Selecting right fuse for the short pulse application
Basically, fuses blow because they get locally hot.  Ditto anything else subjected to pulsed power.
You can kind of infer the time constants involved by looking at a current (or power, for some devices) vs. time plot, like the &quot;Average Time Current Curve&quot; in that datasheet.  The lines aren't very curved for the first one second or so, from which I infer that the fuse's &quot;main&quot; time constant is over 1s (I'm guessing 2s, by where the line sorta-kinda curves).  After that, given that the line is curved up to 10000 seconds, I'm guessing that there's a bazzilion different time constants involved, making life difficult.
If you know the current vs. time as the capacitors charge, then find $$\int_0^{\mathrm{100ms}} i^2 dt$$  This is the size of the current-squared pulse that the fuse undergoes.  Divide it by \$100\mathrm{ms}\$ for the behavior of the fuse after \$100\mathrm{ms}\$, and divide it by \$2\mathrm{s}\$ for your &quot;one cycle every \$2\mathrm{s}\$&quot; case.  (i.e., find \$\frac{1}{2\mathrm{s}}\int_0^{\mathrm{100ms}} i^2 dt\$)
For the case where the relay fails, find $$\frac{1}{T}\int_0^T i^2 dt$$ for the &quot;average&quot; current up to time \$T\$.  Based on the straightness of the current vs. time plot for the first second, this should be pretty good for \$T &lt; 1\mathrm{s}\$ and not too bad out to \$T &lt; 3\mathrm{s}\$ -- I suspect that after that the current will be pretty constant anyway, and you can just read the chart.