[bearnard1212 (OP)]

As we can see the most advanced and the most frequently used propulsion system  for spacecrafts is nuclear. But can you name propulsion system that is rather good for space journeys as nuclear and in some time of development can substitute the most frequently used propulsion system?

[Halc]

As we can see the most advanced and the most frequently used propulsion system  for spacecrafts is nuclear.

Reference?

I may be behind the times with the news, but my current count of known spacecraft with nuclear propulsion is zero. I may be wrong about that, but calling such a low number 'most frequent' is quite a stretch.

Nuclear propulsion has been the subject of numerous research projects since the 50's, but none of those projects seems to have produced an actual spacecraft.

[syhprum]

A few are working with nuclear power generation and ionized gas propulsion but they are very rare

[charles1948]

Perhaps we haven't had atomic energy long enough to develop practicable methods for using it to propel spacecraft.

Looking back in history, steam energy took about only 150 years to progress from its primitive origin in the 1690's, to the first really practicable and widely-utilisable steam locomotives of the 1830/40's.

And of course these days, scientific progress has speeded up.  There were only 52 years between the primitive small, slow,  propeller-driven Wright "Flyer "of 1903, and the giant turbojet-driven intercontinental-range 600 mph B-52 "Stratofortress" strategic bomber.

So, mightn't such progress encourage us to envision a future where atomic-powered space-ships become real?

[Kryptid]

Perhaps we haven't had atomic energy long enough to develop practicable methods for using it to propel spacecraft.

Fission-powered rocket engines were actually developed and tested a long time ago. If I'm not mistaken, politics is why they were never used.

[evan_au]

Surely, nuclear fusion would be the ideal method of propulsion (especially if it could scoop up fuel and reaction mass from the solar wind).
- But we can't get controlled fusion to work on Earth
- Let alone a motor small enough and light enough to fit on a spacecraft.
https://en.wikipedia.org/wiki/Fusion_rocket

A few are working with nuclear power generation and ionized gas propulsion but they are very rare

Dawn spacecraft to the asteroid belt uses ion propulsion, but it gets the power from the Sun (there is still a fair amount of Sunlight at the asteroid belt).
- Spacecraft powered by nuclear energy tend to use thermo-electric generators (TEG), which are not very efficient (but they have no moving parts, which is a bonus in space)
- TEG can't generate the 10 kiloWatts or so required for an ion drive
- For those power levels, you would need a "critical" nuclear reactor, which is a lot more complex.

The Perseverance rover on Mars has a large TEG, which generates just 0.1 kiloWatts
https://en.wikipedia.org/wiki/Perseverance_(rover)#Design

[bearnard1212 (OP)]

Surely, nuclear fusion would be the ideal method of propulsion (especially if it could scoop up fuel and reaction mass from the solar wind).
- But we can't get controlled fusion to work on Earth
- Let alone a motor small enough and light enough to fit on a spacecraft.
https://en.wikipedia.org/wiki/Fusion_rocket

A few are working with nuclear power generation and ionized gas propulsion but they are very rare

Dawn spacecraft to the asteroid belt uses ion propulsion, but it gets the power from the Sun (there is still a fair amount of Sunlight at the asteroid belt).
- Spacecraft powered by nuclear energy tend to use thermo-electric generators (TEG), which are not very efficient (but they have no moving parts, which is a bonus in space)
- TEG can't generate the 10 kiloWatts or so required for an ion drive
- For those power levels, you would need a "critical" nuclear reactor, which is a lot more complex.

The Perseverance rover on Mars has a large TEG, which generates just 0.1 kiloWatts
https://en.wikipedia.org/wiki/Perseverance_(rover)#Design

As we can see nuclear power is the most useful for long space joyrneys. As far as I know Perseverance used such propulsion system to get to the Mars.

