Three-dimensional structure of finite-amplitude ionization wave packets excited in He positive columns

Ohe, K.; Naito, Asako; Kimura, Takashi; Iwama, Naofumi

doi:10.1063/1.859762

Cited by 7 publications

(4 citation statements)

References 21 publications

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“…The reason for this agreement lies in the coincidence of the radial structure of the homogeneous column with the radial structure of the ionization wave. This behaviour was confirmed experimentally by Ohe et al (1991), The solid line shows the exact solution with almost-vanishing nonlinear damping (Im(Q) ≈ 0.01), the long-dashed line correponds to a solution with coefficients calculated when the radial structure is neglected (Im(Q) ≈ 0.16). Finally, the short-dashed line is obtained when the dispersive damping is changed to growth (Im(Q) ≈ −2.5).…”

Section: Resultssupporting

confidence: 61%

“…It turns out that the eigenfunctions are almost independent of the wavenumber k. This partly justifies the previously used reductions to one spatial coordinate, as will also become clear later from the numerical simulations. The radial structure of ionization waves was measured by Ohe et al (1991). Their results also show the almost-identical forms of the radial profils of the positive column and the ionization wave.…”

Section: Linear Equations At First Ordermentioning

confidence: 84%

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Spatial structure of a nonlinear wave of stratification

Rottmann

Spatschek

1998

J. Plasma Phys.

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The positive column of a gas discharge is investigated in the subcritical regime when no self-excited nonlinear ionization wave exists. We derive a model equation for the so-called wave of stratification, which is an externally excited envelope wave. The main point of this work is that, in contrast to previous papers, we take into account the radial structure of the homogeneous column. The mathematical description of the wave of stratification in the form of a complex Ginzburg–Landau equation follows by a systematic reductive perturbation method. The coefficients in the Ginzburg–Landau equation are first calculated in general and are then evaluated explicitly for a low-pressure argon discharge. The results are compared with those obtained from a frequently used simpler model that neglects any radial structure. Finally, the dynamics of the nonlinear wave of stratification is demonstrated via numerical simulations.

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Section: Resultssupporting

confidence: 61%

Section: Linear Equations At First Ordermentioning

confidence: 84%

Spatial structure of a nonlinear wave of stratification

Rottmann

Spatschek

1998

J. Plasma Phys.

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“…P and Q are complex coefficients which have been determined analytically (including the radial structure). It should be mentioned that all the predictions agree very nicely with experimental results [22], even for the three-dimensional structure. The Ginzburg-Landau equation typically expresses what in words is, for example [19], explained as: 'Low-amplitude waves obeying liner theory typically survive under conditions that correspond to moderate penetration into the instability region'.…”

Section: Striated Columns: the Universal Behaviour Of Single Modessupporting

confidence: 81%

On the route to a better understanding of the complex nonlinear dynamics of a plasma

Spatschek¹

1999

Plasma Phys. Control. Fusion

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In many cases, the analytical understanding of the complex nonlinear behaviour of plasmas is simplified by the fact that the plasma dynamics is low-dimensional. Then, quite universal descriptions, which can predict quite sophisticated phenomena, are available. This aspect, and the corresponding appearance of spatially coherent structures, are first discussed for the single-mode dynamics in a weakly unstable (or marginal) regime. The procedure is then generalized to a few modes. The following examples are used to point out the benefits from a low-dimensional description: ionization wave instability, Pierce instability, interchange instability and electron drift instability. Special emphasis is put on the following aspects. Low-dimensional dynamics is quite rich and allows one to apply modern control mechanisms. Coherent structures are present in the dynamics and may contribute to the understanding of transport scalings. The overview is concluded by pointing out some similarities to high-dimensional situations. In the latter, structures (singularities) also have a signature in the dynamical behaviour. They allow us to understand more deeply certain scaling behaviour.

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“…Some observations [20], using an optical absorption technique for spectraJ lines corresponding to the transition of metastables, have shown that the radial profile slightly differs from the charged-particle profile. The optical structure in the radial direction can be detected with good accuracy by an image reconstruction using a CT technique [21,22], because the self-absorption may be neglected as described previously [23,24] optical radiation from the column was detected with a slit-monochromator which was movable in the radial direction at the same axial position as that of the probe installation. Since the grid installation causes an axially symmetric profile, sufficient projection data can be obtained by moving the monochromator from the tube axis to the wall.…”

Section: Methodsmentioning

confidence: 99%

Distortion of plasma due to installation of a grid in homogeneous He positive columns

Ohe¹

1994

J. Phys. D: Appl. Phys.

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Distortion in a weakly ionized homogeneous plasma caused by the installation of a mesh-grid is investigated in a wave-free He positive column. The installation causes distortion in the axial as well as the radial direction, the so-called double-sheath. Such a structure decelerates electrons in a phase of weak electric field, while it accelerates them in that of strong electric field, eventually resulting in a double-humped electron energy distribution function (EEDF). The detected axial variation of the EEDF is compared with a solution of the Boltzmann equation including the spatial derivative.

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Three-dimensional structure of finite-amplitude ionization wave packets excited in He positive columns

Cited by 7 publications

References 21 publications

Spatial structure of a nonlinear wave of stratification

Spatial structure of a nonlinear wave of stratification

On the route to a better understanding of the complex nonlinear dynamics of a plasma

Distortion of plasma due to installation of a grid in homogeneous He positive columns

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