Economic Aspects of the Magnetocaloric Energy Conversion - Magnetocaloric Energy Conversion: From Theory to Applications - page 369

Because of these facts we would like here again to encourage the industry related
to superconducting applications to enter the development of large-scale supercon-
ducting magnetic chillers or heat pumps.
Most of the work that concerns the evaluation of costs for superconducting
magnets regards the superconducting storage of electric energy (SMES). These
systems store electrical energy in the magnetized space, with most of these devices
applying toroidal and cylindrical solenoids. The maximum energy stored per unit
volume at a certain magnetic

eld is calculated using simple mathematical relations.
The procedure to perform an economic analysis on superconducting magnets was
shown by Egolf et al. [ 12 ].
Following the magnetic energy storage, the maximum energy stored in the
magnetized space (gap) of the superconducting magnet can be de ned as [ 12 ]:

¼ l 0

1

2 2

dw

2 dH ðÞ

¼ dB ðÞ ð 9 1 Þ

:

2 l 0

where H 0 represents the applied magnetic eld in the empty gap of the supercon-

ducting coil. Since the empty magnetized space can be considered as a material with
linear magnetic characteristics, a change in the stored energy in a certain space can
be de

ned as [ 12 ]:

Z

1

2 dV

dW ¼ dB ðÞ ð 9 2 Þ

:

2 l 0

V

If the magnetic fl ux density is constant, then it follows from Eq. ( 9.2 ) that:

2

B ðÞ

W ¼ V ð 9 3 Þ

:

2 l 0

With the application of Eq. ( 9.3 ) it is now possible to show the variation of the
magnetic energy depending on the magnetized volume and the magnetic

fl ux

density (Fig. 9.5 ).

Fig. 9.5 The maximum
energy stored per unit volume
for the magnetized space