Proceedings of the 35th Sapporo Symposium on Partial Differential Equations

conf: The 35th Sapporo Symposium on Partial Differential Equations (Room 203, Faculty of Science Building #5, Hokkaido University , August 23-25, 2010

Optimum Arrangement of Resonator in Micro-bunch Free Electron Laser(III. Accelerator, Synchrotron Radiation, and Instrumentation)

Using a short-bunched beam of electrons from a linear accelator, the output of the micro-bunch FEL has been studied experimentally to clarify the optimum arrangement of an open resonator on the electron orbit. The output depends sharply on the arrangement, and the maximum output is observed when the resonator axis intersects the electron orbit with the angle of 3°

Global existence for coupled systems of nonlinear wave and Klein-Gordon equations in three space dimensions

We consider the Cauchy problem for coupled systems of wave and Klein-Gordon equations with quadratic nonlinearity in three space dimensions. We show global existence of small amplitude solutions under certain condition including the null condition on self-interactions between wave equations. Our condition is much weaker than the strong null condition introduced by Georgiev for this kind of coupled system. Consequently our result is applicable to certain physical systems, such as the Dirac-Klein-Gordon equations, the Dirac-Proca equations, and the Klein-Gordon-Zakharov equations.Comment: 31 pages. The final versio