Quantum aspects of accelerator optics

Full text : Charged-particle optics, or the theory of transport of charged-particle beams through electromagnetic systems, is traditionally dealt with using classical mechanics. Though the classical treatment has been very successful, in designing and working of numerous charged-particle optical devices, it is natural to look for a prescription based on the quantum theory, since any system is quantum mechanical at the fundamental level. With this motivation the quantum theory of charged-particle beam optics, is being developed by Jagannathan et al. This formalism is specifically adapted to treat the problems of beam optics. It is found that the quantum theory gives rise to interesting additional contributions to the classical paraxial and aberrating behaviour. These contributions are directly proportional to the powers of the de Broglie wavelength. In the classical limit the quantum formalism reproduces the well-known Lie algebraic formalism of charged-particle beam optics. For spin-half particles, a treatment based on the Dirac equation is presented taking fully into account the spinor character of the wavefunction. The underlying powerful algebraic machinery of the formalism makes it possible to do computations to any degree of accuracy. This formalism is further applied to the study of the spin-dynamics of a Dirac particle with anomalous magnetic moment being transported through magnetic optical element. This naturally leads to a unified treatment of both the orbital (the Lorentz and Stem-Gerlach forces) and the spin (Thomas-Bargmann-Michel-Telegdi equation). This is illustrated, by computing the transfer maps for the phase-space and spin components in the cases of the normal and skew magnetic quadrupole lenses. The quantum mechanics of the concept of the spin-splitter devices, proposed recently for achieving polarized beams, is also understood using our formalisms