Simulation on Control of Beam Halo-Chaos by Selecting Ion Numbers Ratio as Controlling Variable

The ratio of the numbers of ions outside the match radius to the total ion numbers， not root-mean-square radius or others， is selected as variable to simulate the control of beam halo-chaos in high intensity accelerator. Beam halo-chaos for five different initial ion distributions is effectively controlled by a logarithm-function controller based on the variable. The control method may be operational in experiment， because it only needs to probe how many ions are outside the match radius.