Role of magnetic field curvature in magnetohydrodynamic turbulence

Abstract

Magnetic field are transported and tangled by turbulence, even as they lose identity due to nonideal or resistive effects. On balance field lines undergo stretch-twist-fold processes. The curvature field, a scalar that measures the tangling of the magnetic field lines, is studied in detail here, in the context of magnetohydrodynamic turbulence. A central finding is that the magnitudes of the curvature and the magnetic field are anti-correlated. High curvature co-locates with low magnetic field, which gives rise to power-law tails of the probability density function of the curvature field.The curvature drift term that converts magnetic energy into flow and thermal energy, largely depends on the curvature field behavior, a relationship that helps to explain particle acceleration due to curvature drift. This adds as well to evidence that turbulent effects most likely play an essential role in particle energization since turbulence drives stronger tangled field configurations, and therefore curvature.

In Situ Measurement of Curvature of Magnetic Field in Turbulent Space Plasmas: A Statistical Study

“…The probability distribution function shown in figure 2, exhibits two distinct powerlaw regimes: at low values of the curvature field, its distribution scales as κ +1 , while at high curvature values the distribution behaves as κ −2.5 . This is remarkably similar to the empirical and theoretical findings of Yang et al (2019). To further clarify the statistics of the magnetic curvature, Figure 3 shows the joint distributions of curvature and squared magnetic field magnitude, and curvature and normal force.…”

“…Here, we extend this statistical examination of magnetic curvature by analysis of in situ satellite observations in the terrestrial magnetosheath. We employ Magnetospheric Multiscale (MMS) data that reveal distributions and correlations that are consistent with, and in fact very similar to, those observed in the MHD simulations (Yang et al, 2019). These results confirm the theoretical model given in Yang et al (2019), opening the door to new applications such as curvature drift acceleration in turbulence as well as the possible role of local explosive instabilities in turbulence.…”

“…In contrast, low curvature values mainly result from small normal force, more so than from large values of magnetic field. These findings point the way to explain the power-law tails in the curvature distribution in both the high value range, and the low value range, reasoning as follows (Yang et al, 2019).…”

“…Previously (Yang et al, 2019), the above reasoning was found to explain the behavior of the distributions of curvature in three dimensional, isotropic, MHD simulations. We now extend this inquiry to the case of a naturally occurring space plasma, the turbulent magnetosheath.…”

“…Recently, the curvature of magnetic field lines has been studied in the magnetohydrodynamic (MHD) model of plasma turbulence (Yang et al, 2019). In the case of turbulence, it is impractical to study curvature of individual field lines and one may resort to a statistical approach, as is typical in studies of turbulence (Monin & Yaglom, 1971).…”