An MRI elliptical coil with minimum inductance

Abstract

We present an application to elliptical coordinates of Turner's target field method. Coils are designed with their inductance minimized subject to constraints on the magnetic field. This is of value, for example, in magnetic resonance imaging (MRI) where it is desired that high-strengfh gradient coils be rapidly switched on and off Green functions and associated computational toois in elliptic coordinates are developed, We also discuss the advantages d elliptically cylindrical coils compared with circularly cylindrical coils for whole-body MRI applications

Gradient coil with active endcap shielding

“…The approach using the functional Eq. [5] may be connected to the method of Lagrange multipliers by considering it to be the result of an integration over intermediate Lagrange multipliers (which are introduced for all constraints). In our method, a variation is taken with respect to the current densities of the complete coil assembly including the endcap.…”

“…Linear equations for the determination of the ␦b n are found by taking an extremum variation of the functional Eq. [5]. A matrix is formed from the values that one finds by calculating the B field at all constraint points.…”

“…Then the solution of Eq. [5] is obtained by inverting the matrix, which depends on the original b n . Once ␦b n is found, a new value of b n is thus achieved.…”

Gradients: The Heart of the MRI Machine

“…Note also, that while it is convenient to have exact expressions for the FT of the field of coil structures, a number of which exist for simple geometries, circular, cylindrical and elliptical [14,20,21], it is not a necessity, as the fields from elemental currents on any surface can be FT'ed directly [18,19,22].…”

Dispersion of Principal Refractive Indices of CaGa2S4

“…Furthermore, there has been significant work on the design of elliptical cross-section gradient coils and radio frequency coils for use in cylindrical magnets [2][3][4][5][6][7][8].…”