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Experimental Methods for Trapping Ions Using Microfabricated Surface Ion Traps
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Large-amplitude oscillations in the rectangular Fermi accelerator.

Kushal Shah1

  • 1Department of Electrical Engineering, IIT Delhi, Hauz Khas, New Delhi 110016, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 17, 2013
PubMed
Summary
This summary is machine-generated.

The log-normal approximation for energy growth in a rectangular Fermi accelerator is inaccurate at large oscillation amplitudes. New analytical estimates reveal true energy growth rates and optimal bar lengths, especially for high velocities or short bars.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Dynamical Systems

Background:

  • Exponential energy growth in rectangular billiards with oscillating bars is a known phenomenon.
  • Previous analytical estimates relied on the log-normal approximation, valid only for small oscillation amplitudes.

Purpose of the Study:

  • To investigate the validity of the log-normal approximation for larger oscillation amplitudes.
  • To derive new analytical estimates for the true energy growth rate under conditions of large particle velocities or small bar lengths.
  • To analyze the effect of oscillation amplitude on the bar length that maximizes energy growth.

Main Methods:

  • Numerical simulations to demonstrate the invalidity of the log-normal approximation for large oscillation amplitudes.
  • Derivation of analytical estimates for the true energy growth rate.
  • Analysis of the relationship between oscillation amplitude, bar length, and energy growth rate.

Main Results:

  • The log-normal approximation is numerically shown to be invalid for large oscillation amplitudes.
  • Analytical estimates for the true energy growth rate were obtained for specific conditions (high velocities or short bars).
  • The bar length yielding maximum energy growth rate decreases with increasing oscillation amplitude and is smaller than predicted by the log-normal approximation.

Conclusions:

  • The rectangular Fermi accelerator serves as a model system to illustrate the limitations of the log-normal approximation.
  • Accurate energy growth rate predictions require considering larger oscillation amplitudes and specific particle/bar parameters.
  • The study provides a more refined understanding of particle acceleration dynamics in such systems.