Role and Significance of Uniform Distribution in a Study of Ensemble of Particles

Dynamics of an ensemble of particles is often studied by tracking a large number of test particles from a chosen initial state to an adequately defined final state. Random distributions of particles over considered parameters are frequently used to describe an initial state of studied ensemble. Randomness of input data insures that there is no overlapping in test particles visualization; however, it hides the dependencies between various input and output parameters. If non-random, uniformly distributed input data is used, relationships between the input and output variables are revealed. Further, mapping of such an input into its output together with an appropriate interpolation scheme contains description of an output corresponding to any desired distribution of input data. A mapping of non-random uniformly distributed input into its output is combined with
n
-dimensional linear interpolation into a method for studying dynamics of an ensemble of particles. Advantages and efficiency of the method are illustrated using an ion beam interaction with two devices: the four parallel, equally spaced finite wires and the spiral inflector. The method is applicable if interactions between particles within an ensemble are negligible compared to other forces involved.