No abstract

The interaction of magnetohydrodynamic (MHD) waves in a nonuniform, time-dependent background plasma flow is investigated using Lagrangian field theory methods. The analysis uses Lagrangian maps, in which the exact position of the fluid element x * is expressed as a vector sum of the position vector x of the background plasma fluid element plus a Lagrangian displacement ξ(x, t) due to the waves. An exact theory for the wave and background stress energy tensors is developed based on the exact Lagrangian and the exact Lagrangian map. Noether's theorems are used in conjunction with the exact action and Lagrangian maps to determine the general form of conservation laws for the total system of waves and background plasma, corresponding to divergence symmetries of the action. The energy and momentum conservation laws of the system are derived from Noether's first theorem corresponding to the time and space translation symmetries of the action, respectively. As examples of the use of Noether's first theorem, we derive the conservation laws associated with the 10-parameter Galilean group admitted by the MHD equations. This includes the space and time translation symmetries, the space rotations, and the Galilean boosts. A class of solutions of the Lie determining equations for the infinite-dimensional MHD fluid relabeling symmetries are used to discuss the corresponding conservation laws. Ertel's theorem for the conservation of potential vorticity for the system of waves and background gas in ideal gas dynamics is derived from an infinite-dimensional fluid relabeling symmetry of the action.

[1] Alphas (He 4 2+ ) and other ions in the interplanetary medium show a tendency to stream near or below the local Alfvén speed (V A ) relative to the main component of protons. Because V A decreases with increasing distance from the Sun, forces must exist to slow the heavier ions with increasing distance. We have conducted hybrid simulations in a plasma with particle protons and alphas and with a quasineutralizing electron fluid. Simulation runs with other streaming minor ions were also performed. In our simulations, a group of Alfvén waves steepen and generate imbedded rotational discontinuities (RDs) and compressional waves. We examine cases of almost steady waveforms and RDs and ones with evolving waveforms and RDs due to a significantly nonuniform background. When alphas stream with the waves and imbedded RDs faster than the protons, they decelerate more rapidly from higher speeds and heat. We have concluded that alphas do not remain at one streaming speed due to nonlinear Lorentz forces from the wave compressional component and the presence of collisionless dissipation, which dissipates this component so that bulk alpha kinetic energy is ultimately deposited into alpha thermal energy. Imbedded RDs play no significant role in the overall deceleration of alphas. Protons heat similarly to cases without alphas and are slightly accelerated so that the total ion momentum along B 0 is nearly conserved. For small streaming speeds (]0.5 Alfvén speeds), the deceleration rate can be relatively small because the loss of streaming energy competes with the gain in wave kinetic energy required by large-amplitude Alfvén waves. Less proton and more alpha heating is also found since alphas can resonate with the left-handed portion of oblique waves. Starting from rest, alphas and protons can develop a small differential flow in which Lorentz and pressure forces become balanced. The simulation behavior of alphas for streaming speeds near the Alfvén speed is fairly consistent with solar wind observations in high-speed streams. Turbulent Alfvénic fluctuations do have a small compressional component and so might be responsible for the observed deceleration and heating of alphas. Simulations with other streaming minor ions also gave deceleration, suggesting that the behavior of a wide range of solar wind minor ions might be explained by the same processes that affect alphas. INDEX TERMS:7867 Space Plasma Physics: Wave/particle interactions; 7843 Space Plasma Physics: Numerical simulation studies; 2164 Interplanetary Physics: Solar wind plasma; 2109 Interplanetary Physics: Discontinuities; KEYWORDS: solar wind, wave/particle interactions, kinetics, numerical simulations, discontinuities Citation: Kaghashvili, E. K., B. J. Vasquez, and J. V. Hollweg, Deceleration of streaming alpha particles interacting with waves and imbedded rotational discontinuities,

Abstract. The interaction of magnetohydrodynamic (MHD) waves in a nonuniform, time-dependent background plasma flow is investigated using Lagrangian field theory methods. The analysis uses Lagrangian maps, in which the position of the fluid element x * is expressed as a vector sum of the position vector x of the background plasma fluid element plus a Lagrangian displacement ξ(x, t) due to the waves. Linear, non-Wentzel-Kramer-Brillouin (WKB) wave interaction equations are obtained by expansion of the Lagrangian out to second order in ξ and ∆S, where ∆S is the Lagrangian entropy perturbation. The characteristic manifolds of the waves are determined by consideration of the Cauchy problem for the wave interaction equations. The manifolds correspond to the usual MHD waves modes, namely the Alfvén waves, the fast and slow magnetoacoustic waves and the entropy wave. The relationships between the characteristic manifolds, and the ray equations of geometrical MHD optics are developed using the theory of Cauchy characteristics for first-order partial differential equations. The first-order differential equations describing the singular manifolds are the dispersion equations for the MHD eigenmodes, where the wave vector k = ∇φ and frequency ω = −φ t correspond to the characteristic manifolds φ(x, t) = constant. The form of the characteristic manifolds for both time-dependent and steady MHD flows are developed. The bicharacteristics for steady MHD waves in a steady background flow are related to the group velocity surface and Mach cone for the waves, and determine when the flow is elliptic, hyperbolic, or of mixed hyperbolic-elliptic type. The wave interaction equations are decomposed into coupled equations for the compressible and incompressible perturbations.

It is shown that an inhomogeneous Ñow is capable of converting waves escaping from the solar Alfve n atmosphere into other types of MHD waves that can be efficiently dissipated. The efficiency of this process depends on local characteristics of the medium. Using the geometry of the solar wind, it is shown how this mechanism operates in di †erent regions of the solar wind and what the preferred way of the coupling process is in those regions. It is suggested that mode conversion induced by inhomogeneous Ñow, particularly by shear velocity Ñow, could be the basic mechanism required for the solar wind acceleration in the coronal holes. It is shown that this mechanism is most efficient in the fast-expanding regions of polar coronal holes and how it contributes to the detected long-period waves and Alfve n density Ñuctuations in the solar wind. The results demonstrated by numerical simulations coincide with observations.