Following the plasma inductance formula, I understand that the inductance is proportional to meters but I do not understand that the inductance is directly proportional with squared radius and inversely proportional with plasma length. As length increases, inductance decreases? It is said that plasma has a little inductance due to electron inertia.
https://lh6.googleusercontent.com/-I4VYKM99pnk/U0Jwvv2yMjI/AAAAAAAABnA/2Iup38WhD7k/w226-h79-no/Plasma+inductance.png
The explanation is quite simple. If you have a steady direct current along the plasma column, the picture is the same as for a normal conductor with current and its inductance is proportional to the length the conductor. If in a column helical instability is excited, then you get something like a solenoid, which is laid over the length number of turns equal to the number of waves that fit on this length. But solenoid inductance is proportional to the square of its radius and to the number of turns is inversely proportional to the length of it..
It can be truth Vladimir but it generates me following new questions:
1. The column helical instability must be induced.
2. Accordingly the equation only one turn is performed
3. I read that that kind of unstability appear at hollow plasmas, but if a strong magnetic field is generated during the current injection, the electron movement must be confined to the inner part of the plasma (unless it is generated using high frequency current)
The plasma column inductance, is not constant in contrast to conventional wire inductance. In particular, it varies with the current flowing through the column. When the current exceeds some critical value the helical instability develops, leading to the restructuring of the current and hence the column inductance.
Qualitative description of this instability is as follows. When we have current along plasma column in a longitudinal magnetic field, then there is the azimuthal component of the magnetic field and its lines of force twisting more abruptly, with more current. The energy of the magnetic field Increases (curve lines!), which is energetically "unprofitable" for the system.
When the twist exceeds a certain limit (defined in quantitative analysis) system tends to lose excess energy by straightening the lines of force, which is achieved by tightening the current. In the limit we obtain a hollow coil to which the real situation do not usually go - everything can end on "single turn" (the first mode instability). So you should reverse your statement: helical instability tends to make hollow plasma solenoid.
Accordingly that I should measure the plasma inductance during the test.
What method could be better to measure the plasma inductance?
I think it would be interesting using a high power RF signal of about 400 Mhz through a resistor in order to measure plasma inductance and resistance.
It could be used also a measurement of current/voltage delay?
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