Diagnosing collisionless energy transfer using field–particle correlations: Vlasov–Poisson plasmas

Abstract

Turbulence plays a key role in the conversion of the energy of large-scale fields and flows to plasma heat, impacting the macroscopic evolution of the heliosphere and other astrophysical plasma systems. Although we have long been able to make direct spacecraft measurements of all aspects of the electromagnetic field and plasma fluctuations in near-Earth space, our understanding of the physical mechanisms responsible for the damping of the turbulent fluctuations in heliospheric plasmas remains incomplete. Here we propose an innovative field–particle correlation technique that can be used to measure directly the secular energy transfer from fields to particles associated with collisionless damping of the turbulent fluctuations. Furthermore, this novel procedure yields information about the collisionless energy transfer as a function of particle velocity, providing vital new information that can help to identify the dominant collisionless mechanism governing the damping of the turbulent fluctuations. Kinetic plasma theory is used to devise the appropriate correlation to diagnose Landau damping, and the field–particle correlation technique is thoroughly illustrated using the simplified case of the Landau damping of Langmuir waves in a 1D-1V (one dimension in physical space and one dimension in velocity space) Vlasov–Poisson plasma. Generalizations necessary to apply the field–particle correlation technique to diagnose the collisionless damping of turbulent fluctuations in the solar wind are discussed, highlighting several caveats. This novel field–particle correlation technique is intended to be used as a primary analysis tool for measurements from current, upcoming and proposed spacecraft missions that are focused on the kinetic microphysics of weakly collisional heliospheric plasmas, including the Magnetospheric Multiscale (MMS), Solar Probe Plus, Solar Orbiter and Turbulence Heating ObserveR (THOR) missions.

Evidence for electron Landau damping in space plasma turbulence

“…Field-particle correlation technique. The method for measuring the energy transfer is based on a field-particle correlation technique [38,[62][63][64]80] and briefly summarised here. The Vlasov equation,…”

Diagnosing collisionless energy transfer using field–particle correlations: gyrokinetic turbulence

“…The novel approach of using field-particle correlations to diagnose the energy transfer between fields and particles has been described for electrostatic fluctuations in the Vlasov-Poisson system (Howes et al 2017) and been applied to both damped and linearly unstable systems (Klein & Howes 2016;Howes 2017;Klein 2017). Here we describe the application of the field-particle correlation technique to the case of electromagnetic fluctuations in the Vlasov-Maxwell system.…”

“…Since taking the velocity gradient of noisy or low resolution phase-space measurements of particle velocity distribution functions can lead to large errors, one can define a related correlation C that is derived by an integration by parts in velocity (Howes et al 2017). These alternative forms are…”

“…‡ Such structure was seen in the electrostatic simulations of Landau damping described in Klein & Howes (2016) ‡ While C E (τ = 0) is quantitatively similar if we use g p , h p , or f p in its calculation, the additional terms in h p and f p obscure the structure around v = v res in the distributions themselves. and Howes et al (2017). To focus on this v dependence, we calculate the reduced field-particle correlation, integrated over v ⊥ , which for notational simplicity, we write as…”

“…) and the Landau damping of a single kinetic Alfvén wave (Howes 2017) to a system of strong turbulence where the role of resonant interactions is a matter of current debate.…”