On the Closure Relations for Multimoment Fluid Models of the Long-Range Potential in Downward Auroral Current Regions

Recently, we have developed a new fluid theory in the guiding center and gyrotropic approximation that includes the effect of wave-particle interactions for the turbulent, weakly inhomogeneous, non-uniformly magnetized plasma and is applicable to the field-aligned Birkeland current system of the earth's magnetosphere. It is assumed that the turbulence is random and electrostatic, and that the velocity-space Fokker-Planck operator can be used to calculate the correlation functions that describe the wave-particle interactions. This model uses satellite data as a boundary condition; we solve the fluid equations downward to the estimated double layer altitude and upward into the magnetosphere. The results of this calculation depend to a significant extent on how the system of equations is closed. We seek to verify the closure relations in our model by comparing the high-altitude predictions of a run based on FAST data at ~ 4000~km with measurements from Polar at ~ 8 R_E on nearly the same flux tube. We can run our model with different possible closures in order to see which one best predicts the high-altitude observations.