11,284 research outputs found
Long-wavelength limit of gyrokinetics in a turbulent tokamak and its intrinsic ambipolarity
Recently, the electrostatic gyrokinetic Hamiltonian and change of coordinates
have been computed to order in general magnetic geometry. Here
is the gyrokinetic expansion parameter, the gyroradius over the
macroscopic scale length. Starting from these results, the long-wavelength
limit of the gyrokinetic Fokker-Planck and quasineutrality equations is taken
for tokamak geometry. Employing the set of equations derived in the present
article, it is possible to calculate the long-wavelength components of the
distribution functions and of the poloidal electric field to order
. These higher-order pieces contain both neoclassical and turbulent
contributions, and constitute one of the necessary ingredients (the other is
given by the short-wavelength components up to second order) that will
eventually enter a complete model for the radial transport of toroidal angular
momentum in a tokamak in the low flow ordering. Finally, we provide an explicit
and detailed proof that the system consisting of second-order gyrokinetic
Fokker-Planck and quasineutrality equations leaves the long-wavelength radial
electric field undetermined; that is, the turbulent tokamak is intrinsically
ambipolar.Comment: 70 pages. Typos in equations (63), (90), (91), (92) and (129)
correcte
You never surf alone. Ubiquitous tracking of users' browsing habits
In the early age of the internet users enjoyed a large level of anonymity. At
the time web pages were just hypertext documents; almost no personalisation of
the user experience was o ered. The Web today has evolved as a world wide
distributed system following specific architectural paradigms. On the web now,
an enormous quantity of user generated data is shared and consumed by a network
of applications and services, reasoning upon users expressed preferences and
their social and physical connections. Advertising networks follow users'
browsing habits while they surf the web, continuously collecting their traces
and surfing patterns. We analyse how users tracking happens on the web by
measuring their online footprint and estimating how quickly advertising
networks are able to pro le users by their browsing habits
Sources of intrinsic rotation in the low flow ordering
A low flow, gyrokinetic formulation to obtain the intrinsic
rotation profiles is presented. The momentum conservation equation in the low
flow ordering contains new terms, neglected in previous first principles
formulations, that may explain the intrinsic rotation observed in tokamaks in
the absence of external sources of momentum. The intrinsic rotation profile
depends on the density and temperature profiles and on the up-down asymmetry.Comment: 20 page
Quantifying the Inefficiency of the US Social Security System
We quantify the inefficiency of the retirement component of the US social security system within a model where agents receive idiosyncratic labor-productivity shocks that are privately observedsocial security, efficient allocations, idiosyncratic shocks
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
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
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
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