A review is presented of the models of magnetic field line merging defined as the process whereby plasma flows across a surface which separates regions including topologically different magnetic field lines. The models examined are characterized by uniform and antiparallel external magnetic fields. An attempt is made to simplify the presentation of the models, to clarify some doubtful mathematical points, or to extend the results to a different range of physical parameters. The models are described from a hydromagnetic point of view, with the configuration in any given case being determined by the boundary conditions. It is shown that the models developed by Sweet (1958), Parker (1957, 1963), Petschek (1964), Sonnerup (1970), and by Yeh and Axford (1970) are basically consistent, describing different aspects of the same problem; however, there is not a single model that would account for all the cases considered. The singular models and the compressible similarity models are physically not feasible.

Theoretical models of magnetic field line merging

We give a systematic theoretical analysis of trapped nonadiabatic charged particle motion in two-dimensional taillike magnetic field reversals. Particle dynamics is shown to be controlled by the curvature parameter κ, i.e., the ratio κ² = Rmin/ρmax between the minimum radius of curvature of the magnetic field and the maximum Larmor radius in it for a particle of given energy. κ≫1 corresponds to the usual adiabatic case with the magnetic moment μ as a first-order invariant of motion. As κ decreases toward unity, the particle motion becomes stochastic due to deterministic chaos, caused by the overlapping of nonlinear resonances between the bounce- and the gyro-motion. We determine the threshold of deterministic chaos and derive the related pitch angle diffusion coefficient which describes statistically the particle behavior in the limit κ → 1. Such behavior, which for κ ≅ 1 becomes strongly chaotic, applies, e.g., to thermal electrons in Earth's magnetotail and makes its collisionless tearing mode instability possible. We also show that in sharply curved field reversals, i.e., for κ 1. Both types of trapped particle motion in sharply curved magnetic field reversals κ<1 are closely connected with fast oscillations perpendicular to the reversal plane. However, the trajectories are adiabatic only in the case that they permanently remain crossing the reversal plane. The adiabatic are of a ring type, i.e., they resemble rings in phase space and also in real physical space. For ring-type orbits the action integral over the fast oscillations is an adiabatic invariant in the usual sense. On the other hand, the most common particle trajectories in a sharply curved field reversal with κ<1 are essentially of a cucumberlike quasi-adiabatic type. For quasi-adiabatic cucumberlike orbits the action integral over the fast oscillations is an adiabatic invariant only in a piecemeal way between successive traversals in the phase space of the fast motion of a separatrix between orbits which do and those, which do not cross the reversal plane. Due to the effect of separatrix traversals the slow motion shifts between different cucumber orbits with a conservation of the action integral on average but with its chaotic phase space diffusion even for very small perturbation parameters κ. The case κ<1 is applicable, e.g., to thermal ions and high-energy electrons in Earth's magnetotail. Our findings lead to a systematic interpretation of particle observations in Earth's magnetotail and of numerous numerical calculations, carried out in the past. They also explain rather well, e.g., the pitch angle diffusion of plasma sheet particles, the isotropization of the plasma sheet electron distribution immediately before a substorm and provide with the transition to chaos a mechanism for the onset of a large-scale tail instability and the explosion of isolated substorms. Further implications for magnetotail physics, such as acceleration processes and the influence of the particle escape from the field reversal will be discussed in a second related paper.

Regular and chaotic charged particle motion in magnetotaillike field reversals: 1. Basic theory of trapped motion

When the supersonic solar wind reaches the neighborhood of a planetary obstacle it decelerates. The nature of this interaction can be very different, depending upon whether this obstacle has a large-scale planetary magnetic field and/or a well-developed atmosphere/ionosphere. For a number of years significant uncertainties have existed concerning the nature of the solar wind interaction at Mars, because of the lack of relevant plasma and field observations. However, measurements by the Phobos-2 and Mars Global Surveyor (MGS) spacecraft, with different instrument complements and orbital parameters, led to a significant improvement of our knowledge about the regions and boundaries surrounding Mars.

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The plasma Environment of Mars

The properties of charged-particle motion in Hamiltonian dynamics are studied in a magnetotaillike magnetic field configuration. It is shown by numerical integration of the equation of motion that the system is generally nonintegrable and that the particle motion can be classified into three distinct types of orbits: bounded integrable orbits, unbounded stochastic orbits, and unbounded transient orbits. It is also shown that different regions of the phase space exhibit qualitatively different responses to external influences. The concept of 'differential memory' in single-particle distributions is proposed. Physical implications for the dynamical properties of the magnetotail plasmas and the possible generation of non-Maxwellian features in the distribution functions are discussed.

J.W. Eastwood

Papers

Consistency of fields and particle motion in the ‘Speiser’ model of the current sheet