The free electron laser （FEL） gain formulas for a non-resonant case are studied, and some new rigorous analytical formulas are given explicitly. For the mono-energetic and non-resonant electron beam, the exact expre...The free electron laser （FEL） gain formulas for a non-resonant case are studied, and some new rigorous analytical formulas are given explicitly. For the mono-energetic and non-resonant electron beam, the exact expression of the solution of the FEL characteristic cubic equation is obtained with a form much more simple than that in the literatures, and the gain length as the function of the detuning parameter is explicitly given. Then the gain for different detuning parameters and from low to high can be easily calculated. A simplified approximation formula is also given for the exponential gain calculation in the non-resonant case. For the case of the electron beam with an energy spread, the solution of the characteristic cubic equation is given explicitly for rectangular energy distribution and Lorentz distribution, respectively. Moreover the explicit expression also can be used for the solution of the characteristic cubic equation including the impact of the space charge. The transition from the low gain to the high gain is analyzed. The variations of the gain bandwidth and of the detuning parameter for the maximum gain are demonstrated. The applicable ranges of the small signal gain formula and the exponential gain formula are analyzed.展开更多
FLASH at DESY, Hamburg, Germany is the first free-electron laser(FEL) operating in the extreme ultraviolet(EUV)and soft x-ray wavelength range. FLASH is a user facility providing femtosecond short pulses with an unpre...FLASH at DESY, Hamburg, Germany is the first free-electron laser(FEL) operating in the extreme ultraviolet(EUV)and soft x-ray wavelength range. FLASH is a user facility providing femtosecond short pulses with an unprecedented peak and average brilliance, opening new scientific opportunities in many disciplines. The first call for user experiments has been launched in 2005. The FLASH linear accelerator is based on TESLA superconducting technology, providing several thousands of photon pulses per second to user experiments. Probing femtosecond-scale dynamics in atomic and molecular reactions using, for instance, a combination of x-ray and optical pulses in a pump and probe arrangement,as well as single-shot diffraction imaging of biological objects and molecules, are typical experiments performed at the facility. We give an overview of the FLASH facility, and describe the basic principles of the accelerator. Recently,FLASH has been extended by a second undulator beamline(FLASH2) operated in parallel to the first beamline, extending the capacity of the facility by a factor of two.展开更多
基金Supported by Major State Basic Research Development Program(2011CB808301)National Nature Science Foundation of China(11375199)
文摘The free electron laser （FEL） gain formulas for a non-resonant case are studied, and some new rigorous analytical formulas are given explicitly. For the mono-energetic and non-resonant electron beam, the exact expression of the solution of the FEL characteristic cubic equation is obtained with a form much more simple than that in the literatures, and the gain length as the function of the detuning parameter is explicitly given. Then the gain for different detuning parameters and from low to high can be easily calculated. A simplified approximation formula is also given for the exponential gain calculation in the non-resonant case. For the case of the electron beam with an energy spread, the solution of the characteristic cubic equation is given explicitly for rectangular energy distribution and Lorentz distribution, respectively. Moreover the explicit expression also can be used for the solution of the characteristic cubic equation including the impact of the space charge. The transition from the low gain to the high gain is analyzed. The variations of the gain bandwidth and of the detuning parameter for the maximum gain are demonstrated. The applicable ranges of the small signal gain formula and the exponential gain formula are analyzed.
文摘FLASH at DESY, Hamburg, Germany is the first free-electron laser(FEL) operating in the extreme ultraviolet(EUV)and soft x-ray wavelength range. FLASH is a user facility providing femtosecond short pulses with an unprecedented peak and average brilliance, opening new scientific opportunities in many disciplines. The first call for user experiments has been launched in 2005. The FLASH linear accelerator is based on TESLA superconducting technology, providing several thousands of photon pulses per second to user experiments. Probing femtosecond-scale dynamics in atomic and molecular reactions using, for instance, a combination of x-ray and optical pulses in a pump and probe arrangement,as well as single-shot diffraction imaging of biological objects and molecules, are typical experiments performed at the facility. We give an overview of the FLASH facility, and describe the basic principles of the accelerator. Recently,FLASH has been extended by a second undulator beamline(FLASH2) operated in parallel to the first beamline, extending the capacity of the facility by a factor of two.
