Collisional alpha transport in a weakly non-quasisymmetric stellarator magnetic field

Tolman

2021

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A general procedure for understanding plasma behaviour when resonant wave–particle interactions are the sole destabilizing and transport mechanism or only heating and/or current drive source is highlighted without recourse to involved numerical or analytical treatments. These phenomena are characterized by transport that appears to be collisionless even though collisions play a central role in narrow collisional boundary layers. The order of magnitude estimates, which include nonlinear effects, are shown to provide expressions in agreement with the principal results of recent toroidal Alfvén eigenmode (TAE), toroidal magnetic field ripple, and heating and current drive treatments. More importantly, the retention of nonlinearities leads to new estimates of the alpha particle energy diffusivity at saturation for TAE modes, and the ripple threshold at which superbanana plateau evaluations of alpha particle transport are modified by nonlinear radial drift effects. In addition, the estimates indicate when quasilinear descriptions for heating and current drive will begin to fail. The phenomenological procedure demonstrates that in magnetic fusion relevant plasmas, narrow collisional boundary layers must be retained for resonant wave–particle interactions as they enhance the role of collisions, and make stochastic particle motion unlikely to be more important than other nonlinear processes.

Section: Ripple Transport Of Alphassupporting

confidence: 83%

“…Very similar arguments to those in the preceding section are next used to make estimates for ripple transport in the superbanana plateau regime (Galeev et al 1969;Shaing 2015;Catto 2019b). They allow a bound on the ripple amplitude to be estimated.…”

Section: Ripple Transport Of Alphasmentioning

confidence: 99%

Collisional broadening of nonlinear resonant wave–particle interactions

Tolman

2021

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“…This role is directly analogous to that played by collisionality in superbanana plateau tokamak transport (see discussion in Shaing (2015), Calvo et al. (2017) and Catto (2019 a )). It is also similar to the role played by collisionality in the plateau regime of neoclassical transport (see Helander & Sigmar 2005), in the damping of plasma echoes (see Su & Oberman 1968) and in other wave–particle resonance processes (Duarte et al.…”

Section: Plasma Response To Perturbationsmentioning

confidence: 71%

Drift kinetic theory of alpha transport by tokamak perturbations

Tolman

2021

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Upcoming tokamak experiments fuelled with deuterium and tritium are expected to have large alpha particle populations. Such experiments motivate new attention to the theory of alpha particle confinement and transport. A key topic is the interaction of alpha particles with perturbations to the tokamak fields, including those from ripple and magnetohydrodynamic modes like Alfvén eigenmodes. These perturbations can transport alphas, leading to changed localization of alpha heating, loss of alpha power and damage to device walls. Alpha interaction with these perturbations is often studied with single-particle theory. In contrast, we derive a drift kinetic theory to calculate the alpha heat flux resulting from arbitrary perturbation frequency and periodicity (provided these can be studied drift kinetically). Novel features of the theory include the retention of a large effective collision frequency resulting from the resonant alpha collisional boundary layer, correlated interactions over many poloidal transits and finite orbit effects. Heat fluxes are considered for the example cases of ripple and the toroidal Alfvén eigenmode (TAE). The ripple heat flux is small. The TAE heat flux is significant and scales with the square of the perturbation amplitude, allowing the derivation of constraints on mode amplitude for avoidance of significant alpha depletion. A simple saturation condition suggests that TAEs in one upcoming experiment will not cause significant alpha transport via the mechanisms in this theory. However, saturation above the level suggested by the simple condition, but within numerical and experimental experience, which could be accompanied by the onset of stochasticity, could cause significant transport.

“…At low collisionalities, estimates indicate that the transitional ions widen the trapped-passing boundary layer to introduce a regime linear in ν * (Beidler et al 2011;Catto 2019) that cannot be treated by the procedures herein.…”

Section: A Spurious Non-omnigenous Collisional Tangential Drift Modifmentioning

confidence: 97%

Bootstrap current and parallel ion velocity in imperfectly optimized stellarators

Helander

2020

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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.