Nonlinear Dynamics


van der Pol Dynamics

Objective: To measure temporal, spatial, and spatio-temporal signatures of driven-oscillator phenomena.

Significance: Nonlinear oscillator behavior abounds in nature, not just in plasmas. Lack of awareness may result in misinterpretation. Detailed understanding may result in new dynamical control methods.

Long Range Goal: To document and understand the rich dynamics associated with driven nonlinear oscillators.

Collaborators: John Zielinski, Olga Volotskova, Mark Koepke

The experimental device used in this research is a neon glow discharge tube. The device is unmagnetized (B=0) and operates at a pressure of 14 mTorr with a plasma neon atoms ant ions.

Some Terminology

Incomplete Entrainment is associated with quasiperiodicity and is responsible for simultaneous amplitude and phase modulation.

Temporal pulling (frequency, amplitude) Driving force acts within localized region and varies sinusoidally, e.g., ac-biased anode.

Spatial pulling (wavelength, amplitude) Constant, spatially varying driving force acts throughout extended region, e.g., dc-biased electrode array.

Spatio-temporal pulling (wavelength, frequency, amplitude) Driving force acts throughout extended region and varies sinusoidally, e.g., a wave.

Related to the Eckhaus instability, mode transitions, particle and energy transport crossing plasma boundaries, and production of electromagnetic waves from electrostatic waves.

References

1.  M E Koepke and D M Hartley Experimental verification of periodic pulling in a nonlinear electronic oscillator, 1991 Phys. Rev. A 44 6877

Copyright (1991) American Physical Society. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Physical Society.

The listed article appeared in Phys. Rev. A and may also be found here.

2.  M E Koepke and D M Hartley van der Pol behavior of relaxation oscillations in a periodically driven thermionic discharge , 1995 Phys. Rev. E 52 4316

Copyright (1995) American Physical Society. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Physical Society.

The listed article appeared in Phys. Rev. E and may also be found here.