Analysis of the Field Quality in Bent Superconducting Magnets for Hadrontherapy Gantries

In the framework of the European project HITRIplus and the SIGRUM collaboration, the National Centre for Oncological Hadrontherapy (CNAO) has launched initiatives to design and build a superconducting gantry for hadrontherapy. Such a gantry is based on short and strongly bent superconducting dipoles that require an appropriate description of the quality of the produced magnetic field. In accelerator magnets, the field quality is conveniently described by a set of coefficients known as field harmonics or multipole coefficients. Generally, two different approaches can be used for determining the field harmonics. The first is the Fourier expansion of the field component along a circle. The second method provides an estimation of the field harmonics from the coefficients in a suitable Taylor expansion in the case of symmetric fields. These methods are commonly used to analyse the field quality of long accelerator magnets with small apertures. However, in the case of this gantry magnet, a detailed investigation is required since the magnet is short and strongly curved with a relatively large gap. Moreover, the length of the coil heads represents roughly 25% of the total length of the magnet thus the contribution of the introduced non-linear field components cannot be neglected. Both approaches were thoroughly examined in order to determine their applicability. The results revealed that the Fourier expansion of the field components may not be appropriate for the field quality description of a magnet with a small bending radius. Indeed, the vector Laplace equation is not fulfilled due to the presence of an additional term and the interpretation of the coefficients results unclear. In the case of short and strongly curved magnets, the analysis method employed for determining the multipole coefficients considering a field symmetric about the median plane is the Taylor expansion of the magnetic flux density. The multipole coefficients obtained through the Taylor expansion analysis were compared with the field components derived by particle tracking showing an agreement within a few units level. In conclusion, the field derivatives can be effectively used to represent short and strongly bent magnets in accelerator codes.