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A shame these are so expensive...
But this is a cheaper way...
(I might have a go with one of these)
It's a pity that there is no real information on the HP clocks on that site (or at least none that I could find). The manuals for some of them are availabe from Keysight though.
It is my understanding that the caesium beam tube used in the early frequency standards (and maybe later ones) has a finite (and quite short -- about 1 year?) life whether it is used or not. That has rather put me off looking for one. The rubidium unit, which works on a different principle and is not a primary standard, seems a more practical thing to try to run (not that I have one).
I was once told that HP released 3 very significant products almost at the same time. One was the 5061 caesium beam standard (it was one rack unit, 4U high I think, and could be carried by one person, at a time with atomic clocks filled a lab). Another was some kind of interferometer. And the third? A programmble calculator the size of a typewriter, the HP9100A of course.
I think the rubidium tube acts an extremely sharp resonant filter. The electronics generates a signal at that frequency. To get it on-freqeuncy, it is applied to the 'filter' with a slight wobble. If it is on-freqeuncy (at the maximum of the response curve) then there is a component of the output at twice the 'wobble' frequency but nothing at the 'wobble' frequency itself. If it is off-resonance there will be.
The HP59309 is a very practical clock to own (and not hard to find). It normally runs of an internal crystal oscillator, it can be set to run of an external 1MHz, 5MHz or 10MHz signal (which of course determines the timekeeping), so you can run it off one of the atomic standards. It has an HPIB interface (in fact it's one of the first series of HPIB units) and was used with things like the HP9830.
I would love to find out more about the battery backup unit. I have never seen one (other than in that photo). It was designed to keep the 59309 running when the mains failed. I had assumed it was just a box of D cells, but perhaps not.