The development of magnetic field line wander in gyrokinetic plasma turbulence: dependence on amplitude of turbulence

Abstract

The dynamics of a turbulent plasma not only manifests the transport of energy from large to small scales, but also can lead to a tangling of the magnetic field that threads through the plasma. The resulting magnetic field line wander can have a large impact on a number of other important processes, such as the propagation of energetic particles through the turbulent plasma. Here we explore the saturation of the turbulent cascade, the development of stochasticity due to turbulent tangling of the magnetic field lines and the separation of field lines through the turbulent dynamics using nonlinear gyrokinetic simulations of weakly collisional plasma turbulence, relevant to many turbulent space and astrophysical plasma environments. We determine the characteristic time $t_{2}$ for the saturation of the turbulent perpendicular magnetic energy spectrum. We find that the turbulent magnetic field becomes completely stochastic at time $t\lesssim t_{2}$ for strong turbulence, and at $t\gtrsim t_{2}$ for weak turbulence. However, when the nonlinearity parameter of the turbulence, a dimensionless measure of the amplitude of the turbulence, reaches a threshold value (within the regime of weak turbulence) the magnetic field stochasticity does not fully develop, at least within the evolution time interval $t_{2}<t\leqslant 13t_{2}$. Finally, we quantify the mean square displacement of magnetic field lines in the turbulent magnetic field with a functional form $\langle (\unicode[STIX]{x1D6FF}r)^{2}\rangle =A(z/L_{\Vert })^{p}$ ($L_{\Vert }$ is the correlation length parallel to the magnetic background field $\boldsymbol{B}_{\mathbf{0}}$, $z$ is the distance along $\boldsymbol{B}_{\mathbf{0}}$ direction), providing functional forms of the amplitude coefficient $A$ and power-law exponent $p$ as a function of the nonlinearity parameter.

The development of magnetic field line wander by plasma turbulence

“…The companion work to this paper, Bourouaine & Howes (2017), explores the magnetic field line wander over a range of turbulent amplitudes with and to test whether one should indeed always expect turbulent astrophysical plasmas to contain a stochastic magnetic field. We find that the magnetic field becomes fully stochastic when the turbulence amplitude exceeds a threshold value, .…”

Laboratory space physics: Investigating the physics of space plasmas in the laboratory

“…The interplanetary medium, which is dominated by the radially outward flow of the supersonic and super-Alfvénic solar wind, is always observed to be in a turbulent state. This turbulence naturally leads to a very tangled interplanetary magnetic field, [101][102][103][104] and this tangled magnetic field has important implications for the transport of energetic particles through the heliosphere to the Earth, 105,106 including solar energetic particles generated by violent activity at the Sun, 107 anomalous cosmic rays generated through poorly understood mechanisms in the outer reaches of our heliosphere, 108,109 and galactic cosmic rays. 110,111 For particularly extreme space weather events, the copious solar energetic particles that are often generated represent a significant hazard for robotic and human assets in space, so accurate prediction of their propagation through the turbulent solar wind toward the Earth is critical to prevent damage to spaceborne technology and harm to astronauts.…”

A hybrid gyrokinetic ion and isothermal electron fluid code for astrophysical plasma

“…Below we conduct the simulation in two characteristic spatial regions, the MHD inertial range and the ion kinetic range. For the MHD inertial range simulation, the domain is set to L ⊥ = 50πρ i with the number of grid points (n x , n y , n λ , n E ) = (128, 128, 8,16). This gives a wave number range of 0.02 ≤ k ⊥ ρ i ≤ 0.84.…”

“…For the MHD inertial range simulation, the domain is set to L ⊥ = 50πρ i with the number of grid points (n x , n y , n λ , n E ) = (128, 128,8,16). This gives a wave number range of 0.02 ≤ k ⊥ ρ i ≤ 0.84.…”

“…Recently, gyrokinetics has been highlighted as a powerful model in astrophysics as well [8,9]. While many of the past astrophysical studies via gyrokinetics have targeted the solar wind [10,11,12,13,14,15,16,17], gyrokinetics is also expected to be applicable to many other astrophysical objects, such as accretion flows, galaxy clusters, and interstellar media [9].…”