Relativistic dynamics of charges in electromagnetic fields: An eigenspinor approach

Analytical solutions and fresh insights for the relativistic dynamics of charges in classical electromagnetic fields are made possible by an eigenspinor approach. The Lorentz-force equation takes a simple spinorial form when expressed in terms of an amplitude of the Lorentz transformation that describes the motion of the charge in Clifford’s geometric algebra of physical space. Algebraic projectors allow explicit analytical solutions to be found for charges in arbitrary initial motion interacting with monochromatic plane waves, with directed plane-wave pulses, and with pulses superimposed on static axial fields. The treatment tests the classical effective mass of a dressed charge and leads to a refinement of the concept of ponderomotive momentum. Implications for a pulsed autoresonance laser accelerator are briefly discussed.