A Parametric Study of Quasi‐Static Electron Acceleration by Modified Electron Acoustic Wave and Comparison to Knight Relation

A comprehensive understanding of how a magnetic source potential is distributed in the magnetosphere‐ionosphere circuit, and the relationship between the field‐aligned current and the parallel potential, is essential for accurately interpreting the observational characteristics of a quasi‐static arc. In this study, we investigate the formation of quasi‐static electron acceleration led by kinetic Alfvén wave‐electron acoustic wave coupling, based on one‐dimensional kinetic simulations. Various controlling factors of the coupling process are considered, including the hot electron density and temperature, the cold electron density and temperature, the perpendicular wave number, and the ionospheric conductance. The ratio between the parallel potential drop and field‐aligned current is found to be approximately proportional to the square root of the hot electron temperature and inversely proportional to the hot electron density, similar to the Knight relation but with a modified slope factor that depends on the perpendicular wavelength and cold electron parameters. Meanwhile, with smaller perpendicular wavelength, lower hot electron density, higher hot electron temperature, and lower cold electron density, more potential drop is applied to the parallel electron acceleration in the transition region. Plain Language Summary It is believed that above a visible quiet aurora arc, a magnetosphere‐ionosphere circuit is formed to sustain the arc. How this circuit is formed and what are the controlling factors are important to understand the essence of an auroral arc. We investigate the parametric dependence of the potential drop distribution and the ratio between parallel potential drop and field‐aligned current based on 1D kinetic simulations. We found that the ratio of parallel potential drop to field‐aligned current satisfies the well‐known Knight relation and the potential drop distribution, either applied to parallel electron acceleration or to the ionosphere, is dependent on arc width, the temperature, and the density of both hot electron species originated from the magnetosphere and cold electron species originated from the ionosphere, and ionospheric conductance. The results shown here are useful in explaining the formation of an auroral arc and its underlying physics. Key Points A quasi‐static electron acceleration by MEAW can be achieved with typical perpendicular scale of arc The relation between parallel potential drop and current is consistent with the Kni