Interstellar Flight: Perspectives and Patience

>To get around thousand-year generation ships, we are examining some beamed energy solutions that could drive a small sail to Proxima in 20 years.

The odds of a spacecraft hitting a single particle of dust while in space are 100%.

A spacecraft hitting a single particle of dust at 0.2c will impart tens of millions of joules into the body of the spacecraft, the equivalent of getting hit with hundreds of pulses from the most powerful laser ever created by humanity-- simultaneously.

Or concentrating several kilogram's worth of TNT into the size of a particle of dust and detonating it.

alternatively you ionize that particle, may be make in into plasma by laser for ease of "digestion" down in the engine, direct in into the engine where it is used as working mass for your ion thruster, kind of similar to scramjet.

As far as i see with today's tech - like Starlink's ion thruster + classic nuclear reactor - we can get to 300km/s in about 4 stages. Straightforward improvement of ion thrusters - mainly voltage increase and associated engineering (which will immediately happen once we start flying to Mars and beyond as ion thruster currently our best/fastest option inside the Solar system) - can get us to 1000-2000km/s, i.e. under 1000 years to Alpha Centauri (that for a large populated spacecraft, and for just tiny probe to announce our existence (and to send back photos which we'd receive using Sun's gravitational lensing) we can do even better). And using interstellar gas and dust scramjet-style will improve on those numbers (as such ship is mostly limited by the working mass it starts with while the reactors would be able to continue produce the energy much longer).

> alternatively you ionize that particle, may be make in into plasma by laser for ease of "digestion" down in the engine, direct in into the engine where it is used as working mass for your ion thruster, kind of similar to scramjet

This is a Bussard ramjet [1]. The interstellar medium is too thin to make it work. (Maybe we'll find the husk of an ancient ramjet from an earlier era of the universe floating around one day...)

[1] https://en.wikipedia.org/wiki/Bussard_ramjet