I think that the reason I didn't see a clear beam was because I didn't put the detector together properly. The detector consists of a hot tungsten wire and a collector plate. The plate has a hole in it to let the beam of potassium atoms through. They should then hit the hot wire where they lose their outer electron. The remaining potassium ions are then attracted to the plate, which is at a potential of -9V compared to the wire.
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The problem is that when I took another look at the detector the wire wasn't directly beneath the hole in the plate, but had slipped to the side. This means that atoms from the beam could not be detected, only those which had somehow reflected off a wall somewhere.
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You have to click on the image to see it properly! I don't know why it is all black, but it looks interesting anyway. I made the picture with inkscape, and exported it as a .png
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