Asymmetric tesseral shim coils for magnetic resonance

摘要

Tesseral coil with (i) a longitudinal axis and a radius r, which describes a main cylinder surface and (ii) a predetermined volume, in which at least one predetermined tesseral harmonic is produced (the tesseral harmonic volume) and with a plurality of current carrying windings, which are associated with the main cylinder surface, whereby the tesseral coil generates a magnetic field, the linear component is given by: where a_nm and b_nm the amplitudes of the ball surfaces functions are, p_nm(cosθ) associated are legendre''s polynomials, n is the order and m of the degree of the polynomial, and r, θ and ψ polar coordinates are;wherein:(i) the at least one predetermined tesseral harmonic a degree m ''and an order n'', which fulfill the following relationships: $m\; \prime \; 0,\; and$$n\; \text{'}\text{'}\geqq \; 2;$(ii) the main cylinder surface first and second ends having a length 2l therebetween; and(iii) the tesseral harmonic volume extending along the longitudinal axis of z = pl to z = ql,(a) – 1 & p & q 1;(b) | p | ≠ | q | and(c) z = 0 at half the distance between the first and second end of the main cylinder surface is.