509 research outputs found
Quasilinear theory of collisionless Fermi acceleration in a multicusp magnetic confinement geometry
Particle motion in a cylindrical multiple-cusp magnetic field configuration
is shown to be highly (though not completely) chaotic, as expected by analogy
with the Sinai billiard. This provides a collisionless, linear mechanism for
phase randomization during monochromatic wave heating. A general quasilinear
theory of collisionless energy diffusion is developed for particles with a
Hamiltonian of the form , motion in the \emph{unperturbed} Hamiltonian
being assumed chaotic, while the perturbation can be coherent (i.e.
not stochastic). For the multicusp geometry, two heating mechanisms are
identified --- cyclotron resonance heating of particles temporarily
mirror-trapped in the cusps, and nonresonant heating of nonadiabatically
reflected particles (the majority). An analytically solvable model leads to an
expression for a transit-time correction factor, exponentially decreasing with
increasing frequency. The theory is illustrated using the geometry of a typical
laboratory experiment.Comment: 13 pages (.tex file, using REVTeX), 11 figures (.eps files). Sep. 30:
Word "collisionless" added to title, abstract and text slightly revised in
response to referee's comments (to be published in Phys. Rev. E
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 k-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
Cyber-Lisbon? The Impact of the Treaty of Lisbon on European Union Cybersecurity Policy
Cyberspace offers unique opportunities for communication and commerce, but also a wide range of security threats both to individuals and nation states. These threats create specific security challenges. This paper will examine the impact of the Treaty of Lisbon on the EU's response to those challenges. Prior to the coming into force of the Lisbon Treaty in 2009 EU cybersecurity policy was highly fragmented. Responsibility was split between the three Pillars of the European political system: the Communities, justice and home affairs and the common foreign and security policy (CFSP). By abolishing the Pillar system the Lisbon Treaty enabled the EU to develop a single, unified, strategic approach to cybersecurity issues. The 2013 Cybersecurity Strategy was a direct result of this newly-established capacity for coherence. However, the key area of competence relating to the CFSP was left largely undefined in the Lisbon Treaty, limiting the EU's capacity to respond to external cyber-threats. This paper will evaluate how the new legal personality of the Union and the abolition of the Pillar system affected both internal and external cybersecurity policy by examining one of the Treaty's most significant "loose ends": CFSP. It will argue that cybersecurity and external cyber-defence serve as a microcosm of a much wider problem of unresolved and undefined competences. While the Lisbon Treaty facilitated a coherent internal strategy, clarification of EU competence regarding the CFSP was left largely unresolved, a fact demonstrated by the nature of cybersecurity challenges. By examining the EU's cybersecurity policy and strategy this paper will further argue that the EU's approach can be seen as an exemplar of the successes and challenges of post-Lisbon European politics
Generalised action-angle coordinates defined on island chains
Straight-field-line coordinates are very useful for representing magnetic
fields in toroidally confined plasmas, but fundamental problems arise regarding
their definition in 3-D geometries because of the formation of islands and
chaotic field regions, ie non-integrability. In Hamiltonian dynamical systems
terms these coordinates are a form of action-angle variables, which are
normally defined only for integrable systems. In order to describe 3-D magnetic
field systems, a generalisation of this concept was proposed recently by the
present authors that unified the concepts of ghost surfaces and
quadratic-flux-minimising (QFMin) surfaces. This was based on a simple
canonical transformation generated by a change of variable , where and are poloidal and toroidal
angles, respectively, with a new poloidal angle chosen to give
pseudo-orbits that are a) straight when plotted in the plane and
b) QFMin pseudo-orbits in the transformed coordinate. These two requirements
ensure that the pseudo-orbits are also c) ghost pseudo-orbits. In the present
paper, it is demonstrated that these requirements do not \emph{uniquely}
specify the transformation owing to a relabelling symmetry. A variational
method of solution that removes this lack of uniqueness is proposed.Comment: 10 pages. Accepted by Plasma Physics and Controlled Fusion as part of
a cluster of refereed papers in a special issue containing papers arising
from the Joint International Stellarator & Heliotron Workshop and
Asia-Pacific Plasma Theory Conference, held in Canberra and Murramarang
Resort, Australia, 30 January - 3 February, 201
Relaxed plasma equilibria and entropy-related plasma self-organization principles
The concept of plasma relaxation as a constrained energy minimization is reviewed. Recent work by the authors on generalizing this approach to partially relaxed threedimensional plasma systems in a way consistent with chaos theory is discussed, with a view to clarifying the thermodynamic aspects of the variational approach used. Other entropy-related approaches to finding long-time steady states of turbulent or chaotic plasma systems are also briefly reviewed
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