Ideal magnetohydrodynamic stability in stellarators with subsonic equilibrium flow

2021 ◽  
Author(s):  
Carolin Nuehrenberg
Keyword(s):  
Mathematical Formulation ◽  
Radial Electric Field ◽  
Weak Form ◽  
Unstable Flow ◽  
Magnetic Surfaces ◽  
Ideal Mhd ◽  
Mhd Stability ◽  
Ideal Magnetohydrodynamic ◽  
The Stability ◽  
The Ideal

Abstract The effect of a subsonic flow, inherent to most stellarators because of a radial electric field, on their ideal magnetohydrodynamic (MHD) stability properties is studied employing the quasi-Lagrangian picture developed by Frieman and Rotenberg [1960 Rev. Mod. Phys. 32, 898]. The Mach number of the perpendicular ExB flow in stellarators is of order 0.01 and, therefore, admits the usage of a subsonic approximation in form of a static equilibrium. A mathematical formulation of the weak form of the stability equation with flow has been implemented in the ideal-MHD stability code CAS3D. This formulation uses magnetic coordinates and does not involve any derivatives across magnetic surfaces. In addition to the expected Doppler shift of frequencies, properties of the spectrum of the ideal MHD force operator, which are already known for tokamaks, but now also shown in the stellarator case, are: firstly, the appearance of unstable flow-induced continua stemming from the coupling of sound and Alfven continuum branches with equal mode numbers; and, secondly, the existence of flow-induced, global, stable modes near extrema of sound continuum branches, the extrema, in turn, being generated by the influence of a sheared flow on the static sound continua.

scholarly journals Kinetic ballooning modes in tokamaks and stellarators

2018 ◽  
Vol 84 (6) ◽  
Author(s):  
K. Aleynikova ◽  
A. Zocco ◽  
P. Xanthopoulos ◽  
P. Helander ◽  
C. Nührenberg
Keyword(s):  
Plasma Pressure ◽  
Analytical Prediction ◽  
Ion Temperature ◽  
Ion Temperature Gradient ◽  
Large Pressure ◽  
Equilibrium Configurations ◽  
Mhd Stability ◽  
Ideal Magnetohydrodynamic ◽  
General Geometry ◽  
The Ideal

Kinetic ballooning modes (KBMs) are investigated by means of linear electromagnetic gyrokinetic (GK) simulations in the stellarator Wendelstein 7-X (W7-X), for high-$\unicode[STIX]{x1D6FD}$ plasmas, where $\unicode[STIX]{x1D6FD}$ is the ratio of thermal to magnetic plasma pressure. The analysis shows suppression of ion-temperature-gradient (ITG) and trapped particle modes (TEM) by finite-$\unicode[STIX]{x1D6FD}$ effects and destabilization of KBMs at high $\unicode[STIX]{x1D6FD}$. The results are compared with a generic tokamak case. We show that, for large pressure gradients, the frequency of KBMs evaluated by the GENE code is in agreement with the analytical prediction of the diamagnetic modification of the ideal magnetohydrodynamic limit in W7-X general geometry. Thresholds for destabilization of the KBM are predicted for different W7-X equilibrium configurations. We discuss the relation of these thresholds to the ideal magnetohydrodynamic (MHD) stability properties of the corresponding equilibria.

Study of the ideal MHD stability of helical equilibria

1983 ◽  
Vol 25 (11) ◽  
pp. 1257-1269
Author(s):  
L A Charlton ◽  
D K Lee
Keyword(s):  
Ideal Mhd ◽  
Mhd Stability ◽  
The Ideal

MHD Stability of Streaming Jet Using Artificial Intelligence Technique

2012 ◽  
Vol 28 (3) ◽  
pp. 453-459
Author(s):  
Mostafa A. M. Abdeen ◽  
Alfaisal A. Hasan
Keyword(s):  
Magnetic Field ◽  
Artificial Intelligence ◽  
Mathematical Formulation ◽  
Transverse Magnetic ◽  
Field Variation ◽  
Ann Model ◽  
Eigen Value ◽  
Mhd Stability ◽  
Artificial Neural Network Ann ◽  
The Stability

