Growth of harmonic perturbations of an electron shell orbiting a positively-charged wire (Orbitron)

In the present investigation of the negative mass instability of a cylindrical shell of electrons that orbit a positively charged wire, orbital frequency harmonics are noted to grow faster than the fundamental. The growth constant is proportional to the square root of the harmonic number. The equation becomes invalid for very high harmonics, as when wavelength becomes comparable to shell thickness.