Novel Techniques for the Position Calibration of FAUST David Balaban 2014 Cyclotron REU Program Dr. Sherry Yennello’s Group

Problem The Forward Array Using Silicon Technology (FAUST) consists of 68 detectors Detectors identify and measure the energy of charged particles Recently upgraded to position-sensitive detectors Structural tolerances may result in inaccurate relative positioning Position must be accurately known for upcoming experiments

The Detectors Current induced by charged particle Voltage determines position with: X-Position = (Back2-Back1)/(Back1+Back2) Y-Position = (Front2-Front1)/(Front1+Front2) Left picture from: S.N Soisson, et al. "A dual-axis dual-lateral position-sensitive detector for charged particle detection." NIM A, 613, 2, 2010.

The FAUST aRRAY Mask Mask blocks particles and creates striped pattern on detectors Stripes on detectors will be misplaced by detector motion Goal is to find how far detectors are from expected positions 2 phases to accomplish: 1.) Identify stripes on detector 2.) Find set of linear transformations applied to detector which will reposition the stripes to the expected values

Phase 1 Process Noise Removal Rotation Projection onto y-axis 0. Collect Data Noise Removal Rotation Projection onto y-axis K-means algorithm Data Selection and Linear Fit Display Result

1. Noise Removal Collected from 228Th Source X-Position (cm) Y-Position (cm) Count channel number Collected from 228Th Source Cut electrical noise at low energy Stretch out data empirically Trying to understand characteristics of compression

2. Rotation Rotate data by expected angle of slope Makes projecting and fitting easier. X-Position (cm) Y-Position (cm)

3. Project Data onto y-axis Y-Position (cm) Count After projecting onto y-axis, large peaks correspond to stripes.

Description of K-means: 1. Initialize k random points 2. Calculate average position of data associated with each point 3. Reset point to average position 4. Repeat until convergence Picture from: Thomas, Philip. “Midterm Review.” Computer Science 383. University of Massachusetts Amherst, Amherst, MA. 25 Mar. 2014. Lecture.

4. Run K-means Algorithm Use K-means to identify location of stripes Must select best K-value Y-Position (cm) Count Black K=1 Red K=2 Green K=3

5. Data Selection Approximate location of stripe Linear fit to data X’-Position (cm) Y’-Position (cm)

6. Final Result Rotate lines back by 45 degrees Fit line Fit-data center Rotate lines back by 45 degrees Colors show which points were used in fit Left shows plot from step 2 Right shows finished product.

Phase 2 Data collected with 228Th Source and 4He@15MeV/A+ natAu beam source simulation Data collected with 228Th Source and 4He@15MeV/A+ natAu Want to get blue and red data points closer to orange

Geometry Simulation 228Th Source Geometry Simulation “Perfect World” expectation Alpha particle simulation perfect elastic scattering Y-Position X-Position 228Th Source Can see stripes on ring C, not ring A 2-3 stripes on detectors Y-Position X-Position

Geometry Simulation 4He @15MeV/A+ natAu Geometry Simulation “Perfect World” expectation Alpha particle simulation perfect elastic scattering Y-Position X-Position 4He @15MeV/A+ natAu Y-Position X-Position Low stats on ring C Similar stripes to source Agrees with source for ring C

Description of Hill Climbing: Define set of free parameters P Define method eval(P) to evaluate parameters to a single value HC tries to find the global maximum of eval(P) by changing P. The picture to the left shows a successful Hill Climb with one free parameter. Local maxima causes difficulty for successful HC. Picture from: "Hill Climbing." Wikipedia. Wikimedia Foundation, 27 July 2014. Web. 03 Aug. 2014. eval(P) P

Preliminary testing of Hill Climbing algorithm. Setup: Two initially parallel lines are rotated randomly Hill Climbing is told to make them parallel again through rotations 6 free parameters (3 per line) Angle between Lines after Hill Climb (deg) Count

.5˚ Setup: Ring of detectors rotated by .5 degrees about beam-axis Each detector is rotated randomly within a given range Hill Climbing is told to rotate ring such that the set of stripes are as close to expected as possible

eval(P) at the end of Hill Climb θ in degrees (θ-.5)/.5 .5˚ eval(P) at the end of Hill Climb θ in degrees (θ-.5)/.5 Black min/max rotation: [-.05 ˚, .05 ˚] Red min/max rotation: [-.1 ˚, .1 ˚] Green min/max range: [-.2 ˚, .2 ˚] Setup: 1 free parameter Cutting on eval(P) allows better accuracy As the range increases inaccuracy grows

Summary FAUST Detectors measure position but need to be calibrated Mask allows for 2-phase process for calibration Phase one identifies stripes with linear fits Phase two needs to be tested more before implementation

Acknowledgements This work was supported by: Works Cited: the Robert A. Welch Foundation under Grant No. A-1266 U. S. Department of Energy under Grant No. DE-FG03-93ER-40773 National Science Foundation under Grant No. PHY-1263281 Works Cited: S.N Soisson, et al. "A dual-axis dual-lateral position-sensitive detector for charged particle detection." NIM A, 613.2 (2010). F. Gimeno-Nogues, et al. "FAUST: A new forward array detector." Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment 399.1 (1997). Dabney, William. "Local Search." Computer Science Education Lab, UMASS, Amherst. N.p., n.d. Web. 7 Aug. 2014. Thomas, Philip. "Unsupervised Learning." Computer Science Education Lab, UMASS, Amherst. N.p., n.d. Web. 7 Aug. 2014.