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Parameterization of Si Ionization Spectra

Parameterization of Si Ionization Spectra. Nicholas Breznay Stanford Linear Accelerator Center. SLAC-ATLAS Group Meeting 3/21/2006. Simulating track ionization with the Bichsel ‘fold’ technique:. Motivation.

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Parameterization of Si Ionization Spectra

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  1. Parameterization of Si Ionization Spectra Nicholas Breznay Stanford Linear Accelerator Center SLAC-ATLAS Group Meeting 3/21/2006

  2. Simulating track ionization with the Bichsel ‘fold’ technique: Motivation • Bichsel software can calculate by ‘brute force’ single collision spectra for any particle, bg, Energy loss (E) • Comprehensive; uses a combination of atomic theory and data. • Can’t incorporate directly: (Fortran) code is indecipherable, and would be slow to evaluate Single collision spectrum - 45 GeV pion H. Bichsel, Rev. Mod. Phys. Vol 60, 663 (1988) … need a fast way to evaluate spectra for simulation needs ...

  3. Approach Single collision pion spectra • Idea: evaluate single collision spectra at range of E loss, bg values • Use simple functions of E, bg to approximate s(bg,E)

  4. Domain First, need to define the domain of bg, E that we’ll try to ‘parameterize’ Bichsel uses analytic form for E > 30keV Cross section negligible for low E (< 2.3 eV) Parameterize here Program unreliable for small bg (< 0.2)

  5. 1) Consider ‘relative’ energy loss spectra ( Include s(bgMIP) spectrum as an input in final formulation ) Details of Approach Fit Stored data 2) Examine two dimensions of data independently… 1) s vs. bg 2) s vs. E bg sRel(bg,E) … the (s vs. E) dimension is complex; what about (s vs. bg) ? E

  6. s vs. bg “dimension” is fairly simple … Details of Approach … try fitting simple functions …

  7. Details of Approach Approximate s vs. bg at each energy loss E with the following:

  8. … check the quality* of those fits … Details of Approach Grand average for E > 10 eV = 0.00091 *Defined as:

  9. … and also consider the ‘net’ deviation … Details of Approach Grand average for E > 10 eV = 0.000029

  10. Details of Approach Analyze, approximate each fitting parameter in the s vs. E dimension …

  11. Data parameterization And finally … … with a1, a2, …, a8 each a (27-parameter) function of energy. … total of 27*8 = 216 Parameters

  12. Final Check Putting it all together …

  13. Data parameterization … consider deviations …

  14. Next Steps Evaluate “moments” … … where (in particular) M0 determines the average number (n) of collisions of the particles in a thickness t: … and M1 determines the average total energy loss:

  15. Data parameterization Evaluate energy– loss integral (~ M1)

  16. Global View Poisson toss: Determine the number of collisions and collision energies for particle (momentum bg) incident on t microns of Si Calculate energy loss spectrum for bg bg, t sRel(bg,E) parameterization s(bgMIP,E) table Determine <n> (avg. number of collisions) Calculate number of collisions Calculate dE/dx integral Calculate Ei for each collision (E1, E2, …, Em)

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