Hello
In low-pressure glow discharges, two regions which are close to electrodes have relatively stronge electrical field and potential drops occur in this two regions.
What is the physical reason for anode potential drop?
Why is the plasma potential higher than anode potential?
These regions are known as sheats. At the plasma boundary, there is a balance between the diffusion of charged species due to thermal velocity and the coulomb force. This create non neutral region. The thickness of this region is of the order of the Debye length, and the plasma is in at the plasma potential.
These quantities can be calculated by thermodynamic laws. Give a look to the book Fundamental Aspects of Plasma Chemical physics: Thermodynamics, by Capitelli et al, or other books on plasma physics.
In addition to Gianpiero's nice answer:
The anode will attract electrons in order to shield it's potential from the plasma potential. In order to accumulate electrons in front of the anode, the number of attracted electrons must be higher than the number of electrons that are lost over the anode to ground. Hence you get a kind of negatively charged cloud in front of your anode - this is the sheath, Gianpiero was talking about. This electron cloud is highly negatively charged and thus pulls down the value of the space potential between the plasma and the anode - this forms than your anode fall.
As Gianpiero pointed out, those are the "sheath regions". Physically, the potential drop happens because, for example, around the negative electrode (the cathode), a cloud of ions forms, which screens the plasma from the electrode. Being a non-neutral region, its width is of the order of the Debye length. As a consequence, the potential of the electrode is systematically lower than the plasma potential. A similar screening happens at the anode.
In fusion plasmas, where such electrodes are used to measure the plasma potential, and they are known as Langmuir probes, it is a well-known phenomenon: for this reason, in the fusion jargon there is a clear difference between the measured "floating potential" of the electrode, and the (higher) "plasma potential". As you can see in your picture, the plasma potential is pretty flat along the tube length L, and it is determined by the balance between ion and electron fluxes (quasi-neutrality) within the plasma column: as a consequence, the electric field E=0 there.
Near the material electrode, instead, the electrode intercepts particle trajectories, and the ion/electron balance is strongly modified. Electron density goes like exp(e Phi/Te), with Te electron temperature, which means, for a negative biased electrode, that the electron density is decreased exponentially in proximity of the probe (ion cloud). A potential Phi~3.3 Te is required to balance ion and electron fluxes to the probe, and as a consequence the plasma potential Vp = Vf + 3.3 Te, with Vf the "floating potential" of the probe.
A good explanation of this theory (known as the Child-Langmuir theory) is contained in Chapter 1 of the book "Introduction to Plasma Physics" by Rob Goldstone:
http://www.amazon.com/Introduction-Plasma-Physics-R-J-Goldston/dp/075030183X
Thank you so much for your kindness
Your answer was very helpful.
I understood reason of potential drop in vicinity of anode, in book is recommended by dear Gianluca, ion current is saturated. I have another question:
for a gas-filled tube there is a consumption of ions with no feed, does the cathode absorb all(or a significant fraction) of ions in a lot of time?
if answer of above question is true, what is the approximate lifetime in this tubes?
Thank you so much
No, the cathode does not absorb any ions at all (except in the extreme case of ion implantation but for that the ions have to have very high kinetic energies of several keV). What happens is that the ions can either recombine in the gas or on the electrode surface with electrons. Hence neutral particles are formed and the ions disappear.
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