Axisymmetric Equilibrium Models for Tokamak Plasmas PDF Download

Author: Barbara Gloria Epstein
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author: Marco Ferrara
Publisher: LAP Lambert Academic Publishing
ISBN: 9783659532801
Category : Science
Languages : en
Pages : 0

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The vertical position of elongated tokamak plasmas is unstable on the time scale of the eddy currents in the axisymmetric conducting structures. In the absence of feedback control, the plasma would drift vertically and quench on the wall, a situation known as Vertical Displacement Event (VDE), with serious consequences for machine integrity. As tokamaks approach reactor regimes, VDE's cannot be tolerated: vertical feedback control must be robust against system uncertainty and the occurrence of noise and disturbances. At the same time, adaptive routines should be in place to handle unexpected events. The problem of robust control of the vertical position can be formulated in terms of identifying which variables affect vertical stability and which ones are not directly controlled/controllable; identifying the physical region of these variables, and the corresponding most unstable equilibria; and designing the control system to stabilize all equilibria with sufficient margin. The margin should be enough to allow the system to tolerate realistic scenarios of noise and disturbances.

Author: Marco Ariola
Publisher: Springer
ISBN: 3319298909
Category : Technology & Engineering
Languages : en
Pages : 208

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This book is a complete treatment of work done to resolve the problems of position-, current-, and shape-control of plasma in tokamak-type (toroidal) devices being studied as a potential means of commercial energy production by nuclear fusion. Modelling and control are both detailed, allowing non-expert readers to understand the control problem. Starting from the magneto-hydro-dynamic equations, all the steps needed for the derivation of plasma state-space models are enumerated with frequent recall of the basic concepts of electromagnetics. The control problem is then described, beginning with the control of current and position—vertical and radial—control and progressing to the more challenging shape control. The solutions proposed vary from simple PIDs to more sophisticated MIMO controllers. The second edition of Magnetic Control of Tokamak Plasmas contains numerous updates and a substantial amount of completely new material covering areas such as: • modelling and control of resistive wall modes—the most important non-axisimmetric mode; • the isoflux approach for shape control; • a general approach for the control of limiter plasmas; • the use of inner vessel coils for vertical stabilization; and • significantly enhanced treatment of plasma-shape control at JET, including experimental results and introducing a method implemented for operation in the presence of current saturations. Whenever possible, coverage of the various topics is rounded out with experimental results obtained on currently existing tokamaks. The book also includes a presentation of the typical actuators and sensors used for control purposes in tokamaks. Some mathematical details are given in the appendices for the interested reader. The ideas formulated in this monograph will be of great practical help to control engineers, academic researchers and graduate students working directly with problems related to the control of nuclear fusion. They will also stimulate control researchers interested more generally in the advanced applications of the discipline. Advances in Industrial Control aims to report and encourage the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.

Author: R.B. White
Publisher: Elsevier
ISBN: 1483293262
Category : Science
Languages : en
Pages : 374

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This is a graduate textbook on tokamak physics, designed to provide a basic introduction to plasma equilibrium, particle orbits, transport, and those ideal and resistive magnetohydrodynamic instabilities which dominate the behavior of a tokamak discharge, and to develop the mathematical methods necessary for their theoretical analysis.

Author: Jacques Blum
Publisher: Wiley
ISBN: 9780471921875
Category : Technology & Engineering
Languages : en
Pages : 382

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This monograph on modelling, numerical simulation, and optimal control of equilibrium of the plasma in Tokamak fusion reactors covers new generation designs which have just entered service (JET, TFTR, and JT60), are under construction (TORE Supra), or are projected (INTOR and NET). The first five chapters deal with the stationary problem of axisymmetric equilibrium of the plasma--modelling and numerical simulation, mathematical existence of a solution for a simplified model, and identification and static control of the boundary of the plasma. Two final chapters treat the evolution of equilibrium on the time-scale of thermal diffusion in the plasma, and the stability and dynamic control of displacements of the plasma.

Author: Mehmet Artun
Publisher:
ISBN:
Category : Rotating plasmas
Languages : en
Pages : 33

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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 14

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Inductive effects are included in a self-consistent current drive model for axisymmetric tokamak plasmas used in the two-dimensional current drive/MHD equilibrium code, RIP. Previous simulations of current driven equilibria allowed for the steady-state calculation of bootstrap and RF currents. The addition of an inductive current is applied to enhance accurate design and interpretation of tokamak experiments. A convenient expression for the ohmic resistance in a tokamak plasma is derived to aid in the design of reactor grade MHD equilibria. 7 refs., 3 figs., 1 tab.

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 64

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A new linear MHD stability code, NOVA-W, has been developed in order to study feedback stabilization of the axisymmetric mode in deformable tokamak plasmas. The NOVA-W code is a modification of the non-variational MHD stability code NOVA that includes the effects of resistive passive conductors and active feedback circuits. The vacuum calculation has been reformulated in terms of the perturbed poloidal flux to allow the inclusion of perturbed toroidal currents outside the plasma. The boundary condition at the plasma-vacuum interface relates the instability displacement to the perturbed poloidal flux. This allows a solution of the linear MHD stability equations with the feedback effects included. The passive stability predictions of the code have been tested both against a simplified analytic model and against a different numerical calculation for a realistic tokamak configuration. The comparisons demonstrate the accuracy of the NOVA-W results. Active feedback calculations are performed for the CIT tokamak design demonstrating the effect of varying the position of the flux loops that provide the measurements of vertical displacement. The results compare well with those computed earlier using a less efficient nonlinear code. 37 refs., 13 figs.

Author:
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ISBN:
Category :
Languages : en
Pages :

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We deal with the problem of reducing a complicated electromagnetic passive structure model coupled to a linear plasma response model to a size that allows rapid calculations of gains for plasma position and shape control. We find that model reduction through eigenmode decomposition does not reproduce the input-to-output relationship of the system, unless one has a good idea of which eigenmodes are important. Hankel singular mode decomposition, on the other hand, provides an orthogonal basis for the system response, where the modes are ordered by their importance to the input-to-output relationship. A perturbed equilibrium plasma response model is used together with an electromagnetic model of the Alcator C-MOD passive structure to assess the performance of different model reduction schemes. We find that between 10 and 20 modes are required to give an adequate representation of the passive system. Emphasis is placed on keeping the reduction process independent of the parameters of the plasma we are trying to control.

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Tokamaks are sensitive to deviations from axisymmetry as small as [delta]B=B0 ~ 10-4. These non-axisymmetric perturbations greatly modify plasma confinement and performance by either destroying magnetic surfaces with subsequent locking or deforming magnetic surfaces with associated non-ambipolar transport. The Ideal Perturbed Equilibrium Code (IPEC) calculates ideal perturbed equilibria and provides important basis for understanding the sensitivity of tokamak plasmas to perturbations. IPEC calculations indicate that the ideal plasma response, or equiva- lently the effect by ideally perturbed plasma currents, is essential to explain locking experiments on National Spherical Torus eXperiment (NSTX) and DIII-D. The ideal plasma response is also important for Neoclassical Toroidal Viscosity (NTV) in non-ambipolar transport. The consistency between NTV theory and magnetic braking experiments on NSTX and DIII-D can be improved when the variation in the field strength in IPEC is coupled with generalized NTV theory. These plasma response effects will be compared with the previous vacuum superpositions to illustrate the importance. However, plasma response based on ideal perturbed equilibria is still not suffciently accurate to predict the details of NTV transport, and can be inconsistent when currents associated with a toroidal torque become comparable to ideal perturbed currents.