Electrons, the first fundamental particles to be discovered, have played a central role in technological advancements that define the modern world. Their intrinsic charge allows manipulation by electric and magnetic fields, making them essential for efficient data processing and storage in electronic circuits. Beyond their classical role in electronics, electrons, protons and ions can also exist in quantum states, a property that underpins their potential for quantum computing. Importantly, electrons are crucial in advanced imaging techniques such as scanning and transmission electron microscopies (SEM and TEM), X-ray generation, and particle accelerators, advancing our understanding from the structure of matter to the mysteries of our universe.

Despite their importance in processing tasks, the challenge of guiding electrons over long distances in a controlled manner remains unresolved. Modern communication systems rely on converting information into optical signals, which are then transmitted through optical fibers. In materials, electron transport is limited by finite conductivity, with average speeds constrained by scattering mechanisms, effective mass, temperature, electric field strength, material properties, and electron-electron interactions to around ~10⁶ m/s In contrast, vacuum allows electron beams to travel at much higher speeds. However, even though electrons exhibit wave properties, Earnshaw’s theorem prohibits the formation of trapping potentials in a vacuum that would guide them in a manner similar to that an index potential in fibers traps photons. Consequently, most particle accelerators today rely on techniques based on focusing and defocusing beams using electrostatic or magnetic lenses, which are expensive and bulky.

In this article, we introduce a novel approach to realizing electron waveguides in a vacuum for the first time. The guiding mechanism is based on stable Lagrange points, formed by the presence of a twisted wire maintained at a fixed electrostatic potential. Lagrange points, initially identified in reduced three-body systems as stable points where forces on a small mass balance under the action of two massive bodies, have recently inspired our group to realize Trojan waveguides for light. In this manuscript, we extend this concept to guiding charged particles, including electron, proton, and ion beams. Given that beam transport occurs in a vacuum, the nominal loss of the waveguide in the nonrelativistic regime is extremely low, i.e., on the order of 10^-10 dB/km. Similar to an optical fiber, the Lagrange guiding system is by nature passive since the electrostatic potential does not require external energy.

The prospect of a waveguide for electrons, and more broadly for charged particles, opens up numerous new possibilities. These waveguides could significantly advance accelerator physics by enabling high-energy collisions and the observation of extremely rare processes that occur at longer propagations. They could also have a profound impact on the resolution and speed of charged particle imaging techniques, and potentially enable high-energy microwave tubes and undulators. Given their compact and scalable cross-section, this technology could, for the first time, make long-distance charged particle communications a reality. Most importantly, the realization of these waveguides could inspire the development of beam control components like directional couplers, cavities, gratings, and multiplexers, paving the way for new functionalities based on charged particle circuitry, with significant implications for quantum and classical sensing, communication, and computation.

This post was prepared by  Mercedeh Khajavikhan, Haokun Luo, Yunxuan Wei, Georgios Pyrialakos, and Demetrios Christodoulides