Neoclassical theory of collisional transport in the presence of fusion α-particles

Abstract

The neoclassical transport theory is developed for an axisymmetric toroidal plasma containing highly energetic α-particles as produced by fusion events. It is shown that the α-particle fluxes in this case have a weaker dependence on the aspect ratio than at lower energies since the prevailing collisional effect is a drag. The bootstrap current results to be reduced by the presence of fusion α-particles.

A new sawtooth control mechanism relying on toroidally propagating ion cyclotron resonance frequency waves: Theory and Joint European Torus tokamak experimental evidence

“…Finally, barely passing ions contribute to a small orbit current, j 1 , while, due to their small orbit width, deeply passing ions hardly contribute to j 1 at all. Finally, we note that barely passing fast ions also contribute to a bootstrap current, 35 despite being neglected in the above definition of j 1 . However, since pitch angle scattering is very weak for energetic ions, the fast ion bootstrap current is of order ⑀ smaller than the bootstrap current associated with electrons ͑given a like for like pressure profile͒.…”

“…However, since pitch angle scattering is very weak for energetic ions, the fast ion bootstrap current is of order ⑀ smaller than the bootstrap current associated with electrons ͑given a like for like pressure profile͒. 35 Resultingly, the fast ion bootstrap current can be ignored. To summarize, trapped ions cannot contribute to the current due to parallel asymmetry, j 0 , but meanwhile trapped ions strongly dominate the finite orbit width current j 1 .…”

Neoclassical transport of isotropic fast ions

“…However, all these recent treatments, which, in contrast to Ref. [1], emphasized only the pitch angle scattering terms in the collision operator when solving for the fast ions distribution function, are also incomplete. In particular, in Ref.…”

Variational calculation of alpha-driven bootstrap current in a deutrium–tritium tokamak reactor

“…To find the parameter ␣ there is an easier way than a variational way. It is well known, 3 and can be easily shown, that the slowing down only solution G v does not yield alpha bootstrap current to the order ⑀ 1/2 . The function y v , which models G v , should satisfy this known requirement…”

“…It is well known 2 that the pitch angle scattering effect yields bootstrap current of the order ⑀ 1/2 , where ⑀ is the horizontal inverse aspect ratio, while the energy scattering alone can yield bootstrap current of order ⑀ 3/2 only. Earlier evaluation of alpha-driven bootstrap current neglected the pitch-angle scattering effect, 3 thus resulting in an underestimate of the alpha-driven bootstrap current, as pointed out in Ref. 4.…”