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Color online Spatial amplifications for ionization wave modes as a function of wavenumber at different discharge currents.
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A quasi-logistic, nonlinear model for ionization wave modes is introduced. Modes are due to finite size of the discharge and current feedback. 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. Sidebands are predicted by...
Contexts in source publication
Context 1
... Fig. 5. The model parameters in Eq. 1 can be derived from experimental results. The spatial amplification can be derived from measurements see Fig. 5. Since the dispersion of ionization waves f = f is accessible as well, the wave numbers can be determined and the amplification i can be expressed as a function of wave-number i, which is shown in Fig. ...
Context 2
... Fig. 7 indicates, the spatial amplification is well ap- proximated by a unimodal function in the considered param- eter range. The maximum spatial amplification becomes positive above a critical current supercritical Hopf bifurca- tion. Increasing the discharge current leads to an increased maximum and a shift of the maximum to smaller wave ...
Context 3
... is instructive to consider the spatial amplifications for fixed wave numbers under current variations by Fig. 7. First, it is evident that currents exist for which the three wave modes considered have a positive amplification. For a given wave mode an increase of the current results in a minimum and maximum current for which i 0. This is the current region for which a self-excited wave can exist. In between the limiting currents, a current for ...
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Citations
... Recent experiments on ionization waves [69][70][71][72][73][74] provide experimental spatiotemporal patterns with light-emission fluctuations similar to that shown in figure 4, providing independent experimental validation of our numerical results. The impact of the dust particles on the stabilization of the striations has been studied in [75] in the PK-4 system as well as by means of fluid type numerical discharge modeling. ...
The PK-4 system is a micro-gravity dusty plasma experiment currently in operation on-board the International Space Station. The experiment utilizes a long DC discharge in neon or argon gases. We apply our 2D particle-in-cell with Monte Carlo collisions discharge simulation to compute local plasma parameters that serve as input data for future dust dynamics models.The simulation includes electrons, Ne+ions, and Nem metastable atoms in neon gas and their collisions at solid surfaces including secondary electron emission and glass wall charging. On the time scale of the on-board optical imaging, the positive column appears stable and homogeneous. On the other hand, our simulations show that on microsecond time scales the positive column is highly in homogeneous: ionization waves with phase velocities in the range between 500 m s−1and 1200 m s−1dominate the structure. In these waves, the electric field and charged particle densities can reach amplitudes up to 10 times of their average value. Our experiments on ground-based PK-4 replica systems fully support the numerical findings. In the experiment, the direction of the DC current can be alternated, which has been found to favor dust particle chain formation. We discuss possible mechanisms for how the highly oscillatory plasma environment contributes to the dust particle chain formation.
... Ionization instability accompanied by striation was obtained in [22] in nitrogen. Attempts to build a physical model of the spherical ionization instability were made in [23][24][25]. Nevertheless, it was not yet possible to fully understand the conditions for the emergence and maintenance of this type of gas discharge. ...
The conducted study is devoted to the research area of control of high speed flows and shock-wave configurations. Experimental and numerical results on the interaction of a plane shock wave (M = 5–6) with the area formed by ionization instability in gas discharge plasma at a pressure of 3–7 Torr and gas-discharge current of 100–400 mA are presented. The region of ionization instability in plasma of high degree of ionization and non-equilibrium (gas temperature T ∼ 300–600 K, electron temperature Te∼5⋅10³ K) has been obtained experimentally in air. This instability is characterized by spherical strata of changing shape. Two types of a shape of the ionization instability have been obtained: large-scale type and small-scale type. Also, the transitional type from large-scaled strata to low-scaled ones has been obtained. The influence of the ionization instability was established to cause the distortion of an initially plane shock wave up the complete disappearance of its front. Numerical modeling the interaction of the initially plane shock wave with ionization-unstable plasma using the Euler system of equations has been conducted. The area formed by ionization unstable plasma was modeled via a set of thermal layers with varying densities (and temperatures). Changing the physical–chemical properties of the gas medium was taken into account varying the ratio of specific heats. Layered structures with wavy shock-wave and contact discontinuity fronts have been observed. The multiple generations of shear layer instabilities and the Richtmyer–Meshkov instabilities have been obtained as the result of the interaction of a shock wave with thermal strata. It has confirmed that the shapes of the both discontinuities change acquiring an unstable character. Examples of the flow modes with the disappearance of the shock wave front causing by the origination of a structure with cellular order of shear layer instabilities have been presented. A good agreement at the qualitative level with the experimental Schlieren images has been demonstrated.
