# Why don't most electrons hit the anode in a cathode ray tube or electron gun?

In a cathode ray tube or electron gun, electrons liberated from the cathode by thermal emission accelerate towards a ring-shaped anode, from the potential difference between cathode and anode.

If an electron is slightly off-centre, so nearer to one edge of the anode ring than the other, I'd expect the near side of the anode ring to attract it more than the far side, pulling it further off centre (because electrostatic force follows the inverse square law)

So I'd then expect most electrons to end up hitting the anode ring, rather than going through.

Why do electrons go through the hole instead of hitting the ring? Is it z-pinch keeping the beam together, or does a complicated arrangement of anodes at different voltages lead to an inward radial force, and if so how? I'd expect any anode to attract electrons towards itself, moving the beam further from the centre for any anode that's on the outside of the beam.

• Even more interesting is how the electrons are formed into a narrow beam. Don't they like to fly apart because they all repel each other? Or does an invisible quantum mechanical demon cause them to come out in single file? Anyhow, who uses CRT's any more? There is much better display technology in this century. Jun 8, 2022 at 22:37

Electrons have mass, and therefore momentum. As long as they are fast enough, they are not likely to change their direction much. Also, when leaving the cathode, the anode is far enough away, so they are pulled towards the center of the ring anode (because the anode is symmetrical) and are barely accelerated towards the ring itself.

Most important: the electrical field in the plane of the anode ring is almost zero, so there is barely any force on the electrons towards the ring. That's basically the same principle like inside of a Faraday cage.

Furthermore, the inverse-square law applies to point sources of an electrical field, the field in a different geometry can differ significantly - like between charged plates, around a charged rod, between two point sources or inside of a charged ring.

After all, nobody says that none of the electrons hit the anode. Some certainly will and if you measure the current required to sustain the high voltage, you will see some leakage current, which comes from those electrons hitting the anode.

• "field in the plane of the cathode ring" should that be "anode ring"? Jun 2, 2022 at 20:08
• @user20637 yes, indeed Jul 14, 2022 at 16:12

An alternative answer: they hit the anode sooner or later. How much does it matter, where or when?

From an energy standpoint, everything is proceeding as normal. Electrons do gain energy by passing through an electric field gradient, but that energy is not sourced from the neighboring electrode(s)! (Note that the focus ring is first seen by the beam, but very little current indeed is drawn by it. As mentioned in the other answer, basically, electron optics is a thing; the beam doesn't spread out like an electric field does, sure it's influenced by it, but not rigidly following lines of charge or anything.)

The piper only gets paid (so to speak) when that energy is released -- when hitting the anode. Only then is charge delivered across a voltage drop, through a return path to the supply, and the energy being deposited in the screen and phosphors (giving heat and light), as is the observation.

anode leakage is low by design.

CRT's have a plates to accelerate towards screen then a focus zone to tightly focus the beam to a pixel size then high voltage deflection beam from the flyback sawtooth generator to sweep both horizontally fast up to 250 Mpix/s in high res CRT's then slow sweep for vertical or using XY vector text writing with some old scopes between raster scans. Then blanked on Z axis during retrace.

The negative plate polarity repels the fast moving electrons on the focus ring towards a laser like dot so that almost 4k resolutions could be seen on Ilya and Hitachi CRT's with 4:3 aspect ratio. My old PC did 2k horizontal pixels by 2680 vert or more than >5 Megpixels. At 50 Hz NI that was a 250 MHz pixel clock.

A ring's field inside is zero. For symmetry reasons, the field could only be radial, and if it were, charges of one kind would accumulate in the middle. That doesn't happen. So acceleration has no radial component when passing the plane inside of the ring, while passing outside gives the same attraction the ring charge would provide if the whole charge were placed at the center point. When the electron is before the ring, it can be considered mostly inside with regard to the acting forces and thus will have comparatively little incentive to change direction.

• What is wrong with protons being able to accumulate in the middle? Why can we assume that doesn't happen? And that is a 2D picture; in 3D the protons would be pushed away in the 3rd axis. Jun 2, 2022 at 8:45
• There's something bugging me about this. The interior of a hollow sphere has a zero field, assuming the charge is evenly distributed over its surface, so it's easily shown that for any infinitesimal solid angle φ² the unit charge is φ²r²C while the force per unit charge is F/Cr² (in the direction of r), and the radial terms cancel out. But here we're talking about an open ring, not a sphere, so that the net force is an integral over 1/r, where r is a function of angle. So I figure that would make the interior field approximately zero, but not exactly zero. Or have I missed something? Jun 3, 2022 at 0:35