This is much better, so I would say that we agree.
The application of B+ is a necessary condition, but not enough, for the creation of the total electric field in the vacuum.
This is because the problem is often oversimplified, even into the billiard balls model, as electrons and ions are charged particles into an electric field, as I said before kinetic energy is not conserved, kinetic momentum, p=mv, is not conserved, the conserved momentum is
p = p(mechanic) + p(electric) … (1)
No, it cannot, because kinetic energy is not conserved.
Disclaimer: Results recycled from another thread, now with the correct numbers (I hope)
We must take into account the de Broglie wavelength
λ = h / p … (2)
In our daily macroscopic world, most quantum phenomena are not observed because the de Broglie wavelength of common objects is negligible compared with its dimentions.
Let’s consider now a particle, its momentum is given by
E² = p² c² + mo² c⁴ … (3)
Then
Ek = √ [mo² c⁴ + (h² c²) / λ²)] – mo c² … (4)
If the particle collides with the cathode, a reasonable criterion for a classical collision is that its de Broglie wavelength will be negligible compared with atomic radii of the cathode material.
For an electron-calcium atom collision, the limit will be
λ(calcium) ≈ 1.94 x 10⁻¹¹ m
Then
Ek(calcium) ≈ 3.9 KeV
For an electron-nickel atom collision, the limit will be
λ(nickel) ≈ 1.49 x 10⁻¹¹ m
Then
Ek(nickel) ≈ 6.7 KeV
For proton-atom collisions, the lower energy limit is almost zero, so no problem here, unfortunately, for heavier ions things are a bit trickier because nuclei are screened by electrons.
In the limit for high energies, a classical treatment works reasonably well, but for low energies the correct description would require taking into account quantum effects.
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You have consistently misunderstood my posts, Keit. You introduced the term 'electron cloud' to the thread. But its meaning is vague and ambiguous, and shifts context from post to post. It's all things to all men, and for sure all implied meanings used on this thread can't be correct or physically real. Throughout the thread it's clear that I consider the issue of ion bombardment of the cathode and protection thereof an enquiry, FWIW.
Hey! I am the pioneer, introducing the term electron cloud about four years ago on another thread; and it is as vague and ambiguous as space charge. 😀
Exactly right.
You second sentence can confuse. I take it you meant it to read per what I added in brackets. If so, you are again correct.
I entirely agree. Thta's why I try to aviod algebra and calculus in this forum. It turns people off. However, the odd equation that needs only first year high school math skills is ok. For many people it may be 10, 20, 30, 40, years since they did any algebra, but if they are serious about electronics as a hobby they'll retain enough math to cope with simple algebra ok.
Most people can cope with graphs ok.
Sometimes the only satisfactory way to explain things is with math. You can help the reader considerably if:-
1) You explain what each and every symbol means. We all know what R, V, and I means, but apart from that, take nothing for granted.
2) You give the the name of the equation or law (as in Child's Law, Stefan-Boltzmann Law, etc), if it exists, so they can look it up. Then they know it's valid and not just something you dreamed up. So, even if their understanding is a bit shakey, they can have a level of trust in what you are saying.
3) You explain in words the practical significance of each equation.
-and if you are American-
4) do try and use SI units, not US customary units.
I find doing these 4 things not only helps the reader (I write a lot of engineering & R&D reports for executives - a type of person in some ways more technically dumb and mathematically unskilled than many dyi-ers), they significantly help me avoid errors in reasoning as well.
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Yes. Furthermore, barring statistical variance, peak electron and ion energies are only about 300-500 eV typically, it's all pretty low energy stuff.
In a valve, although ions are massive relative to electrons, energy acquired through electrostatic acceleration is the same for ions and electrons, (having the same charge)..........this realisation caused me to revise an estimate of number of required collisions/interactions required to retard an ion significantly. Perhaps only a few 10s required even.........then I wonder whether space charge density due to Ia alone might be sufficient to avoid ion bombardment of the cathode ? Sort of self-regulating. It bugs me that the matter seems to be a non-issue for serious literature......
