Compact accelerators · Free-electron devices

Compact, high-gradient particle accelerators & the inverse free-electron laser (IFEL)

Conventional RF accelerators are large and expensive. The inverse free-electron laser (IFEL) offers a route to compact acceleration: an electromagnetic wave transfers energy to a relativistic electron beam as it wiggles through a helical undulator, reaching high gradients over centimeter-scale interaction lengths.

Watch the IFEL acceleration animation →

The physics

An electron passing through a periodic magnetic (undulator) field acquires a transverse velocity component. When a co-propagating electromagnetic wave (here a circularly-polarized terahertz drive) is phase-matched to that transverse motion, the wave does net work on the electron and it gains energy (the inverse of the free-electron-laser radiation process). Sustaining the energy exchange as the electron accelerates requires tapering the undulator (its period/pitch and field) to hold the resonance condition.

The model

The trajectory is computed from the full relativistic Lorentz-force equation of motion in COMSOL Multiphysics, coupling the helical undulator field and the THz drive. Outputs include the 3-D electron trajectory, the energy-gain curve along the interaction length, and the taper profile required for phase-locked acceleration, which are the inputs for sizing a compact-accelerator stage.

High acceleration gradient

What makes the IFEL attractive is the acceleration gradient: the energy gained per unit length. A high gradient compresses what a conventional RF machine does over meters into centimeters, which is what makes a genuinely compact accelerator possible. It is also decisive when particles must reach energy before they decay: muons, with their microsecond lifetime, are the motivating example for rapid-acceleration schemes and muon-collider concepts.

Selected accelerator & FEL publications

• Magory E, Bratman VL, Balal N. Permanent helical micro-undulators for x-ray free electron lasers. Physics of Plasmas 31, 053301 (2024). doi:10.1063/5.0199053
• Balal N, Bratman VL, Lurie Yu, Magory E. Efficiency of terahertz undulator radiation from short electron bunches moving in the field of permanently magnetized helices. Physics of Plasmas 28, 093301 (2021). doi:10.1063/5.0060778
• Balal N, Bandurkin IV, Bratman VL, Fedotov AE. Helical undulator based on partial redistribution of uniform magnetic field. Physical Review Accelerators and Beams 20, 122401 (2017). doi:10.1103/PhysRevAccelBeams.20.122401
• Balal N, Bandurkin IV, Bratman VL, Magory E, Savilov AV. Negative-mass mitigation of Coulomb repulsion for terahertz undulator radiation of electron bunches. Applied Physics Letters 107, 163505 (2015). doi:10.1063/1.4934495
• Balal N, Bratman VL. Undulator Radiation of Dense Plane Electron Bunches. IEEE Transactions on Plasma Science 43, 532-538 (2015). doi:10.1109/TPS.2014.2381293

The undulator designs behind this work are detailed on the applied magnetism page, and the underlying electron-confinement physics is explored on the particle dynamics page. Klystron and traveling-wave tube models are on the microwave radiation sources page, and further COMSOL examples are collected on the simulations page.

← All research projects