasma waves and high-energy particles, is required. In the case of an isolated single resonance, the problem is homothetic to the so-called Berk-Breizman (B…
A method is developed to analytically determine the resonance broadening function in quasilinear theory, due to either Krook or Fokker-Planck scattering collisions of marginally unstable plasma systems where discrete resonance instabilities are excited without any mode overlap. It is demonstrated that a quasilinear system that employs the calculated broadening functions reported here systematically recovers the nonlinear growth rate and mode saturation levels for near-threshold plasmas previously calculated from kinetic theory. The distribution function is also calculated, which enables precis…
The linear instability and nonlinear dynamics of collisional (resistive) and collisionless (due to electron inertia) double tearing modes (DTMs) are compared with the use of a reduced cylindrical model of a tokamak plasma. We focus on cases where two q = 2 resonant surfaces are located a small distance apart. It is found that regardless of the magnetic reconnection mechanism, resistivity or electron inertia, the fastest growing linear eigenmodes may have high poloidal mode numbers m ~ 10. The spectrum of unstable modes tends to be broader in the collisionless case. In the nonlinear regime, it …
A general criterion is proposed and found to successfully predict the emergence of chirping oscillations of unstable Alfvénic eigenmodes in tokamak plasma experiments. The model includes realistic eigenfunction structure, detailed phase-space dependences of the instability drive, stochastic scattering and the Coulomb drag. The stochastic scattering combines the effects of collisional pitch angle scattering and micro-turbulence spatial diffusion. The latter mechanism is essential to accurately identify the transition between the fixed-frequency mode behavior and rapid chirping in tokamaks and t…
Electron dynamics in the bulk of large band gap dielectric crystals induced by intense femtosecond laser pulses at 800 nm is studied. With laser intensities under the ablation threshold (a few 10 TW/cm\textsuperscript{2}), electrons with unexpected energies in excess of 40-50 eV are observed by using the photoemission spectroscopy. A theoretical approach based on the Boltzmann kinetic equation including state-of-the-art modeling for various particles interactions is developed to interpret these experimental observations. A direct comparison shows that both electron heating in the bulk and a fu…
The saturated state of turbulence driven by the ion-temperature-gradient instability is investigated using a two-dimensional long-wavelength fluid model that describes the perturbed electrostatic potential and perturbed ion temperature in a magnetic field with constant curvature (a $Z$-pinch) and an equilibrium temperature gradient. Numerical simulations reveal a well-defined transition between a finite-amplitude saturated state dominated by strong zonal-flow and zonal-temperature perturbations, and a blow-up state that fails to saturate on a box-independent scale. We argue that this transitio…
A collisional-radiative model describing nonlocal-thermodynamic-equilibrium plasmas is developed. It is based on the HULLAC (Hebrew University Lawrence Livermore Atomic Code) suite for the transitions rates, in the zero-temperature radiation field hypothesis. Two variants of the model are presented: the first one is configuration averaged, while the second one is a detailed level version. Comparisons are made between them in the case of a carbon plasma; they show that the configuration-averaged code gives correct results for an electronic temperature Te=10 eV (or higher) but fails at lower tem…
The aim of this study is to analyze the stability of the Alfven eigenmodes (AE) in the Chinese First Quasi-axisymmetric Stellarator (CFQS). The AE stability is calculated using the code FAR3d that solves the reduced MHD equations to describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moment for the energetic particles (EP) species including the effect of the helical couplings and acoustic modes. The Landau damping and resonant destabilization effects are added in the model by…
We have studied the nonlinear dynamics of whistler waves in magnetized plasmas. Since plasmas and beam-plasma systems considered here are assumed to be weakly collisional, the point of reference for the analysis performed in the present paper is the system of hydrodynamic and field equations. We have applied the renormalization group method to obtain dynamical equations for the slowly varying amplitudes of whistler waves. Further, it has been shown that the amplitudes of eigenmodes satisfy an infinite system of coupled nonlinear Schrödinger equations. In this sense, the whistler eigenmodes for…
The proton temperature anisotropy in the solar wind is known to be constrained by the theoretical thresholds for pressure anisotropy-driven instabilities. Here we use approximately 1 million independent measurements of gyroscale magnetic fluctuations in the solar wind to show for the first time that these fluctuations are enhanced along the temperature anisotropy thresholds of the mirror, proton oblique firehose, and ion cyclotron instabilities. In addition, the measured magnetic compressibility is enhanced at high plasma beta ($β_\parallel \gtrsim 1$) along the mirror instability threshold bu…
A scaling theory of long-wavelength electrostatic turbulence in a magnetised, weakly collisional plasma (e.g., ITG turbulence) is proposed, with account taken both of the nonlinear advection of the perturbed particle distribution by fluctuating ExB flows and of its phase mixing, which is caused by the streaming of the particles along the mean magnetic field and, in a linear problem, would lead to Landau damping. It is found that it is possible to construct a consistent theory in which very little free energy leaks into high velocity moments of the distribution function, rendering the turbulent…
