😀 No ion bombardment, no 'electron cloud', no problems. 😉
@Malcom Irving - I have a 1963 valve Rock-Ola jukebox BTW.
In doing so you are going against well established principles in a a multitude of books and papers in peer reviewed journals, including H/W 1951.
It's no good just repeating yourself, you need to provide alternative explanations that cover ALL of what the physical cloud provides.
None of which refutes a physical cloud, rather it supports it.
I have already explained that emission electron QUANTITY is sensitive to temperature, which is in any case self regulated, but electron launch VELOCITY is not - hence the position of the cloud is fairly stable and mu is thus stable to that extent. Go back and read my post#76. You can read can't you?
I have already explained why the cloud is much MUCH more dense than just the ratio 2.5:1 (queing theory).
Yes you can - it's called (by convention] the "space charge" because it is a cloud of charges in a space. As for the potential (or density, its just a different word for the same thing in this context); as for location, see any text book on calculating mu. There are several methods of calculating the position or inferrring it approximately (or, more correctly, the distance out from the cathode where the electron probability density function is highest), including as I explained in previous posts the slope of the retarding current vs anode voltage, the apparent series combination of R&C in parallel with the static grid-cathode capacitance (covered in my post #76), etc.
Do you just ignore inconvenient truths?
Last edited:
Nope, cathode temperature is not regulated, and one can readily vary it (and emission) without notably varying mu. It's obvious.....
Both potential and location/distribution of the cloud would also obviously depend directly upon total charge ie quantity of electrons ie emission. As it is for an isolated cathode in no external field........... Besides, have you calculated the likely associated potential of such a cloud yet ?
The issue is what happens in grid valves in the presence of an externally applied retarding field, such as negative bias from a grid. Emission is modified, potential barrier associated with cathode work function is essentially added to by the external field. Such that emission itself can essentially be sharply controlled, pinched off by an external retarding field. Fig 14 in the Herrmann/Wagener 1951 book illustrates. I find this convincing and compelling, BTW. Seems that emission per se can be controlled by grid retarding field effect, and this seems entirely plausible and a much better fit to me.
And unfortunately, as suspected, you seem to have space charge and potential concepts a bit confused. Space charge describes carriers generally involved in conduction within valves, not some dense cloud of electrons hanging about near the cathode waiting for a good time - at least not in the presence of real external fields I think 😉
I certainly hope not, and don't see it that way. I haven't found anything contradictory yet......I think it's a matter of our own proper interpretation, and reckon the 'ancient' theoretical writings had it pretty much sorted FWIW.
But every valve textbook ever written talks about the space charge as a dense cloud... aren't you contradicting every one of them?
Space charge describes carriers generally. It's a conceptual construct of convenience when dealing with field potentials arising from distributed charge carriers in a volume. That might be a 'dense cloud', but doesn't mean so necessarily - it's like a 3D version of charge distribution on a surface, a neat way of working out how potential varies with shape.
All operating valves can be modelled as using space charge for conduction - the issue here is whether say in a grid valve in sharp cutoff there is any significant space charge near the cathode surface I think. I really don't see a contradiction, at least so far...........
I think this is the crux of my point, if you get my drift, and I'd be very interested in your opinion, Merlinb :
The issue is what happens in grid valves in the presence of an externally applied retarding field, such as negative bias from a grid. Emission is modified, potential barrier associated with cathode work function is essentially added to by the external field. Such that emission itself can essentially be sharply controlled, pinched off by an external retarding field. Fig 14 in the Herrmann/Wagener 1951 book illustrates. I find this convincing and compelling, BTW. Seems that emission per se can be controlled by grid retarding field effect, and this seems entirely plausible and a much better fit to me.
Last edited:
By way of illustration, Dow (1937) fig 4d, fig 20, fig 49 and Ch5 show potential distributions for triodes. Fig 4 is especially interesting because 4(d) shows triode beyond cut-off. Where potential gradient near the cathode follows a 'space charge free' gradient, ie suggesting space near the cathode is carrier free. But in all of this there is no sign of a potential 'hump' as one might expect if there were a lump of dense space charge hanging out near the cathode. Not under any operational condition. I see no contradiction with what I'm suggesting here, quite the opposite.
