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Glow Discharges in low-pressure gases.

Plasma phenomena are very widespread in our surroundings. You can see them in nature, in everyday life, in your laboratory and in industry. Sun and other stars, aurora, neon lamps in the streets or plasma display of your TV set, ICP or laser in laboratory and so on. You may focus no attention on them. But all this is plasma phenomena. And it is very important and interesting thing to investigate.

Plasmas R. Redmer, Phys. Reports 282, 35 (1997)

The schematics above is from: R. Redmer, Phys. Reports 282, 35 (1997)

They are very different and by their characteristics can be divided into many types. You can see a scheme, illustrating types of plasma with their parameters on the picture below. Left Y axis is logarithm of plasma temperature, evaluated in K. Right Y axis is also temperature, but it has energetic meaning (corresponds with particles energies) and evaluated in eV. High X axis shows so called “plasma frequency”(density of charges divided on density of total gas ). Low X axis shows logarithm of ions density (number of ions in a unit of volume). You can see here not only laboratory plasma (ICP, laser…) parameters, but also characteristics of your everyday plasma. For example, you can find the temperature of solar corona or temperature during supernova explosion, ions densities in flames or in ionosphere. You can compare parameters of solar corona, atmosphere and sun core. Even metals can be seen here! It seems strange, isn’t it?  But remember, that metals have free electrons, forming so called “electron gas”. 
Glow discharge plasma, the type we interested in most of all, is only the small part of all plasma phenomena.


So what are the typical parameters of GD? Here they are:

Pressure 0,01 - 10 Torr
Dimensions 0,1 – 10 cm
Voltage 100 – 2000 V
Current 0,1 – 100 mA
Temperature 300 – 1000 K
Charged particle density 106 – 1013 cm-3
Plasma electrons (energy) 0,1 – 1 eV
Plasma ions kT gas
Ions at cathode 1 – 1000 eV
Low ionisation degree 10-7 – 10-4

Different kinds of particles exist in glow discharge plasma: electrons, ions, metastables, excited atoms and so on. But if we interested in electrical effects in glow discharge, we should concern the charged particles most of all.

Charged Paricles in a Discharge

The particles move under the influence of electric and magnetic fields
                        
Lorentz Force

and experience many collisions with  the background gas.

Collisions.

  •  Elastic Total kinetic energy is conserved.
  • e + Ar e + Ar
  • light
  •  Inelastic Part of the kinetic energy is converted to internal energy.
    • Excitation
    •       e + Ar e + Ar*          leading to  light emission                    
    • Ionisation
    •      e + Ar e + Ar+ + e      leading to charge production

1. All types of collisions have their own characteristics – cross sections (σ)
  
 Hard sphere cross section

Hard Sphere Model


Equation Hard sphere cross section

But reality is more complicated

Cross sections give the probability of collision processes. Compare to electrons velocity, atoms are too slow that’s why they assumed stabile but not like a solid ball. Through strong electrostatic forces there are interactions between atoms, electrons and ions occur. Atoms have electrons, ions and also empty space if electrons approaching to collision. Electrons characteristics like directions, velocities effect these interactions and also caused probability of collisions with the gas density per unit volume (n) and effective collisions area of each molecule (q).

If ideal gas atom has 3 Å radius (or 2.8 10-15 cm2 area) and electron radius is 2.8179 × 10-13 cm, collision has also almost 3 Å radius and this will sweep out a volume of gas as the atom moves.  Total probability of collisions has a value between 0-1 this means there is a collisions or not but there is also different collisions according to electrons energy so probability of that interactions depends on, number of the collisions in unit time and number of the interaction in the same time interval. In hard core model, collisions diameter is equal to summation of projectile and target spheres diameters (see figure above).

Cross sections give the probability of collision processes.

Collional Crossections For Argon


On this figure you can see the order of magnitude for cross sections in argon and its depending on energy. But also you can see what processes can be caused in these conditions. So another parameter that helps us to describe the motion of particles and processes in plasma is energy, gained between collisions. It defines not only by cross sections but also by electrical conditions (electric field intensity E) and density of particles (n).

2.Energy gain between collisions:

 


So we can characterize the motion of particles by E/n.

 

Plasma regimes

First published on the web: 09.12.2007

Marie Curie Research Training Network

Authors: Anna Kravchenko and Hakan Candan. The text is based on a lecture given by Zoltan Donko, RISSP Budapest, at the first Gladnet training course in Antwerp Sept. 2007