Optimization of SMES Coil by Using Virial Theorem
The coil for the superconducting magnetic energy storage (SMES) is
optimized by use of the virial theorem with stored energy and stress.
In this work,
we show the theoretical limit of stored energy
with the maximum stress.
To achieve the ideal limit,
we propose the toroidal coil with helical winding.
It is a hybrid coil
of a toroidal field (TF) coil
and a solenoidal coil helically wound on a torus.
The winding is modulated in such that
the toroidal field is created in the torus
whereas the poloidal field is only out of the tours.
In this case, the electromagnetic force is represented
by the difference in
the poloidal and the toroidal magnetic pressure.
The virial theorem in the magnet is the relation of the magnetic energy
and the averaged stress, and shows that
the best coil to store the magnetic energy
under the weakest averaged stress requires
equal averaged principal stresses in all directions,
the ratio of the poloidal and toroidal current of our toroidal coil.
increases the magnetic energy to 4 times the conventional TF coil
with the same maximum stress.