It has recently been proposed that the inertial interval in magnetohydrodynamic (MHD) turbulence is terminated at small scales not by a Kolmogorov-like dissipation region, but rather by a new ...sub-inertial interval mediated by tearing instability. However, many astrophysical plasmas are nearly collisionless so the MHD approximation is not applicable to turbulence at small scales. In this paper, we propose an extension of the theory of reconnection-mediated turbulence to plasmas which are so weakly collisional that the reconnection occurring in the turbulent eddies is caused by electron inertia rather than by resistivity. We find that the transition scale to reconnection-mediated turbulence depends on the plasma beta and on the assumptions of the plasma turbulence model. However, in all of the cases analyzed, the energy spectra in the reconnection-mediated interval range from to .
Magnetic field fluctuations in magnetohydrodynamic turbulence can be viewed as current sheets that are progressively more anisotropic at smaller scales. As suggested by Loureiro & Boldyrev and Mallet ...et al., below a certain critical thickness, , such current sheets become tearing-unstable. We propose that the tearing instability changes the effective alignment of the magnetic field lines in such a way as to balance the eddy turnover rate at all scales smaller than . As a result, turbulent fluctuations become progressively less anisotropic at smaller scales, with the alignment angle increasing as , where is the resistive dissipation scale. Here L0 is the outer scale of the turbulence, S0 is the corresponding Lundquist number, and is a parameter. The resulting Fourier energy spectrum is , where is the wavenumber normal to the local mean magnetic field, and the critical scale is . The simplest model corresponds to β = 0, in which case the predicted scaling formally agrees with one of the solutions obtained in Mallet et al. from a discrete hierarchical model of abruptly collapsing current sheets, an approach different from and complementary to ours. We also show that the reconnection-mediated interval is non-universal with respect to the dissipation mechanism. Hyper-resistivity of the form leads (in the simplest case of β = 0) to the different transition scale and the energy spectrum , where is the corresponding hyper-resistive Lundquist number.
Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential ...equations, the linearity of quantum mechanics has limited analogous progress for the nonlinear case. Despite this obstacle, we develop a quantum algorithm for dissipative quadratic n-dimensional ordinary differential equations. Assuming Formula: see text, where R is a parameter characterizing the ratio of the nonlinearity and forcing to the linear dissipation, this algorithm has complexity Formula: see text, where T is the evolution time, ϵ is the allowed error, and q measures decay of the solution. This is an exponential improvement over the best previous quantum algorithms, whose complexity is exponential in T. While exponential decay precludes efficiency, driven equations can avoid this issue despite the presence of dissipation. Our algorithm uses the method of Carleman linearization, for which we give a convergence theorem. This method maps a system of nonlinear differential equations to an infinite-dimensional system of linear differential equations, which we discretize, truncate, and solve using the forward Euler method and the quantum linear system algorithm. We also provide a lower bound on the worst-case complexity of quantum algorithms for general quadratic differential equations, showing that the problem is intractable for Formula: see text Finally, we discuss potential applications, showing that the Formula: see text condition can be satisfied in realistic epidemiological models and giving numerical evidence that the method may describe a model of fluid dynamics even for larger values of R.
ABSTRACT
We investigate the spectral properties of the electromagnetic fluctuations of sub-ion scale turbulence in weakly collisional, low-beta plasmas using a two-field isothermal gyrofluid model. ...The numerical results strongly support a description of the turbulence as a critically balanced Kolmogorov-like cascade of kinetic Alfvén wave fluctuations, as amended by previous studies to include intermittency effects. The measured universal index of the energy spectra from systems with different flux-unfreezing mechanisms excludes the role of tearing mediation in determining the spectra. The fluctuations remain isotropic in the plane perpendicular to the strong background magnetic fields as they cascade to smaller scales, which explains the absence of tearing mediation. The calculation of high-order, multipoint structure functions of magnetic fluctuations suggests that the intermittent structures have a quasi-2D, sheet-type morphology. These results are useful for explaining recent observations of the spectrum and structure of magnetic and density fluctuations in the solar wind at sub-proton scales, and are relevant for modelling the energy dissipation in a broad range of astrophysical systems.
