Stretched Field Lines Research Articles

A study of weak anisotropy in electron pressure in the tail current sheet

We adopt a magnetotail model with stretched field lines where ion motions are generally nonadiabatic and where it is assumed that the pressure anisotropy resides only in the electron pressure tensor. We show that the magnetic field lines with p⊥ > p∥ are less stretched than the corresponding field lines in the isotropic model. For p∥ > p⊥, the magnetic field lines become more and more stretched as the anisotropy approaches the marginal firehose limit, p∥ = p⊥+B²/μ0. We also show that the tail current density is highly enhanced at the firehose limit, a situation that might be subject to a microscopic instability. However, we emphasize that the enhancement in the current density is notable only near the center of the tail current sheet (z = 0). Thus it remains unclear whether any microscopic instability can significantly alter the global magnetic field configuration of the tail. By comparing the radius of the field‐line curvature at z = 0 with the particle's gyroradius, we suspect that even the conventional adiabatic description of electrons may become questionable very close to the marginal firehose limit.

Loss of MHD equilibrium caused by the enhancement of the magnetic By component in Earth's magnetotail

The purpose of this paper is to propose that an enhancement of the magnetic By component in Earth's magnetotail might lead to the disruption of the near‐Earth cross‐tail currents and thus to the onset of a magnetospheric substorm. We show, within the context of two‐dimensional MHD equilibrium theory, that the magnetic field energy density, By²/2μo, acts as an additional pressure in the tail plasma sheet that is able to shear magnetotail field lines and, thus, to reduce the normal magnetic field component in the equatorial plane, Bze, perpendicular to the tail current sheet. We solve the Grad‐Shafranov equation for two‐dimensional (∂/∂y = 0) magnetospheric MHD equilibria with a nonzero By component. We compute sequences of quasi‐static equilibria by increasing either |By(A)| or the thermal plasma pressure p(A) in a magnetosphere including the Earth's dipolar field. As a result, the magnetosphere can change from a more “dipolar” tail structure to a tail configuration with highly sheared and/or stretched field lines. Furthermore, increasing By beyond critical values may lead to catastrophic configurations in the near‐Earth plasma sheet whereby the equatorial component, Bze, exhibits a minimum or becomes zero. Such magnetic field configurations can also be achieved by an enhancement of the plasma pressure via the process of adiabatic sunward magnetotail convection. Loss of MHD equilibrium occurs when a quasi‐static magnetic field sequence reaches a critical configuration beyond which no acceptable equilibrium solution exists. Such a senario, as a result of an enhanced (toroidal) shear magnetic field, By, has been proposed as a possible mechanism for driving solar flares or prominence eruptions.

A slingshot model for solar flares

Recent observations of intense, impulsive gamma-ray and X-ray-emitting solar flares underline the suddenness of these events. The simultaneous emission of X-rays greater than 40 keV from electron bremsstrahlung and gamma-rays requiring several MeV protons shows that all particles must be accelerated in less than 5 s. This paper proposes a simple model to explain such events, using the energy stored in the stretched field lines of a coronal arch. When reconnection occurs at the top of the arch, field lines retract like stretched rubber bands, sweeping up plasma and acting like a piston or slingshot. When the slug of plasma caught in the magnetic fields strikes the photosphere, it deposits its considerable kinetic energy, heating and compressing the intruding slug. Ten slugs of 100 km radius striking the photosphere may account for the 10 to the 29th ergs radiation from loop flares.

Quasi‐static magnetospheric MHD processes and the “ground state” of the magnetosphere

From the viewpoint of magnetic equilibrium and convection theories, we discuss whether there exists a theoretically well‐defined ground state of the Earth's magnetosphere. As a basis for this discussion, we review the quasi‐static MHD theory and show in a two‐dimensional (2‐D) model that the convecting magnetosphere can (mathematically) reach a steady state. The steady state configuration has fairly stretched magnetotail field lines and is, therefore, likely to be unstable to the tearing mode instability which ultimately leads to substorm onset in magnetotail regions with stretched field lines. We present an interpretation of the substorm phenomenon in terms of sequences of quasi‐static MHD equilibrium states and argue that, under the influence of convection, magnetic substorms occur periodically in Earth's magnetosphere, thus being an integral part of the entire convection cycle. After explosively releasing plasma and magnetic field energies in a substorm, the magnetosphere starts the convection process again from a low‐energy state. In addition to “smooth” tail field configurations, there exist oscillatory equilibrium tail structures with lower potential energy.We discuss the concept of the ground state of the magnetosphere within the context of 2‐D quasi‐static MHD models for the near‐Earth magnetosphere. However, we are unable to find a definition of a single magnetospheric ground state that is conceptually simple and computationally feasible. The term “ground state” denotes the lowest energy state of a system, which for a magnetosphere in quasi‐static force equilibrium is the empty vacuum magnetic field configuration with zero thermal plasma pressure. The real magnetosphere never approaches that state. Therefore we propose the term “average magnetosphere” for defining a baseline configuration that corresponds to average solar wind conditions. Earth's magnetosphere is convectively driven and powered by the solar wind. Thus all potential energy states W = ∫ [P/(γ − 1) + B²/2µ0] dV that belong to a particular convection time sequence between substorm events are transient in time. Therefore the newly defined “average magnetosphere” has a potential energy 〈W − Wvacuum〉 representing the time average of equilibrium states over the substorm cycle. Thus a “quiet” magnetosphere would have a net potential energy lower than the average, whereas an “active” magnetosphere would have a higher energy. It is an unresolved theoretical problem, however, to determine the lowest and highest possible energy states for the magnetosphere that are compatible with the thermodynamic condition of quasi‐static convection.Three‐dimensional (3‐D) magnetospheric equilibria have not been computed yet, but we describe our experience with Stern's stretch transformations and a magnetofrictional method for calculating 3‐D magnetospheric MHD equilibria.

Open and closed magnetospheric tail configurations and their stability

The asymptotic theory valid for magnetospheric tail configurations that vary only weakly in the antisolar direction is used to derive a number of explicit properties. The conditions under which the magnetopause converges to form a closed magnetosphere or diverges (open magnetosphere) are identified and discussed. It is shown that the presence of the high latitude low pressure tail lobes guarantees the open solution. The large value of the Mach-number of the unperturbed solar wind is the reason for the slow variation of the plasma and field quantities along the tail. Criteria for (two-dimensional) stability are discussed and it is shown that they can be expressed in terms of simple topological properties of the equilibria. Closed magnetopheres turn out to be stable, open magnetospheres with sufficiently stretched field lines are subject to an instability which — as shown earlier —may be the cause of magnetospheric substorms.