On the bootstrap current in stellarators and tokamaks

Abstract

The expression for the long-mean-free-path limit of the bootstrap current in stellarators is rederived in such a way that the expansion procedure is identical to that used in the corresponding calculation for a tokamak. In addition, the first correction due to finite collisionality is calculated and shown to vanish in quasi-isodynamic configurations without net current. This correction, which is proportional to the square root of the collisionality, is found to compare well with a numerical solution of the first-order drift kinetic equation in spherical tokamak geometry. Numerically, it appears that there is a similar correction in general stellarator geometry, which however depends on the strength of the radial electric field.

Stellarator and tokamak plasmas: a comparison

“…The bootstrap current is positive in quasi-axisymmetric stellarators, negative in quasi-helically symmetric ones, and is close to zero in quasi-isodynamic devices [29,50,51]. The latter have the additional property that the Pfirsch-Schlüter current closes within each period of the configuration [47].…”

Stellarator bootstrap current and plasma flow velocity at low collisionality

“…However, we find that this result ceases to be valid in the √ ν or ν-regimes, where the component of the drifts tangential to the flux surface causes the appearance of an additional term that needs to be taken into account. It is well known from numerical results [Beidler et al (2011);Helander et al (2011)] that the approach to the lowcollisionality limit is slow, and in the penultimate section of the paper we identify a possible reason for this behaviour and derive a scaling for the deviation from the lowcollisionality result. Our conclusions are summarised in the final section.…”

“…3 of Kernbichler et al (2016). At least sometimes, the finitecollisionality correction appears to scale as ν 0.5 * , which is indistinguishable from ν 0.4 * , see Helander et al (2011).…”

Impurities in a non-axisymmetric plasma: Transport and effect on bootstrap current

“…In a 3D device, a bootstrap current arises due to similar reasons as in a tokamak, but the size of it is typically substantially smaller than the Ohmic current in a tokamak [1,2,20]. The bootstrap current is a consequence of the trapped particle orbits, and is generally larger at low collisionality than at high collisionality [16,21].…”