Simple, general, realistic, robust, analytic tokamak equilibria. Part 2. Pedestals and flow

Part 1 described a wide range of analytic tokamak equilibria modelling smooth limiter surfaces, double- and single-null divertor surfaces, arbitrary aspect ratio, elongation, triangularity and beta. Part 2 generalizes the analysis to further include edge pedestals and toroidal flow. Specifically, edge pedestals are allowed in the pressure, pressure gradient and toroidal current density. Also, an edge-localized contribution to the bootstrap current is treated. In terms of flow, analytic solutions are obtained for two cases: a $\gamma = 2$ adiabatic and a $\gamma = \infty $ incompressible energy conservation relation.

Bootstrap current and parallel ion velocity in imperfectly optimized stellarators

A novel derivation of the parallel ion velocity, and the bootstrap and Pfirsch–Schlüter currents in an imperfectly optimized (that is, almost omnigenous) stellarator magnetic field, $\boldsymbol{B}$ , is presented that somewhat more generally recovers expressions completely consistent with previous analytic results. However, it is also shown that, when the conventional radially local form of the drift kinetic equation is employed, the flow velocity and the bootstrap current acquire a spurious contribution proportional to $\unicode[STIX]{x1D714}/\unicode[STIX]{x1D708}$ , where $\unicode[STIX]{x1D714}$ denotes the $\boldsymbol{E}\times \boldsymbol{B}$ rotation frequency (due to the radial electric field $\boldsymbol{E}$ ) and $\unicode[STIX]{x1D708}$ the collision frequency. This contribution is particularly large in the $\sqrt{\unicode[STIX]{x1D708}}$ regime and at smaller collisionalities, where $\unicode[STIX]{x1D714}/\unicode[STIX]{x1D708}\gtrsim 1$ , and is presumably present in most numerical calculations, but it disappears if a more accurate drift kinetic equation is used.