A Lévy Walk approach to the propagation of solar energetic particles

Abstract

This thesis is dedicated to the problem of energetic particle propagation in the solar wind, with special emphasis on the propagation of solar energetic particles (SEPs). Those particles are accelerated either in the low corona by flares, usually giving rise to so-called impulsive SEP events, or in the higher corona by the shock driven by coronal mass ejections, giving rise to the so-called gradual SEP events. In either case, energetic particles propagate in the solar wind along the spiral magnetic field, and then reach the Earth’s environment, where they can intensify the auroral emission and downgrade or even damage spacecraft operations. Indeed, SEPs represent one of the major hazards of the research programme known as space weather, which aims at reducing the risks associated with the solar and space activities. The fluxes of energetic particles measured in the Earth’s environment depend both on the source strength and on the propagation properties. Traditionally, two limiting transport regimes are considered, that is, di usive transport and scatter-free, i.e., ballistic, transport. However, in the last two decades, anomalous transport regimes in which the mean square displacement grows nonlinearly with time have become more and more common. An anomalous transport regime, either subdi usive or superdi usive, would influence in a fundamental way the flux of solar energetic particles reaching the Earth. To study this problem we have developed two approaches, one based on the analysis of SEP fluxes measured by spacecraft in the solar wind, and the other on the numerical simulation of SEPs in the case of superdi usive transport. In the first approach, we considered SEPs measurements by ACE, Wind and other spacecraft for the case o mpulsive SEP events, and compared the time profile of the energetic particles with that corresponding to the di erent forms which the propagator assumes in the case of superdi usive transport. The comparison gives direct information on the transport regime, showing that electrons propagate in a superdi usive way with anomalous di usion exponent alpha running from 1.2 to 1.75. For protons, quasi-ballistic transport regimes are also found. In the second approach, the statistical mechanism giving rise to superdi usion, namely the Lévy random walk, is investigated numerically. We developed a new numerical code which simulates the Lévy walk while changing the parameters which determine the pace of transport, that is the exponent of the power law tails of the jump probability distribution. This code reproduces well the anomalous transport predictions for the mean square displacement and for the propagator of Lévy walks, while allowing a clear and simple identification of the parameters determining the transport regime. Therefore this code represents a powerful tool to compare the simulation results to spacecraft data. Comparison with the data has been considered both for impulsive and gradual SEP events. In this thesis, we show that the numerical code reproduces well the observations o mpulsive events for the various transport regimes. Additional work is required to apply the code to the propagation of gradual SEP events, as modeling of the shock source is required. While this will be implemented in the near future, the e ectivitiy of the numerical code will allow an important improvement in the understanding of SEP propagation and in the prediction of space weather perturbations