Kolmogorov dissipation scales in weakly ionized plasmas

Abstract

In a weakly ionized plasma, the evolution of the magnetic field is described by a 'generalized Ohm's law' that includes the Hall effect and the ambipolar diffusion terms. These terms introduce additional spatial and time-scales which play a decisive role in the cascading and the dissipation mechanisms in magnetohydrodynamic turbulence. We determine the Kolmogorov dissipation scales for the viscous, the resistive and the ambipolar dissipation mechanisms. The plasma, depending on its properties and the energy injection rate, may preferentially select one of these dissipation scales, thus determining the shortest spatial scale of the supposedly self-similar spectral distribution of the magnetic field. The results are illustrated taking the partially ionized part of the solar atmosphere as an example. Thus, the shortest spatial scale of the supposedly self-similar spectral distribution of the solar magnetic field is determined by any of the four dissipation scales given by the viscosity, the Spitzer resistivity (electron-ion collisions), the resistivity due to electron-neutral collisions and the ambipolar diffusivity. It is found that the ambipolar diffusion dominates for reasonably large energy injection rate. The robustness of the magnetic helicity in the partially ionized solar atmosphere would facilitate the formation of self-organized vortical structures.

Beltrami structures in disk-jet system: alignment of flow and generalized vorticity

“…The Hall effect (scaled by ǫ) or the viscosity/resistivity (scaled by reciprocal Reynolds number) yields a singular perturbation (then, the generalized magneto-Bernoulli mechanism [33,34] may effectively accelerate the jet-flow). In a weakly ionized plasma, the electron equation ( 2) is modified so that the Hall effect is magnified by the ratio of the neutral and electron densities; the ambipoler diffusion effect also yields a higherorder perturbation [24]. The mechanism of singular perturbation and the local structure of the disk-jet connection point may differ depending on the plasma condition near the central object: in AGN, the plasma is fully ionized but rather collisional (we also need a relativistic equation of state with possible presence of pairs), and, in YSO, the plasma is partially ionized; the relevant dissipation mechanisms determine the scale hierarchy in the vicinity of the singularity.…”

Sweet–Parker current slab in a partially ionized plasma

“…To what do the Hall and the ambipolar terms contribute, to the inductive or the resistive parts of the electric field? This question can be answered by finding the rate of dissipation of the total energy, as recently discussed by Krishan & Yoshida (2009), who show that where is the total energy and ε A and ε η are the dimensionless coefficients of the ambipolar and the resistive dissipation, with L 0 and V 0 the normalizing parameters and ω ci is the ion cyclotron frequency. This exercise shows that the ambipolar diffusion is a dissipation mechanism and the Hall effect is not.…”

“…We can now contrast these cases with the physical conditions of the solar atmosphere. First, the condition of a weakly ionized plasma, ν en ≫ν ei , is satisfied in the solar atmosphere up to a height of nearly 800 km above the photosphere (Krishan & Varghese 2008; Krishan & Yoshida 2009). Thus even the Sweet–Parker rate, in the absence of the Hall and the ambipolar effects, with electron–neutral collisions dominating the electron–ion collisions, is enhanced by, for example, two orders of magnitude at a height of 560 km in the solar atmosphere (Singh & Krishan 2009) in comparison to the value obtained by Vishniac & Lazarian (1999).…”