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By utilizing higher harmonics of undulator radiation, harmonic lasing ishelpful in the development of compact x-ray free electron lasers (FELs), i.e.reducing its costs and sizes. Harmonic lasing of FELs have been experimentallydemonstrated in the low-gain FEL oscillators from terahertz, infrared toultraviolet spectral range. Based on the current status and future directionsof short-wavelength FELs in the worldwide, this paper reviews the progresses onharmonic lasing of x-ray FELs, mainly concentrating on the recently proposedharmonic lasing of x-ray FEL oscillators and further ideas on harmonic lasingof single pass x-ray FEL amplifiers.

Harmonic lasing of x-ray free electron laser: on the way to smaller and cheaper