If the center of a mine field is covered by an ion storm you cannot detect it, or sweep it, except through colonial fighter sweep.
I would highly suggest reading the article on donovans on minefields, if you haven't already.
Other articles are;
Minehit Probability
Torp conversion
As a rule of thumb I only travel through as many mines as I can until I reach a 10% chance of hitting a mine. So when cloaked, it's 20ly's through a single minefield, 10 ly's through a double field, and 5 ly's through a triple field.
When sweeping, I get my heaviest high tech and high beam count ships together, load them up with supplies, and plow them into the minefield to clear the way. Yes, they'll take a minehit or two, but you can only do so much sweeping from the outside edges. So an uncloaked ship, like a T-rex/Nova can carry enough supplies and at least one battle salvo (8 - 10x's number of tubes) torps, and still carry enough supplies to repair one minehit, 2 in the case of a nova.
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