Magnetized vortex tubes in the solar wind plasma

Abstract

We make new applications of our previously proposed method for estimating the strainrate tensor and vorticity vector in plasmas (concerning the local deformation and self rotation of the plasma fluid elements, respectively) solely from magnetic field time series. Here we use solar wind measurements of Ulysses spacecraft made in the outer heliosphere, on and off the ecliptic plane, during the period 1990-1998. The application results imply that the solar wind plasma is, to a good approximation, weakly incompressible, being nearly incompressible on the local magnetic field-normal plane, while expanding at maximum strain rate in the magnetic field direction. This property is theoretically expected, at least for low and intermediate beta plasmas, and supports previous arguments for two-dimensional MHD turbulence in the solar wind. In the magnetic induction equation the vorticity term is favoured, being at least an order of magnitude larger than the strain-rate term, thus explaining the magnetic field alignment of the minimum magnetic field variance and the random wandering of the magnetic field's vector tip on a sphere, both being well known, general features of the heliospheric magnetic field fluctuations. Further, the solar wind is found dominated by magnetized vortex sheet structures (MVS), on the tangential plane of which lie the, (not generally aligned) average vectors of magnetic field, vorticity and plasma velocity in the solar-corotating frame of reference. These coplanarity properties are shown to be consistent with a theoretically predicted force-free state, minimizing the total energy while conserving a generalized helicity function. The theory additionally implies that the (not directly measured by Ulysses) electric current density also lies on the MVS tangential plane, hence the MVS also constitute current sheets. The MVS spatial orientation implies that the MVS are wrapped in the form of magnetized vortex tubes with axes aligned to the average magnetic field. The vector couplings, characterizing the MVS, are found to weaken with increasing heliodistance and near the heliospheric current sheet.

A review of magneto-vorticity induction in Hall-MHD plasmas

“…Strauss 1976, Montgomery and Turner 1981, Montgomery 1982, Morrison and Hazeltine 1984, Zank and Matthaeus 1992, Zank and Matthaeus 1993, Bhattacharjee et al 1998. Also, we recently verified, using Ulysses spacecraft magnetic field measurements, that the solar wind plasma is well approximated as being weakly incompressible in the magnetic field normal plane and, additionally, one of the strain-rate tensor eigenvectors is nearly aligned to the local magnetic field, possibly because the magnetic field itself deforms the plasma volume (Polygiannakis and Moussas 1996. As a result, the term (D − (∇ • V )I) • B in the magnetic field induction equation is small compared to the 1 2 ξ × B. Generalizing for any solenoidal field b ideally inducted in a weakly incompressible flow, if…”

“…with db/dt = ∂b/∂t +(V •∇)b being the field time derivative in the local coordinate system comoving with the lines of flow (often called the Lagrangian, material or substantial derivative). Furthermore, splitting the Jacobian tensor ∇V into symmetric and antisymmetric parts, (1) is equivalently written as (Polygiannakis and Moussas 1996 db dt…”

“…If, in addition, one of the (mutually normal) eigenvectors of the strain-rate tensor, D, is parallel to the strong uniform component on the z-axis (as with the magnetic field in plasmas, see e.g. Polygiannakis andMoussas 1999, 2000), then (86) implies that…”

“…However, the magnetic field and vorticity seem to play a complementary role in plasma dynamics, rather than being simply proportional. The magnetic field and vorticity, as derived from the, highly turbulent, solar wind measurements, were not found to be aligned (Polygiannakis and Moussas 1996) but instead both were tangential on tubular flow sheets (Polygiannakis and Moussas 2000). Also, the expulsion of a large-scale magnetic field at flow regions of strong vorticity was reported in a liquid gallium experiment (Odier et al 2000).…”

Model for vortex turbulence with discontinuities in the solar wind

“…It was shown that presence of long-lived organized coherent vortices plays an important role in two-dimensional plasma dynamics. These 2D vortex structures are quite common in space plasmas and were observed in ionosphere (so-called black aurora) (Johnson and Chang, 1995), solar wind (Polygiannakis and Moussas, 2000), the Earth distant magnetotail (Hones et al, 1978) and plasma sheet (Verkhoglyadova et al, 2001). It should be noted that vortex structures were extensively studied in the ionosphere and the magnetosphere of the Earth.…”