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Aesthetics of these wacky early scifi ray guns could have been based on a real device
(lea.hamradio.si)
This is an obscure type of antenna, called sometimes cigar antenna, that works pretty much like Yagi - most of you will know it as (non-satellite) TV antenna - but instead of rods it has disks. It was used in Lunokhod 1 and 2, Soviet moon rovers launched in 1970 and 1973 respectively
Were there any specific benefits to the discs other than that it looked cool?
Yeah - electrically, antenna has broader bandwidth, and mechanically, it's harder to ding it. Broader bandwidth also means that tolerances aren't that critical. Downside is increased weight and wind loading
This specific antenna was used for video downlink, which requires comparatively large bandwidth
Additionally, for frequencies that were practical at that time you can't use simple Yagi, because this would mean choppy signal. Instead you need circular polarization - and that requires either crossed pairs of rods, but this is narrowband, or rings, but this is flimsy and still narrowband but not as badly, or disks. You could ditch these elements entirely and use long helix only (bottom part but extended) but helix has quickly diminishing returns - this design takes good properties of both of these
So the principle is: If the design of your antenna is such that when the signal emitted by one disc reaches the next disc some nanoseconds later, the phases line up (the next disc is adding power because it's exactly in sync with the signal coming off the first disc), each disc will progressively reinforce the signal so the emitted signal adds up to be way more powerful in the exact direction that the antenna is pointed. And likewise for receiving from that specific direction.
Yagi antennas use the same principle, and another poster gave a much more technical explanation of why discs instead of a Yagi or helix, but in case you were asking the more basic question, that's why.