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Free boundary, high beta equilibrium in a large aspect ratio tokamak with nearly circular plasma boundary
An analytic solution is obtained for free-boundary, high-beta equilibria in large aspect ratio tokamaks with a nearly circular plasma boundary. In the absence of surface currents at the plasma-vacuum interface, the free-boundary equilibrium solution introduces constraints arising from the need to couple to an external vacuum field which is physically realizable with a reasonable set of external field coils. This places a strong constraint on the pressure profiles that are consistent with a given boundary shape at high {epsilon}{beta}{sub p}. The equilibrium solution also provides information on the flux surface topology. The plasma is bounded by a separatrix. Increasing the plasma pressure at fixed total current causes the plasma aperture to decrease in a manner that is described
Strong "quantum" chaos in the global ballooning mode spectrum of three-dimensional plasmas
The spectrum of ideal magnetohydrodynamic (MHD) pressure-driven (ballooning)
modes in strongly nonaxisymmetric toroidal systems is difficult to analyze
numerically owing to the singular nature of ideal MHD caused by lack of an
inherent scale length. In this paper, ideal MHD is regularized by using a
-space cutoff, making the ray tracing for the WKB ballooning formalism a
chaotic Hamiltonian billiard problem. The minimum width of the toroidal Fourier
spectrum needed for resolving toroidally localized ballooning modes with a
global eigenvalue code is estimated from the Weyl formula. This
phase-space-volume estimation method is applied to two stellarator cases.Comment: 4 pages typeset, including 2 figures. Paper accepted for publication
in Phys. Rev. Letter
Heliac parameter study
Helical axis stellarators (heliacs) with zero net current are found to possess very good stability properties. Helically symmetric or straight heliacs with bean-shaped cross sections have a first region of stability that reaches to (..beta..) of 30% or more. Those with circular cross sections have second region of stability to Mercier modes. In addition we report on the stability properties of these plasma configurations as functions of pressure profile, helical aspect ratio, and helical period length
Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size
We construct affinization of the algebra of ``complex size''
matrices, that contains the algebras for integral values of the
parameter. The Drinfeld--Sokolov Hamiltonian reduction of the algebra
results in the quadratic Gelfand--Dickey structure on the
Poisson--Lie group of all pseudodifferential operators of fractional order.
This construction is extended to the simultaneous deformation of orthogonal and
simplectic algebras that produces self-adjoint operators, and it has a
counterpart for the Toda lattices with fractional number of particles.Comment: 29 pages, no figure
Gravity - a Geometric Approach
A brief review is given of an adaptation of the coadjoint orbit method
appropriate for study of models with infinite-dimensional symmetry groups. It
is illustrated on several examples, including derivation of the WZNW action of
induced supergravity. As a main application, we present the
geometric action on a generic coadjoint orbit of the deformed group of area
preserving diffeomorphisms. This action is precisely the anomalous effective
WZNW action of matter fields coupled to chiral gravity
background. Similar actions are given which produce the {\em KP} hierarchy as
on-shell equations of motion.Comment: 13 pages, BGU-92/11/July-PH, LaTe
Darboux Coordinates and Liouville-Arnold Integration in Loop Algebras
Darboux coordinates are constructed on rational coadjoint orbits of the
positive frequency part \wt{\frak{g}}^+ of loop algebras. These are given by
the values of the spectral parameters at the divisors corresponding to
eigenvector line bundles over the associated spectral curves, defined within a
given matrix representation. A Liouville generating function is obtained in
completely separated form and shown, through the Liouville-Arnold integration
method, to lead to the Abel map linearization of all Hamiltonian flows induced
by the spectral invariants. Serre duality is used to define a natural
symplectic structure on the space of line bundles of suitable degree over a
permissible class of spectral curves, and this is shown to be equivalent to the
Kostant-Kirillov symplectic structure on rational coadjoint orbits. The general
construction is given for or , with
reductions to orbits of subalgebras determined as invariant fixed point sets
under involutive automorphisms. The case is shown to reproduce
the classical integration methods for finite dimensional systems defined on
quadrics, as well as the quasi-periodic solutions of the cubically nonlinear
Schr\"odinger equation. For , the method is applied to the
computation of quasi-periodic solutions of the two component coupled nonlinear
Schr\"odinger equation.Comment: 61 pg
Privacy, Ethics, and Institutional Research
Despite widespread agreement that privacy in the context of education is important, it can be difficult to pin down precisely why and to what extent it is important, and it is challenging to determine how privacy is related to other important values. But that task is crucial. Absent a clear sense of what privacy is, it will be difficult to understand the scope of privacy protections in codes of ethics. Moreover, privacy will inevitably conflict with other values, and understanding the values that underwrite privacy protections is crucial for addressing conflicts between privacy and institutional efficiency, advising efficacy, vendor benefits, and student autonomy.
My task in this paper is to seek a better understanding of the concept of privacy in institutional research, canvas a number of important moral values underlying privacy generally (including several that are explicit in the AIR Statement), and examine how those moral values should bear upon institutional research by considering several recent cases
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