An improved method has been formulated for generating analytic boundary shapes as input for axisymmetric MHD equilibria. This method uses the family of superellipses as the basis function, as ...previously introduced. The improvements are a simplified notation, reduction of the number of simultaneous nonlinear equations to be solved, and the realization that not all combinations of input parameters admit a solution to the nonlinear constraint equations. The method tests for the existence of a self-consistent solution and, when no solution exists, it uses a deterministic method to find a nearby solution. Examples of generation of boundaries, including tests with an equilibrium solver, are given.
An analytic form to describe the boundary of an axisymmetric plasma is proposed. This new form uses a generalization of the family of superellipses. The plasma boundaries of existing tokamaks are ...well described using the compact notation. The form employs eleven parameters of which five are standard, two are generalizations of a standard parameter and four are introduced here. With these same parameters, a closed-form analytic solution can be used to generate new boundaries without x-points. If the desired boundary has x-points, the analytic form can be extended in a manner for which a closed-form solution has not been found, but does have an exact solution that can be found numerically. This new form should be useful for variety of physics studies that use magnetohydrodynamic equilibria, such as the dependence of plasma stability on shape and design of poloidal field coil sets that can support a defined range of shapes.
The hybrid scenario is a candidate for stationary high-fusion gain tokamak operation in ITER and DEMO. To obtain such performance, the energy confinement and the normalized pressure βN must be ...maximized, which requires operating near or above ideal MHD no-wall limits. New experimental findings show how these limits can affect hybrid operation. Even if hybrids are mainly limited by tearing modes, proximity to the no-wall limit leads to 3D field amplification that affects plasma profiles, e.g. rotation braking is observed in ASDEX Upgrade throughout the plasma and peaks in the core. As a result, even the small ASDEX Upgrade error fields are amplified and their effects become visible. To quantify such effects, ASDEX Upgrade measured the response to 3D fields applied by 8×2 non-axisymmetric coils as βN approaches the no-wall limit. The full n = 1 response profile and poloidal structure were measured by a suite of diagnostics and compared with linear MHD simulations, revealing a characteristic feature of hybrids: the n = 1 response is due to a global, marginally-stable n = 1 kink characterized by a large m = 1, n = 1 core harmonic due to qmin being just above 1. A helical core distortion of a few cm forms and affects various core quantities, including plasma rotation, electron and ion temperature, and intrinsic W density. In similar experiments, DIII-D also measured the effect of this helical core on the internal current profile, providing information useful to understanding of the physics of magnetic flux pumping, i.e. anomalous current redistribution by MHD modes that keeps qmin>1. Thanks to flux pumping, a broad current profile is maintained in DIII-D even with large on-axis current drive, enabling fully non-inductive operation at high βN up to 3.5-4.
In this volume distinguished scholars from both sides of the Atlantic explore the work of Tacitus in its historical and literary context and also show how his text was interpreted in the sixteenth ...through eighteenth centuries. Discussed here, for example, are the ways predilections of a particular age color one's reading of a complex author and why a reexamination of these influences is necessary to understand both the author and those who have interpreted him. All of the essays were first prepared for a colloquium on Tacitus held at Princeton University in March 1990. The resulting volume is dedicated to the memory of the great Tacitean scholar Sir Ronald Syme.
The contributors are G. W. Bowersock ("Tacitus and the Province of Asia"), T. J. Luce ("Reading and Response in theDialogus"), Elizabeth Keitel ("Speech and Narrative inHistories4"), Christopher Pelling ("Tacitus and Germanicus"), Judith Ginsburg ("In maiores certamina: Past and Present in theAnnals"), A. J. Woodman ("Amateur Dramatics at the Court of Nero"), Mark Morford ("TaciteanPrudentiaand the Doctrines of Justus Lipsius"), Donald R. Kelley ("Tacitus Noster: TheGermaniain the Renaissance and Reformation"), and Howard D. Weinbrot ("Politics, Taste, and National Identity: Some Uses of Tacitism in Eighteenth-Century Britain").
Originally published in 1993.
ThePrinceton Legacy Libraryuses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
A set of >100 DIII-D ITER demonstration discharges was analysed with the goal of characterizing the tearing stability of ITER baseline scenario plasmas on the energy and resistive evolution time ...scales. In DIII-D these discharges are limited by the appearance of an
n
= 1 tearing instability, after the discharge has run at constant pressure for several confinement times (τ
E
≲ 200 ms). Since the resistive time is ≳1 s, the current profile is still evolving when the modes appear. Across the ranges of pressure explored around the ITER design value, the probability of a discharge remaining stable equals that of encountering a mode; therefore, it seems that the tearing stability boundary cannot be characterized as a pressure limit. The internal inductance, a measure of the current distribution, does not contain enough detail to describe the tearing stability limits precisely, despite clear evidence that the evolution of the current profile is the cause of the instability and not the reaching of a β limit. The onset of the instability does not seem to be correlated with the plasma rotation or the presence of ELMs.
PDF
