Magnetic Field Expansion Out of a Plane: Application to Inverse Cyclotron Muon Cooling
Abstract
In studies of the dynamics of charged particles in a cyclotron magnetic field, the specified field is generally Bz in the z = 0 midplane where Br and Btheta are zero. Br(r, theta, z) and Btheta(r, theta, z) are simple to determine through a linear expansion which assumes that Bz is independent of z. But, an expansion to only first order may not be sufficient for orbit simulations at large z. This paper reviews the expansion of a specified Bz(r, theta, z = 0) out of the z = 0 midplane to arbitrary order, and shows simple examples worked out to 4th order.
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