Generation of auroral kilometric radiation by electron horseshoe distributions

High time resolution of rocket and satellite electron distribution functions within the source region of auroral kilometric radiation display a characteristic crescent shaped or horseshoe distribution. Such distribution functions are created by a field aligned electron beam moving into an increasing magnetic field, conservation of the first adiabatic invariant causes an increase of their pitch angle. This produces a broad region on the distribution function where ${\mathrm{\partial f}}_e{\mathrm{/\partial v}}_{\perp }\text{>0,}$ and is a possible source of free energy leading to radio wave emission by the cyclotron maser instability, which is more efficient than the conventional loss-cone maser instability. The stability of these electron horseshoe distribution functions is examined for right-hand extraordinary mode $\mathrm{(R–X}$ mode) radiation close to the electron cyclotron frequency propagating perpendicular to the magnetic field.