How does one calculate the diameter of a 'space fountain'?

I need to know how wide the diameter of a space fountain's* particle stream is in relation to the mass it's trying to support. It would have to lift its mass at least 40000 kilometers. The vacuum tubes wouldn't necessarily be part of that mass. The planet I'm using it for spins very slowly around its axis so rotational energy couldn't be used/doesn't matter (well at least not for the solution I want).

The principal reason that I'm asking this question is to find out how heavy the space fountain's vacuum tubes would be.

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How does one calculate the diameter of a 'space fountain'?

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