# UBA-FNAL QSS-Geant4 Meeting¶

## Parameters for simple tests for the proof of principle(prepared by Soon)¶

### Equation of Motion of a charged particle in the magnetic field (the Lorentz Equation)¶

``m d/dt gamma dx/dt = q (v x B)  ``
``(For the relativistic treatment, please see   http://www-geant4.kek.jp/lxr/source/geometry/magneticfield/src/G4EqMagElectricField.cc#L58 )``

where

x = position vector (x,y,z)
v = momentum vector (vx, vy, vz)
B = magnetic field vector (Bx, By, Bz)
t = time
m = mass of particle
q = charge of particle
c = speed of light
gamma = 1/sqrt(1-beta*beta) where beta = magnitude(v)/c

### Initial conditions for an electron in the uniform magnetic field and stepping parameters¶

use (unit-less) parameters following the Geant4 system of units mm = 1, MeV = 1, nanosecond (ns) = 1, eplus=1

c = 299.792458 mm/ns ;
m = M/c^2 where M = 0.5109989 MeV (elctron_mass_c2)
x = (0,0,0)
v = (0.999c,0,0) this is equivalent to (kinetic) energy = M * (gamma -1) = M * (22.366272 - 1) ~ 10.9181415106 MeV
B = (0,0,0.001) 1 tesla = 1E-3 (MeV/eplus)*(ns/mm*mm)
q = - eplus = - 1 (for electron)
the default step size to trial = 1 mm
the truncation error or the QSS quantum = 0.01 mm / 100 (the default step) = 0.0001 mm