Charge-tube method for space charge in beams

The charge-tube method is an accurate and efficient way of assigning the space-charge of a beam in computational simulations of charged particle systems. The method makes use of the trajectory steps that result from the process of trajectory integration. The space-charge associated with each step of each trajectory is assigned to a narrow cylindrical tube that surrounds the step. The total space-charge of a beam is then the sum of the charges in all the resulting the tubes. In systems of 2-dimensional axial symmetry the charge tubes become conical sheets of charge, and for some purposes these need to be given a finite thickness. The charge-tube method is particularly useful for simulating the space-charge of beams that are very narrow compared with their length. The implementation of the method is described and results obtained with it are compared with those obtained by the traditional charge-cell method.