Launched on 12 Aug. 2018, NASA’s Parker Solar Probe had completed 13 of its scheduled 24 orbits around the Sun by Nov. 2022. The mission’s primary science goal is to determine the structure and dynamics of the Sun’s coronal magnetic field, understand how the solar corona and wind are heated and accelerated, and determine what processes accelerate energetic particles. Parker Solar Probe returned a treasure trove of science data that far exceeded quality, significance, and quantity expectations, leading to a significant number of discoveries reported in nearly 700 peer-reviewed publications. The first four years of the 7-year primary mission duration have been mostly during solar minimum conditions with few major solar events. Starting with orbit 8 (i.e., 28 Apr. 2021), Parker flew through the magnetically dominated corona, i.e., sub-Alfvénic solar wind, which is one of the mission’s primary objectives. In this paper, we present an overview of the scientific advances made mainly during the first four years of the Parker Solar Probe mission, which go well beyond the three science objectives that are: (1) Trace the flow of energy that heats and accelerates the solar corona and solar wind; (2) Determine the structure and dynamics of the plasma and magnetic fields at the sources of the solar wind; and (3) Explore mechanisms that accelerate and transport energetic particles.

Motivated by prior remote observations of a transition from striated solar coronal structures to more isotropic “flocculated” fluctuations, we propose that the dynamics of the inner solar wind just outside the Alfvén critical zone, and in the vicinity of the first surface, is powered by the relative velocities of adjacent coronal magnetic flux tubes. We suggest that large-amplitude flow contrasts are magnetically constrained at lower altitude but shear-driven dynamics are triggered as such constraints are released above the Alfvén critical zone, as suggested by global magnetohydrodynamic (MHD) simulations that include self-consistent turbulence transport. We argue that this dynamical evolution accounts for features observed by Parker Solar Probe (PSP) near initial perihelia, including magnetic “switchbacks,” and large transverse velocities that are partially corotational and saturate near the local Alfvén speed. Large-scale magnetic increments are more longitudinal than latitudinal, a state unlikely to originate in or below the lower corona. We attribute this to preferentially longitudinal velocity shear from varying degrees of corotation. Supporting evidence includes comparison with a high Mach number three-dimensional compressible MHD simulation of nonlinear shear-driven turbulence, reproducing several observed diagnostics, including characteristic distributions of fluctuations that are qualitatively similar to PSP observations near the first perihelion. The concurrence of evidence from remote sensing observations, in situ measurements, and both global and local simulations supports the idea that the dynamics just above the Alfvén critical zone boost low-frequency plasma turbulence to the level routinely observed throughout the explored solar system.

We present a fully three-dimensional magnetohydrodynamic model of the solar corona and solar wind with turbulence transport and heating. The model is based on Reynolds-averaged solar wind equations coupled with transport equations for turbulence energy, cross helicity, and correlation scale. The model includes separate energy equations for protons and electrons and accounts for the effects of electron heat conduction, radiative cooling, Coulomb collisions, Reynolds stresses, eddy viscosity, and turbulent heating of protons and electrons. The computational domain extends from the coronal base to 5 au and is divided into two regions: the inner (coronal) region, 1–30 R _☉, and the outer (solar wind) region, 30 R _☉–5 au. Numerical steady-state solutions in both regions are constructed by time relaxation in the frame of reference corotating with the Sun. Inner boundary conditions are specified using either a tilted-dipole approximation or synoptic solar magnetograms. The strength of solar dipole is adjusted, and a scaling factor for magnetograms is estimated by comparison with Ulysses observations. Except for electron temperature, the model shows reasonable agreement with Ulysses data during its first and third fast latitude transits. We also derive a formula for the loss of angular momentum caused by the outflowing plasma. The formula takes into account the effects of turbulence. The simulation results show that turbulence can notably affect the Sun’s loss of angular momentum.

Modelling the transport of cosmic rays (CRs) in the heliosphere represents a global challenge in the field of heliophysics, in that such a study, if it were to be performed from first principles, requires the careful modelling of both large scale heliospheric plasma quantities (such as the global structure of the heliosphere, or the heliospheric magnetic field) and small scale plasma quantities (such as various turbulence-related quantities). Here, recent advances in our understanding of the transport of galactic cosmic rays are reviewed, with an emphasis on new developments pertaining to their transport coefficients, with a special emphasis on novel theoretical and numerical simulation results, as well as the CR transport studies that employ them. Furthermore, brief reviews are given of recent progress in CR focused transport modelling, as well as the modelling of non-diffusive CR transport.

Direct evidence of an inertial-range turbulent energy cascade has been provided by spacecraft observations in heliospheric plasmas. In the solar wind, the average value of the derived heating rate near 1 au is , an amount sufficient to account for observed departures from adiabatic expansion. Parker Solar Probe, even during its first solar encounter, offers the first opportunity to compute, in a similar fashion, a fluid-scale energy decay rate, much closer to the solar corona than any prior in situ observations. Using the Politano–Pouquet third-order law and the von Kármán decay law, we estimate the fluid-range energy transfer rate in the inner heliosphere, at heliocentric distance R ranging from 54 R _⊙ (0.25 au) to 36 R _⊙ (0.17 au). The energy transfer rate obtained near the first perihelion is about 100 times higher than the average value at 1 au, which is in agreement with estimates based on a heliospheric turbulence transport model. This dramatic increase in the heating rate is unprecedented in previous solar wind observations, including those from Helios, and the values are close to those obtained in the shocked plasma inside the terrestrial magnetosheath.

The investigation of the diffusive transport of charged particles in a turbulent magnetic field remains a subject of considerable interest. Research has most frequently concentrated on determining the diffusion coefficient in the presence of a mean magnetic field. Here we consider the diffusion of charged particles in fully three-dimensional isotropic turbulent magnetic fields with no mean field, which may be pertinent to many astrophysical situations. We identify different ranges of particle energy depending upon the ratio of Larmor radius to the characteristic outer length scale of turbulence. Two different theoretical models are proposed to calculate the diffusion coefficient, each applicable to a distinct range of particle energies. The theoretical results are compared to those from computer simulations, showing good agreement.