Quantum transport of vortex electrons in bending magnets and circular accelerators

Abstract

Controlling the sizes and phase structure of single-particle wave packets in accelerators remains an experimental challenge and requires understanding how bending magnets transform these states. An important example is transporting relativistic vortex electrons through the magnets to a collision point while keeping a narrow orbital-angular-momentum (OAM) distribution. We derive an effective Hamiltonian that accounts for the packet acceleration, employ it to obtain a generalized BMT-like equation, match the electron state at both magnet boundaries, and calculate the mean OAM and its variance. A half turn can reverse the mean OAM relative to the momentum while broadening its distribution, so recovering the mean does not ensure state recovery. We identify windows in packet sizes and bend angles for a small OAM spread and show that weak bends can produce narrow distributions with the mean OAM tilted relative to the momentum, making these states candidates for spatiotemporal vortices. For a few MeV electrons, we propose to use half-turn magnets that leave the mean OAM nearly antiparallel to the momentum while keeping its distribution narrow. For a circular orbit in a uniform field, the OAM variance after the exit grows as $N^2$ over $N$ turns, favoring linear accelerators, such as LINAC at JINR, for first experiments in MeV range.