Effect of a strong equilibrium electric field on the zonal flow residual in quasisymmetric stellarators

It was recently shown [1] that several neoclassical formulae for tokamaks can be significantly modified if the radial electric field is as large as that observed in a pedestal -- specifically, if $d\Phi/dr \sim T/(e \rho_{\mbox{pol}})$, where $\rho_{\mbox{pol}}$ is the poloidal ion gyroradius. In the present work, we consider the same modification of neoclassical quantities in quasisymmetric stellarators, beginning with the zonal flow residual [2]. The tokamak analysis in [1] exploited the conservation of canonical angular momentum. The analysis therefore requires modification in stellarators, in which canonical angular momentum is not conserved. In its place, one can use the ``helical momentum'' which is known to be conserved if the magnetic field is quasisymmetric [3].\\[4pt] [1] Kagan and Catto, \emph{Phys. Plasmas} {\bf 16}, 056105 (2009).\\[0pt] [2] Rosenbluth and Hinton, \emph{Phys. Rev. Lett.} {\bf 80}, 724 (1998).\\[0pt] [3] Boozer, \emph{Phys. Fluids} {\bf 26}, 496 (1983).