Electrons colliding with gas molecules

[PORFIRIO I]

My concern is an electron tube.

From what I understood so far, gas molecules will have an average velocity derived from the Maxwell distribution, and that velocity will influence in the electron collision frequency.

I can't see clearly though how the electron velocity itself in the presence of an electric field will influence the collisions, are there equations describing this specifically?

Maybe the electrons need collisions with the gas to be less frequent so they can acquire more energy while traveling across the tube. When the have enough energy, they will collide more violentlly. Is this correct?

 

[trurle]

From what I understood so far, gas molecules will have an average velocity derived from the Maxwell distribution, and that velocity will influence in the electron collision frequency.
I can't see clearly though how the electron velocity itself in the presence of an electric field will influence the collisions, are there equations describing this specifically?
Maybe the electrons need collisions with the gas to be less frequent so they can acquire more energy while traveling across the tube. When the have enough energy, they will collide more violentlly. Is this correct?

This question is related to "bremsstrahlung" radiation calculations. For low-speed electrons, the energy transmitted per "collision" is roughly proportional to energy of electron, with energy of colliding molecules/atoms negligible unless you are in the temperature range of tens thousands degrees or more.