Plasma undulator may be created by the plasma wakefields excited by the beating of several Hermite-Gaussian modes propagating in a plasma channel. Electrons injected into the plasma wakefields will experience both betatron and undulator motion. Control over both betatron and undulator forces is achieved by tuning the amplitude ratios, colors and order numbers of the modes. Additionally, controlling the relative phase between the laser modes allows for the polarization control of the plasma undulator.
Synchrotron radiation shone by electrons travelling in bending magnets or insertion devices is essential for our understanding of the microcosm. X-ray pulses produced by the synchrotron facilities are widely used in, for example, chemistry, biology and material science. The brightest X-ray pulses are generated using the free- electron lasers (FELs) - a combination of a high-quality linear accelerator (LINAC) and magnetic undulators. Presently, the lower limit to the undulator period $\lambda_u$ for magnetic undulators is on the order of 1 mm. Reducing $\lambda_u$ is highly beneficial as it will decrease the required electron energy for the same specified radiation wavelength and, hence, decrease the size of the light source. Undulators with periods on the order of a millimeter, often referred to as micro-undulators, are, therefore, of great interest.
In this report, we propose a novel type of the undulator for the narrowband photon emission based on the beating of two or more higher-order laser modes in the parabolic plasma channel. Electrons injected into the wakefield created by the laser pulse consisting of mixture of Hermite-Gaussian or Laguerre-Gaussian modes propagating inside a parabolic plasma channel, wiggle with the characteristic wavelength of $\lambda_u=2\pi Z_R$, where $Z_R$ is the Rayleigh length of the laser pulse. It is theoretically possible to achieve high undulator strength $a_u\sim 1$ for undulator periods of 1~mm or less. This makes such a plasma undulator or plasma wiggler (PIGGLER) a promising way towards a ”table-top” bright incoherent soft X-ray source, and, theoretically a ”table-top” FEL with tunable polarization.
Using linear plasma theory and numerical simulations, the field structure of the plasma undulator is examined, electron trajectories and emitted radiation are calculated. Polarization control, achieved by the phase difference of the laser modes, is demonstrated.
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