Alpha-particle orbits near rational flux surfaces in stellarators

In modern stellarator designs, confinement of the bounce-averaged drift motion of fusion-born alphas is achieved by optimising the magnetic field for omnigeneity. Recently, concerns have been raised that additional optimisation may be required for adequate confinement of certain classes of alpha particles with unusual orbits. One such class is particles near rational flux surfaces. Simulations have shown that the orbits of passing alpha particles near rational surfaces can contain islands, even when the magnetic field possesses nested toroidal flux surfaces [1,2]. Meanwhile, trapped alpha particles undergoing resonant motion near a rational surface have been found to exhibit poor conservation of the second adiabatic invariant [3]. We give a theoretical account of these unusual orbits by deriving simple equations for the orbits of energetic particles near rational surfaces in a general stellarator. These orbits are determined by conservation of an adiabatic invariant associated with the closed rational-surface field lines. The resulting theory agrees extremely well with guiding-centre and full-orbit simulations conducted using the ASCOT code.

[1] R. White, A. Bierwage and S. Ethier, Phys. Plasmas 29, 5 (2022).

[2] R. White, Phys. Plasmas 29, 9 (2022).

[3] E. Paul et al., Nucl. Fusion 62, 12 (2022).