Perhaps these days the concept of space charge might mean different things to different people, but for sure Dow had the grasp of it in 1937 IMO.
Perhaps these days the concept of space charge might mean different things to different people, but for sure Dow had the grasp of it in 1937 IMO.
Don't be rediculous.
Cathode temperature IS self regulating, as 1) any increase in temperature of the heater wire increases its' electric resistance per Worthing's Equation, thereby reducing current and power dissipation, and 2) per Stefan-Boltzman law, the heat radiated by the cathode rises as the 4th power of temperature. So any increase in temperature causes a quite dramatic increase in the heat lost to the surroundings, holding down the temperature rise.
This is aspect is just high-school science stuff. In any case many textbooks on vacuum tubes give a graph or table of how cathode temperature varies with heater voltage, eg Eg C E Haller, Tube Filament and Heater Characteristics, 1944. On Page 344 Haller derives an approximate equation for cathode temperature and on page 345 there is a nice graph plotting the result that clearly illustrates the self regulating property of heater and filament wire.
Wrt location. what complete and utter nonsense.
Go back and read my schoolboy throwing rocks analogy.
Presumably you mean Fig 14 in Vol 2 on Page 28, as Fig 14 in Vol 1 is a photo of a machine for coating wire.
If so, then you have taken Fig 14 out of context. As is made clear in the following text in Vol 2 and in the intro text in Vol 1 where the same graph appears as Fig 2, what has been translated from the German as "emission density" is actually more accurately translated as "cathode current per unit cathode area" to use common terminology in English. Writing about the current drawn by the cathode from the external circuit is inherently a bit unwieldy in both languages as not all this current exits via the anode, except in diodes.
Again you are contradicting yourself - you have admitted that in the case of zero anode voltage, there is an electron cloud. Does this cloud then dissappear immediately the slightest voltage is applied to the anode?
It doesn't matter how many times you claim otherwise, the conventional term for the electron cloud is "space charge" - because electrons are basically points in space having an electric charge.
You still haven't provided alternative explanations for ALL the principle tube behavior that is explained by the presence of the electron cloud.
An if there is no electron cloud, then the well established "electron gas" theory in metals must be invalid as the thermal/brownian-like movement of electrons is the origin of the random direction and launch velocity of thermionically emitted electrons. And that has all sorts of unacceptable issue, such as Hall Effect.
In your previous post, you stated that you couldn't find a book that mentions or descibes any electron cloud. You might like to look at Rider, Inside the vacuum tube, 1945. This is a college level book. Rider has a diagram on Page 55 clearly depicting the space charge as an electron cloud some distance out from the cathode surface. Rider has drawn each electron with cute little outstretched armas and legs to depict that they are continually flying about. The text just above this diagram talks about an "accumulation of eletrons outside the cathode and near it". It then explains why this accumulation of electrons (the cloud) is conventionally given the more "academic" term space charge.
Then on Page 57, Rider has another version of the diagram emphasising the continual recycling of electrons between the cathode and the electron cloud. On this page he talks about increased cathode temperature increasing the space charge/electron cloud DENSITY.
On Page 59, there is yet another variant of the diagram depicting any value of anode current below saturation. He's got a few electrons going to the anode, a great thick cloud of them lurking between cathode and anode, and electrons going from cathode to cloud, and going from cloud to cathode.
You also, if you want to insist there is no electron cloud, need to explain the field potential diagrams shown in every textbook on tube operation, including H/W 1951. These "J-curve" diagrams always show that, when the anode current is less than the cathode's emitting capability, there is, some distance out from the cathode, a point that is more negative than the cathode. This more negative region is always shown disappearing when the anode draws off all the available emission. The region is more negative when, because, and ONLY because, electrons have accumulated there.
Last edited:
Member
Joined 2009
Paid Member
So I am trying to draw some conclusions.
Firstly, the risk of cathode damage appears to be from ion bombardment of the cathode leading to sputtering of the oxide which reduces the effectiveness of the cathode and can also contaminate the grid resulting in higher grid emission. The ions are created when electrons are accelerated towards the anode and strike neutral gas atoms. These gas atoms are a feature of an imperfect vacuum and the getter is what helps minimize the gas pressure. The getter in most receiving tubes is a flash getter, often Barium and it is highly reactive/effective at capturing most gas atoms/molecules from inside the tube. I haven't seen any physics to explain how an electron cloud / space charge regions adjacent to the cathode can significantly affect the rate of ion bombardment of the cathode.
