Demonstration of Shafranov Shift by the Simplest Grad–Shafranov Equation Solution in IR-T1 Tokamak

2009 ◽  
Vol 29 (1) ◽  
pp. 73-75 ◽  
Author(s):  
A. Rahimirad ◽  
M. Emami ◽  
M. Ghoranneviss ◽  
A. Salar Elahi
Keyword(s):  
Equation Solution ◽  
Shafranov Equation ◽  
Shafranov Shift

Effect of plasma flow on the equilibrium of an axisymmetric toroidal magnetic trap

1997 ◽  
Vol 58 (3) ◽  
pp. 421-432 ◽  
Author(s):  
ZH. N. ANDRUSHCHENKO ◽  
O. K. CHEREMNYKH ◽  
J. W. EDENSTRASSER
Keyword(s):  
Plasma Flow ◽  
Magnetic Trap ◽  
Plasma Equilibrium ◽  
Plasma Rotation ◽  
Stationary Plasma ◽  
Shafranov Equation ◽  
Nonlinear Vector ◽  
Analytical Expressions ◽  
Poloidal Rotation ◽  
Shafranov Shift

The effect of finite plasma rotation on the equilibrium of an axisymmetric toroidal magnetic trap is investigated. The nonlinear vector equations describing the equilibrium of a highly conducting, current-carrying plasma are reduced to a set of scalar partial differential equations. Based on Shafranov's well-known tokamak model, this set of equations is employed for the description of a kinetic (stationary) plasma equilibrium. Analytical expressions for the Shafranov shift Δ are found for the case of finite plasma rotation, where two regions of possible plasma equilibria are found corresponding to sub- and super-Alfvénic poloidal rotation. The shift Δ itself, however, turns out to depend essentially on the toroidal rotation only. It is shown that in the case of a stationary plasma flow, the solution of the Grad–Shafranov equation is at the same time also the solution of the stationary Strauss equation.

On the accuracy of the symmetric ergodic magnetic limiter map in tokamaks

2010 ◽  
Vol 76 (5) ◽  
pp. 777-794 ◽  
Author(s):  
A. R. SOHRABI ◽  
S. M. JAZAYERI ◽  
M. MOLLABASHI
Keyword(s):  
Delta Function ◽  
Mapping Technique ◽  
Error Criterion ◽  
Flux Function ◽  
Energy Error ◽  
Chaotic Field ◽  
Shafranov Equation ◽  
Field Lines ◽  
Poloidal Flux ◽  
Shafranov Shift

AbstractA new symmetric symplectic map for an ergodic magnetic limiter (EML) is proposed. A rigorous mapping technique based on the Hamilton–Jacobi equation is used for its derivation. The system is composed of the equilibrium field, which is fully integrable, and a Hamiltonian perturbation. The equilibrium poloidal flux function is a solution of the Grad–Schlüter–Shafranov equation. This equation is written in polar toroidal coordinate in order to take into account the outward Shafranov shift. The static perturbation field breaks the exact axisymmetry of the equilibrium field and creates a region of chaotic field lines near the plasma edge. The new symmetric EML map is compared with the conventional (asymmetric) EML map which is derived by applying delta-function method. The accuracy of the maps is considered through mean energy error criterion and maximal Lyapunov exponents. For asymmetric and symmetric maps the approximate location of the main cantorus near the edge of plasma is determined with high accuracy by using mean energy error. The forward–backward error criterion is applied to show the relation between the accuracy of the symmetric EML map and the number of EML rings. We also report on the effect of the number of EML rings on the maximal Lyapunov exponent of the symmetric EML map.

Płyty kołowe Hencky’ego–Bolle’a spoczywające na podłożu sprężystym Własowa

2020 ◽  
Vol 29 (4) ◽  
pp. 444-453
Author(s):  
Mykola Nagirniak
Keyword(s):  
Differential Equation ◽  
Circular Plate ◽  
Significant Influence ◽  
Single Layer ◽  
Medium Thickness ◽  
Cross Sectional ◽  
Equation Solution ◽  
Integral Characteristics ◽  
Two Parameter ◽  
Plate Deflection

The work presents the equations of the theory of symmetrical plates, resting on one-way, single-layer, two-parameter Vlasov’s subsoil. Two cases of differential equation solution of the plate deflection of thin and medium thickness on the ground substrate were analyzed depending on the size of the integral characteristics UÖD and 6ÖD. The example of loading the circular plate with a Pk load evenly distributed over the edge was considered and shows dimensionless graphs of deflection, bending torques and transverse forces in the plate and in the ground subsoil. The effect of the Poisson’s coefficient of the plate on deflection values and cross-sectional forces was investigated. The Poisson’s number has been shown to have a significant influence on deflection values and bending torque, however shown negligible effect on transverse forces values.

Solving the Grad–Shafranov equation with spectral elements

2014 ◽  
Vol 185 (5) ◽  
pp. 1415-1421 ◽  
Author(s):  
E.C. Howell ◽  
C.R. Sovinec
Keyword(s):  
Spectral Elements ◽  
Shafranov Equation
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