Larmor Orbits: Charged Particles in a Magnetic Field

Plasma in a Magnetic Field

Magnetic field B 1.2

Plasma temperature 1.0

Particle density 70

Electric field E (drift) 0.0

Larmor radius (ion)

–

Cyclotron freq. (ion)

–

E×B drift speed

–

Active particles

–

How it works

A charged particle in a uniform magnetic field feels the Lorentz force F = q(E + v×B). The velocity component along the field lines is untouched, so the particle drifts freely in that direction, while the velocity perpendicular to B rotates at a fixed angular rate — the cyclotron (Larmor) frequency. The combination traces a helix that spirals along the field line: exactly what the orange (ions) and cyan (electrons) points do here. Because electrons are far lighter than ions, at the same speed their gyro-circles are tighter — you can see the two species separate into fine and coarse spirals as soon as B is turned up.

r_L = m v_perp / (|q| B)      Larmor radius
f_c = |q| B / (2π m)         cyclotron frequency
v_drift = (E × B) / B²     E×B drift velocity

Magnetic field B — stronger field tightens every gyro-orbit (r_L shrinks as 1/B) and speeds up the spiral (f_c grows with B).
Plasma temperature — sets the thermal (perpendicular) speed of the particles; hotter plasma means larger Larmor radii and looser spirals, exactly as r_L ∝ v_perp predicts.
Particle density — how many ions/electrons are simulated at once; a denser plasma makes the collective spiral pattern easier to read.
Electric field E — added perpendicular to B, it makes every particle's guiding centre drift sideways at v_drift = E/B, in the same direction and speed regardless of charge sign or mass — the defining signature of E×B drift, unlike ordinary acceleration which pushes ions and electrons opposite ways.

Real-world relevance: this same helical gyration is what confines the plasma column inside a tokamak or stellarator, reflects charged particles in Earth's Van Allen belts, and lets the solar wind couple into the magnetosphere via E×B drift at the magnetopause.

Ions (heavy, +) Electrons (light, −) Field lines (B)

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.