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Eddy currents in a gradient coil, modeled as circular loops of strips. (English) Zbl 1126.78005

The coil is modeled as a number of coaxial circular strips of zero thickness (the thickness is smaller than the penetration depth). The Maxwell equations in the quasi-stationary case (zero displacement current and zero electric charge) together with constitutive equations are written in circular-cylindrical coordinates \((r,\varphi,z)\). The symmetry is such that the components \(E_r,E_z, B_\varphi\) vanish. An integral equation for the current distribution is established, its kernel involves \(Q_{1/2}\), the Legendre function of the second kind and order \(\tfrac 12\). A splitting of the kernel into a singular and a regular part is introduced; the former is treated analytically and the second numerically. In addition to the current distribution, the authors consider resistance and inductance. Numerical calculations are carried out for the frequencies \(0.1\), \(0.4\), \(0.7\), \(1.0\)kHz, in three cases. First, one ring is considered. The next case is the so-called Maxwell pair, i.e., two rings with opposite currents such that the derivative \(\partial B_z/\partial z\) is as nearly constant as possible near the center of symmetry. Finally, as an improvement of the Maxwell pair, a coil of 24 rings is considered. This is a realistic model of a coil used for a MRI-scanner, and an almost constant gradient is obtained over a considerable portion of the axis.

MSC:

78A30 Electro- and magnetostatics
78M25 Numerical methods in optics (MSC2010)
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