Tens to hundreds of keV electron precipitation driven by kinetic Alfv\'en waves during an electron injection

Electron injections are critical processes associated with magnetospheric substorms, which deposit significant electron energy into the ionosphere. Although wave scattering of $<$10 keV electrons during injections has been well studied, the link between magnetotail electron injections and energetic ($\geq$100 keV) electron precipitation remains elusive. Using conjugate observations between the ELFIN and Magnetospheric Multiscale (MMS) missions, we present evidence of tens to hundreds of keV electron precipitation to the ionosphere potentially driven by kinetic Alfv\'en waves (KAWs) associated with magnetotail electron injections and magnetic field gradients. Test particle simulations adapted to observations show that dipolarization-front magnetic field gradients and associated $\nabla B$ drifts allow Doppler-shifted Landau resonances between the injected electrons and KAWs, producing electron spatial scattering across the front which results in pitch-angle decreases and subsequent precipitation. Test particle results show that such KAW-driven precipitation can account for ELFIN observations below $\sim$300 keV.