Coherent Betatron Oscillation Systematic Study (x-Position)
This project is part of the G-2 experiment*. This is one part in a larger project to determine the acceptance (detection rate) of positrons, created by decaying muons, by the calorimeters as a function of the muon position in the x, x-prime and y, y-prime phase-spaces at the time of decay.
(The note and presentation below were written for the members of the G-2 experiment. Therefore, there is little background in the note and jargon may be used.)
GitHub code: https://github.com/EmptyBucket9000/BNL_Acceptance_Tracking
Technical note: cbo_systematic_study_status_report.pdf
Presentation: cbo_systematic_study_status_report_presentation.pdf
Presentation (addendum): cbo_systematic_study_status_report_addendum_presentation.pdf
DoE Poster (Required as part of the SULI program): doe_suli_poster.pdf
In E821, the previous G-2 experiment at BNL, the relationship was assumed to be linear. However, due to the current project’s (E989) need for increased precision, this assumption can no longer be made. My task is to show whether or not the relationship between position and acceptance is actually linear or if higher-order terms must be taken into account. Then, assuming the function can be expanded into a power series, find the coefficients for the linear and second order terms. This is important as there is a non-negligible coherent betatron oscillation (CBO) in the muon beam (the mean muon position in the beam oscillates at the betatron oscillation frequency) due to the limitations in the available beam injection methods.
The Python code tracks the positrons (on the order of 1 GeV) as they curl towards the center of the ring due to the magnetic field. Unfortunately, the positrons will often pass through aluminum, Macor, and/or some material similar to brass before possibly striking the calorimeters. This matter can cause Bremsstrahlung events and sometimes subsequent pair-production from the x-rays that then pass through the matter. The ‘shower’ of particles and x-rays must be tracked since if multiple low-energy particles/x-rays strike the same calorimeter withing a short period of time, the calorimeter will interpret these multiple strikes as a single high-energy particle.
I received a data file of about 5,000 muons at 100 microseconds after they enter the storage ring. The data file contains the momentum and phase-space information used to determine the possible positron starting positions and momentum. I then use Runga-Kutta 4th to integrate and track the particle.
* I was an intern working with William M. Morse at Brookhaven National Lab (BNL). More information on this experiment can be found at the Fermilab and BNL websites.