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Register a new userInverse cascade and magnetic vortices in kinetic Alfven-wave turbulence
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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.
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Understanding the nature of the turbulent fluctuations below the ion gyroradius in solar-wind turbulence is a great challenge. Recent studies have been mostly in favor of kinetic Alfven wave (KAW) type of fluctuations, but other kinds of fluctuations with characteristics typical of magnetosonic, whistler and ion Bernstein modes, could also play a role depending on the plasma parameters. Here we investigate the properties of the sub-proton-scale cascade with high-resolution hybrid-kinetic simulations of freely-decaying turbulence in 3D3V phase space, including electron inertia effects. Two proton plasma beta are explored: the intermediate $beta_p=1$ and low $beta_p=0.2$ regimes, both typically observed in solar wind and corona. The magnetic energy spectum exhibits $k_perp^{-8/3}$ and $k_|^{-7/2}$ power laws at $beta_p=1$, while they are slightly steeper at $beta_p=0.2$. Nevertheless, both regimes develop a spectral anisotropy consistent with $k_|sim k_perp^{2/3}$ at $k_perprho_p>1$, and pronounced small-scale intermittency. In this context, we find that the kinetic-scale cascade is dominated by KAW-like fluctuations at $beta_p=1$, whereas the low-$beta$ case presents a more complex scenario suggesting the simultaneous presence of different types of fluctuations. In both regimes, however, a non-negligible role of ion Bernstein type of fluctuations at the smallest scales seems to emerge.
We show that oppositely directed fluxes of energy and magnetic helicity coexist in the inertial range in fully developed magnetohydrodynamic (MHD) turbulence with small-scale sources of magnetic helicity. Using a helical shell model of MHD turbulence, we study the high Reynolds number magnetohydrodynamic turbulence for helicity injection at a scale that is much smaller than the scale of energy injection. In a short range of scales larger than the forcing scale of magnetic helicity, a bottleneck-like effect appears, which results in a local reduction of the spectral slope. The slope changes in a domain with a high level of relative magnetic helicity, which determines that part of the magnetic energy related to the helical modes at a given scale. If the relative helicity approaches unity, the spectral slope tends to $-3/2$. We show that this energy pileup is caused by an inverse cascade of magnetic energy associated with the magnetic helicity. This negative energy flux is the contribution of the pure magnetic-to-magnetic energy transfer, which vanishes in the non-helical limit. In the context of astrophysical dynamos, our results indicate that a large-scale dynamo can be affected by the magnetic helicity generated at small scales. The kinetic helicity, in particular, is not involved in the process at all. An interesting finding is that an inverse cascade of magnetic energy can be provided by a small-scale source of magnetic helicity fluctuations without a mean injection of magnetic helicity.
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.
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 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 cascade in the energetically relevant part of the wave-number space essentially fluid-like. The velocity-space spectra of free energy expressed in terms of Hermite-moment orders are steep power laws and so the free-energy content of the phase space does not diverge at infinitesimal collisionality (while it does for a linear problem); collisional heating due to long-wavelength perturbations vanishes in this limit (also in contrast with the linear problem, in which it occurs at the finite rate equal to the Landau-damping rate). The ability of the free energy to stay in the low velocity moments of the distribution function is facilitated by the anti-phase-mixing effect, whose presence in the nonlinear system is due to the stochastic version of the plasma echo (the advecting velocity couples the phase-mixing and anti-phase-mixing perturbations). The partitioning of the wave-number space between the (energetically dominant) region where this is the case and the region where linear phase mixing wins its competition with nonlinear advection is governed by the critical balance between linear and nonlinear timescales (which for high Hermite moments splits into two thresholds, one demarcating the wave-number region where phase mixing predominates, the other where plasma echo does).
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