# 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.

## Error plots¶

### Geant4¶

#### 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¶

#### 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

• TBD