Abstract
In the last few years, the relationship between reconnection and
turbulence has received significant attention. A surprising recent
result is that laminar reconnection has been shown to exhibit a power
law spectrum consistent with the Kolmogorov law of turbulence1. However,
there still exists an unanswered question: “Is magnetic reconnection
fundamentally an energy cascade?”. The energy cascade can be measured
directly as a function of spatial scale length using the generalized
von-Karman Howarth equation based on the framework of incompressible
Hall MHD2. In this study, we apply this technique to 2.5D kinetic
particle-in-cell (PIC) simulations of strong turbulence and laminar
reconnection, comparing the two to study the flow of energy across
spatial scales (lags). Both the turbulence and reconnection simulations
show similar behavior, implying that reconnection fundamentally involves
an energy cascade. The largest lags are dominated by a steady decrease
in energy (second order structure functions) which drives the global
system dynamics. At smaller lags, a relatively constant flow (cascade)
of energy occurs from large to small scales which can be associated with
an MHD inertial range. At still smaller lags, the rate of energy flow
decreases considerably, and this energy flux is dominated by Hall
physics. In the reconnection simulation, the cascade of energy is
strongly correlated with the reconnection rate, with both shutting off
at similar times. References: Adhikari et al., Phys. Plasmas 27, 042305
(2020); https://doi.org/10.1063/1.5128376 Hellinger et al., ApJ Letters
857, L19 (2018); http://doi.org/10.3847/2041-8213/aabc06