Stability analysis of relativistic electron dynamics in Lagrange waveguides

Recently, the prospect of guiding charged particles by means of Lagrange points has been put forward. What makes this methodology possible is the action of Coriolis forces that dynamically provide stability in static helicoidal potential landscapes. In such an environment, particle guidance can occur indefinitely with minimal losses, without the need for magnetic fields, in a manner analogous to photon transport in optical fibers. Here, we provide a rigorous stability analysis of the relativistic charged-particle dynamics when launched into a Lagrange waveguide—an aspect crucial in establishing the necessary criteria for stable trapping. By considering all the force components involved, our results delineate the stability boundaries under both attractive and repulsive electrostatic conditions. A first-order perturbation approach yields both the spectral eigenvalues and their corresponding eigenvectors associated with the stability of particle dynamics in a six-dimensional phase space. The Larmor radiation is also investigated in terms of pertinent parameters, along with the radiated energy spectral density. Our results enable the design and realization of this new class of Lagrange systems capable of guiding charged particles across a wide range of energy scales, with potential utility in a broad spectrum of applications.