625 research outputs found
Reduction and approximation in gyrokinetics
The gyrokinetics formulation of plasmas in strong magnetic fields aims at the
elimination of the angle associated with the Larmor rotation of charged
particles around the magnetic field lines. In a perturbative treatment or as a
time-averaging procedure, gyrokinetics is in general an approximation to the
true dynamics. Here we discuss the conditions under which gyrokinetics is
either an approximation or an exact operation in the framework of reduction of
dynamical systems with symmetryComment: 15 pages late
Energetic Consistency and Momentum Conservation in the Gyrokinetic Description of Tokamak Plasmas
Gyrokinetic field theory is addressed in the context of a general
Hamiltonian. The background magnetic geometry is static and axisymmetric, and
all dependence of the Lagrangian upon dynamical variables is in the Hamiltonian
or in free field terms. Equations for the fields are given by functional
derivatives. The symmetry through the Hamiltonian with time and toroidal angle
invariance of the geometry lead to energy and toroidal momentum conservation.
In various levels of ordering against fluctuation amplitude, energetic
consistency is exact. The role of this in underpinning of conservation laws is
emphasised. Local transport equations for the vorticity, toroidal momentum, and
energy are derived. In particular, the momentum equation is shown for any form
of Hamiltonian to be well behaved and to relax to its magnetohydrodynamic (MHD)
form when long wavelength approximations are taken in the Hamiltonian. Several
currently used forms, those which form the basis of most global simulations,
are shown to be well defined within the gyrokinetic field theory and energetic
consistency.Comment: RevTeX 4, 47 pages, no figures, revised version updated following
referee comments (discussion more strictly correct/consistent, 4 references
added, results unchanged as they depend on consistency of the theory),
resubmitted to Physics of Plasma
High-m Kink/Tearing Modes in Cylindrical Geometry
The global ideal kink equation, for cylindrical geometry and zero beta, is
simplified in the high poloidal mode number limit and used to determine the
tearing stability parameter, . In the presence of a steep
monotonic current gradient, becomes a function of a parameter,
, characterising the ratio of the maximum current gradient to
magnetic shear, and , characterising the separation of the resonant
surface from the maximum of the current gradient. In equilibria containing a
current "spike", so that there is a non-monotonic current profile,
also depends on two parameters: , related to the ratio
of the curvature of the current density at its maximum to the magnetic shear,
and , which now represents the separation of the resonance from the point
of maximum current density. The relation of our results to earlier studies of
tearing modes and to recent gyro-kinetic calculations of current driven
instabilities, is discussed, together with potential implications for the
stability of the tokamak pedestal.Comment: To appear in Plasma Physics and Controlled Fusio
Omnigenity as generalized quasisymmetry
Any viable stellarator reactor will need to be nearly omnigenous, meaning the
radial guiding-center drift velocity averages to zero over time for all
particles. While omnigenity is easier to achieve than quasisymmetry, we show
here that several properties of quasisymmetric plasmas also apply directly or
with only minor modification to the larger class of omnigenous plasmas. For
example, concise expressions exist for the flow and current, closely resembling
those for a tokamak, and these expressions are explicit in that no magnetic
differential equations remain. A helicity (M,N) can be defined for any
omnigenous field, based on the topology by which |B| contours close on a flux
surface, generalizing the helicity associated with quasisymmetric fields. For
generalized quasi-poloidal symmetry (M=0), the bootstrap current vanishes,
which may yield desirable equilibrium and stability properties. A concise
expression is derived for the radial electric field in any omnigenous plasma
that is not quasisymmetric. The fact that tokamak-like analytical calculations
are possible in omnigenous plasmas despite their fully-3D magnetic spectrum
makes these configurations useful for gaining insight and benchmarking codes. A
construction is given to produce omnigenous B(theta, zeta) patterns with
stellarator symmetry.Comment: 37 pages, 8 figure
A natural fuzzyness of de Sitter space-time
A non-commutative structure for de Sitter spacetime is naturally introduced
by replacing ("fuzzyfication") the classical variables of the bulk in terms of
the dS analogs of the Pauli-Lubanski operators. The dimensionality of the fuzzy
variables is determined by a Compton length and the commutative limit is
recovered for distances much larger than the Compton distance. The choice of
the Compton length determines different scenarios. In scenario I the Compton
length is determined by the limiting Minkowski spacetime. A fuzzy dS in
scenario I implies a lower bound (of the order of the Hubble mass) for the
observed masses of all massive particles (including massive neutrinos) of spin
s>0. In scenario II the Compton length is fixed in the de Sitter spacetime
itself and grossly determines the number of finite elements ("pixels" or
"granularity") of a de Sitter spacetime of a given curvature.Comment: 16 page
Unsupervised machine learning of integrated health and social care data from the Macmillan Improving the Cancer Journey service in Glasgow
Background: Improving the Cancer Journey (ICJ) was launched in 2014 by Glasgow City Council and Macmillan Cancer Support. As part of routine service, data is collected on ICJ users including demographic and health information, results from holistic needs assessments and quality of life scores as measured by EQ-5D health status. There is also data on the number and type of referrals made and feedback from users on the overall service. By applying artificial intelligence and interactive visualization technologies to this data, we seek to improve service provision and optimize resource allocation.Method: An unsupervised machine-learning algorithm was deployed to cluster the data. The classical k-means algorithm was extended with the k-modes technique for categorical data, and the gap heuristic automatically identified the number of clusters. The resulting clusters are used to summarize complex data sets and produce three-dimensional visualizations of the data landscape. Furthermore, the traits of new ICJ clients are predicted by approximately matching their details to the nearest existing cluster center.Results: Cross-validation showed the model’s effectiveness over a wide range of traits. For example, the model can predict marital status, employment status and housing type with an accuracy between 2.4 to 4.8 times greater than random selection. One of the most interesting preliminary findings is that area deprivation (measured through Scottish Index of Multiple Deprivation-SIMD) is a better predictor of an ICJ client’s needs than primary diagnosis (cancer type).Conclusion: A key strength of this system is its ability to rapidly ingest new data on its own and derive new predictions from those data. This means the model can guide service provision by forecasting demand based on actual or hypothesized data. The aim is to provide intelligent person-centered recommendations. The machine-learning model described here is part of a prototype software tool currently under development for use by the cancer support community.Disclosure: Funded by Macmillan Cancer Support</p
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Plasma transport near the separatrix of a magnetic island
The simplest non-trivial model of transport across a magnetic island chain in the presence of collisionless streaming along the magnetic field is solved by a Wiener-Hopf procedure. The solution found is valid provided the boundary layers about the island separatrix is narrow compared to the island width. The result demonstrates that when this assumption is satisfied the flattened profile region is reduced by the boundary layer width. The calculation is similar to the recent work by Fitzpatrick but is carried out in the collisionless, rather than the collisional, limit of parallel transport, and determines the plasma parameters on the separatrix self-consistently
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
A New, Explicitly Collisional Contribution to the Gyroviscosity and the Radial Electric Field in a Collisional Tokamak
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