Role of reconnection in inertial kinetic-Alfvén turbulence

Abstract

In a weakly collisional, low-electron-beta plasma, large-scale Alfvén turbulence transforms into inertial kinetic-Alfvén turbulence at scales smaller than the ion microscale (gyroscale or inertial scale). We propose that at such kinetic scales, the nonlinear dynamics tends to organize turbulent eddies into thin current sheets, consistent with the existence of two conserved integrals of the ideal equations, energy and helicity. The formation of strongly anisotropic structures is arrested by the tearing instability that sets a critical aspect ratio of the eddies at each scale a in the plane perpendicular to the guide field. This aspect ratio is defined by the balance of the eddy turnover rate and the tearing rate, and varies from (de/a) 1/2 to de/a depending on the assumed profile of the current sheets. The energy spectrum of the resulting turbulence varies from k −8/3 to k −3 , and the corresponding spectral anisotropy with respect to the strong background magnetic field from kz k 2/3 ⊥ to kz k ⊥ .PACS numbers: 52.35. Ra, 52.35.Vd, 52.30.Cv Introduction. Large-scale low-frequency fluctuations in astrophysical systems such as the interstellar medium, the solar wind, and others, are associated with nearly incompressible magnetohydrodynamic (Alfvén) turbulence [e.g., 1-3]. The nonlinear Alfvén wave packets that compose such turbulence are three-dimensionally anisotropic: elongated along the strong background magnetic field and resembling current sheets in the perpendicular plane [1,[4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. At scales smaller than the plasma microscales, such as the ion gyroscale or ion inertial scale, the shear-Alfvén modes transform into kinetic Alfvén modes. The character of turbulence then changes qualitatively. Numerical and analytical studies suggest that the energy spectrum becomes relatively steep in the sub-proton range, with the spectral index between −7/3 and −8/3, and fluctuations become compressible, with density and magnetic field fluctuations comparable to each other [e.g., 22-27]. Available solar wind measurements broadly agree with these predictions, with the measured energy spectral slope scattered around a slightly steeper value −2.8 [28][29][30][31][32].

The onset of electron-only reconnection

“…They then argue that this means that the turbulence favours the creation of highly sheet-like structures, but that this is limited by the tearing instability, which then sets a particular critical aspect ratio (as does our analysis). Despite the overall similarity of the results, there are some important differences in the two pictures: in ours, the nonlinear interaction actively produces increasingly sheet-like structures, while in Boldyrev & Loureiro (2019), its role is to rapidly remove non-sheet-like structures. Our method has the advantage that it also works for sheets thicker than the ion scales, and we can therefore predict when one expects to see electron-only versus ion-coupled reconnection, depending on the characteristic aspect ratios of sheets as a function of their thickness.…”

“…In turbulence models that include the phenomenon of dynamic alignment (Boldyrev 2006;Chandran et al 2015;Mallet & Schekochihin 2017), the turbulent structures at scale λ are sheet like in the perpendicular plane, with aspect ratios ∝ (λ/L ⊥ ) −1/4 , where L ⊥ is the outer scale at which energy is injected into the system. Thus, for electron-only reconnection to be observed in turbulence, energy must be injected relatively close to the ion scales: in the magnetosheath, this injection could potentially come in the form of Alfvén vortices (Alexandrova 2008), perhaps driven by density gradients (Sundkvist & Bale 2008).…”

“…We should also mention here that Boldyrev & Loureiro (2019) have used a set of fluid equations derived for k ⊥ ρ i 1, β i ∼ 1, β e 1 to study the small-scale tearing instability and its effect on turbulence, obtaining some results similar to ours (which is an additional source of reassurance that our low-β i ordering does not invalidate the basic picture of tearing-induced reconnection onset): we have used KREHM instead because, first, we want a set of equations covering the ion-scale transition at k ⊥ ρ i ∼ 1 to describe the transition between the ion-coupled and electron-only reconnection regimes, and second, the electron heating channel as encoded by (2.3) is important for a realistic picture of reconnection.…”

Constraints on ion versus electron heating by plasma turbulence at low beta

“…The scalings for a critically balanced ICW cascade are perhaps less well established, but also known, in the guise of the scalings for rotating hydrodynamic turbulence (Nazarenko & Schekochihin 2011). Assuming constant energy flux ε ICW and using the first equation in (5.37), we find the Kolmogorov scaling (which is no surprise, the 18 Various theoretical considerations (Boldyrev & Perez 2012;Boldyrev et al 2013;Meyrand & Galtier 2013;Loureiro & Boldyrev 2017;Boldyrev & Loureiro 2019), prompted by observational evidence (Alexandrova et al 2009;Sahraoui et al 2010;Chen 2016), suggest that these "naïve" scalings may need some subtle corrections. We shall opt for simplicity over modernity and ignore those subtleties.…”

“…While Φ is still the stream function for the E × B velocity, this is now the velocity of the electron flow (ions are much slower because of gyroaveraging). These equations describe what is sometimes referred to as the turbulence of Kinetic Alfvén Waves (KAW)-although, like the Alfvénic (RMHD) turbulence in the inertial range, it is expected to be strong and critically balanced and so does not literally consist of waves (see S09- §7.5 and Cho & Lazarian 2004Boldyrev & Perez 2012;TenBarge et al 2013;Boldyrev & Loureiro 2019). If we consider cold ions, Z/τ ≫ 1 (but not so cold as to break β e ≪ 1), there is an intermediate regime with…”