[bearnard1212 (OP)]

Surely, nuclear fusion would be the ideal method of propulsion (especially if it could scoop up fuel and reaction mass from the solar wind).
- But we can't get controlled fusion to work on Earth
- Let alone a motor small enough and light enough to fit on a spacecraft.
https://en.wikipedia.org/wiki/Fusion_rocket

A few are working with nuclear power generation and ionized gas propulsion but they are very rare

Dawn spacecraft to the asteroid belt uses ion propulsion, but it gets the power from the Sun (there is still a fair amount of Sunlight at the asteroid belt).
- Spacecraft powered by nuclear energy tend to use thermo-electric generators (TEG), which are not very efficient (but they have no moving parts, which is a bonus in space)
- TEG can't generate the 10 kiloWatts or so required for an ion drive
- For those power levels, you would need a "critical" nuclear reactor, which is a lot more complex.

The Perseverance rover on Mars has a large TEG, which generates just 0.1 kiloWatts
https://en.wikipedia.org/wiki/Perseverance_(rover)#Design

I found an artcle about a month ago that tells about ``hybrid`` rocket.  This kind of propulsion is not so advanced and used for small space journeys 

[Janus]

Surely, nuclear fusion would be the ideal method of propulsion (especially if it could scoop up fuel and reaction mass from the solar wind).
- But we can't get controlled fusion to work on Earth
- Let alone a motor small enough and light enough to fit on a spacecraft.
https://en.wikipedia.org/wiki/Fusion_rocket

A few are working with nuclear power generation and ionized gas propulsion but they are very rare

Dawn spacecraft to the asteroid belt uses ion propulsion, but it gets the power from the Sun (there is still a fair amount of Sunlight at the asteroid belt).
- Spacecraft powered by nuclear energy tend to use thermo-electric generators (TEG), which are not very efficient (but they have no moving parts, which is a bonus in space)
- TEG can't generate the 10 kiloWatts or so required for an ion drive
- For those power levels, you would need a "critical" nuclear reactor, which is a lot more complex.

The Perseverance rover on Mars has a large TEG, which generates just 0.1 kiloWatts
https://en.wikipedia.org/wiki/Perseverance_(rover)#Design

As we can see nuclear power is the most useful for long space joyrneys. As far as I know Perseverance used such propulsion system to get to the Mars.

Perseverance was launched to Mars by an Atlas V-541 rocket.  This is a two-stage rocket with boosters attached to the first stage.
The first stage main engine burns kerosene and liquid oxygen and the boosters burn solid fuel.
The second stage (Centaur) burns hydrogen and liquid oxygen. All of these are chemical rockets.

[Janus]

Surely, nuclear fusion would be the ideal method of propulsion (especially if it could scoop up fuel and reaction mass from the solar wind).
- But we can't get controlled fusion to work on Earth
- Let alone a motor small enough and light enough to fit on a spacecraft.
https://en.wikipedia.org/wiki/Fusion_rocket

A few are working with nuclear power generation and ionized gas propulsion but they are very rare

Dawn spacecraft to the asteroid belt uses ion propulsion, but it gets the power from the Sun (there is still a fair amount of Sunlight at the asteroid belt).
- Spacecraft powered by nuclear energy tend to use thermo-electric generators (TEG), which are not very efficient (but they have no moving parts, which is a bonus in space)
- TEG can't generate the 10 kiloWatts or so required for an ion drive
- For those power levels, you would need a "critical" nuclear reactor, which is a lot more complex.

The Perseverance rover on Mars has a large TEG, which generates just 0.1 kiloWatts
https://en.wikipedia.org/wiki/Perseverance_(rover)#Design

I found an artcle about a month ago that tells about ``hybrid`` rocket.  This kind of propulsion is not so advanced and used for small space journeys 

What kind of hybrid rocket are you talking about?  There are hybrid chemical rockets which combine solid fuel with liquid oxygen( Solid fuels typically contain their own oxidizer). Nuclear-electric hybrids which use a nuclear reaction to power something like an ION engine and on the more hypothetical side, Fusion-fission hydbrids, and anitmatter-Fusion hybrids. 

As far as nuclear rockets go, this gives a pretty good overview of proposed types:
http://www.projectrho.com/public_html/rocket/enginelist2.php