Particle acceleration at shocks and magnetic turbulence in the interplanetary space

Abstract

The solar wind is a supersonic and super-alfvenic flow of plasma that propagates in space up to the Earth and throughout the heliosphere reaching speeds of about 400 ð€€€ 800 km sð€€€1. It permeates the heliosphere and is a fantastic laboratory for plasma physics, since it is the only astrophysical environment in which spacecrafts can provide in situ measurements of the relevant physical parameters. Embedded within the solar wind plasma is the interplanetary magnetic field. The interaction of the interplanetary field with the magnetic field of the Earth determines the formation of a magnetosphere, in which the magnetic field of the Earth is confined, bounded by a discontinuity between the two fields, called magnetopause. Magnetic field is at the origin of most of the phenomena that are observed in the various layers of the solar atmosphere, called solar activity. Flares and coronal mass ejections (CMEs) are some of the most spectacular and interesting manifestations of solar activity that can generate shock waves in interplanetary space. A shock is a discontinuity, characterized by a sudden change in pressure, temperature and density of the medium. Solar flares and CMEs can release energetic particles (Solar Energetic Particles - SEPs) that travel faster than the particles already present in the interplanetary space plasma. SEPs, following the interplanetary magnetic field, can reach the Earth in an hour or less and are of particular interest because they can cause damage to the electronic instruments on board the space probes, influence communications and navigation systems and endanger astronauts’ life in orbit, especially the particles with energy greater than 40 MeV. During its expansion, the solar wind develops a strong turbulent character, which evolves towards a state similar to that of hydrodynamic turbulence, described by Kolmogorov (1941). The low frequency fluctuations are generally described by magnetohydrodynamics (MHD). The magnetohydrodynamic turbulence in the solar wind has been studied in great detail in recent years, thanks to the numerous spacecrafts that have been launched in the interplanetary space since the beginning of the space age. This work concerns the study of energetic protons at interplanetary shocks, the related acceleration mechanisms and the connection to magnetic turbulence in the upstream and downstream regions of the shocks. In particular, we performed a correlation analysis between the particle flux enhancements and the magnetic field turbulence observed in the upstream and downstream regions of interplanetary shocks. The data used in the analysis are taken by the Stereo Ahead spacecraft and cover a period from 2009 to 2016. The interplanetary shocks selected are divided into two lists: the first contains 24 events that show an increase of the proton flux close to the shock itself; instead, the second includes 14 events that present flux enhancements more distant from the shocks. In order to quantify the magnetic field turbulence, we used the total wave power, calculated from the standard spectral analysis methods. Because of the low correlation obtained, in the case of the first list we separated shocks occurring on the wake of a SEP event from NO SEP events. On the contrary, this is not possible for the shocks of the second list due to the smaller number of events. We also performed a parametric and non-parametric correlation analysis to study the degree of compressibility in the upstream and downstream regions of interplanetary shocks for both lists of selected events, using the variance of the magnetic field. Moreover, in order to have information on the propagation and acceleration of particles in the interplanetary space, we studied the evolution of the particle energy spectra for shocks associated with the SEP events of the first list. In particular, we identify two types of distribution that well fit the spectra: a Weibull functional form, obtained for quasi-perpendicular shocks and a double power law in the case of quasi-parallel shocks. Thanks also to the combined study of the proton flux enhancements with the Mach number and the shock angle, we identify the shock surfing acceleration as the acceleration mechanism suitable to explain the particle spectra at interplanetary quasi-perpendicular shocks. Finally, concerning fluctuations of the magnetic field in the interplanetary space, we studied high-frequency dynamics, a problem that is still open and not entirely clear. Unlike magnetic fluctuations in the range of kinetic scales, those at low frequencies have been extensively investigated and show a universal scaling behavior, described in the nonlinear turbulent energy cascade framework At small scales (high frequencies), instead, the plasma dynamics in the interplanetary space is extremely complex, since it exhibits simultaneously a dispersive and dissipative character. Therefore, we introduced a Brownian approach that provides a simple description of the high-frequency dynamics of magnetic fluctuations, which is able to successfully reproduce the spectra of the fluctuations observed at high frequencies. This framework allows an interpretation of the observed high frequency magnetic spectra with no assumptions about dispersion relations from plasma turbulence theory