Plasma Beta Dependence of the Ion-Scale Spectral Break of Solar Wind Turbulence: High-Resolution 2d Hybrid Simulations

Abstract

We investigate properties of the ion-scale spectral break of solar wind turbulence by means of twodimensional high-resolution hybrid particle-in-cell simulations. We impose an initial ambient magnetic field perpendicular to the simulation box and add a spectrum of in-plane, large-scale, magnetic and kinetic fluctuations. We perform a set of simulations with different values of the plasma β, distributed over three orders of magnitude, from 0.01 to 10. In all the cases, once turbulence is fully developed, we observe a power-law spectrum of the fluctuating magnetic field on large scales (in the inertial range) with a spectral index close to −5/3, while in the sub-ion range we observe another power-law spectrum with a spectral index systematically varying with β (from around −3.6 for small values to around −2.9 for large ones). The two ranges are separated by a spectral break around ion scales. The length scale at which this transition occurs is found to be proportional to the ion inertial length, d i , for β 1 and to the ion gyroradius, ρ i = d i √ β, for β 1, i.e., to the larger between the two scales in both the extreme regimes. For intermediate cases, i.e., β ∼ 1, a combination of the two scales is involved. We infer an empiric relation for the dependency of the spectral break on β that provides a good fit over the whole range of values. We compare our results with in situ observations in the solar wind and suggest possible explanations for such a behavior.

Solar Wind Turbulent Cascade from MHD to Sub-ion Scales: Large-size 3D Hybrid Particle-in-cell Simulations

“…The transition (break) occurs around ion scales,k d 2 i , just as in the 2D case with the same ion plasma beta. This support our previous 2D numerical study, in which we provided numerical evidence that the plasma beta controls the position of the break (Franci et al 2016). …”

“…In particular, Franci et al (2015aFranci et al ( , 2015b produced extended turbulent spectra with well-defined power laws for the magnetic, ion bulk velocity, density, and electric fluctuations, in agreement with solar wind observations. Moreover, Franci et al (2016) unambiguously determined the ion-scale break in the magnetic field spectrum and recovered the observed dependence on the ion characteristic scales.…”

“…On the one hand, it validates the use of 2D simulations for all those cases where the study of spectral properties is involved and the use of a large collection of simulations with different values of parameters is required, e.g., for convergence studies (Franci et al 2015a), or for parameter studies (Franci et al 2016). On the other hand, it suggests that the dominant process(es) responsible for the ion-scale spectral break in the magnetic field and for the kinetic-scale turbulent cascade are likely not inhibited in a reduced 2D geometry.…”

“…Observational results suggest that the transition likely occurs in correspondence with the larger of the two when they are well separated (Chen et al 2014) or a combination of the two in the intermediate-beta regime (Bruno & Trenchi 2014). Although the nature of the power-law behavior of the solar wind fluctuations at kinetic scales is still under debate, an increasing consensus has recently emerged about the fundamental role of coherent structures and magnetic reconnection in shaping the magnetic field spectrum near and below the ion scales (e.g., Franci et al 2016Franci et al , 2017bLoureiro & Boldyrev 2017;Mallet et al 2017).…”

Electric and magnetic spectra from MHD to electron scales in the magnetosheath

“…Howes et al 2011;Franci et al 2015a). Note however that recent observational (Chen et al 2014) and numerical (Cerri et al 2016;Franci et al 2016) investigations suggest that the quantitative agreement with KAW predictions is fulfilled better at high ( 1) than low beta; this aspect will be the subject of a forthcoming study.…”