  The mathematical foundation is laid for a relatively new type of magnets
generating uniform transverse field - tilted coil magnets. These consist of
concentric nested solenoidal coils with elliptical turns tilted at a certain
angle to the central axis and current flowing in opposite directions in the
coils tilted at opposite angles, generating a perfectly uniform transverse
field. Both superconducting wire-wound and resistive Bitter tilted coils are
discussed. An original analytical method is used to prove that the wire-wound
tilted coils have the ideal distribution of the axial linear current density -
"cosine-theta". Magnetic fields are calculated for a tilted Bitter coil magnet
using an original exact solution for current density in an elliptical Bitter
disk. Superconducting wire-wound tilted coil magnets may become an alternative
for traditional dipole magnets for accelerators, and Bitter tilted coil magnets
are attractive for rotation experiments with a large access port perpendicular
to the field.
