Plasma stability theory including the resistive wall effects

2015 ◽  
Vol 81 (6) ◽  
Author(s):  
V. D. Pustovitov
Keyword(s):  
Stability Theory ◽  
Nonlinear Function ◽  
Thin Wall ◽  
Conducting Wall ◽  
Resistive Wall ◽  
Energy Sink ◽  
The Stability ◽  
Resistive Wall Modes ◽  
Complex Growth Rate ◽  
Plasma Stabilization

Plasma stabilization due to a nearby conducting wall can provide access to better performance in some scenarios in tokamaks. This was proved by experiments with an essential gain in${\it\beta}$and demonstrated as a long-lasting effect at sufficiently fast plasma rotation in the DIII-D tokamak (see, for example, Straitet al.,Nucl. Fusion, vol. 43, 2003, pp. 430–440). The rotational stabilization is the central topic of this review, though eventually the mode rotation gains significance. The analysis is based on the first-principle equations describing the energy balance with dissipation in the resistive wall. The method emphasizes derivation of the dispersion relations for the modes which are faster than the conventional resistive wall modes, but slower than the ideal magnetohydrodynamics modes. Both the standard thin wall and ideal-wall approximations are not valid in this range. Here, these are replaced by an approach incorporating the skin effect in the wall. This new element in the stability theory makes the energy sink a nonlinear function of the complex growth rate. An important consequence is that a mode rotating above a critical level can provide a damping effect sufficient for instability suppression. Estimates are given and applications are discussed.

scholarly journals Tokamak elongation – how much is too much? Part 1. Theory

2015 ◽  
Vol 81 (6) ◽  
Author(s):  
J. P. Freidberg ◽  
A. Cerfon ◽  
J. P Lee
Keyword(s):  
Numerical Analysis ◽  
Variational Principle ◽  
Stability Problem ◽  
Feedback System ◽  
Stability Parameter ◽  
Real Experiment ◽  
Conducting Wall ◽  
Vertical Field ◽  
Resistive Wall ◽  
Resistive Wall Modes

In this and the accompanying paper, the problem of the maximally achievable elongation${\it\kappa}$in a tokamak is investigated. The work represents an extension of many earlier studies, which were often focused on determining${\it\kappa}$limits due to (i) natural elongation in a simple applied pure vertical field or (ii) axisymmetric stability in the presence of a perfectly conducting wall. The extension investigated here includes the effect of the vertical stability feedback system which actually sets the maximum practical elongation limit in a real experiment. A basic resistive wall stability parameter,${\it\gamma}{\it\tau}_{w}$, is introduced to model the feedback system which although simple in appearance actually captures the essence of the feedback system. Elongation limits in the presence of feedback are then determined by calculating the maximum${\it\kappa}$against$n=0$resistive wall modes for fixed${\it\gamma}{\it\tau}_{w}$. The results are obtained by means of a general formulation culminating in a variational principle which is particularly amenable to numerical analysis. The principle is valid for arbitrary profiles but simplifies significantly for the Solov’ev profiles, effectively reducing the 2-D stability problem into a 1-D problem. The accompanying paper provides the numerical results and leads to a sharp answer of ‘how much elongation is too much’?

Effect of plasma-wall separation on the stability of resistive wall modes in the JT-60U tokamak

2006 ◽  
Vol 49 (1) ◽  
pp. 95-103 ◽  
Author(s):  
G Matsunaga ◽  
M Takechi ◽  
G Kurita ◽  
T Ozeki ◽  
Y Kamada ◽  
...  
Keyword(s):  
Resistive Wall ◽  
The Stability ◽  
Resistive Wall Modes

The Effect of Electromagnetic Pulse Treatment on Thin – Wall Bearing Ferrules Dimensional Accuracy

2014 ◽  
Vol 887-888 ◽  
pp. 1328-1332
Author(s):  
Wang Biao Qiu ◽  
Wei Xing Chen
Keyword(s):  
Residual Stress ◽  
Electromagnetic Pulse ◽  
Optical Measurement ◽  
Dimensional Accuracy ◽  
Magnetic Treatment ◽  
Thin Wall ◽  
Pulse Treatment ◽  
The Difference ◽  
The Stability ◽  
Frequency Pulse

The article based on different frequency pulse equiponderance electromagnetic destressing comparison experiment, using vertical optical measurement to survey the changes of bearing ferrules size, study the difference between the effect of different frequency electromagnetic in removing residual stress, find the frequency of magnetic treatment pulse that help to maintain the stability of the thin-wall bearing collars' size, effectively improve the cycle of bearing ferrules process .

Basic Concepts in the Stability Theory of Thin-walled Structures

2010 ◽  
Author(s):  
A. Guran ◽  
L. Lebedev ◽  
Michail D. Todorov ◽  
Christo I. Christov
Keyword(s):  
Stability Theory ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
Basic Concepts ◽  
The Stability

Coupling Between a 3-D Integral Eddy Current Formulation and a Linearized MHD Model for the Analysis of Resistive Wall Modes

2008 ◽  
Vol 44 (6) ◽  
pp. 1654-1657 ◽  
Author(s):  
R. Albanese ◽  
Y.Q. Liu ◽  
A. Portone ◽  
G. Rubinacci ◽  
F. Villone
Keyword(s):  
Eddy Current ◽  
Current Formulation ◽  
Resistive Wall ◽  
Mhd Model ◽  
Resistive Wall Modes

Investigation of the stability of boundary layers by a finite-difference model of the Navier—Stokes equations

1976 ◽  
Vol 78 (2) ◽  
pp. 355-383 ◽  
Author(s):  
H. Fasel
Keyword(s):  
Finite Difference ◽  
Stability Theory ◽  
Stokes Equations ◽  
Time Dependent ◽  
Linear Stability Theory ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
The Stability ◽  
Small Periodic

The stability of incompressible boundary-layer flows on a semi-infinite flat plate and the growth of disturbances in such flows are investigated by numerical integration of the complete Navier–;Stokes equations for laminar two-dimensional flows. Forced time-dependent disturbances are introduced into the flow field and the reaction of the flow to such disturbances is studied by directly solving the Navier–Stokes equations using a finite-difference method. An implicit finitedifference scheme was developed for the calculation of the extremely unsteady flow fields which arose from the forced time-dependent disturbances. The problem of the numerical stability of the method called for special attention in order to avoid possible distortions of the results caused by the interaction of unstable numerical oscillations with physically meaningful perturbations. A demonstration of the suitability of the numerical method for the investigation of stability and the initial growth of disturbances is presented for small periodic perturbations. For this particular case the numerical results can be compared with linear stability theory and experimental measurements. In this paper a number of numerical calculations for small periodic disturbances are discussed in detail. The results are generally in fairly close agreement with linear stability theory or experimental measurements.

scholarly journals Active Sliding Mode for Synchronization of a Wide Class of Four-Dimensional Fractional-Order Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Wang ◽  
Yuangui Zhou ◽  
Jianyi Xue ◽  
Delan Zhu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Wide Class ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Order System ◽  
Fractional Order Calculus ◽  
Simulation Results ◽  
The Stability

We focus on the synchronization of a wide class of four-dimensional (4-D) chaotic systems. Firstly, based on the stability theory in fractional-order calculus and sliding mode control, a new method is derived to make the synchronization of a wide class of fractional-order chaotic systems. Furthermore, the method guarantees the synchronization between an integer-order system and a fraction-order system and the synchronization between two fractional-order chaotic systems with different orders. Finally, three examples are presented to illustrate the effectiveness of the proposed scheme and simulation results are given to demonstrate the effectiveness of the proposed method.

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