Probability of field-aligned currents observed by the satellite cluster in the magnetotail

Field-aligned current (FAC) density distribution at the plasma sheet boundary layers is statistically studied. The FAC is calculated by the so-called curlometer technique with the data from FGM onboard the four Cluster spacecraft in 2001. By calculation we obtain a large number of FAC samples. In the samples, most of calculated FAC densities were very small and around zero caused by some errors or noise. In order to get the real FAC density distribution in the magnetotail, we use a three-Gaussian distribution to fit the errors, then subtract the estimated error contribution from the full distribution and obtain the FAC density distribution. The result shows that the FAC occurrence versus its density has a distribution consisting of a Gaussian distribution with an additional decreasing exponential distribution. The most probable value of the FAC density is 3.45 pT/km.