X-ray production - maximum pressure

[Plat]

What is the maximum practical or theoretical pressure at which x-rays can be produced, as in a Crookes tube or cathode ray tube? I know Crookes tubes operate at 0.1pa and lower, but I need to know if I am at risk of producing x-rays with high voltage (60kv+) discharges at medium vacuum, as low as 5pa.

Does the electron mean free path have anything to do with this? Maybe when the e-mean free path equals or exceeds the gap between cathode and anode, x-rays can be produced by electrons traveling across without being slowed by gas molecules? How do I calculate the electron mean free path in air at 5pa and 298k?

In the vacuum chamber at maximum vacuum, I can still see a slight movement of tissue paper placed in front of a computer fan, which makes me think there must still be too much air to allow x-rays to be produced, but I want to make sure before it's too late!

 

[mfb]

The free path for atoms at room temperature is roughly $\lambda \approx 1cm\frac{1 Pa}{p}$ with pressure p, I wouldn't expect the value for electrons to be completely different. It is an expectation value, so some electrons will have longer acceleration distances. A longer distance between the electrodes can help.

 

[Plat]

Thanks for the reply. So basically, if the gap from cathode to anode is much larger than the mfp then there should be little potential to produce x-ray photons? That makes sense because the mfp of air at 5pa(my setup) is 7mm, and at 0.1pa as in a Crookes tube, it approaches 1 meter, that would make a big difference.

 

[mfb]

Well, "much larger" - if the total gap is 70 centimeters, you still have 600 V per calculated mean free path, so some electrons will gain keVs of energy. To make it worse, I would expect electrons (especially accelerated ones) to have a longer mean free path than atoms. A factor of 4 (suggested by geometry - electrons are smaller than atoms) would be sufficient to get many electrons up to 10 keV. You are certainly still in a pressure range where a more detailed analysis (or sufficient shielding) is necessary.

 

[Plat]

I assume it would be safe if I maintain a much higher pressure, like keeping a container of water under the vacuum so that the pressure cannot drop below 600pa? I will use lead shielding if/when I remove the water to allow much lower pressures.Hopefully this is not too off-topic, but why does the color of the plasma change as the pressure drops? (Because I am using A/C, there are no striations, dark spaces, etc in the discharge.)

https://www.dropbox.com/s/kzks9caltx0rfs1/plasme discharge mason jar high pressure - pink.png?dl=0

It looks like this, pink mostly from nitrogen's emission lines, but then as the vacuum gets very pure, it turns ghostly white like this:

https://www.dropbox.com/s/g3kz9etdgwq62tl/plasme discharge mason jar low pressure - white.png.png?dl=0

I know this is from lower pressure, but if the same gas is present, shouldn't the emission spectrum and color be the same? Why does it change color?

(Sorry I could not get the images to show up in the post directly)