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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

Expected Radius and Period (please check)

Radius = (M/c^2) * gamma * v/ B = 0.5109989 * 22.366272 *0.999 * 1000 / 299.7922458 ~ 38.0854 [mm]
Period = 2*pi/w = 2*pi /(B/((M/c^2) * gamma)) = 6.283185 * 1000 * (0.5109989/(299.7922458*299.7922458)) * 22.366272 ~ 0.7990 [ns]

see the repository for the N02 based tracking only example