| The principle of the neutrino production in the beta-beams relies on the beta-decay of the radioactive ions Neon 18 and Helium 6 in a storage ring. After decaying, the daughter particles have their magnetic rigidity significantly changed (-33 % for Helium and +11 % for Neon). Therefore, the decay products will be quickly lost on the walls of the decay ring after entering a dipole. Absorbers have been inserted in the decay ring in order to collect most decay products. Their optimization implies to calculate the trajectories of the decay products in the dipoles for very large momentum differences with a good accuracy. For pure dipoles without fringe field as in the decay ring, an analytic treatment can be used to simulate the transport. It is then possible to obtain the equivalent dipole which gives the beam sizes of the daughter particles. In a first part, we will describe the analytic treatment of the central trajectory and the motion of the ions around. In a second part, we will compare this treatment with the one with matrices for different orders in the case of the beta-beam decay ring. |
