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Experimentation using a non-static magnetic field

Settings and definitions

  • {G4,QSS}_x_err is the maximum of all the absolute errors in x: max(abs({G4,QSS}x_i - ANx_i))
  • {G4,QSS}_rMSE_err = sqrt(MSE) = 1/N * sum_{i=1}^{N} ({G4,QSS}x_i - ANx_i)^2 + ({G4,QSS}y_i - ANy_i)^2
  • {G4,QSS}_B_diff is the maximum of all the errors in B: max(B - {G4,QSS}B_i) = max(1 - {G4,QSS}B_i) (measured in teslas)
  • Distance used: 100 m
  • Common parameters for G4 simulations:
    • stepMax: 20 mm
    • deltaChord: 0.25 mm
    • deltaOneStep: 1e-2 mm
    • deltaInt: 1e-5 mm (although no crossing planes were used)

Trajectory and velocity plots

  • The purpose of this section is to ensure that both methods are simulating the same system.

Geant4

x vs. distance

v_x vs. distance

Scatter plots

Magnetic field

QSS3

x vs. distance

v_x vs. distance

Scatter plots

Magnetic field

Error plots

Geant4

G4_x_err

G4_r_err

G4_v_err

Summary

epsilon t_sim [s] G4_x_err [mm] G4_rMSE_err [mm] G4_B_diff [tesla]
1.0e-09 0.58 0.113962 0.0597824 4e-06
1.0e-08 0.41 0.113962 0.0597824 4e-06
1.0e-07 0.32 0.113961 0.0597819 4e-06
1.0e-06 0.23 0.113951 0.0597758 4e-06
1.0e-05 0.21 0.113901 0.0597459 4e-06
1.0e-04 0.13 0.114339 0.059998 4e-06
1.0e-03 0.13 0.114339 0.059998 4e-06

QSS3

QSS_x_err

QSS_r_err

QSS_v_err

Summary

dQRel t_sim [s] QSS_x_err [mm] QSS_rMSE_err [mm] QSS_B_diff [tesla]
1.0e-09 9.26438 1.6654 0.718012 2.225324839999e-05
1.0e-08 4.29012 1.66539 0.718009 2.225324580007e-05
1.0e-07 2.00152 1.66532 0.717983 2.225322139993e-05
1.0e-06 0.938851 1.66392 0.717332 2.225316079996e-05
1.0e-05 0.432917 1.65683 0.714325 2.225311149995e-05
1.0e-04 0.206787 2.21839 1.02821 2.225275149992e-05
1.0e-03 0.0914118 12.899 7.60053 2.226413060014e-05

Error and simulation time comparison

  • TBD