... In plasma systems, hysteresis has been theoretically pre- dicted and verified experimentally 10 in cylindrical 10,11 glow dis- charge plasmas. Hysteresis in discharge current was observed 12 in an unmagnetized plasma by varying the discharge voltage and attributed to a negative differential resistance in the current voltage characteristic. ...
Floating potential fluctuations associated with an anode fireball in a glow discharge plasma in the
toroidal vacuum vessel of the SINP tokamak are found to exhibit different kinds of oscillations
under the action of vertical magnetic field of different strengths. While increasing the vertical
magnetic field, the fluctuations have shown transitions as: chaotic oscillation ! inverse homoclinic
transition ! intermittency ! chaotic oscillation. However, on decreasing the magnetic field, the
fluctuations are seen to follow: chaotic oscillations ! homoclinic transition! chaotic oscillation;
that is the intermittent feature is not observed. Fireball dynamics is found to be closely related to
the magnetic field applied; results of visual inspection with a high speed camera are in close
agreement with the fluctuations, and the fireball dynamics is found to be closely related to the
transitions. The statistical properties like skewness, kurtosis, and entropy of the fluctuations are
also found to exhibit this hysteresis behaviour.
... [24][25][26][27][28][29] Presently, such approaches have also found acceptance in treating localized structures and nonlinear properties of ionization instabilities in dc-driven gas discharge systems. [30][31][32][33] The purpose of the present work was to solve the problem formulated by Pekarec, namely, to develop, around the strategy proposed in Ref. 22, modern calculation techniques for basic properties of positive-column plasma; to provide a uniform description to the conditions of spatial homogeneity of plasma column; to consider, within a unified approach, the formation of striations and the emergence of jumps and hysteresis in the current; to place the physical states and properties of positive-column plasma of noble d.c. gas discharges in their proper framework (How does all this fit into the general scheme of things?); and to investigate into the various plasma states more deeply than ordinary deductions from experimental observations usually go. ...
... The origin of the various terms in (33) can be figured out considering the following. By way of illustration, consider the case in which the ionization is caused by step plasma reactions. ...
... However, it can be used for a good approximation not only over these regions, but, surprisingly, for the analysis of regions numbered 1 and 2 as well. In the latter case, the condition r d ≥ R is valid, electrons would be partially 'free' and quasi-free and we should take into account only the first terms of Eq. (33). Equations (33) and (57) contain some basic properties of 1 and 2 regions, that is to say that the processes under review is primarily responsible for the properties of the gas discharge. ...
A one-dimension model for positive-column plasma is analyzed. In the framework of this model, a complete, self-consistent set of equations for the plasma column is proposed and justified. Basic prerequisites for the model and the equations used in it are discussed at length to clarify the mathematics and physics that underlie the proposed generalized description of plasma states. A study of the equations has unveiled the existence of two structurally stable types of steady states and three integrals of motion in the plasma system. The first type of states corresponds to spatially homogeneous plasma, and the second type, to the self-forming plasma structure with striations. Analysis of spatio-temporal plasma structures (spatially homogeneous and stratified stationary plasma states) and their attendant phenomena is given in detail. It is shown that the equations offer a more penetrating insight into the physical states and properties of positive-column plasma in dc-driven gas discharges, and into the various phenomena proceeding in the discharge system. Such a behavior is intimately related to the influence which the electric field has on the rate of ionization reactions. The theoretical results are compared to experimental data and can be used for to place the great body of experimental data in their proper framework. The modern fluid bifurcation model proposed to describe the properties of non-isothermic positive-column plasma in dc-driven low-pressure noble-gas discharges proved to be rather realistic, capable of adequately reproducing the basic properties of real field-plasma systems.
