Toroidal plasma equilibrium with arbitrary current distribution

1990 ◽  
Vol 44 (2) ◽  
pp. 303-311 ◽  
Author(s):  
M. Y. Kucinski ◽  
I. L. Caldas ◽  
L. H. A. Monteiro ◽  
V. Okano
Keyword(s):  
Aspect Ratio ◽  
Cross Section ◽  
Current Distribution ◽  
Successive Approximations ◽  
Large Aspect Ratio ◽  
Poloidal Field ◽  
Plasma Equilibrium ◽  
Toroidal Plasma ◽  
Poloidal Flux ◽  
New System

A new System of co-ordinates is found and a method developed to determine the toroidal equilibrium of plasmas with arbitrary current distribution and plasma cross-section. The method depends on knowledge of the equilibrium of a straight plasma column of similar cross-section and similar current distribution. A large aspect ratio is assumed. By successive approximations, better solutions can be obtained. An explicit formula is presented for the poloidal flux of a nearly circular plasma. This can be written in terms of a function related to the asymmetry of the poloidal field due to toroidality. The method works provided that there is only one magnetic axis.

Plasma equilibrium in toroidal l = 3 stellarators

1980 ◽  
Vol 24 (3) ◽  
pp. 453-478 ◽  
Author(s):  
P. J. Fielding ◽  
W. N. G. Hitchon
Keyword(s):  
Magnetic Field ◽  
Aspect Ratio ◽  
Plasma Pressure ◽  
Large Aspect Ratio ◽  
Plasma Equilibrium ◽  
Density Profiles ◽  
Vertical Field ◽  
Mhd Equilibrium ◽  
Vacuum Fields

The equations of MHD equilibrium are solved by including plasma pressure and current in a large aspect-ratio ordering scheme for the calculation of toroidal, l = 3 stellarator vacuum fields. The extended ordering unifies the low-beta equilibrium theory for tokamaks and l = 3 stellarators, and allows solutions to be obtained simply for arbitrarily prescribed pressure and current density profiles. Expressions are given for the equilibrium magnetic field and the equation for the flux surfaces is calculated, including the effects of l = 3 shaping and toroidal displacement. These results are used to calculate equilibria for the parameters of CLEO stellarator, and we examine the role of an externally applied vertical field in reducing pressure-induced flux surface distortion and destruction.

Structure of the compressible MHD equations for the internal kink mode in a toroidal plasma with large aspect ratio

1999 ◽  
Vol 62 (2) ◽  
pp. 165-178 ◽  
Author(s):  
C. WAHLBERG
Keyword(s):  
Aspect Ratio ◽  
Perturbation Expansion ◽  
Mhd Equations ◽  
Marginal Stability ◽  
Large Aspect Ratio ◽  
Direct Expansion ◽  
Energy Principle ◽  
Toroidal Plasma ◽  
Kink Mode ◽  
Compressible Mhd Equations

The equations for the ideal, internal m = n = 1 kink mode in a toroidal plasma are derived from a direct, large-aspect-ratio perturbation expansion of the compressible magnetohydrodynamic (MHD) equations. The derivation complements earlier investigations of the internal kink mode based either on the energy principle or on direct expansions of the incompressible MHD equations. It is shown that five poloidal harmonics (m = −1, 0, 1, 2 and 3) have to be retained in a direct expansion of the compressible MHD equations, as compared with the three poloidal harmonics m = 0, 1 and 2 needed in the case of an incompressible plasma, or when working from the energy principle. Furthermore, the sound velocity is found to replace the Alfvén velocity in the generalized Pfirsch–Schlüter factor (the kinetic energy enhancement factor in a toroidal plasma) previously derived for an incompressible plasma. Taking this factor fully into account in the calculation of the growth rate of the m = n = 1 mode, it is shown that, while the Bussac result γB is recovered near marginal stability, growth rates of the order of 30% larger than γB are obtained when γB becomes of the order of the sound frequency.

Nanopillar Fabrication with Focused Ion Beam Cutting

2014 ◽  
Vol 20 (5) ◽  
pp. 1581-1584 ◽  
Author(s):  
Oleksii V. Kuzmin ◽  
Yutao T. Pei ◽  
Jeff T.M. De Hosson
Keyword(s):  
Aspect Ratio ◽  
Radiation Damage ◽  
Cross Section ◽  
Focused Ion Beam ◽  
Incident Angle ◽  
Ion Beam ◽  
Large Aspect Ratio ◽  
Milled Surface ◽  
Key Features ◽  
The Cross

AbstractA versatile method to fabricate taper-free micro-/nanopillars of large aspect ratio was developed with focused ion beam (FIB) cutting. The key features of the fabrication are a FIB with an incident angle of 90° to the long axis of the pillar that enables milling of the pillar sideways avoiding tapering and the FIB current can be reduced step by step so as to reduce possible radiation damage of the milled surface by Ga ions. A procedure to accurately determine the cross-section of each pillar was developed.

Approximate static aeroelastic analysis of composite wings

2019 ◽  
Vol 15 (2) ◽  
pp. 365-386 ◽  
Author(s):  
Vladimir Kobelev
Keyword(s):  
Aspect Ratio ◽  
Closed Form ◽  
Cross Section ◽  
Gas Flow ◽  
Complex Analysis ◽  
Unmanned Aircraft ◽  
Large Aspect Ratio ◽  
Content Type ◽  
Analysis And Design ◽  
Thin Walled

PurposeThe purpose of this paper is to consider divergence of composite plate wings as well as slender wings with thin-walled cross-section of small-size airplanes. The main attention is paid to establishing of closed-form mathematical solutions for models of wings with coupling effects. Simplified solutions for calculating the divergence speed of wings with different geometry are established.Design/methodology/approachThe wings are modeled as anisotropic plate elements and thin-walled beams with closed cross-section. Two-dimensional plate-like models are applied to analysis and design problems for wings of large aspect ratio.FindingsAt first, the equations of elastic deformation for anisotropic slender, plate-like wing with the large aspect ratio are studied. The principal consideration is delivered to the coupled torsion-bending effects. The influence of anisotropic tailoring on the critical divergence speed of the wing is examined in closed form. At second, the method is extended to study the behavior of the large aspect ratio, anisotropic wing with box-like wings. The static equations of the wing with box-like profile are derived using the theory of anisotropic thin-walled beams with closed cross-section. The solutions for forward-swept wing with box-like profiles are given in analytical formulas. The formulas for critical divergence speed demonstrate the dependency upon cross-sectional shape characteristics and anisotropic properties of the wing.Research limitations/implicationsThe following simplifications are used: the simplified aerodynamic theory for the wings of large aspect ratio was applied; the static aeroelastic instability is considered (divergence); according to standard component methodology, only the component of wing was modeled, but not the whole aircraft; the simplified theories (plate-lime model for flat section or thin-walled beam of closed-section) were applied; and a single parameter that defines the rotation of a stack of single layers over the face of the wing.Practical implicationsThe simple, closed-form formulas for an estimation of critical static divergence are derived. The formulas are intended for use in designing of sport aircraft, gliders and small unmanned aircraft (drones). No complex analysis of airflow and advanced structural and aerodynamic models is necessary. The expression for chord length over the span of the wing allows for accounting a board class of wing shapes.Social implicationsThe derived theory facilitates the use of composite materials for popular small-size aircraft, and particularly, for drones and gliders.Originality/valueThe closed-form solutions for thin-walled beams in steady gas flow are delivered in closed form. The explicit formulas for slender wings with variable chord and stiffness along the wing span are derived.

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