We present the first observation of self-amplified spontaneous emission (SASE) in a free-electron laser (FEL) in the vacuum ultraviolet regime at 109 nm wavelength (11 eV). The observed free-electron laser gain (approximately 3000) and the radiation characteristics, such as dependency on bunch charge, angular distribution, spectral width, and intensity fluctuations, are all consistent with the present models for SASE FELs.

A numerical approach for the solution of Maxwell's equations is presented. Based on a finite difference Yee lattice the method transforms each of the four Maxwell equations into an equivalent matrix expression that can be subsequently treated by matrix mathematics and suitable numerical methods for solving matrix problems. The algorithm, although derived from integral equations, can be considered to be a special case of finite difference formalisms. A large variety of two and three-dimensional field problems can be solved by computer programs based on this approach: electro statics and magnetostatics, low-frequency eddy currents in solid and laminated iron cores, high-frequency modes in resonators, waves on dielectric or metallic waveguides, transient fields of antennas and waveguide transitions, transient fields of free-moving bunches of charged particles etc.

Trapping of particles in nonlinear resonances in the presence of space charge and synchrotron motion may be a source of beam halo generation and beam loss in high intensity synchrotrons, in particular for extended storage times at the injection plateau as planned for the SIS100 synchrotron of the FAIR project. Although extensive simulation studies have theoretically demonstrated this mechanism, experimental evidence was so far limited to demonstration experiments at the CERN Proton Synchrotron (PS) in 2002-2003 using an octupolar resonance. Here we describe new experiments at the SIS18 synchrotron at GSI, where the resonance is driven by a sextupolar field error and horizontal static tune scans are taken across the resonance stop band. The new data significantly extend the previous observations by a complete set of measurements comparing beams with and without rf, both at low and high intensity. The correlation between transverse beam loss and simultaneous bunch length shortening provides strong evidence that the measured emittance and the loss in intensity are indeed caused by periodic resonance crossing, leading to the main effect of scattering but also to a lesser extent to the trapping of particles due to the combined effect of the nonlinear resonance and the space charge.

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