ABSTRACT
It has been recently shown numerically that there exists an inverse transfer of magnetic energy in decaying, non-helical, magnetically dominated, magnetohydrodynamic turbulence in three ...dimensions (3D). We suggest that magnetic reconnection is the underlying physical mechanism responsible for this inverse transfer. In the two-dimensional (2D) case, the inverse transfer is easily inferred to be due to smaller magnetic islands merging to form larger ones via reconnection. We find that the scaling behaviour is similar between the 2D and 3D cases, i.e. the magnetic energy evolves as t−1, and the magnetic power spectrum follows a slope of k−2. We show that on normalizing time by the magnetic reconnection time-scale, the evolution curves of the magnetic field in systems with different Lundquist numbers collapse on to one another. Furthermore, transfer function plots show signatures of magnetic reconnection driving the inverse transfer. We also discuss the conserved quantities in the system and show that the behaviour of these quantities is similar between the 2D and 3D simulations, thus making the case that the dynamics in 3D could be approximately explained by what we understand in 2D. Lastly, we also conduct simulations where the magnetic field is subdominant to the flow. Here, too, we find an inverse transfer of magnetic energy in 3D. In these simulations, the magnetic energy evolves as t−1.4 and, interestingly, a dynamo effect is observed.
Electron heating in kinetic-Alfvén-wave turbulence Zhou, Muni; Liu, Zhuo; Loureiro, Nuno F
Proceedings of the National Academy of Sciences - PNAS,
2023-Jun-06, Letnik:
120, Številka:
23
Journal Article
Recenzirano
Odprti dostop
We report analytical and numerical investigations of subion-scale turbulence in low-beta plasmas using a rigorous reduced kinetic model. We show that efficient electron heating occurs and is ...primarily due to Landau damping of kinetic Alfvén waves, as opposed to Ohmic dissipation. This collisionless damping is facilitated by the local weakening of advective nonlinearities and the ensuing unimpeded phase mixing near intermittent current sheets, where free energy concentrates. The linearly damped energy of electromagnetic fluctuations at each scale explains the steepening of their energy spectrum with respect to a fluid model where such damping is excluded (i.e., a model that imposes an isothermal electron closure). The use of a Hermite polynomial representation to express the velocity-space dependence of the electron distribution function enables us to obtain an analytical, lowest-order solution for the Hermite moments of the distribution, which is borne out by numerical simulations.
Recently, it has been realized that magnetic plasma turbulence and magnetic field reconnection are inherently related phenomena. Turbulent fluctuations generate regions of sheared magnetic field that ...become unstable to the tearing instability and reconnection, thus modifying turbulence at the corresponding scales. In this contribution, we give a brief review of some recent results on tearing‐mediated magnetic turbulence. We illustrate the main ideas of this rapidly developing field of study by concentrating on two important examples—magnetohydrodynamic Alfvén turbulence and small‐scale kinetic‐Alfvén turbulence. Due to various potential applications of these phenomena in space physics and astrophysics, we specifically try not to overload the text by heavy analytical derivations but rather present a qualitative discussion accessible to a non‐expert in the theories of turbulence and reconnection.
Key Points
Magnetic turbulence and magnetic reconnection are inherently related phenomena
Tearing instability modifies energy cascades in both magnetohydrodynamic and kinetic plasma turbulence
Conservation laws play an important role in governing tearing instability effects in magnetic turbulence
Turbulence in Magnetized Pair Plasmas Loureiro, Nuno F.; Boldyrev, Stanislav
Astrophysical journal. Letters,
10/2018, Letnik:
866, Številka:
1
Journal Article
Recenzirano
Odprti dostop
Alfvénic-type turbulence in strongly magnetized, low-beta pair plasmas is investigated. A coupled set of equations for the evolution of the magnetic and flow potentials are derived, covering both ...fluid and kinetic scales. In the fluid (magnetohydrodynamic) range those equations are the same as for electron-ion plasmas, so turbulence at those scales is expected to be of the Alfvénic nature, exhibiting critical balance, dynamic alignment, and transition to a tearing-mediated regime at small scales. The critical scale at which a transition to a tearing-mediated range occurs is derived, and the spectral slope in that range is predicted to be (or , depending on details of the reconnecting configuration assumed). At scales below the electron (and positron) skin depth, it is argued that turbulence is dictated by a cascade of the inertial Alfvén wave, which we show to result in the magnetic energy spectrum .
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