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

Abstract

Properties of the turbulent cascade from fluid to kinetic scales in collisionless plasmas are investigated by means of large-size 3D hybrid (fluid electrons, kinetic protons) particle-in-cell simulations. Initially isotropic Alfvénic fluctuations rapidly develop a strongly anisotropic turbulent cascade, mainly in the direction perpendicular to the ambient magnetic field. The omnidirectional magnetic field spectrum shows a double power-law behavior over almost two decades in wavenumber, with a Kolmogorov-like index at large scales, a spectral break around ion scales, and a steepening at sub-ion scales. Power laws are also observed in the spectra of the ion bulk velocity, density, and electric field, at both magnetohydrodynamic (MHD) and kinetic scales. Despite the complex structure, the omnidirectional spectra of all fields at ion and sub-ion scales are in remarkable quantitative agreement with those of a 2D simulation with similar physical parameters. This provides a partial, a posteriori validation of the 2D approximation at kinetic scales. Conversely, at MHD scales, the spectra of the density and of the velocity (and, consequently, of the electric field) exhibit differences between the 2D and 3D cases. Although they can be partly ascribed to the lower spatial resolution, the main reason is likely the larger importance of compressible effects in the full 3D geometry. Our findings are also in remarkable quantitative agreement with solar wind observations.

Kinetic Plasma Turbulence: Recent Insights and Open Questions From 3D3V Simulations

“…This is essentially the result of KAWs developing a certain degree of magnetic compressibility at sub-ion scales, which sets the relation between δB ⊥ and δB , and requiring that compressive magnetic fluctuations are pressure balanced, which in turn provides a relation between δB and δn (see, e.g., Schekochihin et al, 2009;Boldyrev et al, 2013). As found in previous studies (e.g., Salem et al, 2012;TenBarge et al, 2012;Chen et al, 2013;Cerri et al, 2017b;Franci et al, 2018b;Grošelj et al, 2018), the spectral field ratios are overall consistent with KAW-like turbulence at sub-ion scales. This is not completely surprising, as both in CAMELIA and OSIRIS simulations, Alfvénic fluctuations are injected.…”

“…So are the sub-ion-scale field polarizations indeed KAW-like? As discussed above, recent observations and kinetic simulations are consistent with such idea, although linear wave predictions are not necessarily satisfied precisely (e.g., Kiyani et al, 2013;Chen et al, 2013;Cerri et al, 2017b;Franci et al, 2018b). Chen et al (2013) report an average value of 0.75 for the normalized ratio C 2 δn 2 /δB 2 ⊥ , whereas (asymptotic) KAW theory predicts a value of unity.…”

“…Unless otherwise specified, parallel ( ) and perpendicular (⊥) directions are defined with respect to the global mean magnetic field B 0 = B 0 e z . Franci et al (2018b) employed the CAMELIA code to investigate freely decaying, Alfvénic fluctuations in a cubic box (L = L ⊥ = 128d i with 512 3 grid points and 2048 particles per cell (ppc)) for β i = β e = 0.5, where β s = 8πn 0 T s /B 2 0 is the species beta. Cerri et al (2017b) instead adopted the HVM code to study freely decaying compressive fluctuations in an elongated box (L = 2L ⊥ 63d i with 384 2 × 64 grid points in real space, and 51 3 points in a velocity space bounded by |v/v th,i | ≤ 5) for β i = β e = 1 and with a reduced ion-electron mass ratio of m i /m e = 100 (viz.…”

Statistical Analysis of Ions in Two-Dimensional Plasma Turbulence

“…It has been suggested, indeed, that these reduced models of collisionless plasmas share several similarities with full 3D systems [Servidio et al, 2015, Li et al, 2016. From recent works, it has been suggested that 2D and 3D are in quantitative agreement [Franci et al, 2018].…”

Nonlinear Evolution of Ion Kinetic Instabilities in the Solar Wind

“…The advantage of the hybrid models over other kinetic modeling methods, such as full PIC and Vlasov solvers is that they can model the nonlinear evolution of the ion kinetic instabilities for parameter ranges, physical size, and duration not accessible by other methods, relaxing the approximations on mass ratio and speed of light used in PIC methods (the trade-off is the limitation of hybrid modeling to plasmas where electron kinetic evolution or instabilities could be neglected or are uncoupled from the ions), and the severe resolution limitations in velocity space of multi-dimensional Vlasov codes (e.g., Perrone et al, 2014). Three-dimensional hybrid codes were developed for the study of SW e − p plasma turbulence with more general (than 2.5D) description of the wave-particle interactions (e.g., Vasquez, Markovskii, and Chandran, 2014;Vasquez, 2015;Franci et al, 2018).…”