... Striations originate due to growing instability during the ionization process, which may be caused by step-wise ionization when metastable atoms are produced by electron impact decay as a result of diffusion to the wall. 13 In earlier studies, ionization wave in dc discharge of rare gases 14,15 have been extensively studied. Striations depend on system parameters, i.e., discharge current, the neutral gas pressure, length and diameter of the plasma column etc. ...
... Recently, study on hysteresis of ionization wave has suggested that the maximum spatial amplification becomes positive above a critical current (supercritical Hopf bifurcation), which means that bifurcation take place after a certain value of current. 15 With the help of the above given studies for dc discharges, different structures of surface wave produced plasma column can be explained in which striations are achieved in inert gas (argon) which is filled at 0.03 to 0.10 mbar in 30 cm long and 3 to 5 cm diameter of glass tube in which coupled power is varied from 40 to 50 W keeping constant driven frequency of 5 MHz. Although the experiments are performed with different gases such as nitrogen, oxygen, air, and argon, striations are formed only in argon gas. ...
A 30 cm long plasma column is excited by a surface wave, which acts as a plasma antenna. Using plasma properties (pattern formation/striations in plasmas) single plasma antenna can be transformed into array, helical, and spiral plasma antenna. Experiments are carried out to study the power patterns, directivity, and half power beam width of such different plasma antennas. Moreover, field properties of plasma and copper antenna are studied. Further, wireless communication and jamming capability of plasma antenna are tested. Findings of this study suggest that directivity and communication range can be increased by converting single plasma antenna in to array/helical/spiral plasma antenna. Field frequencies of plasma antenna determine the communication and jamming of radio frequency waves. Therefore, this study invokes applications of pattern formation or striations of plasmas in plasma antenna technology.
... [3][4][5][6][7][8] In the context of nonlinear phenomenon, striations have been studied in different plasmas with different discharge mechanisms such as dc discharges, rf plasmas, [9][10][11] laser plasmas, 12 ionospheric plasmas, 13 plasma display cells, 14 instabilities, and pattern formations in low temperature plasmas 15,16 for academic interest due to its several manifestations which are challenging to the scientists. In general, striations are periodic changes in electron density and are caused not by the redistribution of a fixed number of electrons but by alternate regions of predominant production and removal of electrons, which can survive in a limited range of current values, pressure, gas species, and tube radius. 2 It has been established that the striations are caused by ionization instability or manifestations of ionization oscillations and waves, [17][18][19][20][21][22] which may be caused by stepwise ionization, the maximization of the electron distribution function, and by any agent-causing enhancement in inhomogeneities in plasma. Generally, on the basis of visual observations, two types of striations have been classified: standing ͑stationary͒ striations having static appearance and moving striations at a certain velocity. ...
... 21 Moreover, complex behavior is observed ranging from regular to chaotic states. [25][26][27] However, several types of striations have been identified and various instabilities responsible for the striations based on the results of numerous studies 21,22 have been pointed out. In spite of long research history, striations are not yet fully understood or classified because of their diverse phenomena. ...
... Striations originate due to growing instability during the ionization process, which may be caused by stepwise ionization when metastable atoms produced by electron impact decay as a result of diffusion to the wall. 2 In earlier studies, ionization wave in dc discharge of rare gases 21,22 have been extensively studied by using numerical analysis, 34 mode transitions, 35,36 scaling laws, 37 etc., considering that the nonlinear phenomenon or striations depend on system parameters, i.e., discharge current, the neutral gas pressure, length, and diameter of plasma column. Most analytical and numerical calculations are based on a hydrodynamic model that is simplified by some reasonable assumptions. ...