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The electron interacts with the electron shells around the ion through mutual electrostatic repulsion. The ion and electron may approach each other from a large distance. They will approach closely, interacting through this repulsive force and then move apart again. This interaction can be described using classical physics as an elastic collision.
Interestingly, the treatment of a collision between two billiard balls is the same. And on a microscopic scale it is the repulsive force between the electron shells around the atoms at the surface of the balls that dominates their interaction.
Normally it is at the limit for high energies that a classical treatment falters and you need to account for relativistic effects. Classical treatments are more useful at low energies.
How did you reason this? The massive difference in their mass is actually why energy transfer from the ion to the electron in such a collision is tiny unless the collision is inelastic - implying excitation of the ion or further ionization (e.g to double + ions). Most of the collisions will be elastic and little energy can be lost. I'm quite curious how you reasoned that only a few 10's are required ?
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For repulsive collisions, there is rarely a true 'collision' AFAIK, rather an electrostatic encounter. Excitation is the main non-classical outcome - all IIRC but its some time ago so caveats apply. But in any event, for the purposes of working out retardation via collisions I agree a classical approach seems a far simpler place to start, unless there's reason to think grossly out. Needs a smaller envelope 😉
Utter nonsense. When I write "electron cloud" I mean exactly that. A cloud of electrons. A cloud of electrons that is much more dense than electrons streaming to the anode.
"Space charge" is a term that does mean somewhat different things depending on who is talking - even in textbooks. That is not my doing. However, others have pointed out that any group of electrons in a space will have a group effect charge or 'space charge' and thus distort the main electric field established by the anode to some degree.
Generally though, when textbooks talk about a "space charge", they are talking about the electron cloud between the cathode and grid, or the electron cloud between the accelerator grid and control grid in a space charge enhanced vacuum tube (you probably have not heard of them - they were once used in applications employing very low anode voltages), the space charge just beyond the screen in beam tetrodes, and in some converter tubes.
The space charge effects of electrons accelerating to the anode is in most applications mimimal due to their low density - that is why most authors do not refer to them as a space charge. The density of the electron cloud between the cathode and the grid is, by comparison, very dense under normal oiperation, and thus the space charge effects of this cloud are very significant.
I note that you still have not identified any error in the words or graphs I presented in my post #159 - which show how the electron cloud affects the electric field as shown in typical J-curves.
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As I said before, mathematics is THE language of physics, if we want to discuss seriously about physics, “math” is unavoidable, unless we talk about philosophy.
The reason for 190 posts without more convincing conclusions is just that, too much philosophy and so less physics. IMHO
BTW, my doodles are not intended as physics, but I am just a TV repairman, and most of you are electronic engineers.
This is perfectly valid and used daily, e.g. Rutherford scattering, provided that the electron behaves like particle, i.e. at high energies.
At low energies, coincidentally into the range that we use in our beloved valves, the electron behaves like wave, as proved experimentally Davisson and Germer, (by accident) at about 54 eV.
My original assumption is only a rough estimate, because it must be compared the de Broglie wavelength with interatomic distances, that is not easy, then atomic radii or diameters are reasonable approximations.
For nickel, the distance between planes in a crystal is about
D ≈ 3.52 x 10⁻¹⁰ m
Radius of nickel atom
r ≈ 3.52 x 10⁻¹⁰ m
Then, the distance between atoms
d = D – 2 r ≈ 0.54 x 10⁻¹⁰ m ≈ λ(nickel)
Then
Ek(nickel) ≈ 516 eV
Relativity is a classical theory. AFAIK
Classical treatment means NO quantum mechanics.
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Erratum:
Radius of nickel atom
Wrong copy-paste, sorry, other results are right.
My editor for equations does not work here, and I must make a previous word document with strange characters and all kind of fonts, it is a mess.
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Last estimate, Ek(nickel) ≈ 516 eV, looks reasonable, even for ion-atom collisions; because most cathode sputtering theories based on the billiard balls model, fail at low energies.
