ALBERT

Notes: 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. © 2002 American Institute of Physics.

Notes: The properties of fully nonlinear ion-acoustic solitons are investigated by interpreting conservation of total momentum as the structure equation for the proton flow in the wave. In most studies momentum conservation is regarded as the first integral of the Poisson equation for the electric potential and is interpreted as being analogous to a particle moving in a pseudo-potential well. By adopting an essentially gas-dynamic viewpoint, which emphasizes momentum conservation and the properties of the Bernoulli-type energy equations, the crucial role played by the proton sonic point becomes apparent. The relationship (implied by energy conservation) between the electron and proton speeds in the transition yields a locus—the hodograph of the system–which shows that, in the first half of the soliton, the electrons initially lag behind the protons until the charge neutral point is reached, after which they run ahead of the protons. The system reaches an equilibrium point (the center of the soliton) before the proton flow goes sonic. It follows that the critical ion-acoustic Mach number, Mc, above which smooth, continuous solitons cannot be constructed, stems from the requirement that the two equilibrium points of the structure equation coalesce at the proton sonic point of the flow. In general the range of the ion-acoustic Mach numbers, Mep, in which solitons exist, is extended beyond the classical range 1〈Mep〈1.6. In the special case of cold protons and hot electrons with an adiabatic index 2, the structure equation may be integrated in closed form. This analytic solution describes the fully nonlinear counterpart to the sech2 shaped pulses characteristic of weakly nonlinear waves and shows that solitons exist only if 1〈Mep〈2. The corresponding maximum potential, associated with the critical ion-acoustic Mach number, can be between 1.3kTe and 10kTe depending upon the values of the adiabatic indices of the electrons and protons and the proton Mach number. © 2002 American Institute of Physics.

Notes: A fully nonlinear theory for stationary waves, propagating obliquely to the ambient magnetic field in a cold plasma, has been developed. Soliton solutions, representing both compressions and rarefactions in the magnetic field, exist for sub-fast flow conditions and in certain cones of magnetic obliquity. The soliton is explicitly characterized, in terms of the wave speed and its obliquity, by a parameter m (the "soliton number"). Compressive ("bright") solitons are found to have a maximum attainable compression amplitude of three, corresponding to the condition m=1. Rarefactive ("dark") solitons attain complete rarefaction when m=4. The properties of these stationary waves are described both in terms of magnetic hodographs, and of a spatial structure equation, whose equilibrium points yield the maximum compression and rarefaction at the center of the waves. An analytic solution, in terms of elementary transcendental functions, is also presented and highlights the role played by the soliton number m in determining the speed, strength and width of the solitons. © 2001 American Institute of Physics.

Notes: The nonlinear coupling between inertial and Rossby waves is considered accounting for the action of the low-frequency nonlinear force associated with the inertial waves. It is found that this interaction is governed by a pair of equations, which can be useful for studying the modulational instability of a constant amplitude inertial wave as well as the dynamics of nonlinearly coupled inertial and Rossby waves. © 1995 American Institute of Physics.

Notes: [Auszug] The (nonradial) flow of a minor ion species in a purely radial background solar wind containing a spiral interplanetary magnetic field is governed by the equation4: HA2"! jn J +F l_dp p dr Am (D where u and w are respectively the radial and azimuthal velocity components, H is the angular ...

Notes: Abstract This paper provides a comprehensive analysis of the dynamics of the flow of minor ion species in the solar wind under the combined influences of gravity, Coulomb friction (with protons), rotational forces (arising from the Sun's rotation and the interplanetary spiral magnetic field) and wave forces (induced in the minor ion flow by Alfvén waves propagating in the solar wind). It is assumed that the solar wind can be considered as a proton-electron plasma which is, to a first approximation, unaffected by the presence of minor ions. In the dense hot region near the Sun Coulomb friction accelerates minor ions outwards against the gravitational force, part of which is cancelled by the charge-separation electric field. Once the initial acceleration has been achieved, wave and rotational forces assist Coulomb friction in further increasing the minor ion speed so that it becomes comparable with, or perhaps even exceeds, the solar wind speed. A characteristic feature of the non-resonant wave force is that it tends to bring the minor ion flow into an equilibrium where the radial speed matches the Alfvén speed relative to the solar wind speed, whereas Coulomb friction and rotational forces tend to bring the flow into an equilibrium where the radial speed of the minor ions equals the solar wind speed. Therefore, provided that there is sufficient wave energy and Coulomb friction is weak, the minor ion speed can be ‘trapped’ between these two speeds. This inteststing result is in qualitative agreement with observational findings to the effect that the differential flow speed between helium ions and protons is controlled by the ratio of the solar wind expansion time to the ion-proton collision time. If the thermal speeds of the protons and minor ions are small compared to the Alfvén speed, two stable equilibrium speeds can exist because the rapid decrease in the Coulomb cross-section with increasing differential flow speed allows the non-resonant wave force to balance Coulomb friction at more than one ion speed. However, it must be emphasized that resonant wave acceleration and/or strong ion partial pressure gradients are required to achieve radial speeds of minor ions in excess of the proton speed, since, as is shown in Section 4, the non-resonant wave acceleration on protons and minor ions are identical when their radial speeds are the same, with the result that, in the solar wind, non-resonant wave acceleration tends (asymptotically) to equalize minor ion and proton speeds.