Experimental results on the observation of spatial structures appearing in a radio frequency (rf) produced plasma column are presented in this paper. A plasma column of length 30 cm is formed in a glass tube by applying rf power from a cw generator. It is observed that by changing the operating parameters, e.g., input power, working pressure, drive frequency, diameter of glass tube, background gases, etc., single plasma column transforms into stationary/moving striations and helical and spiral structures. For a better understanding of these observations, experiments are also carried out to study the electric field profile of these structures in the plasma. Findings of this study reveal that surface wave produced plasma column transversally bifurcates and transforms into stationary striations. With further increase in working pressure, stationary striations become moving striations with linear and rotational motions and finally rotating plasma column bifurcates longitudinally and a helical structure is formed, which can also be transformed into a spiral structure. Electric field profile of each structure is entirely different from that of the other structure.
Based on the analysis of electron phase trajectories in sinusoidal electric fields, a new point of view on discharge stratification is proposed. It is shown that the positive column can be considered as a spatial resonator in which electric fields with a fundamental period length L S or higher mode length q p L S establish, where p and q are integers and p > q. The fundamental mode length L S is equivalent to the distance on which electrons gain energy equal to the lowest excitation threshold. This distance determines a length of the S-striation. Unlike kinetic theory, in the presented model resonance properties of the discharge column are not connected with elastic collision energy losses. A point map is used to obtain the resonance trajectories of electrons in the phase plane. Stable points for the positions of inelastic collisions in the resonance trajectories have been found at the positions of field maxima in the case of integer ratios p q . For non-integer ratios p q , multiple resonance trajectories arise according to a more complex stability criterion. From this point of view, S-, P-, and R-striations in noble gas discharges can be explained. Due to energy losses in elastic collisions, initial electron energy distribution functions converge to the resonance trajectories (the so-called “bunch effect”). The findings of the discrete model agree with results of kinetic theory and experiment. The new approach avoids difficulties of the kinetic theory in the case of exceptionally large relaxation lengths which can even exceed the positive column length.
Plasma stratification and excitation of ionization waves is one of the
fundamental problems in gas discharge physics. Significant progress in
this field is associated with the name of Lev Tsendin. He advocated the
need for the kinetic approach to this problem contrary to the
traditional hydrodynamic approach, introduced the idea of electron
bunching in spatially periodic electric fields, and developed a theory
of kinetic resonances for analysis of moving striations in rare gases.
The present paper shows how Tsendin's ideas have been further developed
and applied for understanding the nature of the well-known S-, P-, and
R-striations observed in glow discharges of inert gases at low pressures
and currents. We review numerical solutions of a Fokker-Planck kinetic
equation in spatially periodic electric fields under the effects of
elastic and inelastic collisions of electrons with atoms. We illustrate
the formation of kinetic resonances at specific field periods for
different shapes of injected Electron Distribution Functions (EDF).
Computer simulations illustrate how self-organization of the EDFs occurs
under nonlocal conditions and how Gaussian-like peaks moving along
resonance trajectories are formed in a certain range of discharge
conditions. The calculated EDFs agree well with the experimentally
measured EDFs for the S, P, and R striations in noble gases. We discuss
how kinetic resonances affect dispersion characteristics of moving
striations and mention some non-linear effects associated with glow
discharge stratification. We propose further studies of stratification
phenomena combining physical kinetics and non-linear physics.
A neon glow-discharge plasma supports multimode oscillation in the form of traveling normal modes of p-type neon-ionization waves. The modes compete as coupled spatiotemporal oscillators, each capable of driving the other or being driven. Competition is modulated by neon-resonant laser light chopped almost synchronously with the subdominant wave mode resulting in quasiperiodic mode hopping between neighbor wave modes. This process repeats indefinitely without adjustment of the discharge plasma or chopped laser-light parameters. The mode-amplitude normalization of the driving-force term in the governing differential equations, inherent in driven-oscillator phenomena and responsible for quasiperiodic mode hopping, is validated by experimental observations.
In experimental investigations array, helical and spiral patterns of a plasma column are formed by changing the operating parameters e.g., input power, working pressure, drive frequency, diameter of the glass tube, background gases, etc. Further, theoretical formulations are attempted using a hydrodynamic model to explain the bifurcation of a plasma column in the transverse and longitudinal axis considering two-step ionization in surface wave produced plasma. Findings of this study reveal that metastable atoms provide two-step ionization which in turn excites weak instability, which bifurcate plasma column in such a way that different patterns are formed.
