The direct hand of the magnetosphere in controlling small-scale auroral plasma turbulence: Introducing the renormalization group

Abstract. Studies of high-latitude plasma turbulence in Earth's upper atmosphere fundamentally focus on the differential response of electrons and ions to strong external electric fields generated during geomagnetic storms. Because ions in the E region are heavy and highly collisional, they remain largely tied to the neutral gas, whereas magnetized electrons undergo rapid E×B-drift. Microscopic polarization electric fields are generated when the relative drift velocity between these streaming electrons and the background ions exceeds the local ion-acoustic speed, triggering two-stream plasma instabilities, producing Farley Buneman waves. We propose a new theory that explicitly considers thousands, or millions, of such waves being excited inside a limited volume of space around aurorae, subject to the renormalization group. The resulting theory constitutes an effective field-theory for Farley-Buneman turbulence in the Martin-Siggia-Rose formalism. At the core of this theory is a statistical description of Farley-Buneman waves, where we allow each individual wave to produce a polarization electric field. We treat the sum total of these "micro-fields" that occur inside a turbulent volume as a stochastic variable, or simply noise. That noise, now a thermodynamic property, becomes the basis for anomalous diffusion, and an effective diffusion tensor, and we recover the expression for Bohm diffusion. In support of this theory, we present a large statistical analysis of how auroral electrojet turbulence responds to magnetospheric driving,  revealing a clear tendency for the observed number density of turbulent waves to scale linearly with driving power, matching the predictions made by our field theory's overdamped equations of motion. Crucially, the effective field theory offers closed-form calculations of macroscopic transport relations that are uniquely suitable for sub-grid parameterization in space weather modeling, mimicking the success of stochastic parameterization in hydrodynamic Earth-system models. The derivation of these parameterized equations demonstrates how Bohm diffusion arises from a statistical-mechanical treatment of turbulent volumes, at the expense of an explicit treatment of the turbulent cascade. The equations should be investigated further, and in future, they may model the evolution of momentum and energy in numerical treatments of global magnetohydrodynamic circulation, below the scale-sizes normally considered accessible to fast, predictive models.