Abstract
A plasma channel undulator/wiggler may be created through the plasma wakefield excited by the beating of several Hermite-Gaussian laser modes propagating in a parabolic plasma channel. Control over both the betatron and undulator forces is conveniently achieved by tuning the amplitude ratios, colors, and order numbers of the modes. A special structure of the undulator/wiggler field without the focusing force near the propagation axis is generated inside the plasma wakefield by matching the strengths of the fundamental and first-order Hermite-Gaussian modes. The electron beam only experiences forced undulator oscillations in such a field, which significantly improves the quality of the emitted radiation. Since the value of the undulator strength parameter could be in a wide range, less or larger than unity, it is capable of generating narrow bandwidth x-ray, as well as the synchrotronlike high-energy $\mathrm{x}/\ensuremath{\gamma}$-ray, radiation by harmonics. Additionally, controlling the relative phases between the laser modes allows for polarization control of the plasma undulator. High-order harmonics produced from a circularly polarized plasma undulator clearly show the vortex nature and carry well-defined orbital angular momentum.
Highlights
Extreme ultraviolet (XUV) and x-ray pulses produced by electrons traveling through magnetic undulators have become an indispensable tool for experimental studies in chemistry, biology, material science, warm dense matter, etc
Since the value of the undulator strength parameter could be in a wide range, less or larger than unity, it is capable of generating narrow bandwidth x-ray, as well as the synchrotronlike high-energy x=γ-ray, radiation by harmonics
The wavelength of the on-axis radiation generated by an electron with relativistic Lorentz factor γ traveling through a linearly polarized undulator is equal to λ 1⁄4 λuð1 þ a2u=2Þ=ð2γ2Þ, where λu is the undulator period, au 1⁄4 eBuλu=ð2πmecÞ is the undulator strength, Bu is the magnetic field amplitude, e and me are the absolute values of electron charge and mass respectively, and c is the speed of light in vacuum
Summary
Extreme ultraviolet (XUV) and x-ray pulses produced by electrons traveling through magnetic undulators have become an indispensable tool for experimental studies in chemistry, biology, material science, warm dense matter, etc. It was mentioned that using the superposition of two (odd and even) higher-order Hermite-Gaussian modes may (1) lead to a better control over the strength of the focusing forces, relaxing the conditions for the electron beam emittance for generation of a narrow-bandwidth photon spectrum; and (2) provide more control for the parameters of the plasma undulator (its strength and wavelength) It is the purpose of this paper to extend previous work [37,39,41] and provide detailed analytical derivations for the case where the plasma undulator is created by the superposition of higher-order laser modes propagating inside the parabolic plasma channel.
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