1. Making the second section undulator of optical klystron resonant with the higher harmonic of the laser, the harmonic emission can be enhanced.

2. The effects of undulator phase errors on the Free Electron Laser small signal gain is analyzed and discussed.

3. Undulator oar, boating on the lake, Fun for all at.

4. But the effects on the beam are strong when the undulator is located in the 4th straight section, and the storage ring will not work if the compensation methods are not implemented in the ring.

5. The analysis and discussion of the effect of the undulator magnetic field error on the modulation of the electron beam energy in an optical klystron are presented in this paper.

6. We have derived the formulas of harmonic spontaneous emission power density, small signal gain of this undulator FEL and the coupling coefficients between the electrons and the radiation field.

7. For a coherent harmonic generation experiment the electron energy, the OK undulator gap and the wavelength of the seed laser must meet the requirement of resonance bondition.

8. A Hall probe magnetic field measurement device is used to measure the undulator of The Project 2 inNSRL.

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9. The advanced photon source, especially the synchrotron radiation photon exited from undulator is equipped with extremely high power density.

10. Undulator rms phase error is expressed as function of the magnet peak field distribution. It can be used as the objective function for practical undulator performance optimization.

11. Choosing the BFEL parameters, we simulated the effects on FEL spontaneous spectrum due to field errors, and obtained the acceptable condition of all kinds of field errors in undulator.

12. The angular spectrum of spontaneous emission in a wo-dimensional undulator free-electron laser is analyzed theoretically.