Thermionic emission and current density

[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

 

[mfb]

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.

 

[Abimbola1987]

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.

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.

 

[mfb]

If there is nothing else neutralizing the setup: Yes.

 

[Abimbola1987]

If there is nothing else neutralizing the setup: Yes.

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?

 

[anorlunda]

If there is nothing else neutralizing the setup: Yes.

And your reply tried to introduce something to neutralize the setup.

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.

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

 

[Abimbola1987]

And your reply tried to introduce something to neutralize the setup.

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

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.

 

[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."

 

[tech99]

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.

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.

 

[sophiecentaur]

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.

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.

 

[Abimbola1987]

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.

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.

 

[Abimbola1987]

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.

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.

 

[Abimbola1987]

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."

Thank you, "electromigration" - interesting subject.

 

[sophiecentaur]

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.

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.

 

[Abimbola1987]

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.

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.

 

[sophiecentaur]

That symbolic representation is just the sort of thing we all need, even though it may seem 'obvious' to you - thanks.

"static electron starvation"

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.

 

[Abimbola1987]

Dear sophiecentaur,

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.

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.

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.

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

 

[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.

 

[Abimbola1987]

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.

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

 

[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).

 

[mfb]

You can maintain an electric field of maybe 1 kV/mm. That gives you a surface charge of 8.8μC/m². A 100 μm sheet of aluminium foil has an electron density of 13 MC/m². You reduce the number of electrons by about 1 in a trillion. That is the magnitude of the effect we are talking about.

 

[Abimbola1987]

@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.

View attachment 238600

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

Dear klystron,

Thank you. I have posted this question https://www.physicsforums.com/threads/vacuum-diode-electron-flow.966059/ maybe you can help me with that?

Indeed vacuum tube technology is still useful, look at this cool device http://www.think-grid.org/hvdc-breaker-comeback-gas-discharge-tubes

 

[Abimbola1987]

You can maintain an electric field of maybe 1 kV/mm. That gives you a surface charge of 8.8μC/m². A 100 μm sheet of aluminium foil has an electron density of 13 MC/m². You reduce the number of electrons by about 1 in a trillion. That is the magnitude of the effect we are talking about.

Thank you and duly noted.

 

[Dr Dr news]

What you are describing here is close to what we called thermionic energy conversion in the 1960's. The object was to place two electrodes in close proximity, heat one of them until thermionic electron emission occurs. The electrons with sufficient kinetic energy could cross the gap and be collected by the cool electrode. The output power was realized across a resistor connecting the two electrodes. The output characteristic was like that of a battery, with a short circuit current and an open circuit voltage. The process was made more efficient by introducing cesium vapor into the inter-electrode space which served several functions. Adsorption of Cs on the emitter lowered its work function and thermal ionization produced Cs ions which reduced the space charge enhancing the transit of electrons. Photo-voltaic conversion seems to have won the competition.

 

[Abimbola1987]

What you are describing here is close to what we called thermionic energy conversion in the 1960's. The object was to place two electrodes in close proximity, heat one of them until thermionic electron emission occurs. The electrons with sufficient kinetic energy could cross the gap and be collected by the cool electrode. The output power was realized across a resistor connecting the two electrodes. The output characteristic was like that of a battery, with a short circuit current and an open circuit voltage. The process was made more efficient by introducing cesium vapor into the inter-electrode space which served several functions. Adsorption of Cs on the emitter lowered its work function and thermal ionization produced Cs ions which reduced the space charge enhancing the transit of electrons. Photo-voltaic conversion seems to have won the competition.

Dear Dr Dr news,

Thank you for your kind input, I remember I have read about it on wiki https://en.wikipedia.org/wiki/Thermionic_converter

One question though, by which factor did the efficiency increase due to the introduction of cesium vapor? I mean I have learned in this thread that thermionic emission is very ineffective.

 

[tech99]

Thermionic emission can be considerable.
For instance, take the little battery operated vacuum tube 3A4, which is designed as a power amplifier and has a 3V filament. From memory, the filament current is around 100mA whilst the anode current can be 50mA. This causes problems for the designer because there is noticeable heating of the filament by the anode current. I encountered a particular problem with a stable oscillator when it had a slow chirp at switch-on; this was caused by the filament warming up a little in response to anode current.