Theory of using magnetic deflections to combine charged particle beams

Several radiation effects projects in the Ion Beam Lab (IBL) have recently required two disparate charged particle beams to simultaneously strike a single sample through a single port of the target chamber. Because these beams have vastly different mass-energy products (MEP), the low-MEP beam requires a large angle of deflection toward the sample by a bending electromagnet. A second electromagnet located further upstream provides a means to compensate for the small angle deflection experienced by the high-MEP beam during its path through the bending magnet. This paper derives the equations used to select the magnetic fields required by these two magnets to achieve uniting both beams at the target sample. A simple result was obtained when the separation of the two magnets was equivalent to the distance from the bending magnet to the sample, and the equation is given by: B_s= 1/2(r_c/r_s) B_c, where B_s and B_c are the magnetic fields in the steering and bending magnet and r_c/r_s is the ratio of the radii of the bending magnet to that of the steering magnet. This result is not dependent upon the parameters of the high MEP beam, i.e. energy, mass, charge state. Therefore, once the field of the bending magnet is set for the low-MEP beam, and the field in the steering magnet is set as indicted in the equation, the trajectory path of any high-MEP beam will be directed into the sample.