Mean free path problem

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Chia-Yu Yuan
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Real name: Chia-Yu Yuan

Mean free path problem

Post by Chia-Yu Yuan »

My team recently encountered difficulties in classifying the different discharge modes for estimating the mean free path of nitrogen ions. Our chamber is CF 35 TEE, and the inner diameter of the chamber is 34.4 mm. We think that the mean free path in star mode is close to or larger than the chamber size, the halo mode may be 10 mm, and the glow discharge is roughly 1 mm, but this part we're not sure whether this is correct, and would appreciate some opinions.
We are currently using the ideal gas equation to estimate the gas density, but we are not sure whether the temperature T should be substituted into the temperature of the ion or the temperature of the background gas (maybe close to room temperature?) because the degree of ionization of our gas should be <10%. We think that the mean free path should be related to the pressure, ionization degree, ion temperature, and background gas temperature, but we had no choice but to estimate these quantities by the applied voltage and pressure. Assuming that our chamber pressure is 30 mTorr, and the applied rms voltage is 1880 V, what degree of ionization and ion temperature do we expect?
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Dennis P Brown
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Re: Mean free path problem

Post by Dennis P Brown »

First, this post should not be in fusor construction section. Second, the ideal gas law is useless for a plasma and cannot be used. There are specialized computer programs for that and a few here have posted on this subject.
That all said, for the gas before you apply a voltage, then standard 'mean free path' formulas in any Physical Chemistry book would apply. The number of molecules does not change due to a plasma; however, their behavior (Collison rate) changes a great deal when ionized.
This topic should have been posted in the "New User Chat section"
Last edited by Dennis P Brown on Wed May 10, 2023 1:55 pm, edited 1 time in total.
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Liam David
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Re: Mean free path problem

Post by Liam David »

This question is in the wrong section.

Some plasmas can be accurately described with equations including the ideal gas law, notably those in the multi-fluid and MHD regimes. There are likely plasma sub-populations in a "star mode" fusor that can be described thermally. A high-pressure glow discharge like "glow mode" or "halo mode" is likely predominantly thermal with minor beam components.

Some cross-section data that can be used to calculate MFP can be found here: viewtopic.php?t=14157

The background molecular deuterium density can be found using the ideal gas law. The temperature is the gas temperature (likely near the temperature of the chamber), not the ion or electron temperature. The law is a per-species equation.

The ionization fraction is likely <1%. There are some simple ways to estimate this, but one would need to know the electron temperature.

Collisionality between ions and electrons in a plasma is a more complicated process. Heating a gas at constant volume will increase the collisionality, but after ionization, the collisionality scales strongly inversely with temperature.
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