Got it. Note that this advice refers to when operating at saturation current in the presence of high voltage gradients. Neither of these things is a serious concern in receiving circuits.
Correct. It is long-term standby operation that leads to the problem, and with a standby switch it is all too tempting to leave the heaters running.
No, my comments are in accordance with all the standard books. Slumping performance can be due to ordinary barium evaporation, or gas poisoning. It is these effects that can be rejuvenated by heating. Interface resistance can't, or not nearly to the same extent. See for example page 57 in: https://archive.org/details/ElectronTubeDesign
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Interface layer formation is discussed in a paragraph on the right side column of page 57, and there's another paragraph about it on page 60. In neither case does it say or suggest that the interface layer is permanent.
It is easy to tell the difference between changes in tube caracteristics due to barium (or strontium) depletion and the changes due to the interface layer. As the interface layer is very thin, it functions as a capacitor in parallel with a resistance. Hence with emission layer metal depletion the effect is loss in emission but no so much change in gm until emission is really bad. With the formation of an interface layer, the gm as measured by the grid shift method (a DC test) falls off dramatically, but the gm measured at a high audio frequency is little changed.
Yes, running a low emission tube on a high heater voltage can free up some more metal atoms and improve emission. But when I say I've rejuvinated tubes with an interface layer problem, I mean just that - I do know how to tell the difference.
The early TV IF amplifier tubes (eg 6CB6) can develop an interface layer if the TV was in a strong signal area and the AGC held the tube almost cutoff. The emission as tested in the standard way is little changed. It makes little difference to the TV, as the in-circuit gm is normal due to interface layer capacitance. In any case the AGC would, if gm did fall, back off and increase the gain. These tubes, because of their high gm (allowing lowish load resistors and thus wide bandwidth) , were used in some lab grade AC millivoltmeters and oscillators, where the loss in low audio frequency gain due to the interface layer does matter. Provided emission is ok, 30 minutes or so at 120% heater voltage and these old tubes recovered from TV's are good as new.
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Yup, I don't know either and suspect the other way. I'm hoping for substance as to why because on the face of it I don't think it obvious that a 'thermionic cloud' of electrons would necessarily stop an ion of reasonable mass and energy at issue. Thermionic emission is endothermic and probabilistic, ie not really abundant AFAIK, and I doubt the space-density that could be occupied by what should be a relatively sparse population of very small low mass low energy electrons ........happy to be wrong, but would love to see some substance as to why either way.
Hmmm, yet if we deplete population of thermionic electrons by x2.5 max Ia it's said we expose cathode to stripping.......? I think that defines the available or 'significant' population of thermionic electrons, and then I venture the tiny space density of them makes multiple collisions with ions unlikely ?keit said:
I agree about the rule of thumb being 'common wisdom', I just don't see the reasoning since it hangs on a 'thermionic cloud' retarding an ion which I question. I wonder if it might be one of those rules of lore that is difficult to verify and 10x as difficult to disprove ? I don't doubt manufacturers seemed to work by such rules, from hints in texts and by anacdote if one looks at heater requirements in valves like EL36 capable of large short term Ik max for example.....keit said:
Thought to add that electron mass is c x25,000 smaller than Nitrogen ion mass........even several collisions seems totally immaterial in shielding the cathode ?
I can't quite see what you meant to say in your fisrt sentence quoted above. But it appears you missed my point that:-
a) under temerature limitted conditions that apply momentarily during warmup. the electron cloud bear the cathode is significantly less dense than the normal amount a bit past the grid under normal operating conditions.
b) under normal operation, the x2.5 rule of thumb means, via queing theory, the density of electrons near the cathode is much much greater than 2.5 times the density just after the grid. Not just double or someting, MUCH greater.
There's another minor factor I forgot to mention. Tubes have the cathode in the centre, the control grid around it, and the other electrode around the grid some distance away. So the physical space between grid and cathode is much less that the area just outside the grid before significant electron acceleration.
The way to resolve this is to calculate the density of electrons just after the grid - that's easy - we just need the typical current density and the charge of an electron. Then calculate the actual density of electrons in the cloud near the cathode. There's several approaches we could take. One way would be to infer it from the anode current under retarding field (anode negative, grids at zero grid current) conditions. First we would have to measure the retarding field current over a range of negative anode voltages - it isn't listed in data sheets. Its not easy to measure - it's pico amps even with only a few volts on the anode, at which point leakage on the micas takes it all.
I'm too lazy.
Googling "space charge density" gave me nothing relavent.
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What I mean is that, if we are to believe, increase by a factor of x2.5 in Ik is sufficient to depopulate the cathode's 'protective' thermionic cloud. Then we know the difference in density deemed to be significant, and it seems too small to be relevent IMO if somehow a 'dense cloud of electrons' is to prevent ions from penetrating it even at normal Ik. Seems one of those things that sounds plausible until put under scrutiny I think..........?
