There are different optimal power sources for probes and spaceships for different kinds of missions.
- Well suited for many missions in the inner solar system. Only limited degradation over time but have to be adjusted towards to sun for optimal performance
- relatively cheap but don't like cold very much and deplete quite quickly af not recharged in some way
- can't be recharged but provide a steady (but declining) source of heat and power over decades
- Fission rectors
- Don't know anything about that
Now if we want to send probes on interstellar cruises we need to power them for centuries or even millenia. They are too far away from the sun or any other star to get any useful power from solar panels, batteries would be depeted before the probe reached the outer solar system and even an RTG with todays technology would only deliver miniscule amounts of power after a century in space.
So what could be the solution? Are there power sources that provide useful amounts of power over such timeframes? Could we use materials with a longer halflife for an RTG and thus increase the time it works? Could we use solar and just put the probe to deep sleep during transfer and it would wake up as soon as it gets close enough to the target star (I see some risks there)?