Quantum mechanics of charged-particle beam transport through magnetic lenses.

Abstract

The quantum theory of charged-particle beam transport through a magnetic lens system with a straight optic axis, at the level of single-particle dynamics and disregarding spin (or, when nonzero, assuming it to be an independent spectator degree of freedom), is presented, based on the Schr\"odinger and Klein-Gordon equations in a form suitable for analyzing the paraxial and aberration aspects in a systematic way using a Lie algebraic approach. In the classical limit, the well known Lie algebraic treatment of the corresponding classical theory is obtained. As examples, quadrupole and axially symmetric magnetic lenses are considered. An extension of the theory to the cases of electrostatic and other electromagnetic lens systems is outlined. This work is complementary to an already known similar approach to the spinor electron optics based on the Dirac equation and provides the corresponding framework when the optics of charged particles, with or without spin, is described with scalar wave functions in the nonrelativistic and relativistic situations.