Abstract: Auroral electron precipitation is a key mechanism in traditional aurora. These electrons are responsible for excitation emissions which create the visible light of the aurora, and are linked to ionospheric conductivity. The relationship between precipitation and conductivity has been explored by Robinson (1987) to determine the height integrated conductance. In the local form, the conductivity ties currents to the electric field through Ohm’s law J=𝝈⋅E. Distributed in situ measurements of the electric field and magnetic field in the ionosphere around the aurora are planned in ARCS (Auroral Reconstruction CubeSwarm), a NASA mission concept involving 32 cubesats. During passes over Alaska there will also be tomography and ground based auroral imaging that will measure the 3D plasma density; however these ground based observations will not exist for every pass and can be obscured by weather. A case study of working with conductivity without precipitation is found in STEVE (Strong Thermal Emission Velocity Enhancement). STEVE is a newly observed ionospheric phenomenon characterized by a visible purple or mauve band without auroral electron precipitation. It is also associated with strong ionospheric flows (and thus a localized  electric field) and reduced plasma density [Nishimura et al, 2019]. This thesis works toward a method to determine auroral region volumetric plasma density (which drives conductivity) from plasma flow and E, by exploring different pairings (governed by the current continuity equation) of J, E, and plasma densities in GEMINI (Geospace Environment Model of Ion-Neutral Interactions) [Zettergen 2012] to find common patterns, preparatory to developing a direct inversion method using GEMINI.  Examples for simple arc systems are compared against expectations from the idealized Robinson inversion method. This will allow plasma density reconstructions from in situ field data when the ARCS tomography and ground based imaging measurements are unavailable; and will help understand the volumetric current structure of STEVE. In particular we look to determine if shears in the strong ionospheric flows of STEVE events are sufficient to source field-aligned currents sufficiently strong to cause tearing mode instabilities.