An alpha-particle-driven Alfvén wave instability in a tandem mirror reactor

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Abstract
Because their energies greatly exceed the plug potential, fusion reaction alpha particles in a tandem mirror reactor will be mirror confined rather than electrostatically confined by the end plugs. Hence, the alpha particle distribution function will have a loss cone. This anisotropy in the distribution function is shown to destabilize Alfvén waves in the central section of a tandem mirror reactor. The wave equation with a modified cold plasma response is used to determine the radial mode structure and real frequency of the Alfvén waves in cylindrical geometry. The growth rate is calculated from the resonant particle part of the plasma response. Destabilization of the wave occurs due to a cyclotron resonance of the alpha particles. The resonant interaction of the wave with the alpha particles will pitch‐angle scatter the alphas into the loss cone, effectively widening the loss cone. The instability will cause a substantial loss of alpha particle energy unless the central cell is characterized by small diameter, sharply peaked radial profile, low magnetic field, and large mirror ratio. A recent ‘‘axicell’’ reactor design is found to be stable.