There is the question of whether the getter is more effective at higher temperatures. From what information I can find, over the typical range of glass envelope temperatures the adsorption rate might vary by a factor of 2 which to me doesn't seem that significant [Leybold Vacuum Handbook - K. Diels, R. Jaeckel, figure 2.4.23] given that the tube spends way more time at its normal operating temperature than during warm up. If I accept this, then I haven't found facts to support the premise that ion bombardment is a significant function of the glass envelope temperature.
There is however, the question of excessive turn-on transient current flow that might occur when the tube starts conducting heavily if external voltages are such to produce excessive current until they have settled to normal operating levels (e.g. capacitors to charge, especially those connected to the grid). With high transient current flows there will be higher rates of ion generation and so higher sputtering rates at the cathode. This can be avoided by allowing applied potentials to establish normal operating conditions before significant current flow through the tube.
Firstly, the risk of cathode damage appears to be from ion bombardment of the cathode leading to sputtering of the oxide which reduces the effectiveness of the cathode and can also contaminate the grid resulting in higher grid emission. The ions are created when electrons are accelerated towards the anode and strike neutral gas atoms. These gas atoms are a feature of an imperfect vacuum and the getter is what helps minimize the gas pressure. The getter in most receiving tubes is a flash getter, often Barium and it is highly reactive/effective at capturing most gas atoms/molecules from inside the tube. I haven't seen any physics to explain how an electron cloud / space charge regions adjacent to the cathode can significantly affect the rate of ion bombardment of the cathode.
There is the question of whether the getter is more effective at higher temperatures. From what information I can find, over the typical range of glass envelope temperatures the adsorption rate might vary by a factor of 2 which to me doesn't seem that significant [Leybold Vacuum Handbook - K. Diels, R. Jaeckel, figure 2.4.23] given that the tube spends way more time at its normal operating temperature than during warm up. If I accept this, then I haven't found facts to support the premise that ion bombardment is a significant function of the glass envelope temperature.
There is however, the question of excessive turn-on transient current flow that might occur when the tube starts conducting heavily if external voltages are such to produce excessive current until they have settled to normal operating levels (e.g. capacitors to charge, especially those connected to the grid). With high transient current flows there will be higher rates of ion generation and so higher sputtering rates at the cathode. This can be avoided by allowing applied potentials to establish normal operating conditions before significant current flow through the tube.
Last edited:
DF96 answered that one in his post #24 above. I pointed out in my post #70 that RCA internal engineer training books say the same thing: The electron cloud is sufficiently dense during normal operation that ions (or atoms produced from the ions by charge equalisation) typically undergo sufficient collisions to bring their kinetic energy down. And their direction of travel will thereby change from heading straight for the cathode to shooting off in some random direction.
Transients in coupling capacitors are a non-issue. The time constant of coupling capacitors associated with their follwing grid resistor is, or should be (if not it causes several other problems) so short compared to the time the tube spends ramping up its cathode temperature that no significant grid voltage transient can occur.
Maybe due my Tarzan-English I can not understand even a single word that you are saying; do you mean that electrons of the cloud do not produce an electric field?
I did.
I hate the term “space charge” because it sounds to me Sy-Fy, I prefer instead “electron cloud”, anyway, starting from Maxwell equations (cgs units)
∇ . D = 4π ρ … (1)
∇ . B = 0 … (2)
∇ x E + (1/c) ∂B/∂t = 0 … (3)
∇ x H - (1/c) ∂D/∂t = (4π / c) J … (4)
Assumptions
1.- The cathode is an infinite plane plate on the yz plane at x=0, at a potential φ=0
2.- The anode is an infinite plane plate parallel to cathode, and placed at x=d, at a potential φ=V
3.- Both are into vacuum, i.e. D=E, B=H
4.- Conservation of charge and energy.
5.- Steady state; all physical quantities are taken to be time independent.
6.- Non-relativistic electron velocities.
7.- Electrons are initially at rest.
