The equation for stored energy in an arbitrary magnetic field is:  formula_18  Here, formula_12 is the permeability of free space, formula_20 is the magnitude of the field, and formula_21 is an infinitesimal element of volume. Now for an electromagnet with a cylindrical bore of radius formula_22, producing a pure multipole field of order formula_10, this integral becomes:  formula_24 Ampere's Law for multipole electromagnets gives the field within the bore as:  formula_25  Here, formula_26 is the radial coordinate. It can be seen that along formula_26 the field of a dipole is constant, the field of a quadrupole magnet is linearly increasing (i.e. has a constant gradient), and the field of a sextupole magnet is parabolically increasing (i.e. has a constant second derivative). Substituting this equation into the previous equation for formula_28 gives:  formula_29  formula_30  formula_31  formula_32  formula_33     Hans A. Bachor  Professor Hans-Albert Bachor, Member of the Order of Australia (AM), is a German-born Australian research physicist. He was chairperson of the National Youth Science Forum in Australia, and is an Emeritus Professor in the Department of Quantum Science, Research School of Physics and Engineering at the Australian National University, Canberra, Australia. Bachor was born in Wolfenbüttel, Germany in 1952. He studied Physics in Hannover, Germany, where he received his diploma and doctorate, supervised by Prof. Dr. Manfred Kock. He took up a position at the Australian National University in 1981. Bachor established experimental quantum optics in Australia and created a widely known group for optics and laser physics, exploring the possibilities of harnessing the quantum nature of light. He has pioneered techniques for sensitive measurements beyond the quantum noise limit, for the improvement of optical sensors, interferometers, optical communication and data storage. Bachor has mentored and graduated a number of Australia's leading scientists. His former graduate students include Professor Ping Koy Lam (CQC2T), Professor Timothy Ralph (UQ), and Professor Andrew White (UQ). Bachor was Head of the Department of Physics at the Australian National University in the late 1990s, and took a leading role in teaching and inspiring undergraduate students. He is active in the professional management of science, a former member of the expert panels of the Australian Research Council (1997-2001, 2010-2012) and the European Research Council (2009-2013), through leading roles in the Australian Optical Society, as chair and organiser of several international science conferences, and as a member of the advisory boards of international research Centres.