The effect of tail stretching on the ionospheric accessibility of relativistic electron beam experiments

New accelerator technologies have made it possible to install a lightweight electron beam accelerator onto small to medium satellites. Electron beams fired along the geomagnetic field would be able to carry energy flux into the ionosphere if they were fired into the loss cone, making these particles observable from the ground. Such an experiment would provide a way to accurately map field lines. One of the important challenges to utilizing this concept is understanding accessibility of these electrons to the ionosphere. While relativistic electron beams are generally more stable than lower energy beams, they are more sensitive to the effects of field-line curvature, which can significantly modify the loss cone [Porazik et al., 2014] making accessibility to the ionosphere sensitive to the launch angle with respect to the magnetic field. We examine the loss cone for 1 MeV electrons in a realistic magnetospheric geometry considering, in particular, the role of field-line stretching. To map the loss cone, we consider conservation of the first adiabatic invariant to second order in ρ/L using the asymptotic series derived by Gardner [Phys Fluids, 1966], which is valid on the midnight meridian. We investigate the loss cones for different magnetic field models controlled by a stretching parameter over the entire midnight meridian. We found that, because tail stretching increases field line curvature near the midplane but decreases curvature elsewhere, accessibility to the ionosphere is increased by tail stretching in regions above and below the midplane, although accessibility of particles passing through the midplane is reduced. This result implies that satellites armed with electron beam accelerators may be able to visibly affect the atmosphere from distances greater than previously anticipated.