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And even if you can build the scoop a Bussard Ramjet has a theoretical efficiency limit of .12c unless you can somehow reclaim the energy of the infalling matter.

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0.12c would still be incredibly useful. Proxima Centauri in 35 years? Game changing.

for a travel time of 35 years, you'd not get very long at Proxima Centauri, because you'd still be doing 0.12c when you arrived

If you could keep an acceleration of 1g, it would take about 40 days to accelerate to 0.12c, and as much to decelerate.

The problem, of course, that with a Bussard ramjet, you won't be able to achieve nearly as much acceleration.

What would happen if you entered its orbit at that speed?

edit: according to https://rechneronline.de/g-acceleration/orbital-speed.php, if I got my numbers right (0.12 x solar mass star, .12c = 36000 km/s), the orbit radius would be 1230 km, so you'd be almost at the core of the star since its radius is ~ 100 000 km.

Because if you don't reclaim the energy of matter infalling at 0.12c your craft gets shredded by dust. At that velocity it's like flying through sandpaper.

And if you're flying through a cometary halo, your odds of hitting something bigger are much higher.

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