AbstractMathematical formulation for Magnetohydrodynamic (MHD) stability of a streaming cylindrical model penetrated by varying transverse magnetic field is presented. Eigen value relation is derived and discussed analytically. In the current paper, Artificial Neural Network (ANN) model, one of the artificial intelligence techniques, is developed to simulate the stability of streaming jet penetrated by magnetic field. The ANN results presented in the current study showed that ANN technique, with less effort and time, is very efficiently capable of simulating and predicting the effect of magnetic field variation and axial exterior field on the stability of the streaming jet. The influence of magnetic field has a stabilizing effect for all short and long wavelengths. However the streaming is strongly destabilizing.

The ideal MHD stability of time-dependent Z-pinch equilibria

1989 ◽  
Vol 31 (9) ◽  
pp. 1443-1449 ◽  
Author(s):  
I D Culverwell ◽  
M Coppins
Keyword(s):  
Time Dependent ◽  
Ideal Mhd ◽  
Mhd Stability ◽  
Z Pinch ◽  
The Ideal

Structures of reconnection layers based on the ideal magnetohydrodynamic equations

1994 ◽  
Vol 51 (3) ◽  
pp. 381-398
Author(s):  
Wenlong Dai ◽  
Paul R. Woodward
Keyword(s):  
Numerical Simulations ◽  
Quantitative Agreement ◽  
Mhd Equations ◽  
Riemann Solver ◽  
Magnetohydrodynamic Equations ◽  
One Dimensional ◽  
Ideal Mhd ◽  
Ideal Magnetohydrodynamic ◽  
The One ◽  
The Ideal

A Riemann solver is used, and a set of numerical simulations are performed, to study the structures of reconnection layers in the approximation of the one- dimensional ideal MHD equations. Since the Riemann solver may solve general Riemarin problems, the model used in this paper is more general than those in previous investigations on this problem. Under the conditions used in the previous investigations, the structures we obtained are the same. Our numerical simulations show quantitative agreement with those obtained through the Riemann solver.

scholarly journals A Dissipative Model of Plasma Equilibrium in Toroidal Systems

1986 ◽  
Vol 41 (9) ◽  
pp. 1101-1110
Author(s):  
H. Wobig
Keyword(s):  
Magnetic Field ◽  
Existence Theorem ◽  
Plasma Pressure ◽  
Magnetic Islands ◽  
Plasma Equilibrium ◽  
Magnetic Surfaces ◽  
Ideal Mhd ◽  
Friction Term ◽  
Dissipative Terms ◽  
The Ideal

In order to describe a steady-state plasma equilibrium in tokamaks, stellarators or other non-axisymmetric configurations, the model of ideal MHD with isotropic plasma pressure is widely used:0 = - ∇p + j x B .The ideal MHD-model of a toroidal plasma equilibrium requires the existence of closed magnetic surfaces. Several numerical codes have been developed in the past to solve the three-dimensional equilibrium problem, but so far no existence theorem for a solution has been proved. Another difficulty is the formation of magnetic islands and field line ergodisation, which can only be described in terms of ideal MHD if the plasma pressure is constant in the ergodic region. In order to describe the formation of magnetic islands and ergodisation of surfaces properly, additional dissipative terms have to be incorporated to allow decoupling of the plasma and magnetic field. In a collisional plasma, viscosity and inelastic collisions introduce such dissipative processes. In the model used a friction term proportional to the velocity v of the plasma is included. Such a term originates from charge exchange interaction of the plasma with a neutral background. With these modifications, the equilibrium problem reduces to a set of quasilinear elliptic equations for the pressure, the electric potential and the magnetic field. The paper deals with an existence theorem based on the Fixed-Point method of Schauder. It can be shown that a self-consistent and unique equilibrium exists if the friction term is large and the plasma pressure is sufficiently low. The essential role of the dissipative terms is to remove the singularities of the ideal MHD model on rational magnetic surfaces. The problem has a strong similarity to Bénard cell convection, and consequently a similar behaviour such as bifurcation and exchange of stability is expected.

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