Accelerating electrons

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One of the main reasons for the development of quantum mechanics was the fact that classical electrodynamics predicted that electrons orbiting around atoms would quickly radiate away all of their energy and spiral into the atom.

Well, it occurs to me that this should be a very easy experiment to test: Take an electron in a vacuum, eg an electron from an evacuated cathode ray tube, apply a magnetic field parallel to the tube so that the electrons start spiraling, and measure the resulting radiation. It should be an easy test of Larmor's formula.

Here's where things get weird. I can't find a single paper describing an experiment like this, even though cathode ray tubes have been around for at least a century, so presumably this should have been done a long time ago.

When I start digging into how the radiation of an accelerated charge is calculated at an arbitrary point, physicists start saying schizo shit like "oh this can't really be calculated except for very particular cases"... the fuck? Has this radiation ever actually been observed? Can someone point me to an experiment that measures the charge from an accelerating electron? Not a formula, an experiment with measurements.

Google is giving me extremely schizo results that don't seem to make any fucking sense, and my suspicion is aroused. It's a simple question. Do accelerating electrons radiate? Let's get to the bottom of this.