Abstract
Mathematical foundation is laid for a relatively new type of magnets generating uniform transverse magnetic field-tilted coil magnets. These consist of concentric nested 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 current density-"cosine-theta". To program coil fabrication tooling, a parametric description of the helical path of the conductor within a tilted coil is given. Magnetic fields are calculated for a tilted Bitter coil magnet using an original exact solution for current density in an elliptical Bitter disk.
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