# Model electron movement in an electric field (Magic Eye tube)

• interestedperson
In summary, the author is modeling the visible output of a magic eye tube, which is composed of two concentric circles of anode (screen) material, with a small circular cathode in the center. Around the cathode is a grid to dampen electron flow, and if possible, the author wants to ignore the extra anode and grid for signal amplification. If the voltage on the two small circles next to the cathode is controlled, the screen will emit green light. The author is also interested in modeling the velocity of electrons moving between the charged plates, and is willing to compute the end result if it is too difficult for math to do accurately.
interestedperson
Hello there,

I'd like to model a simplified version of a "Magic Eye" tube (e.g. without the amplification triode, and for a start, 2 dimensions only), or the visible display behavior.

What I'm talking about:
https://en.wikipedia.org/wiki/Magic_eye_tube#Operation

Here is a nicer depiction of how it's actually constructed, and also an animation of what it looks like, the EM34 tube (which is my target). As can be seen, it's not exactly straight lines on that screen anode, next to other welcome imperfections.

Source: (Text in German only, sorry)
http://www.netzmafia.de/skripten/hardware/Roehren/mag_eye.html

Using the German page's images for labels:
So, if viewed as a 2d case from above for now: Basically, there's a small circular cathode (K) in the very center, at 0 Volt. Around it is a grid (g) to somewhat dampen the electron flow (I've seen it electrically tied to the cathode in a particular radio receiver circuit). If we can, I'd like to ignore the extra anode (A) and its grid (G) which are for signal amplification, of the signal that goes to those 2 rods (St), in our 2d case even smaller circles spaced somewhat apart from the cathode. If we can, let's pretend I can control the voltage on those two (St) directly.
Then there is the screen (L) which acts as anode for the display function of the device - usually at 250 Volt.
This screen has a layer that will visibly emit green light if hit by sufficient number of electrons per time unit.
In the 2d case, it is the largest diameter ring, concentrically placed around the cathode.
In the function description it says, if both rods (St) are at the same voltage as the screen anode, they will not cause an "electron shadow", and the whole screen "ring" will be illuminated.
The lower the voltage gets on the rods, the more of a "shadow" (2 of them) is said to be produced.
Resulting in the display behavior as seen in the gif animation on the second linked site.

I Have searched a bit about calculating acceleration of electrons and found one on this site:
https://www.physicsforums.com/threads/velocity-of-electron-moving-between-charged-plates.360134/

This is a straight forward field between two plates. I guess my scenario is a bit more complicated.
I only had high school physics, and I don't even have an idea of how to model this, and what to compute. Well I imagine lots of vectors in different directions, but that's about it.

My goal, for now, is to make a simulation with "electrons moving" at human-observable speeds, and play around with voltages to see changes. (I'm a software dev of the rather less mathematical sort, I'd like to get somewhat more mathsy if it's not too late, though ;))
So I'd be fine with some stepped, discrete interval calculation of what happens.

I guess computing the end result (which parts of the screen "ring" are hit how much) could be computed with less effort with some fancy math, which is probably above my head or I have forgotten in all those years.
(By "compute end result" I mean, the display as a function of voltage(s) on the rods as parameters).

Since it's only about the humanly observable effects, this probably does not need to be extremely accurate - if corners can be cut to simplify things, let's do that.
What too much corner cutting would look like: Just drawing sections of a 2d ring with a fixed angle, and all at the same intensity. Which works without any physical calculations :)
If this turns out not to be way over my head, extending this to "3d enough" to get the irregularities, and different intensities, the glowing, at least somewhat convincingly, that would be a later goal.

Those irregularitities / glow on an already weakened tube (the different reaction curves of the left/right angles to the input signal is deliberate - how this is done exactly in the physical setup, I do not know)

Well, how could one go about this?

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I suggest looking at electron optics. Fro memory, Terman "Radio Engineers Handbook" gives some examples of electron paths in triodes etc.
The magic eye seems to be have a simple grid having two rods which deflects electron paths away from itself, so I presume they follow a hyperbolic path into the illuminated region. I think this could be modeled quite easily. The differing sensitivity of the rods may be produced by their distance from the cathode, in other words, each one has a different amplification factor.

For modeling the 'magic-eye' output the description of the triode in the (English) article provides advice: output resembles a Lissajou pattern. Presuming access to an oscilloscope and reference signal generator, you can model the 2D output pattern on the o'scope.

## 1. How does an electric field affect electron movement in a Magic Eye tube?

When an electric field is applied to a Magic Eye tube, it causes the electrons within the tube to move in a specific direction. This movement is due to the force exerted on the electrons by the electric field.

## 2. What is the purpose of modeling electron movement in a Magic Eye tube?

Modeling electron movement in a Magic Eye tube allows scientists to better understand how the tube functions and how different factors, such as electric fields, can affect its operation. This knowledge can then be used to improve the design and performance of the tube.

## 3. How is the movement of electrons in a Magic Eye tube visualized?

The movement of electrons in a Magic Eye tube is visualized through the use of a phosphor screen. When the electrons hit the screen, they cause the screen to emit light, creating the familiar glowing green image seen in the tube.

## 4. What factors can impact electron movement in a Magic Eye tube?

Aside from electric fields, other factors that can impact electron movement in a Magic Eye tube include the voltage applied to the tube, the type of gas within the tube, and the distance between the electrodes within the tube.

## 5. How does the model of electron movement in a Magic Eye tube relate to other scientific principles?

The model of electron movement in a Magic Eye tube is based on fundamental principles of electromagnetism and quantum mechanics. Understanding how these principles apply to the movement of electrons in the tube can also help us understand other phenomena in the natural world, such as the behavior of particles in a magnetic field.

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