Using the Virial Theorem to Analyze Effects of Energy Dynamics in the Magnetosphere

The solar wind couples with Earth’s magnetosphere driving plasma dynamics which can create magnetic perturbations at Earth’s surface impacting life on the ground. One classic way of understanding this process is via the Dungey cycle where magnetic flux is injected into the magnetosphere on the dayside via a dayside reconnection site. This flux is then transported downstream and is released from the magnetosphere via a tail reconnection site, bringing high hydrodynamic energy plasma earthward which becomes trapped in the ring current, leading to intense sustained magnetic perturbation.

In this work, we take a closer look at this process using 3D MHD results from the Space Weather Modeling Framework. Building off previous work by Brenner et al. 2021, the magnetopause surface is identified in the simulation domain to a fixed downstream tail distance. This 3D volume is then split into regions based on magnetic topology and L shell location. From here two methods are used to describe the magnetic perturbation resulting from each region. The first is using the Biot-Savart law that integrates current density vectors weighted by position and direction. The second uses the virial theorem which employs the scalar product of momentum with the position vector integrated over the magnetosphere. The latter formulation is advantageous since it directly relates the magnetic perturbation with stress terms at the magnetopause boundary and volume integrated energy density in the magnetosphere.

Results from the Biot Savart integration and virial theorem are compared with observations of ground based magnetic perturbations to study the effects of energy transport within the system during a simulated storm event.