In situ observations from solar and heliospheric spacecraft missions measure power spectra of the solar wind plasma and electromagnetic field fluctuations which show a power-law behaviour over several decades in frequency. This is interpreted as the manifestation of a turbulent cascade of energy from large fluid scales to small kinetic scales, characteristic of the motion of the ions and the electrons. Direct numerical simulations of turbulent plasmas are not only important for interpreting the nature of the solar wind fluctuations at large scales, but also a fundamental tool to understand how energy is channelled to protons and electrons. In particular, the hybrid particle-in-cell model, which treats the ions as particles and the electrons as a charge-neutralizing massless fluid, has proved to be the most appropriate and efficient method to follow the turbulent cascade down to sub-ion scales, retaining ion kinetic effects [1].
Figure 1. Left panel: Pseudocolor plot of the power of the perpendicular (with respect to the mean field) magnetic fluctuations when turbulence is fully developed in a 2D 4096×4096 simulation. Middle panel: The same as in the left panel, but for a 3D 512x512x512 simulation. Right panel: Omnidirectional 1D power spectra of magnetic field B, electric field E, ion bulk velocity u, parallel magnetic field Bz, and ion density n, from the 3D simulation. Power laws with different slopes represent theoretical predictions and/or observational results, as reference. In the insets, a direct comparison from 2D and 3D simulations shows a remarkable agreement.
We have used DiRAC resources to perform a collection of state-of-the-art two-dimensional (2D, Fig. 1 left panel) and three-dimensional (3D, Fig. 1 middle) hybrid simulations of plasma turbulence, investigating the processes responsible for coronal heating and solar wind heating and acceleration. We have analysed, among other things, the spectral properties (Fig. 1, right), the spectral anisotropy [2], the intermittency properties, and the nature of fluctuations at kinetic scales. We also investigated the interplay between plasma turbulence and the proton firehose instabilities in a slowly expanding plasma, performing the first 3D hybrid simulation employing the expanding-box model, to take into account the solar wind expansion [3].
Our numerical results are being used to interpret in situ observations in the Earth’s magnetosheath and in the solar wind from the Magnetospheric Multiscale (MMS) mission [4], as well as to predict upcoming results from Parker Solar Probe (PSP) and Solar Orbiter.
More recently, we have produced high-resolution high-cadence 2D and 3D data exploring the conditions encountered by PSP on its first perihelion. Analysis of the results is ongoing and it will provide a large amount of information on many different aspects of plasma turbulence, to be directly compared with present and upcoming spacecraft observations.
[1] Franci et al., Solar Wind Turbulent Cascade from MHD to Sub-ion Scales: Large-size 3D Hybrid Particle-in-cell Simulations, ApJ 853(1):26, 2018
[2] Landi et al., Spectral anisotropies and intermittency of plasma turbulence at ion kinetic scales, submitted to ApJL, 2019
[3] Hellinger et al., Turbulence vs. fire hose instabilities: 3-D hybrid expanding box simulations, submitted to ApJ, 2019
[4] Franci et al., Predicting and interpreting data of solar wind turbulence with numerical modelling: hybrid simulations vs. MMS observations, in preparation, 2019
