| |
The drift tubes shape choice which provides the require distribution of the spatial harmonics amplitudes of RF field is an important problem in the design of RF focusing accelerators. It is necessary to have various relationships of the main (accelerating) and the first (as main focusing) harmonics of RF field for different types of accelerators. High order harmonics should be negligible for accelerators with an external focusing, and this ratio should be E1/E0 = 3-5 for the efficient operation of the axially symmetric RF focusing accelerator. Thus, the distribution and harmonic amplitude's ratios at the accelerator axis which provides stable beam dynamics are always known. The drift tubes shape study problem cannot be solved directly by ordinary methods because of unknown boundary conditions belongs to a class of ill-posed problem. At present, this problem can be solved by using genetic algorithms (GA). For this purpose, the electrode shape will be represent as the polynomial function, and then solve the Laplace equation with boundary conditions of Dirichlet and Neumann. The necessary electrodes shape can be quickly and easily simulated using the adaptive search.
|
|