According to Earnshaw’s theorem an electrostatic potential cannot have stable equilibria, i.e. the minima, since such potentials are harmonic functions. However, the 1989 Nobel Prize in physics was awarded to W. Paul for his invention of the trap for suspending charged particles in an oscillating electric field. Paul’s idea was to stabilize the saddle by “vibrating” the electrostatic field, by analogy with the so-called Stephenson-Kapitsa pendulum in which the upside-down equilibrium is stabilized by vibration of the pivot. Instead of vibration, the saddle can also be stabilized by rotation of the potential (in two dimensions); this has been known for nearly a century, since 1918. Particles confined in rotating saddle traps exhibit precession in the laboratory frame, which up to now has been explained by analyzing explicit solutions. Here we show that this precession is actually due to a hidden Coriolis-like force, which we uncover by a normal form transformation. Unlike the conventional Coriolis force, this one is not an inertial force, as it acts in the non-rotating frame. To our knowledge this is the first example of a Coriolis-like force arising in an inertial frame.
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