Theory of stochastic diffusion in Wendelstein-line stellarators in the presence of radial electric field

In optimized stellarators of the Wendelstein line prompt losses of fast ions in superbanana orbits are reduced through a modification of the magnetic configuration by high β (ratio of the plasma pressure to the magnetic field pressure), so that most contours of the longitudinal adiabatic invariant J ∥ of locally trapped particles are closed inside the plasma volume. However, magnetic drift leads to the transformation of some of these particles into the locally passing ones and vice versa. Orbit transformation upon crossing the separatrix between locally trapped and locally passing states is accompanied by jumps in J ∥ that lead to collisionless stochastic diffusion (SD), which was shown to be an important mechanism of the loss of energetic ions in the optimized Wendelstein-line stellarators (C D Beidler et al 2001 Phys. Plasmas 8 2731). The theory of SD that took into account the phase space asymmetry between locally passing particles with opposite signs of v ∥ was developed in (A V Tykhyy 2018 Ukr. J. Phys. 63 (6) 495). This work extends that theory to consider the effect of radial electric field E r on SD. It is found that negative E r of such magnitudes as those observed in W7-X and predicted in Helias reactor can mitigate SD losses from the plasma core of NBI ions in W7-X and α -particles in Helias. This loss mitigation occurs because added E × B drift increases the range of pitch angles for which separatrices are closed inside the plasma volume, even while it increases the SD coefficient. This means that E r can be used in addition to magnetic configuration changes for both loss mitigation and energy deposition profile optimization.