Description of electrons motion in an alpha magnet

It is well known that the beam directly out of the thermionic cathode RFgun is not suitable for injection into a linear accelerator section. This kind of injection would produce an accelerated beam with a large energy spread because of the large phase-spread the particles coming into the accelerator section would have in the absence of compression. Magnetic bunch compression is one solution to this problem, and is most suitable for RF gun. In this paper, an alpha magnet is described, which is an asymmetric quadrupole. The scaled equation of motion and ideal trajectory in an alpha magnet are presented, and how the scaled form of the differential equation can be used to deduce some of the magnet's properties with numerical calculation method is shown.