Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userModeling imbalanced collisionless Alfven wave turbulence with nonlinear diffusion equations
333
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
A pair of nonlinear diffusion equations in Fourier space} is used to study the dynamics of strong Alfven-wave turbulence, from MHD to electron scales. Special attention is paid to the regime of imbalance between the energies of counter-propagating waves commonly observed in the solar wind (SW), especially in regions relatively close to the Sun. In the collisionless regime where dispersive effects arise at scales comparable to or larger than those where dissipation becomes effective, the imbalance produced by a given injection rate of generalized cross-helicity (GCH), which is an invariant, is much larger than in the corresponding collisional regime described by the usual (or reduced) magnetohydrodynamics. The combined effect of high imbalance and ion Landau damping induces a steep energy spectrum for the transverse magnetic field at sub-ion scales. This spectrum is consistent with observations in highly Alfvenic regions of the SW, such as trailing edges, but does not take the form of a transition range continued at smaller scales by a shallower spectrum. This suggests that the observed spectra displaying such a transition result from the superposition of contributions originating from various streams with different degrees of imbalance. Furthermore, when imbalanced energy injection is supplemented at small scales in an already fully developed turbulence, for example under the effect of magnetic reconnection, a significant enhancement of the imbalance at all scales is observed.
rate research
Read More
A two-field Hamiltonian gyrofluid model for kinetic Alfven waves retaining ion finite Larmor radius corrections, parallel magnetic field fluctuations and electron inertia, is used to study turbulent cascades from the MHD to the sub-ion scales. Special attention is paid to the case of imbalance between waves propagating along or opposite to the ambient magnetic field. For weak turbulence in the absence of electron inertia, kinetic equations for the spectral density of the conserved quantities (total energy and generalized cross-helicity) are obtained. They provide a global description, matching between the regimes of reduced MHD at large scales and electron reduced MHD at small scales, previously considered in the literature. In the limit of ultra-local interactions, Leith-type nonlinear diffusion equations in the Fourier space are derived and heuristically extended to the strong turbulence regime by modifying the transfer time appropriately. Relations with existing phenomenological models for imbalanced MHD and balanced sub-ion turbulence are discussed. It turns out that in the presence of dispersive effects, the dynamics is sensitive on the way turbulence is maintained in a steady state. Furthermore, the total energy spectrum at sub-ion scales becomes steeper as the generalized cross-helicity flux is increased.
We apply field-particle correlations -- a technique that tracks the time-averaged velocity-space structure of the energy density transfer rate between electromagnetic fields and plasma particles -- to data drawn from a hybrid Vlasov-Maxwell simulation of Alfven Ion-Cyclotron turbulence. Energy transfer in this system is expected to include both Landau and cyclotron wave-particle resonances, unlike previous systems to which the field-particle correlation technique has been applied. In this simulation, the energy transfer rate mediated by the parallel electric field $E_parallel$ comprises approximately $60%$ of the total rate, with the remainder mediated by the perpendicular electric field $E_perp$. The parallel electric field resonantly couples to protons, with the canonical bipolar velocity-space signature of Landau damping identified at many points throughout the simulation. The energy transfer mediated by $E_perp$ preferentially couples to particles with $v_{tp} lesssim v_perp lesssim 3 v_{tp}$ in agreement with the expected formation of a cyclotron diffusion plateau. Our results demonstrate clearly that the field-particle correlation technique can distinguish distinct channels of energy transfer using single-point measurements, even at points in which multiple channels act simultaneously, and can be used to determine quantitatively the rates of particle energization in each channel.
Weak Alfvenic turbulence in a periodic domain is considered as a mixed state of Alfven waves interacting with the two-dimensional (2D) condensate. Unlike in standard treatments, no spectral continuity between the two is assumed and indeed none is found. If the 2D modes are not directly forced, k^{-2} and k^{-1} spectra are found for the Alfven waves and the 2D modes, respectively, with the latter less energetic than the former. The wave number at which their energies become comparable marks the transition to strong turbulence. For imbalanced energy injection, the spectra are similar and the Elsasser ratio scales as the ratio of the energy fluxes in the counterpropagting Alfven waves. If the 2D modes are forced, a 2D inverse cascade dominates the dynamics at the largest scales, but at small enough scales, the same weak and then strong regimes as described above are achieved.
A Hamiltonian two-field gyrofluid model for kinetic Alfven waves (KAWs) in a magnetized electron-proton plasma, retaining ion finite-Larmor-radius corrections and parallel magnetic field fluctuations, is used to study the inverse cascades that develop when turbulence is randomly driven at sub-ion scales. In the directions perpendicular to the ambient field, the dynamics of the cascade turns out to be nonlocal and the ratio $chi_f$ of the wave period to the characteristic nonlinear time at the driving scale affect some of its properties. For example, at small values of $chi_f$, parametric decay instability of the modes driven by the forcing can develop, enhancing for a while inverse transfers. The balanced state, obtained at early time when the two counter-propagating waves are equally driven, also becomes unstable at small $chi_f$, leading to an inverse cascade. For $beta_e$ smaller than a few units, the cascade slows down when reaching the low-dispersion spectral range. For higher $beta_e$, the ratio of the KAW to the Alfven frequencies displays a local minimum. At the corresponding transverse wavenumber, a condensate is formed, and the cascade towards larger scales is then inhibited. Depending on the parameters, a parallel inverse cascade can develop, enhancing the elongation of the ion-scale magnetic vortices that generically form.
Reduced fluid models including electron inertia and ion finite Larmor radius corrections are derived asymptotically, both from fluid basic equations and from a gyrofluid model. They apply to collisionless plasmas with small ion-to-electron equilibrium temperature ratio and low $beta_e$, where $beta_e$ indicates the ratio between the equilibrium electron pressure and the magnetic pressure exerted by a strong, constant and uniform magnetic guide field. The consistency between the fluid and gyrofluid approaches is ensured when choosing ion closure relations prescribed by the underlying ordering. A two-field reduction of the gyrofluid model valid for arbitrary equilibrium temperature ratio is also introduced, and is shown to have a noncanonical Hamiltonian structure. This model provides a convenient framework for studying kinetic Alfven wave turbulence, from MHD to sub-$d_e$ scales (where $d_e$ holds for the electron skin depth). Magnetic energy spectra are phenomenologically determined within energy and generalized helicity cascades in the perpendicular spectral plane. Arguments based on absolute statistical equilibria are used to predict the direction of the transfers, pointing out that, within the sub-ion range associated with a $k_perp^{-7/3}$ transverse magnetic spectrum, the generalized helicity could display an inverse cascade if injected at small scales, for example by reconnection processes.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
