Our first new physics result is the identification of a linear correlation between position within the bunch and energy of interaction. Since guinea-pig goes through layers in the bunch in sequential order, we can process an output file directly, and output the energy contained in macro-particles that generate events. Physically, this is understandable as the electron/positron at the end of a bunch has crossed more field through more field, and thus has interacted more than the one at the beginning of a bunch.
Since the guinea-pig algorithm goes through each pair of transverse bunch slices before moving to the next slice, there are several dozens macro particles to process within each slice. For this reason, we average 200 lines of the output file before plotting, thus neglecting the computational artefacts. In figure j below the independent variable, labelled T, is effectively the line number/200.
Figure j: plot of collision energy as a function of position in output file
Another interesting quantity is the fractional decrease in energy over a whole bunch, as a function of beam energy. This decrease in energy is found by running guinea-pig at a range of different energies, and finding the scaled energy loss over the range of the fitted linear trendline.
We find another linear relation: at √s=500GeV,average 2.2% energy loss. But at 1TeV, will have lost ~6%. This is comparable to values found in literature by independent methods: in ref [1Monig reconstruct paper], (p1) the average energy lost for an electron at √s=500GeV is 1.5%, which is compatible with an average loss of ~2% from an electrons at the beginning of the bunch vs those at the end.
Fig k: fractional enegy loss throuh a whole bunch in TESLA, at varying beam energy:
We also plot z-position of electrons around the interaction point, as the software runs through the bunch. As we expect intuitively, at the beginning and the end of the interaction the z-positions of the interacting particles will be less spread, as the bunches are going through each other. Note that the envelope is what is intersting here, rather than the up-down pattern which is a computational effect.
