# The Application of Loss Models to Superconducting Solenoids

• J. T. Broach
• W. D. Lee
Part of the Advances in Cryogenic Engineering book series (ACRE, volume 19)

## Abstract

The use of inductors, both cryogenic and superconductive, for the storage of energy in pulsed power systems of various types has recently attracted considerable attention. The storage element is usually operated in a pool of liquid cryogen but for certain applications, integrated refrigeration using helium gas is desirable. In either case, an estimate of the losses generated during transients is an essential part of the design. The principal loss mechanisms in the superconducting case are eddy currents in the stabilizer and hysteresis in the superconductor, both of which depend upon the magnitude and frequency of the transient field. This presentation presents the results of an application of loss models to a particular configuration of multifilament superconductor. The eddy current loss model is compared separately to loss measurements made on a coil wound from commercial copper wire. Losses calculated using a simple linear model of the field in the winding are compared with those obtained from a more sophisticated calculation using digital computer techniques.

## Keywords

Power Loss Eddy Current Loss Model Field Profile Hysteresis Loss
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Notation

a1

a2

B

= magnetic flux density

Bm

= sinusoidal peak fluxdensity

B0

= central field of solenoid

d

= superconductor filament diameter

E

= electric field strength

I

= rms transport current

Jc

= superconductor critical current density

l

= winding length

n

= scale factor (not necessarily integral) for filament radius specifying spacing of composite

Q

= Power

q

= power density

r

Reff

= effective resistance

rm

= maximum radius of eddy current loop

rw

V

= volume available for eddy current paths

## Greek letters

λ

= ratio of superconductor volume to winding volume

ρ

= resistivity

τ

= charge (or discharge) time

ω

= angular frequency

## References

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3. 3.
C. P. Bean, “A Research Investigation of the Factors that Affect the Superconducting Properties of Materials,” Tech. Rept. No. AFML-TR-65–431 (March 1966).Google Scholar
4. 4.
K. P. Jüngst, G. Krafft, and G. Ries, “Measurements on Pulsed Superconducting Magnets,” paper presented at Third International Conference on Magnet Technology, May 19–22, 1970, Hamburg, Germany.Google Scholar