By 'space density' I mean how much physical space electrons occupy in a given volume ie what's the chance of an ion actually hitting one. ie not 'space charge density' whatever that might be.
It's probabalistic, depending on temperature and work function. But we don't need to know if we take x2.5 Ik max as a significant density depletion level. Knowing what is deemed to be a significant density difference we can readily show it to be unlikely. Reductio ad absurdum, then I doubt the cloud ever provides much protection.........keit said:
No, that's not correct. The density ratio is not 2.5x, if that's what you are trying to say. Its much much greater. Please re-read my analogy in my post #26 above.
Thermionic emission is a probablistic process, but the electron cloud density is an averaging type of phenomena and does not just depend on temperature and work function. It also depends on the Richardson-Dushman constant (this is a constant for all metals but in oxide coated cathodes it depends on both the actual coating formulation, the underlying alloy, and the temperature) and the electron charge. At any given temperature, it works this way:-
Work function: .......decrease causes increase in density
R-D constant: ......increase causes increase in density
Electron charge: .....acts to inhibit the build up of the electron cloud.
The probability of any one ion colliding with an electron, assuming there are far more electrons than ions, is obviously proportional (to a first approximation) to the density of electrons, ie number of electrons in a given volume. Knowing the electron density and the effective ion diameter, one could then calculate the mean distance between between successive collisions until the ion's kinetic energy is significantly dissipated (whether or not the ion has remained an ion, or captured or let go an electron, or whatever) among all the electrons collided with.
By means of my queing analogy, it is easy to see that the mean distance between collisions is going to be dramatically less than it will be under temperature limitted conditions.
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I understand your analogy but don't agree it applies. Thermionic emission density is a probabilistic equilibrium, a balance between random emission and random recombination. Once emitted, any given electron doesn't 'queue' it nips about for a short time before returning to the cathode to recombine under influence of the net field. There isn't a significant 'thermionic' concentration gradient, it's endothermic. Depleting the pool by drawing Ik simply depletes the number (ie density) of electrons in a thermionic state at any given time. There are approximately as many electrons as probability dictates, not 'many more' , and there is no queue - if one is looking for a 'shopping analogy' how about 'when they're gone they're gone ' ?! Otherwise one could never fully deplete thermionic emission, nor would there be any rhyme to the x2.5 rule for better or worse - again by reductio ad absurdum it can't be so. Plus the x2.5 rule can't be argued to both apply and not apply........
Besides, would not the average N ion require about 10000 electron collisions to lose half its energy ? I just don't see it stands scrutiny.
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Electrons are, to a very good approximation, points so they occupy no space at all.luckythedog said:
'Space charge density' is the number of electrons per unit volume in the space charge. You need to know that to calculate the probability of a collision between an electron and an ion/atom. I have been trying to think of a way of producing a rough estimate of the density, but no inspiration yet.
I think we can assume that a positive ion will be quickly neutralised, and then assume that the collision cross-section for an atom is about equal to the size of the atom?
The total charge in the space charge may be another way in. We may be able to treat it as a thin sheet at the cathode surface, and simply estimate how many electrons fit into the cross-sectional area of an atom. I'm thinking Gauss' Law?
Back of envelope calcs suggest mean inter-electron spacing in thermionic zone might be c 1um. N ion size c 30pm. Do we feel lucky, suggests there might be the odd collision, but not the number needed to afford protection I think? Probably not worth the used envelope its written on, but supports what I'm thinking. Based on the x2.5 rule to find thermionic electron density, FWIW.
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The supermarket analogy, like all analogies, is not perfect, but it is a good analogy. Customers arrive at the store at random intervals, and at teh checkout counter at random intervals. If they see the checkout queue is too long, they leave without purchasing. I for one have done excatly that. This is very similar to electrons being repelled by the space charge and returning to the cathode. If the space charge is depleted by drawing off some to the anode, then less electrons will return to teh cathode - they will remain in the electron cloud.
If you are still not satisfied by my supermarket analogy, as electrons do not actually queue at the grid, but just keep moving on their individual trajectories, then amend it this way: Many of the electrons, having each selected some purchases, go towards the checkout, but randomly change their minds - some return to the shelves and grab extra things they nearly forgot, and some decide their husbands will be cross at the money they've wasted on lollies and go back and return them to the shelves. So, the queue at the checkout is still averaging about the same, but it isn't the same electrons there each time you look. It doesn't change the big picture. It's still 2.5 electrons arriving per minute, the checkout chick is still only clearing one electron per minute, and after a while there's a heck of a lot in the queue making new electrons go home in disgust.
