# B Thermionic emission and current density

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1. Feb 10, 2019

### Abimbola1987

Dear Sirs,

Maybe this is general knowledge, but I couldn't find the answer where I looked, so please bear with me.

Consider a circuit consisting of a mechanical generator (some spinning magnets and coils) and a wire across the generators output. At some point the wire gets hot and starts a thermionic emission of electrons.

My assumption is that if electrons continuously disappears from the circuit, the current density must diminish over time.

Would the above be a correct assumption?

Regards
Abim

2. Feb 10, 2019

### Staff: Mentor

You won't be able to make that loses a relevant fraction of electrons. It gets charged quickly, stopping further emission unless the electrons return in some way.

3. Feb 10, 2019

### Abimbola1987

Dear mfb,

Are you saying that a space charge quickly builds up, stopping any further emissions? If not, then I haven't quite understood what you said.

4. Feb 10, 2019

### Staff: Mentor

If there is nothing else neutralizing the setup: Yes.

5. Feb 10, 2019

### Abimbola1987

Dear mfb,

Yes that would obviously happen, please allow me to rephrase:

Consider a circuit consisting of a mechanical generator (some spinning magnets and coils) and a wire across the generators output. At some point the wire gets hot and starts a continuous thermionic emission of electrons due to external conditions e.g. an E-field like in a vacuum tube.

My assumption is that if electrons continuously disappears from the circuit, the current density must diminish over time.

Would the above be a correct assumption?

6. Feb 10, 2019

### Staff: Mentor

How the neutralization occurs doesn't matter. It is neutralized or not.

7. Feb 10, 2019

### Abimbola1987

Yes, my question is basically what happens with the current density when electrons leave the circuit over time?

How the electrons leave the circuit is not important here, I was just using thermionic emission as an practical example.

8. Feb 10, 2019

### Klystron

This excerpt from the wikipedia entry for current density offers this information possibly relevant to your circuit:

"High current densities have undesirable consequences. Most electrical conductors have a finite, positive resistance, making them dissipate power in the form of heat. The current density must be kept sufficiently low to prevent the conductor from melting or burning up, the insulating material failing, or the desired electrical properties changing. At high current densities the material forming the interconnections actually moves, a phenomenon called electromigration."

9. Feb 10, 2019

### tech99

If we place a positive electrode (positive with respect to one end of the wire using a battery, for instance) near the wire than a current will flow to it via the thermionic emission. The current in the wire is now split between the two circuits.

10. Feb 10, 2019

### sophiecentaur

It would help if you were to post a diagram of the circuit. What will happen depends on precisely what you are trying to describe verbally.

11. Feb 11, 2019

### Abimbola1987

I appreciate that, but I was trying to describe a logical experiment not an actual detailed circuit. A generator and a wire with some electrons dissipating from the wire, what is the effect on the current in the wire? I believe tech99 answered my question.

12. Feb 11, 2019

### Abimbola1987

So any electron emission from the wire would mean a reduction in the wire's current carrying capacity, which could be considered permanent as the only way the electrons in the wire could be replenished is by random impact of free electrons in the atmosphere.

13. Feb 11, 2019

### Abimbola1987

Thank you, "electromigration" - interesting subject.

14. Feb 11, 2019

### sophiecentaur

This is where a diagram could have helped and the NUMBERS count, here. If you were to take just a tiny fraction of the valence electrons from the conducting wire, due to thermionic emission, the potential would increase significantly - the wire would become positively charged. What proportion of the number of available electrons be reduced for a typical space charge due to thermionic emission? A quick comparison of the density of the metal with the density of the surrounding air implies that the density of electrons surrounding the metal surface (space charge) will be a minute fraction of the available conduction electrons inside the metal. Every atom in the metal can contribute to the conductivity.

If you allow the thermionic electrons to flow away (as in a rectifier diode) then things will change; the Cathode Current for a thermionic diode can be much higher than the current flowing through the cathode heating circuit so you could perhaps measure a difference in the heater current for a given Diode current. I am sure there are some PF members with some experience of this (looking at how the heater current could be modulated by the amplifying action in a triode valve perhaps. (We could wait for some input here . . . . . . .?)
But that effect would only be due to Kirchoff'c Current sharing law, rather than static 'electron starvation' which is what you seem to be proposing.

15. Feb 11, 2019

### Abimbola1987

Dear sophiecentaur,

This is the conceptual situation I'm describing, the electron(s) have already left the circuit, what happens with the current in the wire? As to the number of electrons leaving; then it would be the maximum number that is physically possible by any means.

I'm not proposing anything, I'm asking out of doubt. I mentioned "static electron starvation" as my suggestion, if this is wrong then I would obviously appreciate to be corrected.

16. Feb 11, 2019

### sophiecentaur

That symbolic representation is just the sort of thing we all need, even though it may seem 'obvious' to you - thanks.
It's purely a matter of the actual quantities involved. Removing a single electron would in principle make a difference to the resistance in the circuit. However, there will be something in the order of at least 1020 electrons available in a typical piece of metal equipment. To remove just 1% of available electrons would require far more energy than would be provided by the thermionic effect - in fact the thermionic effect only applies to the surface atoms. The lower atoms would only lose electrons if the metal were hot enough to be so the model would not apply.
Something I only just thought of is that the temperature of the metal would have more effect on its resistivity than any tiny number of 'lost' thermionic electrons could account for. As I pointed out before, the NUMBERS count in all Science. I cannot see any way that the thermionic effect on resistivity could be measured; it's many orders of magnitude less than other effects.

I notice that you mention 'other' methods of removing electrons. It is possible to discharge electrons from an insulated circuit but the static voltages involved would have to be of lunatic proportions in order to distort the Electric Fields within the circuit enough to alter its function.

17. Feb 11, 2019

### Abimbola1987

Dear sophiecentaur,

So if I understand correctly you are saying that the situation I'm describing would not occur under normal operating conditions, yes I can concur.

Purely theoretical then, if tension of lunatic proportions were present, in what way would it alter the circuits function?

18. Feb 11, 2019

### sophiecentaur

1. Massive static fields needed to remove sufficient electrons would not be practical even if possible in principle.
2. Heating current passed through a thermionic electrode in a thermionic valve would cause a Voltage drop. The current through the diode(say) would also cause Voltage drop across the filament. But this is not a static situation. You may need to read around about thermionic valves if you aren’t familiar with them. Google is your friend.

19. Feb 11, 2019

### Abimbola1987

Thank you. I'm currently reading the "radiotron designers handbook", but one doubt remains, which I will seek to clear in another post.

20. Feb 11, 2019

### Klystron

@Abimbola1987 When I first read your thread, I immediately thought of an early device called a thyratron largely replaced in practice by solid-state devices but still useful.

But was unsure of your level of understanding, etc. from the OP (original post).