11,773 research outputs found
Flow damping in stellarators close to quasisymmetry
Quasisymmetric stellarators are a type of optimized stellarators for which
flows are undamped to lowest order in an expansion in the normalized Larmor
radius. However, perfect quasisymmetry is impossible. Since large flows may be
desirable as a means to reduce turbulent transport, it is important to know
when a stellarator can be considered to be sufficiently close to quasisymmetry.
The answer to this question depends strongly on the size of the spatial
gradients of the deviation from quasisymmetry and on the collisionality regime.
Recently, formal criteria for closeness to quasisymmetry have been derived in a
variety of situations. In particular, the case of deviations with large
gradients was solved in the regime. Denoting by a parameter
that gives the size of the deviation from quasisymmetry, it was proven that
particle fluxes do not scale with , as typically claimed, but
with . It was also shown that ripple wells are not necessarily the main
cause of transport. This paper reviews those works and presents a new result in
another collisionality regime, in which particles trapped in ripple wells are
collisional and the rest are collisionless.Comment: 14 pages, 2 figures. To appear in Plasma Physics and Controlled
Fusio
Optimizing stellarators for large flows
Plasma flow is damped in stellarators because they are not intrinsically
ambipolar, unlike tokamaks, in which the flux-surface averaged radial electric
current vanishes for any value of the radial electric field. Only
quasisymmetric stellarators are intrinsically ambipolar, but exact
quasisymmetry is impossible to achieve in non-axisymmetric toroidal
configurations. By calculating the violation of intrinsic ambipolarity due to
deviations from quasisymmetry, one can derive criteria to assess when a
stellarator can be considered quasisymmetric in practice, i.e. when the flow
damping is weak enough. Let us denote by a small parameter that
controls the size of a perturbation to an exactly quasisymmetric magnetic
field. Recently, it has been shown that if the gradient of the perturbation is
sufficiently small, the flux-surface averaged radial electric current scales as
for any value of the collisionality. It was also argued that when
the gradient of the perturbation is large, the quadratic scaling is replaced by
a more unfavorable one. In this paper, perturbations with large gradients are
rigorously treated. In particular, it is proven that for low collisionality a
perturbation with large gradient yields, at best, an deviation
from quasisymmetry. Heuristic estimations in the literature incorrectly
predicted an deviation.Comment: 24 pages, 2 figures. To appear in Plasma Physics and Controlled
Fusio
The effect of tangential drifts on neoclassical transport in stellarators close to omnigeneity
In general, the orbit-averaged radial magnetic drift of trapped particles in
stellarators is non-zero due to the three-dimensional nature of the magnetic
field. Stellarators in which the orbit-averaged radial magnetic drift vanishes
are called omnigeneous, and they exhibit neoclassical transport levels
comparable to those of axisymmetric tokamaks. However, the effect of deviations
from omnigeneity cannot be neglected in practice. For sufficiently low
collision frequencies (below the values that define the regime), the
components of the drifts tangential to the flux surface become relevant. This
article focuses on the study of such collisionality regimes in stellarators
close to omnigeneity when the gradient of the non-omnigeneous perturbation is
small. First, it is proven that closeness to omnigeneity is required to
preserve radial locality in the drift-kinetic equation for collisionalities
below the regime. Then, it is shown that neoclassical transport is
determined by two layers in phase space. One of the layers corresponds to the
regime and the other to the superbanana-plateau regime. The
importance of the superbanana-plateau layer for the calculation of the
tangential electric field is emphasized, as well as the relevance of the latter
for neoclassical transport in the collisionality regimes considered in this
paper. In particular, the tangential electric field is essential for the
emergence of a new subregime of superbanana-plateau transport when the radial
electric field is small. A formula for the ion energy flux that includes the
regime and the superbanana-plateau regime is given. The energy
flux scales with the square of the size of the deviation from omnigeneity.
Finally, it is explained why below a certain collisionality value the
formulation presented in this article ceases to be valid.Comment: 36 pages. Version to be published in Plasma Physics and Controlled
Fusio
Dual branes in topological sigma models over Lie groups. BF-theory and non-factorizable Lie bialgebras
We complete the study of the Poisson-Sigma model over Poisson-Lie groups.
Firstly, we solve the models with targets and (the dual group of the
Poisson-Lie group ) corresponding to a triangular -matrix and show that
the model over is always equivalent to BF-theory. Then, given an
arbitrary -matrix, we address the problem of finding D-branes preserving the
duality between the models. We identify a broad class of dual branes which are
subgroups of and , but not necessarily Poisson-Lie subgroups. In
particular, they are not coisotropic submanifolds in the general case and what
is more, we show that by means of duality transformations one can go from
coisotropic to non-coisotropic branes. This fact makes clear that
non-coisotropic branes are natural boundary conditions for the Poisson-Sigma
model.Comment: 24 pages; JHEP style; Final versio
Intrinsic rotation with gyrokinetic models
The generation of intrinsic rotation by turbulence and neoclassical effects
in tokamaks is considered. To obtain the complex dependences observed in
experiments, it is necessary to have a model of the radial flux of momentum
that redistributes the momentum within the tokamak in the absence of a
preexisting velocity. When the lowest order gyrokinetic formulation is used, a
symmetry of the model precludes this possibility, making small effects in the
gyroradius over scale length expansion necessary. These effects that are
usually small become important for momentum transport because the symmetry of
the lowest order gyrokinetic formulation leads to the cancellation of the
lowest order momentum flux. The accuracy to which the gyrokinetic equation
needs to be obtained to retain all the physically relevant effects is
discussed
When omnigeneity fails
A generic non-symmetric magnetic field does not confine magnetized charged
particles for long times due to secular magnetic drifts. Stellarator magnetic
fields should be omnigeneous (that is, designed such that the secular drifts
vanish), but perfect omnigeneity is technically impossible. There always are
small deviations from omnigeneity that necessarily have large gradients. The
amplification of the energy flux caused by a deviation of size is
calculated and it is shown that the scaling with of the
amplification factor can be as large as linear. In opposition to common wisdom,
most of the transport is not due to particles trapped in ripple wells, but to
the perturbed motion of particles trapped in the omnigeneous magnetic wells
around their bounce points.Comment: 6 pages, 2 figure
- …