\title{On the current-voltage relationship in Auroral Breakups\\ and Westward Travelling Surges} \author{\underline{A. Olsson}\footnotemark[1], A.I. Eriksson\footnotemark[1], P. Janhunen\footnotemark[2,1]} \footnotetext[1]{Swedish Institute of Space Physics, Uppsala, Sweden} \vspace{2cm} Auroral precipitating electrons often go through an acceleration region before entering the atmosphere. Regardless of what produces it, a parallel electric field is assumed to cause the acceleration. With considerations taken to this potential difference a fairly complex expression for the corresponding upward field-aligned current is derived from kinetic theory {\it [Knight, 1973]}. However, for a value of ${\it eV}/{\it kT}$ between 10 and 100 a linear simplification between the upward current density and the voltage, ${\it j}_{\rm{||}}$=$\it KV$, can be calculated to hold. The {\it K } constant, referred to the Lyans-Evans-Lundin constant, depends on the source density and the characteristc energy of the magnetospheric electrons and is an important parameter in magnetosphere-ionosphere coupling models. However, the {\it K }-value is still a rather unknown parameter and values are found in a wide range of $10^{-8}-$ $10^{-10}$ $\left[\frac{\rm{S}}{\rm{m^2}}\right]$. We'll here study if the type of auroral structure affects the {\it K }-values and how the spatial distribution of the {\it K }-value changes over the auroral structure. In the study we look at onset and westward travelling surge, WTS, events and compare them with earlier results from observations of more stable auroral arcs. Measurements are done with the EISCAT radar, and through an inversion technique of EISCAT density data flux-energy spectra are calculated. From fittings of accelerated Maxwellian distributions, the source densities, characteristic energies and the potential drops are estimated and discussed. The study indicates that the linearization of the Full-Knight formulation holds even for the very high potential drops and characteristic temperatures found in dynamic onset and WTS events. The values of K are in both the onset cases, and the WTS events found to be very low, around $10^{-11} \left[\frac{\rm{S}}{\rm{m^2}}\right]$.