A Basic Silicon Xray Absorption MC and Considerations

A Basic Silicon X-ray Absorption MC and Considerations for an APS Run Argonne/Los Alamos UMA Meeting 12/5/18 Bruce Schumm, SCIPP, UC Santa Cruz

The SCIPP X-ray Absorption MC Inputs • Overall attenuation length and PE vs. Compton fraction • Above 10 ke. V: Photon Cross Sections, Attenuation Coefficients, and Energy Absorption Coefficients from 10 ke. V to 100 Ge. V, NSRD-NBS 29, August 1969, p 50 • Below 10 ke. V: https: //physics. nist. gov/Phys. Ref. Data/Xray. Mass. Coef/Elem. Tab/z 14. html; extraplate Compton fraction from above reference. • Choose the values that don’t include coherent (Thomson) scattering • Modeling of PE effect • Photoelectron given energy E - EK (EK is K-shell energy of 1. 84 ke. V) and sin 2 distribution • 94. 5% of time remaining energy goes into single Auger electron • 5. 5% of time remaining energy goes into fluorescence photon of energy 1. 80 ke. V and Auger of 0. 04 ke. V • Fluorescence fraction and mean energy from R. T. Berger, The X- or Gamma-Ray Energy Absorption or Transfer Coefficient: Tabulations and Discussion, Radiation Research, Vol. 15, No. 1 (Jul. , 1961), pp. 1 -29

The SCIPP X-ray Absorption MC cont’d More Inputs • Compton Scattering given by Klein-Nishina Formula; for ease of reference: • Cross section from https: //en. wikipedia. org/wiki/Klein%E 2%80%93 Nishina_formula • Electron angular distribution from https: //en. wikipedia. org/wiki/Compton_scattering • Electron d. E/d. X • Total path length from stopping-power values at https: //physics. nist. gov/Phys. Ref. Data/Star/Text/ESTAR. html • Assume single deposition at point ¾ along the path (mean point of deposition for nonrelativistic particle with stopping power proportional to 1/ 2 • Electron path length is less than 1 m for E < 6 ke. V • Multiple interactions • If absorption process generates final-state photon, continue simulation • Allow up to 4 photon scatters

Attenuation Length and Overall Absorption Probability in 1 cm of Silicon INTERACTION PROBABILITY IN 1 CM DEPTH VS ENERGY (KEV) ATTENUATION LENGTH (�M) VS X-RAY ENERGY (KEV) 1. 2 100000 1 10000 0. 8 1000 0. 6 100 0. 4 K edge 10 0. 2 1 0 1 10 100 1000

Compton Fraction and Interaction Probability in 100 m Thick Sensor INTERACTION PROBABILITY VS X -RAY ENERGY (KEV) COMPTON FRACTION VS X-RAY ENERGY (KEV) 1 10 100 1 1000 0. 1 0. 01 0. 001 10 1000

Energy deposited in a 100 m 3 cube around incoming path Compton Fraction: 4. 4% Compton Fraction: 20. 5% Compton Fraction: 35. 0%

APS Beamline 14 Rates Some calculations based on https: //www. aps. anl. gov/Beamlines/Directory/Details? beamline_id=14 3 x 1013 photon/s over 3 mm 2 (unfocused) 2. 5 X 1012 p/s into half-millimeter pixel Max energy is 32 ke. V. At that energy, Compton fraction is 16% and single-layer scattering probability in 100 um is 2. 7% Rate of scatter in a given pixel would be 2. 5 x 1012 X 0. 027 = 6. 75 x 1010 p/s This is quite a lot, although the rate was for 10 ke. V photons. What is the beam spill structure for this flux? I didn’t see that.

BACKUP Compton Fraction vs X-ray Energy (ke. V) 1 0. 01 0. 001 1 10 1000