J.J. Thomson discovered the electron because electrons are negatively charged after observing the CRT reaction to a magnetic field/electromagnetic field. If that is the case, wouldn't the charged electrons in the ray repel each other? Note that I am referring to simple experiments where there is only a cathode in one side and an anode on the other side of a tube. No electromagnetic coils are used on these experiments, yet the ray remains straight or at least whole and relatively uniform across the beam. Is there a relativistic or quantum mechanic explanation for how the electrons stay aligned? Is this due to a property of the electromagnetism and how waves behave?
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$\begingroup$ Kind of guessing here but my hunch is that the density of the electrons in a CRT beam probably isn't high enough for electron-electron repulsion to be a big problem. Think that there may be much more of a problem with electron synchrotrons where probably much higher densities of electrons are used in order to maximize the emitted x-ray intensities. I think that those facilities often employ physicists to specifically look into the problem of focussing and controlling high densities of electrons whirling around a synchrotron ring. $\endgroup$– user93237Commented Jun 9, 2017 at 0:24
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1$\begingroup$ @SamuelWeir - indeed, you are correct. A more common (well, for scientists) place to 'worry' would be a transmission electron microscope, with less than a microAmp of current at 200keV. You run the real numbers, and you get 1 to a few electrons between the electron source and the camera at any point in time. So single-electron-at-a-time diffraction is a real and normal thing... $\endgroup$– Jon CusterCommented Jun 9, 2017 at 0:29
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Electrons in a beam DO repel each other. In order to focus in a cathode ray tube, tricks are employed (axial magnetic field) that cause convergence at the screen surface. The beam originates at a point, diverges, then reconverges.
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$\begingroup$ Thanks @Whit3rd , I do however refer not to most modern CRT in tvs, I am referring to simple experiments where there is only a cathode in one side and an anode on the other side of a tube, yet the ray remains straight. $\endgroup$ Commented Jun 8, 2017 at 22:06
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2$\begingroup$ @ErnestoMelo - The trick is that there are many fewer electrons in flight then your intuition might be telling you. Current densities where space charge effects are noticeable are far in excess of what JJ Thompson, or even a CRT worry about. $\endgroup$ Commented Jun 8, 2017 at 22:45
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$\begingroup$ The 'straight ray' always diverges. When long travel in a narrow space is intended (like, in a linear accelerator or cyclotron/synchrotron) other lens-like systems are used. Quadrupole and sextupole focusing is the only reason the big accelerators (CERN, Fermilab, SLAC) have a tight beam to play with. $\endgroup$– Whit3rdCommented Jun 10, 2017 at 0:22