Quantum theory of charged-particle beam optics

Charged-particle beam 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 deeper understanding 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 currently by Jagannathan et al.; this formalism is specifically adapted to treat the problems of beam optics. The present thesis is an elaboration of this new formalism of the quantum theory of charged-particle beam optics with illustrations of applications to several practically important systems. The essential content of the thesis can be summarized briefly as follows. Quantum mechanics of the optics of charged-particle beams transported through an electromagnetic lens or other such optical systems is analyzed, at the level of single-particle dynamics, treating the electromagnetic fields as classical and disregarding the radiation aspects, using essentially an algebraic approach. The formalism is based on the basic equations of quantum mechanics appropriate to the situations. For situations when either there is no spin or spin can be treated as a spectator the scalar Klein-Gordon and Schrödinger equations are used as the basic equations for relativistic and nonrelativistic cases respectively. For spin2 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 in any situation from electron microscopy to accelerator optics. The power of the formalism is demonstrated by working out the examples which include the axially symmetric magnetic round lens (of importance for electron microscopy and other micro-electron-beam device technologies) and the magnetic quadrupole lens (of importance for accelerator optics). It is found that the quantum theory at the scalar (spin-less) level gives rise to interesting small additional contributions to the classical paraxial and aberrating behaviours. These contributions are directly proportional to powers of the de Broglie wavelength. The Dirac theory further gives rise to spinor contributions which are also directly proportional to powers of the de Broglie wavelength.. Thus, it is clear that these quantum contributions are of significance only at very low energies; this explains the grand success of the classical theory so far.