Abstract
It has been shown [1] with the aid of the virial theorem that, regardless of configuration, an energy storage magnet would be prohibitively expensive if all structural supports were built with known fabricated materials. Accordingly, it has been proposed that the magnet be buried in tunnels in bedrock, a less expensive structure.
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Abbreviations
- α 0, α 2, and α 4 :
-
= Legendre polynomial coefficients
- B M :
-
= maximum magnetic field
- E :
-
= stored energy
- h 1 :
-
= height of the central section of the C-shaped solenoid
- h 2 :
-
= length of the horizontal end sections of the C-shaped solenoid
- J :
-
= current per unit length
- l :
-
= length of the magnet
- n :
-
= number of turns
- Q c :
-
= fractional virial theorem mass
- Q fr :
-
= radial force factor
- Q fv :
-
= total vector force factor
- Q fz :
-
= axial force factor
- R 1 :
-
= radius of the central section of the C-shaped solenoid
- R 2 :
-
= inner radius of the horizontal end sections of the C-shaped solenoid
- Z :
-
= axial distance from the median plane
- β :
-
= aspect ratio = length/average diameter
- θ :
-
= angle of the end sections on the horizontal plane
References
R. W. Boom, “Wisconsin Superconductive Energy Storage Project, Feasibility Study Report,” Vol. I, University of Wisconsin,.Madison, Wisconsin (July 1974).
M. N. El-Derini, R. W. Boom, and M. A. Hilal, in Advances in Cryogenic Engineering, Vol. 23, Plenum Press, New York (1978), p. 88.
R. L. Willig and R. W. Moses Jr., IEEE Trans. Magn. Mag-13(5):1122 (1977).
M. N. El-Derini, Doctoral Dissertation, University of Wisconsin, Madison, Wisconsin (1978).
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El-Derini, M.N., Boom, R.W. (1980). Shape Optimization Study for a Three-Tunnel Superconductive Energy Storage Magnet. In: Timmerhaus, K.D., Snyder, H.A. (eds) Advances in Cryogenic Engineering. Advances in Cryogenic Engineering, vol 35 A. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-9856-1_13
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DOI: https://doi.org/10.1007/978-1-4613-9856-1_13
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