The following report concerns the application of a relaxation mesh method for the determination of the average flux within the moderator of a light water moderated, 1.027 per cent U-235, hexagonal lattice with a volume ratio (V_H2O + V_Al)/V_Uranium of 4:1. It was hoped that the calculation would enable one to determine any differences in flux which might result from the fact that the unit cell is a hexagon instead of a cylinder. Because we were primarily interested in the effect due to geometry we applied the same theory, diffusion theory, to the hexagon by means of the mesh method and to the equivalent cylinder.

The proton beam in the Cosmotron is accelerated to an energy of 2.3 billion electron volts by a radio frequency voltage which is impressed across an insulated gap in the ferrite loaded accelerating cavity of the vacuum chamber. To maintain a constant orbit radius as the beam is accelerated, the frequency of the accelerating voltage must increase from the initial value of 370 kc/sec to 4200 kc/sec during the one second magnet pulse. Over the entire 11:1 frequency range, a minimum gap voltage of 2000 volts rms must be maintained. At every instant throughout the magnet pulse, the frequency of this voltage must be a predetermined function of the magnet field to a high degree of accuracy. Frequency errors greater than about .2 percent result in loss of beam due to excessive radius changes. Smaller errors than this however, can excite fatal phase oscillations in the beam if they occur rapidly. As little as .005 percent frequency modulation can result in total beam loss if it occurs at a rate of several kc/sec, where the beam is most sensitive to such disturbances.