Effect of longitudinal aberration in an ion-optical system on the properties of a focused beam

Modelling of the processes involved in the passage of a beam through a system of high-voltage electrodes with allowance made for the thermal and grid spreads of transverse particle velocities constitutes a three-dimensional problem that is difficult to solve with modern computers. In the present work, an analytic method has been developed that reduces this problem to a two-dimensional one. The method corresponds to approximating a marked longitudinal aberration in an ion-optical system (IOS), when the effective emittance of the beam during its high-voltage shaping increases severalfold, this being characteristic of all IOS know thus far. Fully justified in this case is the statement that a unique relationship exists between the coordinates r and z, which respectively characterize the location of the particle on the emitter and the point of intersection of the axis by the particle (or the point of maximum approach of the particle to the axis), and also between r and {alpha} ({alpha}being the angle between the particle trajectory in the focusing region and the axis of the system). This statement leads to a hyperbolic law of increase in current density in the central portion of the focused beam and thus confirms the validity of this law.more » The calculations were compared with experimental data on the focusing of a 0.4-MeV proton beam with a current of 20-75 mA and a diameter of 2-5 mm in the crossover under conditions in which the effective emittance of the beam, as a result of aberrations during its high-voltage shaping, increased by a factor of 3 or more (in kilovolts), and the calculated trajectories for 20 of 40 mm at the emitter are shown, where the markers D8 and D9 denote the positions of multiwire beam profile sensors.« less