Velocity of Electrons and Protons in Plasma Loops

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Discussion Overview

The discussion centers on the velocities of electrons and protons in a plasma loop when a current is induced. Participants explore the relationships between particle velocities, mass, and momentum conservation in different plasma compositions, including mixtures of protium and deuterium.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about the equation for determining the velocities of electrons and protons in a plasma loop, questioning whether their velocities are equal in magnitude and opposite in direction or if they depend on mass.
  • Another participant suggests that conservation of momentum implies a velocity ratio of approximately 1:1800 for electrons to protons, assuming singly ionized particles, and notes that this would vary with the total mass of the ions.
  • A further inquiry is made about the velocity ratio in a plasma mixture of protium and deuterium, proposing a ratio of 3600:2:1 for electrons, protium, and deuterium, respectively.
  • One participant expresses uncertainty about the validity of the proposed ratios for a mixture, suggesting that while momentum conservation might hold for pure plasmas, the situation could be more complex in mixtures. They propose that the kinetic energy of ions might lead to different velocity ratios and introduce a paradox regarding momentum conservation.
  • The same participant revises their earlier assertion about momentum conservation, suggesting that in a non-isolated system, the momentum of ions and electrons need not sum to zero, and proposes that energy considerations might yield different velocity ratios.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of momentum conservation in mixed plasmas and the resulting velocity ratios. The discussion remains unresolved, with no consensus on the correct approach or ratios.

Contextual Notes

Participants note potential limitations in their assumptions regarding the nature of the plasma and the interactions between particles, particularly in mixed compositions.

skullcracker
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Is there an equation to find out the velocity of electrons and protons in a loop of plasma when a current is induced through it?Is the velocity just equal in magnitude and opposite in direction or is it opposite in direction and the velocity dependent on mass of the particles?(implying that an equal amount of force is exerted on the electrons and protons)
 
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Conservation of momentum would tell you that the relative magnitudes of velocities would be around 1:1800ma, where ma is the 'atomic' mass of the ions. (Big ions slow, small electrons fast)
Your suggestion would only apply to a Hydrogen plasma so you need to consider the total mass of the ions. I have assumed singly ionised particles, of course.
 


So if I had a plasma which is a mixture consisting of an equal amount of protium and deutrium would the ratio of the velocities of electron, protium and deutrium (respectively)be 3600:2:1 ?
 


I think we need to think again about this.
Your numbers agree with momentum conservation so you may be right but I wondered whether they would hold for a mixture. Then, as I wrote the following, I came to a bit of an impasse. Here is my general thinking - I think it's worth sharing this sort of thing:

A protium plasma would have the ratio 1800:1 and a Deuterium plasma would have the ratio 3600:1 but could you be sure that the ion velocities would be 2:1 in ratio in a mixture? I should have thought that the KE of the ions would be the same so their velocities would be in the ratio 1:√2. But then the electrons would also have different velocities due to momentum conservation. This is a paradox.

I think my initial glib statement about momentum consideration could be at fault. This is not an isolated system and momentum can be transferred to the equipment / rest of the world so momentum of ions and electrons need not add up to zero. It would probably be better to assume that the work done on all the charges is the same. It would certainly be the case if the plasma were subject to an electric field across a gap - the eV would be the same for all. So I think, from energy considedrations, the ratios of velocity would be √(1800):1:1/√2 and to hell with momentum conservation.
 

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