Increase voltage = increase in intensity of electrons - X-ray tube

[nousername]

Hey,

In x-ray tubes, how come an increase in the voltage results in an increase in the intensity of the electrons. i.e. the no. of electrons emitted per unit time per unit second.

Thanks.

 

[ZapperZ]

Hey,

In x-ray tubes, how come an increase in the voltage results in an increase in the intensity of the electrons. i.e. the no. of electrons emitted per unit time per unit second.

Thanks.

There are two different answers to your question, depending on the range of voltage that is being applied.

In the beginning, as you are increasing the voltage from zero, you are starting to collect more and more of the electrons that have been emitted from the thermionic cathode. Electrons that would have gone off into a different direction and not hitting the anode would now be collected at a higher potential. At some point, you'll reach a "plateau" where all the electrons emitted would be collected.

However, this is not a flat plateau. As you continue to increase the potential even higher, you now get into a "Schottky" effect. This is where the applied potential is large enough that it is starting to lower the effective work function of the surface. The larger the applied potential, the lower the effective work function. The lower the effective work function, the more electrons emitted from the cathode.

Thus, you see a higher electron intensity at a larger voltage.

BTW, this effect is not "classical".

Zz.

 

[nousername]

Hey ZapperZ,

Thanks for your explanation mate. it was awesomne! With the second point about the increased potential difference resulting in a decrease in effective work function of the metal surface... is that because the electrons are now being attracted by the positive potential (anode) and so less energy is required to remove them?

Thanks!

 

[ZapperZ]

Hey ZapperZ,

Thanks for your explanation mate. it was awesomne! With the second point about the increased potential difference resulting in a decrease in effective work function of the metal surface... is that because the electrons are now being attracted by the positive potential (anode) and so less energy is required to remove them?

Thanks!

Sort of. Remember that for metals (which is the normal material for these thermionic cathodes), the external field can only penetrate up to the skin depth. So here, the external field changes the field, and thus the surface barrier potential also changes. All of these affect the work function.

So yes, one can sort of say that the electrons are more "attracted" to the anode, but a more accurate description should be in terms of the barrier potential.

Maybe this figure might help. This is a viewgraph from one of my talks that I've used frequently. In terms of the image potential that can be used to represent the work function, one can see that the potential barrier is lowered when an external field (-eEz) is applied on the surface, thus lowering the effective work function.

Zz.