MICROPARTICLE DRIVEN BY PARAMETRIC AND RANDOM FORCES - THEORY AND EXPERIMENT

The confined motion of a charged microparticle within the Pad Trap (al so known as the electrodynamic levitator trap) in an atmosphere near t he standard temperature rand pressure P-atm is studied both theoretica lly and experimentally. The suggested theoretical model is based on th e Mathieu differential equation with damping term and stochastic sourc e. This equation describes the damped microparticle motion subjected t o the combined periodic parametric and random external excitations. To solve the equation in an experimentally investigated regime of extrem ely strong damping and periodic excitations, the singular perturbation theory (WKB theory) is applied. In order to compare experimental data obtained in the long-time imaging limit with an analytical solution o btained for the autocorrelation function, the last is averaged by empl oying the Bogoliubov general averaging principle. This comparison is p erformed in terms of the standard deviation of the microparticle confi ned stochastic motion. It results almost in the perfect agreement betw een the analytical result and the data obtained experimentally in an e ntire region of the investigated experimental parameters. The only the oretical restrictions imposed on the model parameters are 1/alpha << 1 and 4 beta/alpha(2) << 1 (where alpha and beta are the dimensionless drag and drive parameters). It is discovered both experimentally and t heoretically that there is a minimum equal to [8kT/(m omega(2))](1/2) in the standard deviation of the microparticle confined stochastic mot ion (mi is the microparticle mass and omega is the drive force frequen cy). The presence of this minimum, which takes place at beta approxima te to 1.518 alpha, reduces the thermal noise effects, providing unique opportunities for the spectroscopic studies. Comparison with the nume rical simulation schemes developed in papers [Arnold, Folan, and Kern, J. Appl. Phys. 74, 4291 (1993); Blatt et al.,Z. Phys. D 4, 121 (1986) ; Zerbe, Jung, and Hanggi, Phys. Rev. E 49, 3626 (1994)] is discussed.