Analytic solutions for constant-tension coil shapes

Journal Article · Tue Jun 01 04:00:00 EDT 1976 · J. Appl. Phys.; (United States)

DOI:https://doi.org/10.1063/1.322993· OSTI ID:7194660

Gralnick, S L; Tenney, F H

An analytical solution of the differential equation describing the shape of a flexible filamentary conductor (incapable of supporting bending stresses) in a toroidal magnetic field has been obtained: previously only numerical solutions were available. The solution derives from a series expansion of modified Bessel functions of integer order. The characteristics of toroidal field magnets for proposed tokamak devices are obtainable by term integration of the solution series. General expressions are given for the following coil characteristics: the conductor turn length, the solenoid inductance, the area enclosed by the coil, and the coil support dimensions. For several particular cases of interest these coil chararacteritics are obtained as closed-form analytical formulas. A new type of coil, called a compound-constant-tension coil, is proposed. It is formed by selecting and matching (point and slope) segments chosen from two or more members of the one parameter family of solution curves found for the shape equation. These coils may be supported by tension members at the intersections of the solution curves or by a compression ring support and provide a unique and highly attractive solution to the toroidal field coil centering force support problem of tokamak designs. (AIP)

• Research Organization: Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08540
• OSTI ID: 7194660
• Journal Information: J. Appl. Phys.; (United States), Journal Name: J. Appl. Phys.; (United States) Vol. 47:6; ISSN JAPIA
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700202* -- Fusion Power Plant Technology-- Magnet Coils & Fields
ANALYTICAL SOLUTION
ANNULAR SPACE
BESSEL FUNCTIONS
CLOSED PLASMA DEVICES
CONFIGURATION
DIFFERENTIAL EQUATIONS
ELECTRIC COILS
ELECTRICAL EQUIPMENT
EQUATIONS
EQUIPMENT
FUNCTIONS
MAGNET COILS
MAGNETIC FIELDS
MAGNETS
SHAPE
STRESSES
THERMONUCLEAR DEVICES
TOKAMAK DEVICES
TOROIDAL CONFIGURATION