Magnetic fields with photon beams: planar-current-induced magnetic fields

Strong transverse magnetic fields can produce very large dose enhancements and reductions in localized regions of a patient under irradiation by a photon beam. In this work we consider planar-current-induced magnetic fields ("PCIMFs") generated by arbitrary electric currents in one or two parallel planes, and pose two questions: how much arbitrariness is there in specifying a PCIMF, and how can we solve the "inverse problem" of determining the current distribution which generates a chosen PCIMF? We have completely answered both questions, and have applied the general formulas which we have developed to the case of cylindrical symmetry, giving a concrete example of our method. The present work provides the theoretical tools for designing PCIMFs, but a great deal of systematic research will be required in order to understand and design magnetic fields which produce desired distributions of dose enhancement and dose reduction in photon beams treating patients.