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Dimensionless teaching units: the magnetic field confines ions radially, the electric quadrupole confines them axially.
Ions
Model checks
The science
What is modelled
Non-interacting ions in an ideal uniform axial magnetic field B and an ideal electrostatic quadrupole. The motion splits into three independent oscillations: a fast reduced cyclotron motion, a slow magnetron drift around the axis, and an axial oscillation along B.
Equations
- Axial
ωz = sqrt((q/m) κ), cyclotronωc = (q/m) B. ω± = (ωc ± sqrt(ωc2 - 2ωz2)) / 2, stable only ifωc2 > 2 ωz2.- Boris scheme: half electric kick, exact magnetic rotation, half kick.
Honest limits
Dimensionless units; no space-charge, no field imperfections, collisions are a simple random isotropic scattering. Not a calibrated instrument model.
What to try
- Choose Weak magnetic field: the cyclotron frequency drops below the stability threshold and the cloud is lost to the walls.
- Raise the trap voltage (curvature) and watch the axial frequency grow as its square root.
- Flip the charge sign: the magnetron and cyclotron rotation reverse, the confinement stays.