Combining (1) and (3) we obtain Poisson’s equation
∇²φ = - 4π ρ … (5)
By symmetry, this reduces to
d²φ(x)/dx² = - 4π ρ(x) … (6)
Taken the divergence on (4)
∂ρ/∂t + ∇ . J = 0 … (7)
Being ∂ρ/∂t=0, it needs ∇ . J = 0, hence J = Jx = constant, furthermore
J = ρ(x) v(x) … (8)
By conservation of energy
½ m v(x)² = e φ(x) ... (9)
Combining (6), (8) and (9)
d²φ(x)/dx² = - 4 π J √ (m / 2e) [φ(x)]^(- ½) … (10)
Solving
φ(x) = C x^(4/3) … (11)
For boundary conditions φ(x=0)=0, and φ(x=d)=V
φ(x) = V (x / d)^(4/3) … (12)
J = (1 / 9 π) √ (2e / m) (1 / d²) V^(3/2) … (13)
ρ(x) = (1 / 9 π) (V / d²) (d / x)^(2/3) … (14)
Then, the number of electrons per unit volume will be
n(x) = ρ(x) / e ... (15)
Result (13) is known as Child-Langmuir law or 3/2 power law.
If we add a grid, it is said that Maxwell, making some simplifying assumptions, he showed that the electric field as seen at the cathode is equivalent to an anode voltage of
Veff = Vg + (Va / μ) … (16)
Using the effective anode voltage, we can calculate the current density that will flow in the triode following Child-Langmuir law, but we also need to know the value to use for the cathode-anode distance, a good approximation is given by
deq = dcg + (dcg + dga) / μ … (17)
Combining (13), (15) and (16)
J = (1 / 9 π) √ (2e / m) {1 / [dcg + (dcg + dga) / μ]²} [Vg + (Va / μ)]^(3/2) ... (18)
It is still a 3/2 power law...
Hi popilin, no worries. I mean if there were a dense free electron cloud separate from the cathode it must possess associated potential, and have an associated electric field. But no such thing shows up in triode potential maps in cut-off, quite the opposite (Dow 1937 fig 4(d), Fig 20, Fig 49, Ch5). What does show up, correctly, is the effect of space charge during conduction, electron carriers have their own potential and field of course. And in any event, I venture any such dense free carrier cloud would be disruptive, because of likely high potential/field associated.
Space charge and 'electron cloud' are not quite the same thing. I'm beginning to think that is a crux of a general misunderstanding, not just of what I'm posting but of many excellent vintage texts. Space charge describes carriers generally. It's a conceptual construct of convenience when dealing with field potentials arising from distributed charge carriers in a volume. That might be a free electron cloud, but doesn't mean so necessarily - it's like a 3D version of charge distribution on a surface, a neat way of working out how potential varies with shape.
Very nice concise and clear maths as ever, poplilin. You've derived ρ(x), charge carrier density as a function of distance from cathode, and no surprise confirmed Child/Langmuir into the bargain. ρ(x) is essentially space charge density associated with anode potential V, and φ(x) potential at distance x from the cathode.
I think it is correct and very nice. From equation (14) charge carrier (space charge) density depends solely on cathode-anode spacing and cathode-anode potential difference.
Last edited:
F arises from correlations. Electrons leaving the cathode surface are uncorrelated, presumably because the cathode shields them from 'seeing ' each other. Electrons leaving the cathode space charge are fully exposed to each other - they feel Coulomb repulsion to every other electron in the space charge so they are highly correlated.luckythedog said:
I think you will find that it is the existence of the cloud and its location which affects mu, not the density of the cloud. Hotter cathode just means denser cloud, but in approximately the same place.luckythedog said:
That's strange, as I thought all the usual valve textbooks show the drop in potential due to the cathode space charge.
My point is that if one chooses to one can intentionally vary cathode temperature, and demonstrate a relatively insensitive dependence for mu. And that contradicts your position that mu should depend strongly on emission........
