The solar wind is a magnetized plasma and as such exhibits collective plasma behavior associated with its characteristic spatial and temporal scales. The characteristic length scales include the size of the heliosphere, the collisional mean free paths of all species, their inertial lengths, their gyration radii, and their Debye lengths. The characteristic timescales include the expansion time, the collision times, and the periods associated with gyration, waves, and oscillations. We review the past and present research into the multi-scale nature of the solar wind based on in-situ spacecraft measurements and plasma theory. We emphasize that couplings of processes across scales are important for the global dynamics and thermodynamics of the solar wind. We describe methods to measure in-situ properties of particles and fields. We then discuss the role of expansion effects, non-equilibrium distribution functions, collisions,

We use particle-in-cell (PIC) simulations to study the nonlinear evolution of ion velocity space instabilities in an idealized problem in which a background velocity shear continuously amplifies the magnetic field. We simulate the astrophysically relevant regime where the shear timescale is long compared to the ion cyclotron period, and the plasma beta is β ∼ 1 − 100. The background field amplification in our calculation is meant to mimic processes such as turbulent fluctuations or MHD-scale instabilities. The field amplification continuously drives a pressure anisotropy with p ⊥ > p and the plasma becomes unstable to the mirror and ion cyclotron instabilities. In all cases, the nonlinear state is dominated by the mirror instability, not the ion cyclotron instability, and the plasma pressure anisotropy saturates near the threshold for the linear mirror instability. The magnetic field fluctuations initially undergo exponential growth but saturate in a secular phase in which the fluctuations grow on the same timescale as the background magnetic field (with δB ∼ 0.3 B in the secular phase). At early times, the ion magnetic moment is well-conserved but once the fluctuation amplitudes exceed δB ∼ 0.1 B , the magnetic moment is no longer conserved but instead changes on a timescale comparable to that of the mean magnetic field. We discuss the implications of our results for low-collisionality astrophysical plasmas, including the near-Earth solar wind and low-luminosity accretion disks around black holes.

We investigate the scattering of strahl electrons by micro-instabilities as a mechanism for creating the electron halo in the solar wind. We develop a mathematical framework for the description of electron-driven microinstabilities and discuss the associated physical mechanisms. We find that an instability of the oblique fastmagnetosonic/whistler (FM/W) mode is the best candidate for a micro-instability that scatters strahl electrons into the halo. We derive approximate analytical expressions for its instability threshold and confirm their accuracy through comparison with numerical solutions to the hot-plasma dispersion relation. We find that the strahl-driven oblique FM/W instability creates copious FM/W waves under low-β c conditions when U 0s 3w c , where β c is the ratio of the core electrons' thermal pressure to the magnetic pressure, U 0s is the strahl speed, and w c is the thermal speed of the core. These waves have a propagation angle of about 60 • with respect to the background magnetic field and a frequency of about half the local electron gyro-frequency. We also derive an analytical expression for the strahl-driven oblique FM/W instability for β c values approaching unity. The comparison of our theory results with data from the Wind spacecraft confirms the relevance of the oblique FM/W instability for the solar wind. We show that the whistler heat-flux, ion-acoustic heat-flux, kinetic-Alfvénwave heat-flux, and electrostatic electron-beam instabilities cannot fulfill the requirements for self-induced scattering of strahl electrons into the halo. We make predictions for the electron strahl close to the Sun, which will be testable against measurements from Parker Solar Probe and Solar Orbiter.

In low-collisionality plasmas, velocity-space instabilities are a key mechanism providing an effective collisionality for the plasma. We use particle-in-cell (PIC) simulations to study the interplay between electron-and ion-scale velocity-space instabilities and their effect on electron pressure anisotropy, viscous heating, and thermal conduction. The adiabatic invariance of the magnetic moment in low-collisionality plasmas leads to pressure anisotropy, ∆p j ≡ p ⊥,j − p ||,j > 0, if the magnetic field B is amplified (p ⊥,j and p ||,j denote the pressure of species j [electron, ion] perpendicular and parallel to B). If the resulting anisotropy is large enough, it can in turn trigger small-scale plasma instabilities. Our PIC simulations explore the nonlinear regime of the mirror, ion-cyclotron, and electron whistler instabilities, through continuous amplification of the magnetic field |B| by an imposed shear in the plasma. In the regime 1 β j 20 (β j ≡ 8πp j /|B| 2 ), the saturated electron pressure anisotropy, ∆p e /p ||,e , is determined mainly by the (electron-lengthscale) whistler marginal stability condition, with a modest factor of ∼ 1.5 − 2 decrease due to the trapping of electrons into ion-lengthscale mirrors. We explicitly calculate the mean free path of the electrons and ions along the mean magnetic field and provide a simple physical prescription for the mean free path and thermal conductivity in low-collisionality β j 1 plasmas. Our results imply that velocity-space instabilities likely decrease the thermal conductivity of plasma in the outer parts of massive, hot, galaxy clusters. We also discuss the implications of our results for electron heating and thermal conduction in low-collisionality accretion flows onto black holes, including Sgr A* in the Galactic Center.