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• W2079479987 abstract "Calculations based on coupled Mathieu-Coulomb equations indicate that the transition from transient to stationary chaos for two ions in a Paul trap near the edge of the stability region is due to a boundary crisis. Numerical simulations reproduce the long-lived chaotic transients observed in ion trap experiments, obeying the power-law dependence T(q)ensuremath{propto}(${mathit{q}}_{mathit{c}}$-q${)}^{mathrm{ensuremath{-}}ensuremath{gamma}}$ where T is the average transient lifetime and q the dimensionless trap voltage. The unstable, periodic orbits which are fundamental to a heteroclinic boundary crisis were identified and the intersection of their invariant manifolds in the four-dimensional phase space was located, yielding a prediction for ${mathit{q}}_{mathit{c}}$, the transition point between transient and stationary chaos, that agrees well with the experimental value. This provides a theoretical understanding of a transition which previously has been a subject of controversy. Finally, a heuristic derivation is given for the critical exponent ensuremath{gamma}, based on the stability properties of the mediating periodic orbits. Thus solutions of the deterministic, time-dependent equations of motion can be used to accurately describe the duration of transient two-ion chaos near criticality, with only a single free scale factor." @default.
• W2079479987 created "2016-06-24" @default.
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• W2079479987 date "1994-11-01" @default.
• W2079479987 modified "2023-09-23" @default.
• W2079479987 title "Chaotic transients of two particles in a Paul trap: Interpretation as a boundary crisis" @default.
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• W2079479987 doi "https://doi.org/10.1103/physreva.50.4157" @default.
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