Die Schichterscheinungen in der positiven Säule der Sauerstoff‐Niederdruck‐Entladung

Sabadil, H.

doi:10.1002/ctpp.19660060503

Cited by 22 publications

(17 citation statements)

References 14 publications

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“…Actually,the same behavior is observed experimentally at the transition from the H-mode to the T-mode [8], [14] at the upper critical current. Furthermore, there appears apronounced hysteresis right at this transition.…”

Section: Third Perturbation Ordersupporting

confidence: 74%

“…[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.…”

mentioning

confidence: 96%

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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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Section: Third Perturbation Ordersupporting

confidence: 74%

mentioning

confidence: 96%

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

Bruhn

May

Marbach

2011

Contrib. Plasma Phys.

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“…By increasing the current, a mode selection (with a high modulation degree) occurs resulting in a periodic oscillation of the electric field and a discrete frequency spectrum. As discussed above, this is the T-mode with low averaged electric fields (here about 3.7 V cm −1 ) 5 . At higher discharge currents the discharge jumps into the H-mode, characterized by higher values of the electric field (here about 12 V cm −1 ), and a discrete frequency spectrum with small modulation degree which is comparable to the modulation degree of moving striations in noble gases [14,15].…”

Section: The H-and T-mode Of the Positive Column In Oxygenmentioning

confidence: 69%

“…In particular, the T-mode is characterized by different kinds of dynamic operation states, besides others, the so-called T-waves. These waves have a phase velocity in the cathode to anode direction (forward waves) and show no dispersion [5]. A long-standing problem is the deeper understanding of the transition between these two operation modes, i.e.…”

Section: Introductionmentioning

confidence: 99%

Investigations on the stability of the low pressure positive column in oxygen

Testrich

Pasedag

Navrátil

et al. 2009

J. Phys. D: Appl. Phys.

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The stability of the low pressure positive column in oxygen was investigated in a pressure range from 0.5 to 0.9 Torr within a discharge current interval from 0.5 to 90 mA. The transition between the well-known T-and H-modes has been studied. The H-to T-mode transition showed a marked hysteresis in the E(I) characteristic which is affected by wall processes. For the first time temporally resolved electric field measurements were realized. At small discharge current the electric field showed a significant modulation, characterized by incoherent fluctuations with a broadband Fourier spectrum. With increasing current the discharge operates in the T-mode, where a mode selection with high modulation degree occurred, resulting in a periodic oscillation of the electric field at a discrete frequency spectrum. The dynamic state in the T-mode is expressed by T-waves moving from the cathode to the anode. It seems that they were excited by oscillations in the cathode region. The waves were damped in the direction of the anode and show no dispersion. The discharge stability was studied using a hydrodynamic model considering electrons, positive and negative ions as well as metastable O 2 (a 1 g) molecules. Here the negative O −-ions play a crucial role. In good agreement with the experiments the transition between the Hand T-modes was explained as a linear unstable equilibrium state where the energy dependence of the corresponding rate coefficients is the driving mechanism (attachment-induced instability).

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“…Depending on the discharge conditions the positive column of an oxygen discharge exists in two modes [26]. For higher values of the discharge current the positive column of the discharge is maintained by higher electric fields (a so-called H-mode with E about 10 V cm −1 ).…”

Section: Resultsmentioning

confidence: 99%

Dynamic behaviour of an oxygen dc discharge

et al. 2009

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The dynamic behaviour of a positive column oxygen plasma is investigated both experimentally and theoretically. In the experiment the response of the discharge current to small external perturbations of the electrical field is measured. Using these data the electrical impedance of the plasma is obtained dependent on the frequency of the external perturbation. A drift approximation model is presented, which covers the experimental findings over a wide range of the perturbation frequency. It appears that the influence of the fluctuations of the neutral species is negligible and the dynamic behaviour of the plasma is mostly governed by the charged particles. This provides a simple expression for the plasma impedance which allows the reaction rate and transport coefficients, as well as discharge parameters, to be validated.

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Die Schichterscheinungen in der positiven Säule der Sauerstoff‐Niederdruck‐Entladung

Cited by 22 publications

References 14 publications

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

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

Investigations on the stability of the low pressure positive column in oxygen

Dynamic behaviour of an oxygen dc discharge

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