A family of two variable polynomials naturally emerges from the expansion in multipoles of a magnetic field. The order of the expansion fixes the polynomial degree and the multipolar content: dipole, quadrupole, sextupole and so on. The associated polynomials share analogies with Hermite-type families. The relevant properties are studied, within an umbral framework, which simplifies the derivation of the associated mathematical technicalities. We take advantage from this analogy to present a fairly general discussion about the properties of the “magnetic” polynomials. We touch on the possibility of embedding the results of the present study in a dedicated algorithm for the analysis of the transport of a charged beam in a magnetic structure.
A note on the magnetic multipole polynomials
Dattoli G.;Carpanese M.;Di Palma E.;Petralia A.
2024-01-01
Abstract
A family of two variable polynomials naturally emerges from the expansion in multipoles of a magnetic field. The order of the expansion fixes the polynomial degree and the multipolar content: dipole, quadrupole, sextupole and so on. The associated polynomials share analogies with Hermite-type families. The relevant properties are studied, within an umbral framework, which simplifies the derivation of the associated mathematical technicalities. We take advantage from this analogy to present a fairly general discussion about the properties of the “magnetic” polynomials. We touch on the possibility of embedding the results of the present study in a dedicated algorithm for the analysis of the transport of a charged beam in a magnetic structure.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
