Penninga

Penninga, an armoured warden, holds a single charged particle captive in a glowing cage of orbits.

The Physics

Earnshaw's theorem says no arrangement of static electric charges alone can hold a charge in stable equilibrium. A Penning trap gets around it by adding a strong, uniform magnetic field to an electric quadrupole field. A trapped particle then has three motions: a fast modified cyclotron circle (ω₊), an axial bounce along the field (ω_z), and a slow magnetron drift (ω₋). L. S. Brown and G. Gabrielse showed that, even in an imperfect trap, the three combine to give the true cyclotron frequency (“Geonium theory”, Rev. Mod. Phys. 58, 233, 1986).

ω_c² = ω₊² + ω_z² + ω₋²

• ω_c: free-space cyclotron frequency, qB/m (rad/s)
• ω₊: modified cyclotron frequency (rad/s)
• ω_z: axial frequency (rad/s)
• ω₋: magnetron frequency (rad/s)

Because ω_c = qB/m, measuring it gives a particle's charge-to-mass ratio, and Penning traps make some of the most precise mass and magnetic-moment measurements in physics.

Honest caveat: The invariance theorem holds for small misalignment and ellipticity of the trap. Large imperfections and field anharmonicities still need corrections.

On the sticker

Penninga, in armour, holds glowing atom-style orbits, a stylised picture rather than the trap's three motions. Printed text: PENNINGA with the line ωc² = ω+² + ωz² + ω−². Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.