The properties of fast and slow oblique solitons in a magnetized plasma

Abstract

This work builds on a recent treatment by McKenzie and Doyle [Phys. Plasmas 8, 4367 (2001)], on oblique solitons in a cold magnetized plasma, to include the effects of plasma thermal pressure. Conservation of total momentum in the direction of wave propagation immediately shows that if the flow is supersonic, compressive (rarefactive) changes in the magnetic pressure induce decelerations (accelerations) in the flow speed, whereas if the flow is subsonic, compressive (rarefactive) changes in the magnetic pressure induce accelerations (decelerations) in the flow speed. Such behavior is characteristic of a Bernoulli-type plasma momentum flux which exhibits a minimum at the plasma sonic point. The plasma energy flux (kinetic plus enthalpy) also shows similar Bernoulli-type behavior. This transonic effect is manifest in the spatial structure equation for the flow speed (in the direction of propagation) which shows that soliton structures may exist if the wave speed lies either (i) in the range between the fast and Alfven speeds or (ii) between the sound and slow mode speed. These conditions follow from the requirement that a defined, characteristic “soliton parameter” m exceeds unity. It is in this latter slow soliton regime that the effects of plasma pressure are most keenly felt. The equilibrium points of the structure equation define the center of the wave. The structure of both fast and slow solitons is elucidated through the properties of the energy integral function of the structure equation. In particular, the slow soliton, which owes its existence to plasma pressure, may have either a compressive or rarefactive nature, and exhibits a rich structure, which is revealed through the spatial structure of the longitudinal speed and its corresponding transverse velocity hodograph.

Kinetic slow mode-type solitons

“…It is seen from this figure that for large propagation angles the slow mode soliton velocity may vary between the speeds c slow of the slow magnetosonic wave and c I =v A cos θ (v A Alfven velocity) of the intermediate wave, both in the k=0 limit. It should be pointed out here that McKenzie and Doyle (2002) erroneously calculated the extended interval c slow <V <c s as constraint for the velocity of slow mode solitons. With respect to polarization, the soliton exhibits elements of both the slow magnetosonic and the intermediate wave.…”

“…In order to examine solitary solutions of the Hall-MHD equations one may proceed in two distinct ways. A rather direct way uses the stationary wave approximation of the basic system (all variables depend only on x−V t), from which solitary waves can be isolated with the help of the fixed-pointanalysis (Hau and Sonnerup, 1991;Baumgärtel et al, 1997;McKenzie and Doyle, 2002). An alternative method derives first an evolution equation from the superior system, containing nonlinearity and dispersion only to lowest order, and tries to apply inverse scattering theory in order to find 'genuine' solitons.…”

Nonlinear model for magnetosonic shocklets in plasmas

“…Observations reveal that SM solitons [6] are associated with large amplitude compressional (rarefactional) magnetic field (plasma density) variations. On the other hand, FMS shocklets are accompanied with compression of the plasma density and magnetic field perturbations.…”

Finite Larmor radius influence on MHD solitary waves

“…Focus has been on extending the Hall-MHD model (McKenzie and Doyle, 2002) with dispersive effects of thermal origin. Such effects are embodied in the finite Larmor radius extension to the pressure tensor (MacMahon, 1965;Yajima, 1966).…”

“…MHD solitons, i.e., stationary localized travelling structures theoretically derived from MHD models extended with terms introducing dispersion, have recently received some attention (Baumgärtel, 1999;McKenzie and Doyle, 2002;Stasiewicz et al, 2003;Stasiewicz, 2004;Mjølhus, 2006;Baumgärtel et al, 2007). Reasons for this are space observations that have recently been interpreted this way (Baumgärtel, 1999;Stasiewicz et al, 2003;Stasiewicz, 2004).…”