[Paper Review] Superconducting and Resistive Tilted Coil Magnets

Andrey Akhmeteli, A.V. Gavrilin|ArXiv.org|Sep 30, 2004

Superconducting Materials and Applications5 references3 citations

TL;DR

This paper proposes a novel design for superconducting and resistive tilted coil magnets that generate a highly uniform transverse magnetic field using concentric solenoidal coils with elliptically shaped, oppositely angled turns. By employing a cosine-theta current distribution and exact analytical solutions for current density in elliptical Bitter disks, the method achieves ideal field uniformity, offering a promising alternative to traditional dipole magnets for particle accelerators and large-aperture experiments.

ABSTRACT

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.

Motivation & Objective

• To develop a new class of magnets that produce a highly uniform transverse magnetic field using tilted coil geometry.
• To address limitations of conventional dipole magnets, particularly in providing large access ports perpendicular to the field.
• To establish a mathematical foundation for both superconducting wire-wound and resistive Bitter-type tilted coil magnets.
• To demonstrate that the axial linear current density distribution in wire-wound coils follows an ideal 'cosine-theta' profile.
• To provide an exact analytical solution for current density in elliptical Bitter disks to enable precise field calculations.

Proposed method

• The design uses concentric nested solenoidal coils with elliptical turns tilted at a specific angle relative to the central axis.
• Current flows in opposite directions in coils tilted at opposite angles, enabling field cancellation outside and uniformity within the bore.
• An analytical method proves that the axial linear current density distribution in wire-wound coils follows a 'cosine-theta' profile, essential for field uniformity.
• For Bitter coils, an exact solution for current density in an elliptical Bitter disk is derived to model the magnetic field precisely.
• The method leverages symmetry and analytical integration to solve for the magnetic field in both superconducting and resistive configurations.
• Field uniformity is validated through mathematical derivation and numerical evaluation of the resulting field expressions.

Experimental results

Research questions

• RQ1 Can a tilted coil geometry with elliptical turns produce a highly uniform transverse magnetic field suitable for accelerator applications?
• RQ2 What current distribution in the coils ensures optimal field uniformity, and can it be analytically derived?
• RQ3 How can the magnetic field of a resistive Bitter-type tilted coil magnet be accurately calculated using an exact solution for elliptical current density?
• RQ4 Can superconducting wire-wound tilted coils achieve performance comparable to traditional dipole magnets?
• RQ5 What advantages do tilted coil magnets offer over conventional dipole magnets in experiments requiring large access ports perpendicular to the field?

Key findings

• The axial linear current density in wire-wound tilted coils follows an ideal 'cosine-theta' distribution, which is critical for achieving uniform transverse fields.
• An exact analytical solution for current density in an elliptical Bitter disk is derived, enabling precise magnetic field calculations for resistive Bitter magnets.
• The magnetic field generated by the tilted coil configuration is proven to be perfectly uniform in the central region, validating the design's theoretical foundation.
• Superconducting wire-wound tilted coil magnets are shown to be a viable alternative to traditional dipole magnets in accelerator systems.
• Resistive Bitter tilted coil magnets are particularly well-suited for experiments requiring large access ports perpendicular to the magnetic field direction.
• The method ensures high field uniformity without requiring complex winding techniques or external shimming, simplifying magnet fabrication.