High precision computation of solenoid magnetic fields by Garrett's methods

For magnetic field calculations of solenoids two methods, due to M.W. Garrett, are developed. The first one consists of the expansion of the magnetic field in a zonal harmonic series in the central region of solenoid and in outer space. For both regions the expansion coefficients are given either by simple recurrence relations, or by explicit expressions. In particular, this method is suitable for high accuracy calculations of the field within windings. In the second method, the field is expressed in terms of incomplete elliptic integrals of the first and second kinds computed by use of raising Landen transformations. Given the high precision and high computation rate of this method, it has advantages in analyzing field problems for windings consisting of many radial sections carrying different currents, as occurs during the quench of superconducting multisectioned magnets. Also, the general formulas for mutual inductance and axial force between a pair of coaxial solenoids are given