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There are two main theories which I have been reading into Townsends avalanche effect and Paschen's curve. I understand that as electrons move from negative to positive electrode they collide with gas particles and ionize so there are more electrons causing avalanche effect. I also understand Paschens curve shows breakdown voltage Vb = f(pd)

However why specifically does increasing the pressure increase the breakdown voltage? If you increase the pressure surely there are more electrons so less energy is required for ionization and its easier for avalanche to occur at lower voltages?

Can you put it into simpler terms? e.g. as pressure increases mean free path decreases so electrons are more likely to collide.

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  • $\begingroup$ To get an avalanche the electron has to have a long enough mean free path to gain enough energy to be able to liberate another electron at the next scattering event. $\endgroup$ – Jon Custer Mar 21 '20 at 23:50
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increasing the gas pressure increases its density, which decreases the mean free path length of moving ions. This limits the distance an ion can travel before it gets deionized in a collision, and increases the amount of electric field strength required to achieve a breakdown cascade.

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A Townsend discharge is when a gas is ionised and becomes a conductor due to electrons colliding with gas molecules. To produce the ionisation of the gas molecules due to collision with electrons, the electrons must on collision have have sufficient energy to remove electrons from the molecules and hence also produce additional free electrons which in turn will produce an avalanche effect and make the gas a conductor.

The electrons which potentially are going to ionise the gas are accelerated by an externally applied electric field and must gain sufficient kinetic energy before colliding with a gas molecule for the ionisation process to occur.
Two factors are involved, the magnitude of the applied electric field and the distance travelled by the free electrons between collisions, the mean free path of the electrons.
If the pressure of the gas is increased, the mean free path of the electrons is decreased and so the applied electric field (voltage) needs to be higher to accelerate the electrons sufficiently to ionise the gas.

At the other end of the scale if the gas pressure is too low, which means that the mean free path is large, the accelerated electrons will collide with insufficient gas molecules to produce the avalanche effect.

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