The successive production of striations in a glow discharge in hydrogen

The manner of successive production of striations moving from the cathode to the anode in a glow discharge in hydrogen is experimentally investigated. For this purpose use is made of the method of an artifically produced transient process in the positive column. It is shown that the fundamental phenomenon in the production of these striations, similarly as with an inert gas, is the wave of stratification. The wave of stratification in hydrogen, however, differs from that in the plasma of an inert gas in the direction of motion of the striations. This direction in a hydrogen discharge is the same as the direction of the successive production of striations, i. e. from cathode to anode. The phenomenological theory of the successive production of moving striations elaborated earlier is also applicable for the wave of stratification in hydrogen.     

Moving striations in tapered discharge tube

Moving striations in the tapered tube with smoothly changing radius are studied experimentally. The frequency depends on local tube radius by nature and increases toward the narrow end of the tube, independent of direction and magnitude of the discharge current. Radius-frequency versus radius-pressure is compatible with the similarity law for striations in cylindrical tubes. When there appears synchronization, the frequency becomes apparently constant throughout the tube column. The wavelength shows different dependences on radius without and with the synchronization. An important role is played by the feedback through an electric circuit. Also, direction and magnitude of the current have influence on the phenomena. Steady states in the tubes are compared with those in cylindrical tubes. An attempt is made to explain the observed synchronizations and then the remarkable discrepancies between the previous experiments can be eliminated.     

Spherical striations in a glow discharge

The stratification of a volume glow discharge is observed experimentally. Spherically symmetric stationary striations are detected. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 11, 679–682 (10 December 1997)     

THe mechanism of the amplification of moving striations in a d-c discharge

To determine the mechanism of the amplification of moving striations one starts out from the processes which [3] showed to be decisive for the production of stratification of the plasma of a positive column. An analysis of the influence of other processes shows that the main processes leading to the decay of space charges and thus to a smoothing out of the inhomogeneities and thereby to the attenuation of the periodic structure, cannot by overcome by ionization phenomena caused by changes in the concentration of electrons but only partially compensated.It was found that the process which can lead to the predomination of the processes of amplification over the attenuation is the process of the spatial shift of the temperature deflections of the electrons with respect to the additional electric field, which is expressed in a simplified way by Eq. (12).By solving the extremely simplified basic equations it is proved that under favourable conditions this displacement can lead to both a time and a spatial amplification of the striations. Such a possibility is also verified quantitatively by substituting numerical values into the formulae obtained.

---

, [3] . , , , , , ., , (12). , , . .

     

Forced modulation of self excited striations in a discharge tube of varying diameter

Observations on striations contained in a discharge tube of varying diameter are reported and explained in terms of forced modulation.     

Spatial period of moving striations as function of electric field strength in glow discharge

During a systematic investigation of the parameters of a moving stratification in a glow discharge in helium and neon it was found that the spatial period of the striations is a simple, unique function of the d-c (constant) component of the longitudinal electric field strengthE. It was found that this dependence is hyperbolic and that the simple relation (1) or (2) thus holds. In the relation has the significance of a potential fall between the corresponding points of two neighbouring striations and in the measured range of pressures, currents and diameters of discharge tubes it depends only on the sort of gas and type of striations.

---

, , E. , , , (1) (2). (1) (2). , .

---

---

The principal results of this work were reported at the 1st conference on electronics in Prague on April 26, 1960.     

The physical nature of the production of moving striations in a d-c discharge plasma

The physical nature of the stratification of the d-c discharge plasma is found and physically interpreted. The interpretation is based on the mathematical expression of the production of periodic structure in plasma after an aperiodic disturbance, derived from an extremely simplified system of equations. Only three basic phenomena occurring in the plasma of each d-c discharge are included: a) the dependence of the rate of ionization on the electron temperature and hence on the electric field, b) the production of space charges due to the different rates of diffusion of the electrons and ions, c) the creation of additional electric fields due to the creation of space charges. The interactions of these phenomena gives rise to a chain, expanded in time and space, which leads to the production of moving striations. In agreement with experiment this structure is developed only on the side towards the anode from the place where the equilibrium state is disturbed.

---

. (9, 10) (4, ), . , , : ) , , ; ) , ; ) , . , , — — . , .

---

---

In conclusion the authors thank J. Fousek, J. Kaczér and M. Novák for carefully reading this paper and for valuable remarks, and J. Holub for carrying out the numerical and graphical work.     

