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magnitude and direction of
B
are both designed to be as constant as
possible. This requirement is achieved by considering the best winding of
the superconducting wire, plus the use of small assisting magnets (called
shim coils). When we consider the use of a magnetic force, the usual
magnets designed to provide a constant
H
are only of limited utility. This
is because the constancy of
H
and that of
H
2
are mathematically different
from each other. For
H
2
to be constant, the product of
H
and (grad
H
)
should be constant. However, a magnet specifically made for this purpose
did not exist when we conceived the need for it in 1997. We then made
some effort to show that the manufacture of such a magnet is in fact pos-
sible by presenting an actual design of the configuration of coils and by
demonstrating the constancy of the magnetic force distribution inside the
bore of the magnet (Kiyoshi
et al
., 1999).
The same problem was formulated a little differently by Brooks
et al
.
(2000). They pointed out that if we use a conventional superconducting
magnet and if we want to make “a microgravity-equivalent environment”
by counterbalancing the downward force of gravity and the upward mag-
netic force, then a spherical space of only 0.1 mm radius may be used; out-
side of this small volume, the counterbalancing condition will not be
satisfied. This meant that, experimentally, identifying this volume and
reproducibly using it would extremely be difficult. This was another
demonstration that using a conventional magnet would not be easy if one
wants to use an upward magnetic force that will in principle cancel gravity.
This is because the magnetic force distribution in a conventional supercon-
ducting magnet is not uniform whereas gravity is highly uniform on Earth.
Modes of operation of various magnets
Many experiments (such as NMR) on the effects of a magnetic field on
substances have been carried out at the center of a magnet where the field
strength becomes maximal. Usually, the field homogeneity at the center of
a magnet is quite good (i.e. grad
H
0), which means that the magnetic
force does not operate. On the other hand, there are positions off the cen-
ter of the magnet where
H
is not small, and a change in
H
with position
=
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