Formula representation of auroral ionospheric O+ outflows based on systematic simulations with effects of soft electron precipitation and transverse ion heating

Systematic Dynamic Fluid Kinetic (DyFK) model simulations are conducted to obtain a simulation‐based formula representation of the O+ outflow flux level versus the energy flux of soft electron precipitation, and wave spectral density of transverse wave heating in the high‐latitude auroral region. Based on results of 140 DyFK simulations of auroral outflows, we depict the O+ outflows at the ends of these two hour simulation runs in spectrogram form versus these parameters. We also approximate the results by the formula representation: = 8.8(3.0 × 105 + 2fe1.4 × 107)(tanh (8Dwave) + 0.2Dwave0.6), where is the O+ number flux in cm−2/s at 3 RE mapped to 1000 km altitude, fe is the electron precipitation energy flux in ergs cm−2/s, and Dwave is the wave electric field spectral density at O+ gyrofrequency at 1 RE in (mV)2 m−2 Hz−1. This formula representation provides a convenient way to set the boundary conditions of the ionosphere in global magnetosphere simulation since the ionosphere is the important plasma source of the magnetosphere.