Inductance of Bitter Coil with Rectangular Cross-section
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O R I G I N A L PA P E R
Inductance of Bitter Coil with Rectangular Cross-section Yong Ren · Guangli Kuang · Wenge Chen
Received: 1 October 2012 / Accepted: 25 November 2012 / Published online: 7 December 2012 © Springer Science+Business Media New York 2012
Abstract The self-inductance of Bitter coil and mutual inductance between coaxial Bitter coils with rectangular cross-section using semi-analytical expressions based on two integrations were introduced. The current density of the Bitter coil in radial direction is inversely proportional to its radius. The obtained expressions can be implemented by Gauss integration method with FORTRAN programming. We confirm the validity of inductance results by comparing them with finite filament method and finite element method. The inductance values computed by three methods are in excellent agreement. The derived expressions of inductance of Bitter coils with rectangular cross-section allow a low computational time compared with finite filament method to a specific accuracy. The derived mutual inductance expressions can be used to accurately calculate the axial force between coaxial Bitter coils with mutual inductance gradient method. Keywords Bitter coil · Inductance · Storage energy
1 Introduction Steady-state high magnetic field over 20 T can be generated by a water-cooled magnet with Bitter coils or by hybrid magnet combined with an inner water-cooled magnet and an outsert superconducting magnet. During a water-cooled Y. Ren () · G. Kuang · W. Chen High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei, China e-mail: [email protected] Y. Ren Graduate University of Chinese Academy of Sciences, Beijing, China
magnet trip, the induced current in the superconducting outsert coil changes as a function of decay time constant of the water-cooled magnet. The decay time constant is determined by the self-inductance and the resistance of the water-cooled magnet. Thus, an accurate estimation of the inductance of Bitter coil is of primary importance in the hybrid magnet design. For a water-cooled magnet combined with some Bitter coils, there exists a large electromagnetic force in an axial direction. The electromagnetic force between Bitter coils is proportional to their mutual inductance gradient [1]. To optimize the support structure of the Bitter coil, it is vital to have accurate evaluation of the mutual inductance between Bitter coils. Many early contributions on the self-inductance and mutual inductance of solenoid coils with rectangular crosssection are mainly concerned on the coils with uniform current density distribution [2–7]. For Bitter coils with copper disk, we neglect the variations of current density distribution caused by temperature distribution and cooling hole of Bitter coil. The current density distribution of a Bitter coil in radial direction, however, is inversely proportional to the radius of the coil [1]. In this study, we derived the expressions of self-inductance of Bitter coil and mutual inductance between Bitter coils based on two
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