Notes: Abstract The properties of ‘discontinuous’ transitions in a current-carrying plasma are analyzed by formulating the problem in terms of the two-fluid (i.e., electrons and ions) equations. The jump conditions, which connect states on either side of a discontinuity, are derived and it is shown that these are similar to the ordinary gas-dynamic Rankine-Hugoniot conditions except that there are extra terms which represent an enhanced mass flux in the momentum equation, and an additional heat, flux in the energy equation, both of which arise from the existence of a current flow through the discontinuity. the additional heat flux, which is due to collisions between electrons and ions and is carried by the electrons, plays a role analogous to the heat of reaction in the theory of combustion waves and gives rise to Hugoniots (i.e., curves in the pressure-specific volume plane representing the locus of states satisfying conservation of total plasma energy) which may be either ‘exothermic’ or ‘endothermic’ in character. Thus the classification of the various types of discontinuities, permitted by the jump relations, adopted here follows the classical description of detonation and deflagration waves and is based on the nature of the flow (i.e., whether the flow is ‘subsonic’ or ‘supersonic’) ahead of and behind the discontinuity. In an artificial way we show that the effects of reflected particles on such discontinuities can be to alter the nature of the discontinuity. For example in the special case of adiabatic transitions only ‘weak’ transitions are permitted in the absence of reflected particles, whereas in their presence all types (weak and strong) are possible. The end states permitted by the jump conditions must be joined together by a valid internal structure which can be obtained only by solving the full equations of motion. These are set up and we ask what extra conditions must be fulfilled by a transition characterized by a monotonic change in potential going from zero at one end to a constant value at the other, assuming that the plasma is charge neutral outside the transition region. In the case of adiabatic transitions one extra condition is imposed and this turns out to be a generalization of Block's (1972) self-consistency condition for double layers (which in its turn is an extension of Bohm's condition for the existence of wall sheaths). However the inclusion of dissipative effects indicates that adiabatic transitions are degenerate since the inclusion of dissipation shows that no extra conditions are imposed by requirements stemming from considerations of the self-consistency of the internal structure. As an example of how such discontinuities may be fitted into flow problems, we examine the construction of discontinuous periodic solutions for streaming ions and electrons. allowing for collisions with a background neutral gas. The idea here is borrowed from the phenomenon of ‘roll waves’, which occur in water flow along an inclined channel including frictional effects, and consist of a series of hydraulic jumps (or ‘bores’) separated by stretches of smooth flow.

Notes: Abstract This paper extends some previous work on the acceleration of minor ions in the solar wind to include the effects of wave acceleration and heating arising from minor ions interacting via the gyroresonance with ion cyclotron waves. Resonant wave acceleration is made up of two contributions, the first, and generally the more important, is a ‘local’ acceleration which is proportional to the wave power and the number of resonant particles and is also sensitive to the details of the distribution function; while the other contribution is basically ‘fluid dynamic’ in character, arises from the inhomogeneity of the medium and is proportional to the radial gradient of the resonant wave power. Under suitable cir-cumstances both contributions exhibit the feature that heavier ions receive greater acceleration than lighter ones. Also the kinematics of the resonance shows that the resonance wave acceleration switches off above a maximum differential speed, between ions and protons, which increases with increasing ratio of mass to charge. We also examine briefly possible beam instabilities driven by the streaming of minor ions relative to protons.