Parametrically driven microparticle in the presence of a stationary zero-mean stochastic source

Model for thermal equilibrium in the Paul trap

Alexander F. Izmailov, Stephen Arnold, Allan S. Myerson

Research output: Contribution to journalArticle

Abstract

An analytical approach is developed to consider confined motion of a charged microparticle within the Paul trap (an electrodynamic levitator trap) in an atmosphere near the standard temperature and pressure. The suggested approach is based on a second-order linear stochastic differential equation which describes dampled microparticle motion subjected to the combined periodic parametric and random external excitations. To solve this equation a new ansatz is developed. This ansatz is a generalization of the Bogoliubov-Krylov decomposition technique, which is usually used to reduce the order of a differential equation. The solution is obtained in the long time imaging limit by applying the Bogoliubov general averaging principle. In spite of the second-order form of the initial stochastic differential equation, the microparticle motion can be understood as a one-dimensional Markov process. Comparison in the long time imaging limit of the calculated data obtained from the analytically derived expression for the standard deviation of confined microparticle stochastic motion with the experimentally obtained data demonstrates asymptotic agreement for regions where the dimensionless parameter κ is much less than 1 (κ≤0.005). Simple extremum analysis of the expression obtained for the standard deviation reveals that for the particular case of a large drag parameter α (α8 12) there is a minimum in the standard deviation which is only α dependent.

Original languageEnglish (US)
Pages (from-to)702-708
Number of pages7
JournalPhysical Review E
Volume50
Issue number2
DOIs
StatePublished - 1994

Fingerprint

Thermal Equilibrium
microparticles
Trap
traps
Standard deviation
standard deviation
differential equations
Motion
Zero
Differential equation
Stochastic Equations
Imaging
Averaging Principle
Markov processes
Decomposition Techniques
range (extremes)
Electrodynamics
Extremum
Drag
Dimensionless

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

Parametrically driven microparticle in the presence of a stationary zero-mean stochastic source : Model for thermal equilibrium in the Paul trap. / Izmailov, Alexander F.; Arnold, Stephen; Myerson, Allan S.

In: Physical Review E, Vol. 50, No. 2, 1994, p. 702-708.

Research output: Contribution to journalArticle

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