= beam interaction =

Both crossing beams are split in slices (the number of slices of each beam is 'n_slice'). 
At each 'slice-step' there are interacting  pair slices (a 'pair' is made of a slice of one beam and a slice of the other). One has to consider one beam (with slices numbered, for example, from right to left : O, 1, 2, .... n_slices) passing before an other beam (with slices numbered from left to right : 0,1,...., n_slices)
 * At slice-step numbered 0 there is one interacting pair : 0-0 
 * At slice-step numbered 1 two pairs : 0-1 and 1-0, 
 * At slice-step numbered 2 there are three of them : 0-2, 1-1 and 2-0 
 * and so on...
 * until slice-step numbered n_slice-1  (when two beams exactly overlap) where the pairs are : 0-(n_slice_1), ...., (n_slice-1)-0


The beam crossing has to be ended by the following slice-steps :
 * pairs : 1-(n_slice-1), 2-(n_slice-2), ...., (n_slice-1)-1
 * pairs : 2-(n_slice-1), 3-(n_slice-2), ...., (n_slice-1)-2

each slice-step is defined by two values : ''firstSliceOfBeam1'' and ''lastSliceOfBeam2'', treating pairs (''SliceOfBeam1-SliceOfBeam2''), with ''SliceOfBeam1'' running in increasing order from ''firstSliceOfBeam1'' to ''min(n_slice, lastSliceOfBeam2)'' and ''SliceOfBeam2'' running in decreasing order from ''lastSliceOfBeam2'' to ''firstSliceOfBeam1''. The number of pairs at each slice_step is : ''firstSliceOfBeam1 + lastSliceOfBeam2 + 1''.
A slice-step consists of a call to the GUINEA-method : iteration_on_overlaping_slices(int firstSliceOfBeam1, int lastSliceOfBeam2,...) or iteration_on_overlaping_slices_with_trackpair(...,int firstSliceOfBeam1, int lastSliceOfBeam2,...)

Each slice-step (in methods iteration_on_overlaping_slices or iteration_on_overlaping_slices_with_trackpair) is computed by splitting into 'time-steps' (the number of time steps per slice-steps is given through the keyword 'n_t' in the file acc.dat). 
One of these 'time-steps' is a call to the GUINEA-method : make_time_step_on_slices(unsigned int firstSliceOfBeam1, unsigned int lastSliceOfBeam2, ...).
Finally, the interaction of a single pair (''sliceOfBeam1''-''sliceOfBeam2'') is realized by a call to the GUINEA-method : 

[wiki:guiNeaPig/MakeStep make_step(int sliceOfBeam1, int sliceOfBeam2,...)]