Jumps in current, shock waves and hysteresis phenomena in low- pressure gas D.C. discharge plasma.

Jumps in current, shock waves and hysteresis phenomena in low- pressure gas D.C. discharge plasma.

P. F. Kurbatov

Institute of Laser Physics SB RAS, Novosibirsk 630090, Russia, E- mail: ion@laser.nsc.ru

Classical methods developed recently (see, for example, first chapters in [1]) for the description of a discharge plasma have probably reached a certain information limit. One feels the practical need for methods and ideas to be developed to supplement the available approaches and expand our grasp of this condition of substance. The gas discharge description [2-4] originating at the interface between laser physics and plasma physics allows us to look with the exotic party at the processes and various phenomena going on in the self- sustained gas discharge plasma and discern the uniting element of all known types of the discharge. The solution of Pecarek’s program [2,3,5] as a diffusion – plasma reaction theory or basis provides an understanding of the general concept of the phenomena and the discharge plasma in itself as a whole plasma organism. Similar approaches have been useful for describing early classical examples in biology, chemistry, and physics [6-9], among them localized structures in D.C. gas discharge systems [10,11]. They allow us with the exotic party to look at gas discharge physics and reveal the relationship of the phenomena in the gas discharge with classical and statistical mechanics and other aspects of physics. These results produce a theory based on than the one hundreds experimental data. Processes of generation and absorption of charged particles of varied types in a plasma, and their mutual transformations are the processes that not only determine basically the electrical properties of the positive column plasma, but also lead to coming into existence of a self- sustained gas discharge by itself’ [2].

The use of catastrophe theory to describe phenomena in the plasma of a gas discharge [2,3,9,12] shows new possibilities of nonstandard method of attack. The jumps and hysteresis effects in the gas discharge are explained by specific properties of a potential function. A minimum of this potential determines the state of the plasma. The physical whys and wherefores of introducing this potential are given in [2,3]. This gives a new insight into the gas discharge phenomena. The use of diffuse ionization mechanism of the electron multiplication allows us to describe adequately and completely the phenomena observed in the gas discharge with help of the potential.

Equation (9) shows that as  z → +∞  ρ tends exponentially to ρ2 ( E2c ) . The total current density I  in

formula (9) is given in a system of coordinates moving with the shock wave front. In the laboratory system of coordinates I has the following form

I 2 ( E2c ) ρ1 ( E2c ) − I1 ( E2c ) ρ2 ( E2c )

I =                                                      ,                                             (10)

ρ 2 ( E2c ) − ρ1 ( E2c )

where I 1 ( E 2c ) , I 2 ( E 2c ) , ρ1 ( E2c ) and ρ2 ( E2c ) are the drift components of the density current and the

charge densities forward and down- stream of the diffuse ionization shock wave, respectively. The structure of the shock wave that appears in reverse passing through the line of the wrinkle has an analogous form. Their parameters are determined from equations (7), (9), and (10) by replacement ρ1 ( E2c ) → ρ2 ( E1c ) , ρ 2 ( E2c ) → ρ1 ( E1c ) , I1 ( E2c ) → I 2 ( E1c ) and I 2 ( E2c ) → I1 ( E1c ) . In the reverse

passing, the diffuse ionization shock wave appears at the point E1c . In both cases, these changes in the charge density take place in a typical spatial scale

zi = D ρi ( Eic )    
  , (11)  

where i is 1 or 2.With the data previously obtained we can say with reasonable confidence that the change- over from the current state of the gas discharge to the other is performed by the field component or the bias current j (we used the same notations as [3,4])


− u ρ = 1   ∂E = − j ,     (12)  
  4π ∂t        
where ρ is the equivalent density of the bias current. At the critical points E c and E c the diffuse  
1   2    
ionization shock waves propagate through the gas discharge plasma at velocities u1,2 and this can lead  

to catastrophic impacts. For example, they lead to catastrophic failures of the plasma tube, the anode and cathode of the ion laser and of the power supply, too.


[1]  Fortov, V. E. (ed.) 2000 Encyclopedia of Low Temperature Plasma, 2 volumes. Moscow: Nauka. (in Russian)

[2]  Kurbatov, P.F. 2006 J. Plasma Phys. 72(1), 1-17.

[3]  Kurbatov, P. F. 2001 Modern view on physics of low- pressure gas D.C. discharge (Novosibirsk: Institute of Laser Physics SB RAS) Preprint 3 – 2001 (in Russian)

[4]   Kurbatov, P. F. 2005 in Proceedings (of the Fourth International Symposium ‘Modern Problems of Laser Physics’ (Novosibirsk, Russia, August 22-27, 2004, ed. S. Bagayev)). Novosibirsk, 263-276.

[5]  Pecarek, L. 1968 Physics-Uspekhi 94, 463-500.

[6]  Turing, A. M. 1952 Phil. Trans. Roy. Soc. Lond. B237, 37-72.

[7]  Haken, H. 1978 Synergetics. Berlin: Springer- Verlag, New York: Heidelberg.

[8]   Nicolas, G. and Prigogine, I. 1977 Self-organization in nonequilibrium system. From dissipative structures to order through fluctuations. New York, London, Sydney, Toronto: John Wiley & Sons.

[9]  Gilmore, R. 1981 Catastrophe theory for scientists and engineers vol.1,2. New York, Chichester, Brisbane, Toronto: John Wiley & Sons.

[10]  Ammelt, E., Astrov, Yu. A. and Purwings, H.-G. 1998 Phys. Rev. E 58, 7109-7117.

[11]  Gurevich, E. L., Liehr, A. W., Amiranashvily, Sh. and Purwings, H.-G. 2004 Phys. Rev. E 69, 036211 (1-7).

[12]  Knorr, G. 1984 Plasma Phys. Contr. Fusion 26, 949-953.

[13]   Whitham,G. B. 1974 Linear and nonlinear waves. New York, London, Sydney, Toronto: John Wiley & Sons.

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