Abstract
Ignited fusion plasmas have the potential of high-Q performance but only if charged-particle fusion products deposit a large share of their energy within the plasma. The problem of alpha-particle losses in a magnetic configuration having a loss-cone and non-zero alpha Larmor radius is treated. First, an exact analytic solution is found for the zero-dimensional, time-dependent Fokker-Planck equation with a constant plasma reactivity switched on abruptly in time. Several effects are accounted for, including alpha endloss, finite alpha Larmor radius size (compared to the plasma radius), and alpha pitch-angle scattering. The results of the exact solution are then used as a guide in constructing a mocked-up representation of alpha behaviour. This model, based on two coupled first-order time-differential equations, accounts for all the effects contained in the more complicated exact solution; in addition, it allows arbitrary time variation in plasma parameters and reactivity.
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