Kerr-Newman-Jacobi geometry and the deflection of charged massive particles

In this paper, we investigate the deflection of a charged particle moving in equatorial plane Kerr-Newman spacetime, focusing on weak field limit. To end, use Jacobi geometry, which can be described three equivalent forms, namely Randers-Finsler metric, Zermelo navigation problem, and ($n+1$)-dimensional stationary spacetime picture. Based Randers data Gauss-Bonnet theorem, utilize osculating Riemannian manifold method generalized metric method, respectively, to study angle. picture, motion follows null geodesic, thus standard geodesic calculate The methods lead same second-order angle, is obtained for first time. result shows that black hole spin $a$ affects particles both gravitationally magnetically at leading order [$\mathcal{O}([M{]}^{2}/{b}^{2})$]. When $qQ/E<2M$, will decrease (or increase) prograde retrograde) signal. If $qQ/E>2M$, opposite happens, ray divergently deflected by lens. We also show effect magnetic charge dyonic angle independent particle's charge.