Gary P. Zank

Dissipation of pickup‐induced waves: A solar wind temperature increase in the outer heliosphere?

The deposition of energy into the solar wind by the pickup of interstellar neutrals is due to both the creation of hot, nonthermal ions and the associated generation of low frequency magnetohydrodynamic (MHD) waves. Dissipation of some fraction of the free wave energy released by ion pickup and isotropization is possible through nonlinear turbulent processes which may lead to heating of the core thermal solar wind proton distribution. Simple energy budget arguments are utilized to show that pickup ion generated wave dissipation may play a significant role in determining the solar wind radial temperature profile in the outer heliosphere. In particular, depending on the density of interstellar hydrogen in the heliosphere, there will be some radial distance beyond which the thermal solar wind core temperature increases steadily until the termination shock. Existing Pioneer and Voyager temperature profiles are consistent with this interpretation.

An evaluation of perpendicular diffusion models regarding cosmic ray modulation on the basis of a hydromagnetic description for solar wind turbulence

The theory for the perpendicular diffusion of cosmic rays is not well understood which hampers our understanding of cosmic ray modulation. In this paper, a spherically symmetric cosmic ray modulation model is used to evaluate three different theories for perpendicular cosmic ray diffusion in the ecliptic plane, subject to the limitation of negligible cosmic ray transport in the polar direction. In models for the perpendicular diffusion component, it is assumed that perpendicular diffusion due to large-scale field line wandering dominates resonant perpendicular diffusion. To test these models, observations of anomalous and galactic helium obtained during a time of relatively small latitudinal gradients (1996) are used as a guideline. The spatial dependence of the parallel and perpendicular cosmic ray diffusion coefficients is determined completely theoretically using a promising hydromagnetic model for the transport of combined slab plus two-dimensional turbulence in the solar wind [Zank et al., 1996]. The main result of the paper is that the nonperturbative model [Zank et al., 1998] yields the best results. Its success is determined by the following: (1) a perpendicular correlation length derived from two-dimensional solar wind turbulence that is much larger than the parallel correlation length associated with slab turbulence; (2) a modest radial dependence of the radial diffusion coefficient in the outer heliosphere; and (3) a three interval rigidity dependence of the radial diffusion coefficient in the outer heliosphere with the smallest rigidity dependence in the middle interval and a strong rigidity squared dependence in the other two intervals. The nonperturbative model gives a tentative theoretical basis for the cosmic ray modulation simulations by Moraal et al. [1999], who found empirically that a similar spatial and three stage rigidity dependence for the radial diffusion coefficient is important for reproducing observed anomalous and galactic cosmic ray spectra.

Magnetohydrodynamic waves in non-uniform flows. II: stress-energy tensors, conservation laws and Lie symmetries

The interaction of magnetohydrodynamic (MHD) waves in a non-uniform, 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

Transport of energetic charged particles in a radial magnetic field. Part 1. Large-angle scattering

{\bf x}^*

Self‐consistent acceleration of multiply reflected pickup ions at a quasi‐perpendicular solar wind termination shock: a fluid approach

is expressed as a vector sum of the position vector

Predicted timing for the turn‐on of radiation in the outer heliosphere due to the Bastille Day shock

{\bf x}

Transport of energetic charged particles. Part 2. Small-angle scattering

of the background plasma fluid element plus a Lagrangian displacement

Modeling of radial dependence of Fe/O elemental abundance ratio in mixed SEP events with the PATH code

\xib({\bf x},t)

Heliospheric Variation in Response to Changing Interstellar Environments

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. Noethers 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 Noethers first theorem corresponding to the time and space translation symmetries of the action, respectively. As examples of the use of Noethers 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. Ertels 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.

Efficiency of particle acceleration at oblique strong CME shocks from 0.13 to 2.5 AU: PATH modeling

A new approach, the propagating-source method, is introduced to solve the time-dependent Boltzmann equation. The method relies on the decomposition of the particle distribution function into scattered and unscattered particles. It is assumed in this paper that the particles are transported in a constant-velocity spherically expanding supersonic flow (such as the solar wind) in the presence of a radial magnetic field. Attention too has been restricted to very fast particles. The present paper addresses only large-angle scattering, which is modelled as a BGK relaxation time operator. A subsequent paper (Part 2) will apply the propagating-source method to a small-angle quasilinear scattering operator. Initially, we consider the simplest form of the BGK Boltzmann equation, which omits both adiabatic deceleration and focusing, to re-derive the well-known telegrapher equation for particle transport. However, the derivation based on the propagating-source method yields an inhomogeneous form of the telegrapher equation; a form for which the well-known problem of coherent pulse solutions is absent. Furthermore, the inhomogeneous telegrapher equation is valid for times t much smaller than the ‘scattering time’ τ, i.e. for times t [Lt ] τ, as well as for t > τ. More complicated forms of the BGK Boltzmann equation that now include focusing and adiabatic deceleration are solved. The basic results to emerge from this new approach to solving the BGK Boltzmann equation are the following. (i) Low-order polynomial expansions can be used to investigate particle propagation and transport at arbitrarily small times in a scattering medium. (ii) The theory of characteristics for linear hyperbolic equations illuminates the role of causality in the expanded integro-differential Fokker–Planck equation. (iii) The propagating-source approach is not restricted to isotropic initial data, but instead arbitrarily anisotropic initial data can be investigated. Examples using different ring-beam distributions are presented. (iv) Finally, the numerical scheme can include both small-angle and large-angle particle scattering operators (Part 2). A detailed discussion of the results for the various Boltzmann-equation models is given. In general, it is found that particle beams that experience scattering by, for example, interplanetary fluctuations are likely to remain highly anisotropic for many scattering times. This makes the use of the diffusion approximation for charged-particle transport particularly dangerous under many reasonable solar-wind conditions, especially in the inner heliosphere.