No, I mean the coating wire machine 😉 Joking. Fig14 is already for a diode, je is labelled emission density and it's clear from the narrative that emission is the intended meaning. It's also plain in the text of the first few chapters of Hermmann/Waganer 1951 that external field can modify cathode emission per se, effectively raising potential barrier at cathode surface. Then, at a certain external field, apparently emission effectively can become zero - well as near as zero to not matter. Do you disagree ? Then in grid valves under normal operation, only electrons destined to become Ik leave the cathode (well nearly all so as not to matter) I venture. That is why triode potential diagrams don't show any sign of changing local potential due to 'surplus' emission near the cathode surface I suppose.Keit said:
Effectively yes I think so, for practical purposes in real grid valves in operation but not for the 'slightest' voltage obviously. See early chapters of H/W 1951, in a diode (accelerating field) there remains a very thin charge layer (1e-8 to 1e-6 m).Keit said:
Actually, it's more likely the conventional cause of much confusion IMO. Grasping the difference is key to proper interpretation of many vintage writings.Keit said:
To my satisfaction I certainly have. Mu variation with emission - or lack of - actually contradicts 'cloud' notion, space charge smoothing happens because there's always space charge in an operating valve, behaviour retarding field current behaviour is a classical space charge density phemonemum not relevant to the point at issue, and if there is a 'virtual capacitor' involved just work out charge involved in any 'cloud' scheme and work out potential, that should change your mind, Keit !!Keit said:
Very funny 🙂 ! Yup, that is the level of literature that openly portrays 'electron clouds' for the masses. I mean, really.......... 🙄 I don't doubt that notion has somehow become 'common wisdom' and accepted, but it's not a model portrayed in serious literature AFAIK, and upon thinking about it more and more doesn't stand scrutiny IMO.Keit said:
You'd have to point out an example to examine and explain further, I don't see any contradiction in what I've seen so far, and would love to see.Keit said:
So how much charge is in this free cloud in a normally operating triode do you reckon, how far from the cathode is it, and where can I read about it in proper literature ?
Last edited:
Yes you've interpreted correctly, but cathode is conductive and grounded/referenced to other electrodes, and its own charge carriers don't contribute to external potential. Though the cathode bulk acquires an equal and opposite positive charge - so there'll always be potential between cathode surface and dissociated free thermionic electrons and it's that we're interested in. Think capacitor !
Are you getting confused by your own nonsense now? The idea that mu should depend strongly on emission is your idea, not mine.
You must be easily satisfied then. You haven't even mentioned some of the consequences of the electron cloud I cited, and you've provided a coherent alternative explanation for none of them.
1) Lots.
2) The cloud, as I said before, has a probability density function, with a peak density at the effective distance for virtual cathode calculations. It's not a thin sheet, it has an exponential decay out as far as the tube dimensions allow. The point of max density is typically in the range 0.5 to 0.8 of the distance to the grid when the grid and anode are at zero volts and about the same under normal applied voltage conditions.
3) You can read about it in any good book on vacuum tubes, including Herrmann/Wagener 1951 that you like so much, but clearly cannot, or do not want to, understand.
J-curve diagrams, which are a plot of electrostatic field strength vs distance form cathode and have a characteristic J-shape, are common in tube theory books. You'll find a particularly clear one for diodes in Fig 4, page 162 by L Scholz, Calculation of fields and currents, in Electron Tube Design, RCA 1962. You will notice that for space charge limitted operation (ie with anode moderately positive) with the cathode indentified as at zero volts, the electron cloud/space charge distorts the field so a point some distance out from the cathode is more negative than the cathode. A point in space can only be more negative than both boundary conditions (ie cathode and anode) if there is a concentration of electrons there.
This is not a true picture.
You have possibly misinterpreted or placed undue emphasis on something that the more detailed textbooks point out, known as the Schottky effect, aka field emission.
Electron emission occurs when electrons in the electron gas within the metal are given sufficient kinetic energy to overcome the work function and leave the metal. There's actually two ways this increase in kinetic energy can occur: a) by raising the cathode temperature (thermionic emission), and b) by imposing a strong electric field that penetratesd the cathode surface (field emission). It follows that the increase in electron kinetic energy caused by raising the temperature can be opposed by a strong retarding field. However, in the normal operation of typical vacuum tubes, field emission is very small compared to thermionic emission. If it were not so we wouldn't need heaters!
And obviously, as I pointed out before, if the anode (or grid) is moderately negative, it pushes the electron cloud back towards the cathode. If the anode is sufficiently negative, it can push the electron cloud right back into the cathode. Nothing remarkable about that. Like charges repel - you learnt that in high school. In no way does it mean there is no electron cloud under normal tube operation.
