Scaling of the energy of ion beams in the low-altitude plasma sheet boundary layer

The scaling of the energy of ion beams (beamlets) in resonance regions of the low-altitude plasma sheet boundary layer has been analyzed using the measurements made on the Interball-2 and Cluster satellites at distances of 3.0 to 6.0 Earth’s radii and numerical simulations of the acceleration of ions in the current sheet of the Earth's magnetotail. The experimental test of the previously theoretically predicted scaling $W_N \sim N^A$ (where $W_N$ is the energy at the $N$th resonance and $A\sim 1.33$ shows that the real scaling of resonance energies varies in a wide range $A\in [0.61;1.75]$ and is independent of the geomagnetic indices $K_{p}$ and $AE$. Model calculations with allowance for an electric field $E_z$ perpendicular to the current sheet are in good agreement with the experimental data. They indicate that the scaling increases in the case of the dominance of the ion current and decreases in the case of the dominance of the electron current ($A>1.33$ and $A<1.33$, respectively).