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HOPF‐Bifurcations, Global Coupling and Hysteresis in dc‐Driven Oxygen Discharges
Author(s) -
Bruhn B.,
May B.,
Marbach J.
Publication year - 2011
Publication title -
contributions to plasma physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.531
H-Index - 47
eISSN - 1521-3986
pISSN - 0863-1042
DOI - 10.1002/ctpp.201000083
Subject(s) - hysteresis , physics , amplitude , hopf bifurcation , plasma , coupling (piping) , instability , bifurcation , mechanics , condensed matter physics , materials science , quantum mechanics , nonlinear system , metallurgy
Starting from a hydrodynamic model to describe the positive column of a glow discharge in oxygen, we investigate the stability of the homogeneous state. Near the critical points of the instability curve the wave dynamics are approximated by an amplitude equation of the Ginzburg‐Landau type with complex coefficients and an additional integral term. The nonlocal coupling term describes the influence of the external circuit on the plasma properties. The complex coefficients are calculated for selected values of the plasma parameters. For sufficiently large values of the external resistor a subcritical Hopf ‐bifurcation is found. This is in agreement with the observation that in oxygen discharges a strong hysteresis occurs at the transition from the H ‐mode to the T ‐mode. Moreover, a numerical approach is used to study the hysteresis as a transition phenomenon (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)