It seems to me that DF96 is essentially correct. Each electron can be considered a point; each atom/ion can be considered to have a radius. You can look up the effective radii for appropriate gas species in textbooks (Blundell & Blundell Thermal Physics or even Kittel will do) The probability of a collision as a function of atom size is then approx proportional to to the square of the radius. This is all standard, albiet advanced physics.
But what we need to use this is a numerical value for electron density. DF96 says we can start with the total charge. To find total charge we can start with the retarding field current.
The slope of retarding field current when plotted against log anode voltage gives, after some arithmetic work, the cathode temperature and is a calculation well known to factory tube design engineers (they use it to check their design calcs on prototype tubes), but I'm too lazy to re-jig it to find space charge density. If anyone likes I can list a few journal papers on retarding field calcs.
The space charge /electron cloud is NOT a thin sheet. It has a double-exponential distribution with an effective mean distance away from the cathode. That's no big problem. You can calculate the effective mean distance, which is referred to as a "virtual cathode" from the tube plate or screen mu by knowing the distance to the grid and to the plate or screen. Once you know the virtual cathode distance distance, calculating the distribution of electrons vs distance out from the cathode is straightforward statistics.
As with any probability density function, the "tail" of the electron cloud /space charge assymptotes to zero at infinite distance from the cathode (ignoring for the minute that the vacuum stops not that far out). At any finite distance from the cathode there is a non-zero electron density until you reach the anode. That's why the retarding field current occurs. One merely has to connect anode to cathode and a current flows. Somewhat less flows if the anode is held negative by an external battery, but it does flow.
If you are still not satisfied by my supermarket analogy, as electrons do not actually queue at the grid, but just keep moving on their individual trajectories, then amend it this way: Many of the electrons, having each selected some purchases, go towards the checkout, but randomly change their minds - some return to the shelves and grab extra things they nearly forgot, and some decide their husbands will be cross at the money they've wasted on lollies and go back and return them to the shelves. So, the queue at the checkout is still averaging about the same, but it isn't the same electrons there each time you look. It doesn't change the big picture. It's still 2.5 electrons arriving per minute, the checkout chick is still only clearing one electron per minute, and after a while there's a heck of a lot in the queue making new electrons go home in disgust.
It seems to me that DF96 is essentially correct. Each electron can be considered a point; each atom/ion can be considered to have a radius. You can look up the effective radii for appropriate gas species in textbooks (Blundell & Blundell Thermal Physics or even Kittel will do) The probability of a collision as a function of atom size is then approx proportional to to the square of the radius. This is all standard, albiet advanced physics.
But what we need to use this is a numerical value for electron density. DF96 says we can start with the total charge. To find total charge we can start with the retarding field current.
The slope of retarding field current when plotted against log anode voltage gives, after some arithmetic work, the cathode temperature and is a calculation well known to factory tube design engineers (they use it to check their design calcs on prototype tubes), but I'm too lazy to re-jig it to find space charge density. If anyone likes I can list a few journal papers on retarding field calcs.
The space charge /electron cloud is NOT a thin sheet. It has a double-exponential distribution with an effective mean distance away from the cathode. That's no big problem. You can calculate the effective mean distance, which is referred to as a "virtual cathode" from the tube plate or screen mu by knowing the distance to the grid and to the plate or screen. Once you know the virtual cathode distance distance, calculating the distribution of electrons vs distance out from the cathode is straightforward statistics.
As with any probability density function, the "tail" of the electron cloud /space charge assymptotes to zero at infinite distance from the cathode (ignoring for the minute that the vacuum stops not that far out). At any finite distance from the cathode there is a non-zero electron density until you reach the anode. That's why the retarding field current occurs. One merely has to connect anode to cathode and a current flows. Somewhat less flows if the anode is held negative by an external battery, but it does flow.
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Perhaps page 37 of this reference can help here? (Also see the nomograph on page 33):
http://www.tubebooks.org/Books/herrmann_wagener_oxide2.pdf
I'll share my method.......
Applying the 2.5x rule as though it were true, we know Ik needed to effectively consume all thermionic emission. Cathode is always in thermionic equilibrium, so at Ik = 2.5x max we know rate of thermionic charge emission, then we know number of electrons created/absorbed per second, then we know total number of electrons in thermionic zone when Ik=0. We estimate volume of thermionic zone, apply general statistical spacing models et voila !
I never was any good at sums so a double check of figures seems well worthwhile. But really it's reductio ad absurdum illustration that both the 2.5x rule and electron density likely to afford protection can't both be true I think......
