## Plasma physics question - how long does it take for plasma to neutralize after E field turned off?

It may be difficult to separate "theory" from "application," but let''s see if this helps facilitate the discussion.
Arun Luthra
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### Plasma physics question - how long does it take for plasma to neutralize after E field turned off?

How long does it take for a plasma to neutralize after the electric field is turned off? Assume no magnetic field. Assume electron density equal to ion density and Maxwellian velocity distribution with temperature T. The plasma is in a metal chamber with characteristic linear dimension "a".

My thoughts are that we should start with the electron-ion collision frequency, since that drives neutralization. However, the outcome of each collision depends on relative velocity or temperature. So, it is also a question of the plasma cooling rate. Bremstrahlung will cause cooling due to collisions, and wall collisions will cause cooling. Wall collisions occur at different rates for electrons and protons/deutrons, according to their speed. They should lose a lot of speed with each plasma-wall interaction.

It is a complicated problem. Are there rules of thumb that can get us within a factor of 10 for close to 100% neutralization given starting temperature T?
Richard Hull
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### Re: Plasma physics question - how long does it take for plasma to neutralize after E field turned off?

Absolute and complete neutralization of the ideal situation you have posed would be a long time. A large fraction of a second or more would be my answer. In a genuine ideal plasma of a pure gas, Density, (pressure) and temperature (ion velocity) would be the dominant factors. It is easy to speak of theoretically idealized physics situations such as 100% total neutralization of a gas that was an idealized plasma.

Read up on ionized gases in Von Engels book. For a quick rinse read up on how a GM tube works. The modern GM tube is a fine tuned device. It is designed to kill a plasma (deionize it), even in the presence of a fixed e-field in no more than 60 or even 30 usec. This seeming magic is due to clever circuit and mixed gas choices in controlled geometries.

Plasmas require feed energy to maintain them. Electrical current flow in a gas is that most often encountered. We all know that just because you have an e-field you don't necessarily have or create a plasma. We also know there is no way possible to instantly, and ideally, remove an e-field.

In theory, and in practice you cannot instantly remove an e field. (capacitance of the e-field system and circuit characteristics all play a role) This complicates and removes forever the possibility of the approach to the realization of a real world simplification. Due to many factors, generalizations to even order of magnitude best guesses just can't answer your question regarding 100% complete neutralization without full plasma system data.

Richard Hull
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Patrick Lindecker
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### Re: Plasma physics question - how long does it take for plasma to neutralize after E field turned off?

Hello Arun and all,

Some years ago I wrote a paper (in French) published in a Ham journal. The title of this paper is "Etude d’un générateur de signal AM à un seul tube à gaz" ("Study of an AM generator with a gas tube"). The gas tube was a NE2. The principle is to generate a discharge which itself generates oscillations (system called "relaxation oscillator").
In the appendix of this paper, I made a mathematical analysis of the voltage decline (decay rate). In my case, the complete decay takes about 0.4 ms.