Strong pattern selection and amplitude equation of higher order for ionization waves in a neon glow discharge

Bruhn, B.; Koch, B. P.

doi:10.1103/physreve.61.3078

Cited by 13 publications

(18 citation statements)

References 18 publications

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“…Fig. 6 shows that in particular the expansion up to order (j/µ) 3 gives a very good agreement at least within the range of validity of j/µ < ∼ 0.08 or 1.3 · 10 −3 , resp., according to (52). F. Corrections to j/µ-scaling Fig.…”

Section: E Comparison Of Numerical and Analytical Resultsmentioning

confidence: 62%

Transition from Townsend to glow discharge: Subcritical, mixed, or supercritical characteristics

Sijacic

Ebert

2002

Phys. Rev. E

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The transition from Townsend to glow discharge is investigated numerically in one space dimension in full parameter space within the classical model: with electrons and positive ions drifting in the local electric field, impact ionization by electrons (α process), secondary electron emission from the cathode (γ process) and space charge effects. We also perform a systematic analytical small current expansion about the Townsend limit up to third order in the current that fits our numerical data very well. Depending on the two determining parameters γ and system size pd, the transition from Townsend to glow discharge can show the textbook subcritical behavior, but for smaller values of pd, we also find supercritical or some unexpected intermediate "mixed" behavior. Our work shows the same qualitative dependence of U = U (I, pd) for fixed γ as the old experiments by Pokrovskaya-Soboleva and Klyarfeld. Furthermore, the analysis lays the basis for understanding the complex spatio-temporal patterns in short planar barrier discharge systems.52. 80.-s, 05.45.-a, 51.50.+v, 47.54.+r

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Section: E Comparison Of Numerical and Analytical Resultsmentioning

confidence: 62%

Transition from Townsend to glow discharge: Subcritical, mixed, or supercritical characteristics

Sijacic

Ebert

2002

Phys. Rev. E

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“…Moreover, a universal description exists in terms of an amplitude equation of higher order which is valid in the weakly nonlinear region [21]. These methods give information on the global properties of the stability diagram, i.e.…”

Section: Link To Universal Descriptionsmentioning

confidence: 99%

Hysteresis of ionization waves

et al. 2008

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A quasi-logistic, non-linear model for ionization wave modes is introduced. Modes are due to finite size of the discharge and current feed-back. The model consists of competing coupled modes and it incorporates spatial wave amplitude saturation. The hysteresis of wave mode transitions under current variation is reproduced. Side-bands are predicted by the model and found in experimental data. The ad-hoc model is equivalent to a general -so-called universal -approach from bifurcation theory.

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“…terms of fifth power of the modulated amplitude. Let us note without proof that we have www.cpp-journal.org calculated these terms similar to the treatment givenin [27], and the principal result is…”

Section: Third Perturbation Ordermentioning

confidence: 72%

“…Similar investigations can be found in Refs. [26], [27] for aneon glowdischarge. The structure of eq.…”

Section: N Onlinear Stability Propertiesmentioning

confidence: 99%

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HOPF‐Bifurcations, Global Coupling and Hysteresis in dc‐Driven Oxygen Discharges

Bruhn

May

Marbach

2011

Contrib. Plasma Phys.

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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. 1I ntroductionDue to the importance of glowdischarge processes in various technological applications, there is an increasing effort to understand and model such plasmas [1]. This is ar ather challenging task since plasmas of molecular gases are dissipative systems farfrom thermodynamic equilibrium, where alot of nonlinear kinetic processes take place. Typical examples are reaction processes likeelectron attachment and ionization, which depend on the mean electron energy.T he nonlinearity givesr ise to manyi nteresting phenomena likep attern formation outside the equilibrium, butitisalso asource of profound mathematical difficulties. Moreover, the description of the plasma becomese venm ore complexi nt he case of electronegative gases. The presence of twos pecies of negativelycharged particles introduces additional reaction channels, i.e. beyond ionization one also has to accountf or attachment, detachment and recombination. In the vicinity of the wall there are differences to electropositive plasmas, because the heavy negative ions should be much more confined to the central region of the discharge than the electrons [2]. The homogeneous and stationary axial state of electronegative plasmas has been studied in aseries of numerical and analytical investigations, for example in Refs. [3][4][5][6][7]. In particular Ref. [7] contains as tudy of dynamical effects, which can be compared to theoretical results presented in this paper.B ut little is known about the theoretical description of nonlinear dynamical states in such plasmas. On the other hand, there is al ot of experimental data for instabilities, oscillations and wavesi nd c-discharges, as well as in rf-plasmas [8][9][10][11][12][13][14]. The onset of such waves, i.e. the primary instability,can be described by means of linear methods, likein the case of the SF 6 discharge discussed in Ref. [16] or in the case of oxygen givenin [17]. Nonlinear properties, which are responsible for the observable dynamical effects, may be (partially) obtained from alocal bifurcation theory.The HOPF bifurcation is such ageneric mathematical model to describe the phenomenon where areal system depending on ac ontrol parameter mo...

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Strong pattern selection and amplitude equation of higher order for ionization waves in a neon glow discharge

Cited by 13 publications

References 18 publications

Transition from Townsend to glow discharge: Subcritical, mixed, or supercritical characteristics

Transition from Townsend to glow discharge: Subcritical, mixed, or supercritical characteristics

Hysteresis of ionization waves

HOPF‐Bifurcations, Global Coupling and Hysteresis in dc‐Driven Oxygen Discharges

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