Unfortunately, the idea that electrons somehow 'queue' to replace those depleted by Ik isn't how it works I think. The population is simply born of statistics, has a lifetime set by statistics and what doesn't end up as Ik gets reabsorbed promptly. Providing Ik is endothermic for the cathode, BTW - ie it will cool it too.
That's all a load of nonsense. When the anode draws 2.5 times the rated current, at a first approximation the anode is getting every single electron emitted. Presumably that's what you are trying to say. When the anode is drawing rated current, the cathode is STILL emitting the same amount. But 1.5 x the anode stream is continually returning to the cathode, while a quantity of electrons are in flight within the electron cloud. If it wasn't for the electron charge, none would be forced to return. There is negligible net velocity (although there is a sort of brownian motion) in the electron cloud, so the average electron spends significant time in the cloud. The lower the number drawn off to the anode, the longer the electrons not drawn off spend in the cloud. Roughly analogous to customers spending time in the check out queue, with some returning home without buying anything.
You haven't shared you actual calculation, with numbers. Just a so called "method" description in vaguely written words.
If you share your actual calcs, then we can see how you actually arrived at your answer of 1 um for inter-electron spacing. I sense from your comment about "sums" and the fact that you didn't just post your calcs, that the figure is just something you plucked out of thin air.
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So what? What has electron emission cooling got to do with the topic of this thread?
Hopefully you don't think emission cooling cools the cathode sufficient to significantly affect emission and thereby significantly affect electron lifetime in the cloud. The cooling effect is very small, and usually at least partly balanced out by joule (I^2.R) heating in the emission layer radial resistance.
My use of the word "brownian" is perhaps misleading. Brownian motion is the motion of particles in random directions in straight lines between each collision.
Each point on a hot cathode emits electrons in random directions at random times and with random velocity distributed aboot a mean velocity.
The flight of each electron not captured by the acceleration field of the anode is a sort of parabola. Considering the cathode as horizontal, some electrons leave the cathode near vertically, undergoing decelleration due to the net space charge, until they reach zero velocity at some random point within the electron cloud, then accelerate downwards back to the cathode. As their velocity is maximum just as they leave the cathode, and the same maxium again just as the get back to the cathode, most of their flight time is spent within the more dnse parts of the lectron cloud. The cloud is most dense some distance away from the cathode, less dense near it - the virtual cathode effect.
Some electrons are emitted quite slowly at a shallow angle. These electrons can travel some distance horzontally before getting high enough to be effectively repelled by the cloud, and their flight time is thus relatively long.
Each point on a hot cathode emits electrons in random directions at random times and with random velocity distributed aboot a mean velocity.
The flight of each electron not captured by the acceleration field of the anode is a sort of parabola. Considering the cathode as horizontal, some electrons leave the cathode near vertically, undergoing decelleration due to the net space charge, until they reach zero velocity at some random point within the electron cloud, then accelerate downwards back to the cathode. As their velocity is maximum just as they leave the cathode, and the same maxium again just as the get back to the cathode, most of their flight time is spent within the more dnse parts of the lectron cloud. The cloud is most dense some distance away from the cathode, less dense near it - the virtual cathode effect.
Some electrons are emitted quite slowly at a shallow angle. These electrons can travel some distance horzontally before getting high enough to be effectively repelled by the cloud, and their flight time is thus relatively long.
Well yes, that's the nature of reduction ad absurdum arguments, they are devised to show that if a proposition were true, the outcome is nonsense. In this case either the 2.5x rule, or the density of electrons sufficient to 'protect' the cathode from ion bombardment is contradicted I think.
As to how long an electron spends in any 'cloud' - an electron which escaped the cathode surface already overcame a potential barrier - subsequently its motion is defined mostly by the prevailing electric field gradient in the vacuum you'd think (& weakly by its momentum). One might argue that in grid valves the retarding field provided by grid potential is already taken into account in the potential barrier the electron had to overcome to escape, then only electrons destined to become Ik actually leave the surface in any meaningful sense......???
Don't know, I hope the 1951 paper Merlinb linked might hold some answers.
I mentioned Ik generation as endothermic ie cools the cathode because such action would happen at the oxide coating, which is thin, perhaps not very thermally conductive and perhaps mechanically vulnerable to thermal gradient? As an alternate reason for the 2.5x rule maybe, and perhaps as an alternate mechanism for cathode degradation at high Ik other than ion bombardment - since AFAIK one still would need to explain it.
And it seems moot to discuss arithmetic whilst disputing the principles involved ! Actually I'd welcome independant double-check once the principles involved are agreed. I also hope that the paper linked in Merlinb's post might provide some cross-check and insight into likely thermionic electron density near the cathode. I have an open mind, but one or both of the 2.5x rule and/or ion bombardment protection seems unlikely to me.
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