Supposing elastic collisions, heavier ions should make more sputtering, but a result provided for a measurement equipment manufacturer, for a silicon target
This shows how capricious can be low energy collisions.
Radius of nickel atom
r ≈ 1.49 x 10⁻¹⁰ m
Wrong copy-paste, sorry, other results are right.
My editor for equations does not work here, and I must make a previous word document with strange characters and all kind of fonts, it is a mess.
.............................................................................................................
Last estimate, Ek(nickel) ≈ 516 eV, looks reasonable, even for ion-atom collisions; because most cathode sputtering theories based on the billiard balls model, fail at low energies.
Supposing elastic collisions, heavier ions should make more sputtering, but a result provided for a measurement equipment manufacturer, for a silicon target
This shows how capricious can be low energy collisions.
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Yup, I guessed that. And therein lies the problem, Keit. Because it's ambiguous when aspects such as quantity, distribution, location, density, potential, velocity, shape etc etc matter and go undefined. And therefore can be all things to all men unfortunately. Same can be true for space charge out of context. Two people read Romeo and Juliet, with a different understanding of love. One thinks it's a murder story, what can you say..........? 😉
If you mean 'J-FIELDS FOR DUMMIES' I thought the title said it all, since you ask. It's far better to point to established, peer reviewed technical papers for concepts, descriptions, maths and narratives IMO. As I think you said yourself on this thread......Keit said:
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Overcoming a grid induced potential well and overcoming a potential barrier at the cathode can be two separate but related hurdles to Ia I think. Especially since potential barrier at the cathode surface might also be influenced by grid induced field. I really don't know what happens in practice, but suspect that density and distribution of carriers in the vacuum between those two physical locations might depend on potential equilibrium plus two rate equations (one for each potential barrier). The devil is in the detail then, and would be interesting to know since what happens strikes at the crux of the density of charge carriers available as the valve changes from cut-off to carrier limited 'normal' operation. I think.
Well, I used realistic values for space charge, electrode distances, etc. I marked each axis numerically. There's no ambiguity.
More importantly, as Bigun pointed out, for a planar diode, and a planar triode with a close pitched grid, the curve can only be straight lines if there is no electron cloud. Only the presence of an electron cloud can make the J-curve curved in the negative direction. Yet all those peer reviewed papers, and those textbooks you claim to love so much, show the lines just so curved.
There's absolutely NO ambiguity whether or not the J-curve graphs, mine or the books', show straight lines or shown them curved downwards.
The graphs I constructed start with just an electron cloud and the field set up by the anode, and end up shaped just like the J-curves in the textbooks and papers.
Sure. But those papers support the concept of an electron cloud. They don't support your nonsense.
You've claimed that books eg H/W, Dow, support you, but it has been shown that you misread or misunderstood what they said every time.
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The whole topic of ion generation, cathode bombardment and cathode protection afforded by electron collisions is conspicuously absent from a fair raft of serious technical papers which are otherwise definitive - at least as known to this thread. That is very very odd I think. I suspect if we teased at the problem long enough we'd uncover why in practice it apparently is a non-issue and absent from serious technical references, at least for typical domestic valves. It must be staring us in the face. I also note what scant advice there is in serious literature to sequence B+ at warm-up arises because of risk of cathode stripping in certain applications from causes not related to ion bombardment - rather from electrostatic force induced detachment of oxide coating from core cathode metal.
And it was pointed out that that requires field strengths much higher than exist in domestic tubes used in audio applications.
Well, you'd be worried if they didn't, after all valves without charge carriers don't conduct that well 😉 But thanks, I might as well use the proper peer reviewed technical literature then........but in fairness I also think you're making good progress to understanding properly.
Quite possibly, after all it doesn't seem to happen in practice. How do you know grid/anode field strengths that arise in practice in domestic valves, BTW, depending much on flatness of cathode surface according to Harmmann/Waganer ?
Excellent! But do take the care to read carefully and understand them this time!
You might find my graphs, sice I set it out step-by-step, helpfull in grasping what what the technical literature says.
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