Guiding charged particles in vacuum via Lagrange points.

We propose a method for guiding charged particles such as electrons and protons, in vacuum, by employing the exotic properties of Lagrange points. This leap is made possible by the dynamics unfolding around these equilibrium points, which stably capture such particles, akin to the way Trojan asteroids are held in Jupiter's orbit. Unlike traditional methodologies that allow for either focusing or three-dimensional storage of charged particles, the proposed scheme can guide both non-relativistic and relativistic electrons and protons in small cross-sectional areas in an invariant fashion over long distances without any appreciable loss in energy - in a manner analogous to photon transport in optical fibers. Here, particle guiding is achieved by employing twisted electrostatic potentials that in turn induce stable Lagrange points in vacuum. In principle, guidance can be realized within the fundamental mode of the resulting waveguide, thereby presenting a prospect for manipulating these particles in the quantum domain. Our findings may be useful in a wide range of applications in both scientific and technological pursuits. These applications could encompass electron microscopies and lithographies, particle accelerators, quantum and classical communication/sensing systems, as well as methods for shuttling entangled qubits between nodes within a quantum network.