Two Topics in the Physics of the Solar Wind: 1. A Model of Fermi Acceleration at Shock Fronts. 2. Effects of Diffusion on the Composition of the Solar Corona and Solar Wind

Citation

Jokipii, Jack Randolph (1965) Two Topics in the Physics of the Solar Wind: 1. A Model of Fermi Acceleration at Shock Fronts. 2. Effects of Diffusion on the Composition of the Solar Corona and Solar Wind. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/AC5X-KR20. https://resolver.caltech.edu/CaltechETD:etd-01242003-092742

Abstract

1. A Model of Fermi Acceleration at Shock Fronts A model of first order Fermi acceleration at shock fronts is developed. A "fast" hydromagnetic shock is assumed to be propogating toward an isolated magnetic mirror in an otherwise uniform magnetic field which is not parallel to the shock front. The behavior of an ensemble of particles trapped between the mirror and the shock is studied and a differential equation describing the balance of particle injection into the trapping region, loss through the shock or mirror, and energy gain is obtained. A general expression for n(W, t), the number of trapped particles as a function of energy and time is obtained. Useful limiting forms are discussed. Possible sources of particles eligible for acceleration are discussed and an attractive source is shown to be the quasi-thermalized plasma behind the shock, a small fraction of which may leak out in front of the shock and be accelerated. The flux of particles through the shock is found to be small and due mainly to convection with magnetic irregularities behind the shock. The energy spectrum of accelerated particles behind the shock is therefore expected to be nearly the same as in the trapping region. The general theory is then applied to the acceleration of electrons at the earth's bow shock. This leads to an attractive model for the energetic electron pulses which have been observed beyond the magnetopause. The observations and their interpretation are discussed. If a small fraction of the ~ 1 keV electrons in the quasi-thermalized plasma behind the shock escape to the region in front of the shock, many quantitative features of the observed pulses are explained by a model in which each pulse is due to the acceleration of these electrons by a mirror approaching the bow shock. In particular, the cutoff in >30 keV pulses at a few earth radii beyond the shock is readily explained. The theory predicts, further, that cutoffs for more energetic particles should be at smaller distances from the shock. The observed energy spectra are in excellent agreement with the model. Some critical observations are suggested. 2. Effects of Diffusion on the Composition of the Solar Corona and Solar Wind A simple model is developed with which it is possible to estimate quantitatively the effects of radial diffusion on the composition of the solar corona and solar wind. As it flows out to form the solar wind, it is assumed that each constituent satisfies the time independent equation of continuity n[subscript t]v[subscript t]r[superscript 2] = constant, where n[subscript t] and v[subscript t] are the number density and velocity of element t at heliocentric radius r. For typical coronal temperatures of 1 - 2 x 10[superscript 6] [degrees] K and solar wind fluxes of 3 x 10[superscript 8] protons cm[- superscript 2]sec[- superscript 1] at r = 1 AU, the relative diffusion velocities of ions and protons are a substantial fraction of the local solar wind velocity. This diffusion is found to be mostly due to the coronal pressure gradient, with the effect of the temperature gradient relatively unimportant. The large relative velocities together with the above continuity equation lead to substantial changes in the relative composition of the solar wind. Effects of magnetic fields and turbulent mixing are briefly considered. It is concluded that, in conjunction with the diffusion, they may lead to appreciable fluctuations of the composition as a function of time and heliocentric radius. The conclusions are in agreement with the observed behavior of the He/H ratio observed on Mariner-2.

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