Patent ID: 6664879
Filing Date: 2003-12-16
Classification: G01R

Abstract:
A tesseral coil having (i) a longitudinal axis and a radius r describing a primary cylindrical surface and (ii) a predetermined volume in which at least one predetermined tesseral harmonic is generated (the tesseral harmonic volume) and comprising a plurality of current-carrying windings associated with the primary cylindrical surface, the tesseral coil producing a magnetic field, the longitudinal component of which is given by: B&af;(r,Î¸,Ï†)=&Sum;n=0âˆž&it;â€ƒ&it;&Sum;m=0m=n&it;â€ƒ&it;rn&af;[An&it;â€ƒ&it;m&it;cos&af;(m&it;â€ƒ&it;Ï†)+Bn&it;â€ƒ&it;m&it;sin&af;(m&it;â€ƒ&it;Ï†)]&it;Pn&it;â€ƒ&it;m&af;(cos&it;â€ƒ&it;Î¸)where Anm and Bnm are the amplitudes of spherical harmonics, Pnm(cos &thgr;) are associated Legendre polynomials, n is the order and m the degree of the polynomial, and r ,&thgr; and &phgr; are polar co-ordinates; wherein: (i) the at least one predetermined tesseral harmonic has a degree mâ€² and an order nâ€² which satisfy the relationships: mâ€²>0, and nâ€²&gE;2; (ii) the primary cylindrical surface has first and second ends which define a length 2L therebetween; and (iii) the tesseral harmonic volume extends along the longitudinal axis from z=pL to z=qL, where (a) âˆ’1(b) |P|â‰ |q|; and (c) z=0 is midway between the first and second ends of the primary cylindrical surface.