An oscillating Langevin antenna for driving plasma turbulence simulations

Abstract

A unique method of driving Alfvénic turbulence via an oscillating Langevin antenna is presented. This method of driving is motivated by a desire to inject energy into a finite domain numerical simulation in a manner that models the nonlinear transfer of energy from fluctuations in the turbulent cascade at scales larger than the simulation domain. The oscillating Langevin antenna is shown to capture the essential features of the larger scale turbulence and efficiently couple to the plasma, generating steady-state turbulence within one characteristic turnaround time. The antenna is also sufficiently flexible to explore both strong and weak regimes of Alfvénic plasma turbulence.

Introduction

The development of a detailed understanding of plasma turbulence is an outstanding goal of the plasma physics community due to its ubiquity and importance in a variety of environments. In space physics and astrophysics, turbulence mediates the transfer of energy from the large scales at which energy is injected into turbulent motions to the small scales at which the turbulent energy is ultimately dissipated as heat. The resulting heating of the plasma determines the radiation emitted from turbulent astrophysical environments, which constitutes the majority of our observational data. In the heliosphere, turbulence likely plays a key role in the heating of the solar corona and in the launching of the solar wind. The dissipation of turbulent fluctuations in the streaming solar wind plasma impacts the overall thermodynamic balance of the heliosphere.

The near-Earth solar wind is a unique laboratory for the study of plasma turbulence due to its accessibility to direct spacecraft measurements. The Alfvénic nature of the turbulent fluctuations in the solar wind plasma has long been recognized [1], [2], [3]. Modern theories of anisotropic MHD turbulence suggest that the physical mechanism that drives the turbulent cascade of energy from large to small scales is the nonlinear interaction between counterpropagating Alfvén waves [4], [5], [6], [7], [8], [9], [10]. Although spacecraft missions enable detailed in situ measurements of many aspects of the turbulent plasma and electromagnetic fluctuations, measurements are generally possible at only a single point, or at most a few points, in space. The solar wind plasma typically streams past the spacecraft at super-Alfvénic velocities, so a time series of single-point measurements maps to the advection of spatial variations in the turbulent plasma  [11]. These limitations of spacecraft measurements motivate complementary efforts to gain further insight into the nature of Alfvénic turbulence using terrestrial laboratory experiments or numerical simulations. Although the experimental measurement of the nonlinear interaction between counterpropagating Alfvén waves has recently been accomplished in the laboratory [12], the large length scales and low frequencies associated with Alfvénic fluctuations are particularly challenging to realize in the laboratory  [13], and experiments thus far have been limited to the weak turbulence regime  [12]. Numerical simulations of plasma turbulence, therefore, are indispensable tools to explore the fundamental nature of plasma turbulence, the mechanisms of its dissipation, and the resulting plasma heating.

The simulation of a turbulent plasma system typically requires the injection of energy into the turbulence at large scale and the dissipation of the turbulent energy at small scales. For many space and astrophysical plasma systems of interest, the dynamic range between the observed energy injection and dissipation scales exceeds current computational capabilities (a limit of approximately 3 orders of magnitude for 3D turbulence simulations). In addition, on the small scales at which the dissipation mechanisms serve to terminate the turbulent cascade of energy, the plasma dynamics is weakly collisional in many space and astrophysical plasmas of interest, so the dissipation is thought to be governed by some kinetic damping mechanism, such as collisionless wave–particle interactions [14], [15], [16]. Since it is not possible to include, in a single simulation with realistic physical parameters, both the large-scale process driving the turbulence and the kinetic physical dynamics governing the dissipation at small scales, a promising strategy is to focus on a subrange of the complete turbulent cascade.

An exciting frontier in the study of plasma turbulence, one that has engendered vigorous recent activity [17], [18], [19], [20], [21], is the quest to identify the physical mechanisms that govern the dissipation of turbulence under weakly collisional conditions and to determine the resulting heating of the plasma species. The subrange of numerical simulations, in this case, begins with a domain scale that falls within the inertial range of the turbulent cascade and extends down to encompass the small, dissipative scales. Therefore, it is desirable to inject energy into the simulation at the domain scale in a manner that resembles the nonlinear transfer of energy, within the inertial range, from scales slightly larger than the simulation domain. In constructing such a technique for driving plasma turbulence simulations, it is essential to account for the inherent scale-dependent anisotropy of Alfvénic turbulence [7], [8], [9], which becomes more anisotropic as the turbulence cascades to smaller scales. Here we describe such a mechanism for forcing plasma turbulence simulations, the oscillating Langevin antenna, that models the Alfvénic fluctuations at the domain scale generated by the transfer of energy caused by nonlinear interactions between counterpropagating Alfvén waves at scales larger than the simulation domain. The method is effective in generating strong Alfvénic turbulence in kinetic simulations and flexible enough to simulate strong or weak turbulence.

The paper is organized as follows. In Section  2, we introduce some of the basic concepts underlying Alfvénic turbulence. Section  3 discusses the simple case of sinusoidal driving and plasma coupling before moving on to the more complicated oscillating Langevin antenna in Section  4. In the latter section, the antenna is described in detail and its domain of applicability is examined. The implementation of the antenna in AstroGK is explored and the amplitude necessary for driving strong turbulence is given in Section  5. Section  6 briefly discusses driving methods employed in other turbulence simulations. In Section  7, we present a summary of this paper.