Collisionless neoclassical polarization drift in a spatio-temporally sheared radial electric field in a tokamak plasma

Neoclassical polarization drift of plasma ions is of critical importance in the dynamics of a radial electric field $E_r$. Neoclassical polarization drift speed $V_{\rm NP}$ of collisionless single ions is studied using a guiding center code in a time-varying, spatially sheared $E_r$ in a realistic tokamak geometry. It is found numerically that $V_{\rm NP}$ is not only a function of the time derivative $dE_r/dt$, as conventionally understood, but also a strong function of the radial shear $dE_r/dr$ if the shear length is on the same order as the ion banana width. If the radial shear $(\Delta r) dE_r/dr$ has the same sign as $E_r$, where $\Delta r$ is the banana excursion width, then the radial shear effect adds to $V_ {\rm NP}$; but if $(\Delta r) dE_r/dr$ has the opposite sign to $E_r$, then its effect opposes $V_{\rm NP}$. Due to this effect, $V_{\rm NP}$ can even be in the opposite direction from the $dE_r/dr=0$ case for fat banana ions. An analytic investigation reveals that this effect is simply due to the finite banana modification to the orbital average $E_r$. An approximate analytic formula has been presented for majority ions in a conventional tokamak plasma.