超声波在液体中相速与群速的测量

简要叙述了相速与群速的定义,并用实验测量了超声波在不同液体中的相速与群速.     

Experimental verification of the theory of the successive production of striations in a glow discharge

The properties of the wave of stratification in the plasma of the positive column in a glow discharge in neon are measured. The measurements are compared with the results of the theory of the successive production of striations and good agreement is found.

---

. .

---

---

In conclusion the author thanks M. Novák for help in measuring and evaluating the experimental results, and F. Kroupa and V. Krejí for carefully reading this paper and for valuable remarks.     

Electron thermal diffusion instability and standing striations in the plasma of a dc discharge in molecular gases

A linear theory of waves in the positive column of dc discharge in molecular gases is presented. Full account is taken of local electron hydrodynamics (s.c. quasi-homogeneous equations), which is derived on the basis of a local non-equilibrium distribution of the electron gas. The production term on the right-hand-side of the ion balance equation gives the familiar ionization wawes, but the ion drift enhanced by the high value of the logitudinal field strength, together with the modification of the pertubed electric field incurred by the electron thermal diffusion, causes the dispersion curve to inersect thek-axis. This provides a natural explanation of the amplified low frequency anode directed wave commonly observed in molecular gas discharges as well as of the standing striation pattern. Numerical examples are given for the case of nitrogen.     

Thermodiffusional stratification of a continuous microwave discharge plasma

We report the results of investigations of a continuous microwave discharge ignited in a quasioptical resonant cavity. We study a new phenomenon for such a discharge: a small-scale stratification of the plasma in the direction perpendicular to the electric field vector. This stratification is observed in a plasma with electron density higher than the critical density at the microwave frequency and is due to the development of a thermocurrent instability. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 8, 537–542 (25 April 1998)     

The theory of moving striations in a D-C discharge plasma II. High current approximation

The integrodifferential equation of striations, found in the preceding part [1] of this theory, is simplified for the case when the Debye lengthl _D is vanishingly small in comparison with the wave-length of the striations. It then takes the form (51b). The still non-zero space charge field then influences the motion of the charge carriers in such a way that it takes on the character of ambipolar diffusion in the axial direction. This is expressed by the first term on the right-hand side of Eq. (51b). The second and third terms describe the influence of the space charge field on the ionization rate through the changes in the electron temperature. Thus the third (integral) term causes the oscillatory behaviour of the transient process excited by a pulse disturbance, while the second term can lead to growth of the amplitude (i.e. to amplification) of the transient wave.The transient solution of Eq. (51b) is given by the formula (73). It is in full qualitative agreement with the experiment and the quantitative agreement is also sufficient. This shows that processes found to be decisive for the very nature of moving striations [11] and for their amplification [16] do determine with sufficient accuracy even other finer properties of striations. The choice of optimum wave-length, in the conditions studied in this paper, is fulfilled by the ambipolar diffusion in the axial direction, which damps the short wave-length striations, and by the final value of the relaxation length of the electron temperature [1/a ₁, see Eq. (4)] which limits the long-distance effect of the electric space charge field on the ionization rate.In conclusion, the authors thank F. Kroupa and M. Novák for carefully reading the paper and for valuable remarks, and S. Vepek for help in the calculations.     

Theory of moving striations in plasma of D-C discharge I. Basic equation and its general solution

As a base for the theory of moving striations a partial integro-differential equation (26) is derived from the equations of continuity (1), (2), the Laplace-Poisson equation (3) and relation (4) between the electric field and the temperature of the electrons. Apart from the processes necessary for the actual formation of striations according to [1] and for the amplification of the wave of stratification according to [2], the equation also includes the processes defining the Debye length of the electrons, the influence of the axial electric field and of its local deflections on the motion of current carriers and the direct influence of the deviations in concentration of the electrons on the rate of production of current carriers. In deriving the equation the main attention is paid to the physical sense of the mathematical operations applied. The general solution is found by the method of the two-sided Laplace transformation and is described by triple integral convolution (42).

---

I.

(1), (2), - (3) (4) (26). , , [1], , [2], , , . . (42).

     

The connection between moving and standing striations in a d.c. glow discharge in Ne

The paper describes the standing structure (standing ionization waves) in a d.c. glow discharge in Ne at low currents, and its connection with moving ionization waves. We have found three types of standing waves and have associated them with the dispersion curves established from measurements on all three types of moving waves. Thus one wavelength of standing waves is associated with each dispersion curve related to one type of moving ionization waves.