Energy Spectrum of Lost Alpha Particles in Centrifugal Mirror Confinement

In a centrifugal mirror fusion reactor, capturing the energy of alpha particles is essential to sustaining the reaction. However, since alpha particles are born at energies much higher than the confining potential, it is virtually impossible to avoid substantial end losses. The dominant collisional processes that alpha particles experience are drag and pitch-angle scattering by the less energetic bulk population, with drag serving to capture their energy and pitch-angle scattering undermining the process by knocking them into the loss cone. The energy of prematurely lost alpha particles can still be captured via direct conversion, but determining the relative importance of these two processes, as well as designing an effective direct conversion scheme requires understanding at what energies and times alpha particles become deconfined. Here we present analytical solutions for the energy spectrum and confinement times of alpha particles in a centrifugal mirror. We use the high-energy limit of the Landau collision operator to derive a PDE describing energetic transport of alpha particles and find an asymptotic solution to this PDE valid for both DT and p-B11 scenarios. This model is validated via Monte Carlo simulations. Our framework can in principle be applied to any fast ion species subject to any applied potential, in the low collisionality, large mirror ratio and modest potential limits, making this work applicable to cases not previously considered in studies of magnetic mirror transport.