It is well established that under normal operation, many more electrons leave the cathode than get captured by the anode. The surplus sooner or later return to the cathode. A grid sufficiently negative to cut off all flow to the anode is NOT sufficiently negative to drive the electron cloud back into the cathode - a fact easily demostrated by measuring the apparent grid/cathode capacitance, as the electron cloud forms one plate of a capacitor (grid the other). Making the grid still more negative byond cutoff reduces the capacitance still futher. The continual recycling of emitted electrons back to the cathode carries on. That's not in any doubt whatsoever.
Last edited:
I found this chapter particularly lucid:
http://www.tubebbs.com/tubedata/other/docs/PoET/PoET_05.pdf
Gewartowski and Watson, Principles of Electron Tubes, 1965
Last edited:
Luckythedog needs to look at Fig 5.2.5., which shows an example of emission 0.5 A/cm2 and anode current of 0.071 A/cm2, the areas in both cases referring to the cathode. The space charge effective distance is 0.015 mm from the cathode, and the grid 0.042 mm from the cathode. It must be a quite old fashioned low mu tube.
Could I ask that folk citing references give the title & author of the work as well as the url? Some of these books take a long time to download, and when I've done it, it usually turns out I already have it.
Last edited:
---Quote (Originally by luckythedog)---
Then in grid valves under normal operation, only electrons destined to become Ik leave the cathode (well nearly all so as not to matter) I venture. That is why triode potential diagrams don't show any sign of changing local potential due to 'surplus' emission near the cathode surface I suppose.
---End Quote---
---Quote (Originally by Merlinb)---
I've been pondering your assertion that a cloud of electrons between the cathode and grid ought to result in a powerful potential minimum. I'm not sure that it the case, because a cloud outside the cathode's surface is surely less dense than the electron density inside the cathode, so under normal positive anode voltage conditions the electric field strength in the region of the cloud would still be higher (positive) than at the cathode surace. The grid is the only negative-voltage thing in the valve, so it causes a potential minimum close to its plane as we see in the usual textbook diagrams. No?
The electron gas in a metal is more dense that the electron cloud, but that has no relavence.
The grid no not the only thing that's negative. The elctropn cloud exists because electrons heave the cathode by virtue of their inertia, imposed by teh cathode temperature. Their inertain cariies them into the cloud until the accumulated charge turns them around and accelerates them back to the cathode, assisted by the grid. The cloud can not only be more negative than the cathode, it can be more negative than the grid.
And I have no idea why the quote came up in a funny font, or what to do about it.
Then in grid valves under normal operation, only electrons destined to become Ik leave the cathode (well nearly all so as not to matter) I venture. That is why triode potential diagrams don't show any sign of changing local potential due to 'surplus' emission near the cathode surface I suppose.
---End Quote---
---Quote (Originally by Merlinb)---
I've been pondering your assertion that a cloud of electrons between the cathode and grid ought to result in a powerful potential minimum. I'm not sure that it the case, because a cloud outside the cathode's surface is surely less dense than the electron density inside the cathode, so under normal positive anode voltage conditions the electric field strength in the region of the cloud would still be higher (positive) than at the cathode surace. The grid is the only negative-voltage thing in the valve, so it causes a potential minimum close to its plane as we see in the usual textbook diagrams. No?
The electron gas in a metal is more dense that the electron cloud, but that has no relavence.
The grid no not the only thing that's negative. The elctropn cloud exists because electrons heave the cathode by virtue of their inertia, imposed by teh cathode temperature. Their inertain cariies them into the cloud until the accumulated charge turns them around and accelerates them back to the cathode, assisted by the grid. The cloud can not only be more negative than the cathode, it can be more negative than the grid.
And I have no idea why the quote came up in a funny font, or what to do about it.
Member
Joined 2009
Paid Member
DF96 knows his physics (from what I remember) and wouldn't make a claim he wasn't sure about. I went back to post #24 and he says (the highlights are mine):
"... It won't lose much energy/momentum in each collision as electrons are so light, but if there are enough collisions it could work. I don't know, but the books seem to agree ..."
I don't think this answers the point yet.
Never mind what an RCA engineer says in a book - show my the physics!
- Status
- Not open for further replies.