Charged particle dynamicsLorentz-force integration · normalized units

Magnetic bottle

Reflection, energy exchange and the loss cone
3D trajectory
100%
Drag to rotate · scroll or pinch to zoom
Particle orbitB field linesGuiding centrevB vector
65%
Mirror force
User guide

Pitch angle α is the angle between the particle’s initial velocity and the magnetic field. Start at 90°, then lower it slightly to add motion along the field lines and make the helix visible.

Particle controls: Electron switches the charge sign; unchecked means proton. Particle shows or hides the trajectory and velocity arrow. The orbit sizes are normalized and schematic, so they do not compare the physical proton and electron Larmor radii.

Field controls: Field lines shows the magnetic field-line curves; Guiding centre shows the centre of the gyration. Vectors toggles the instantaneous velocity, magnetic field, electric field and drift arrows. Axes toggles the x, y and z orientation marker.

Tabs: Gyromotion shows helical motion; E × B shows drift in crossed fields; Time-varying B shows induction and perpendicular heating; Curvature shows drift from curved field lines; Polarization shows the response to a time-varying electric field; Magnetic bottle shows mirroring and escape.

Module controls: In Magnetic bottle, the mirror ratio sets the maximum-to-minimum magnetic-field strength; it starts at 2 and ranges from 1.5 to 4. In E × B, E-field strength controls the electric field.

Time and view: The Time slider moves through the motion and updates the plots. Drag the 3D view to rotate, use the ↶/↷ buttons to rotate around z, scroll or pinch to zoom, and use Reset view to restore the camera. The plots show kinetic-energy components, velocity-space/loss-cone information for the mirror, or the selected module’s field and drift quantities.