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Abstract
The radiation from SASE FEL has always limited value of the degree of transverse coherence. When transverse size of the electron beam significantly exceeds diffraction limit, the mode competition effect does not provide the selection of the ground mode, and spatial coherence degrades due to contribution of the higher order transverse modes. It is important that the most strong higher modes are azimythally non-symmetric which leads to fluctuations of the spot size and of the pointing stability of the photon beam. These fluctuations are fundamental and originate from the shot noise in the electron beam. The effect of the pointing instability becomes more pronouncing for shorter wavelengths. We analyze in detail the case of optimized SASE FEL and derive universal dependencies applicable to all operating and planned x-ray FELs. It is shown that x-ray FELs driven by low energy electron beams will exhibit poor spatial coherence and bad pointing stability.