Nuclear bomb powered spaceships are technically feasible and could be built. The mass of the spaceships would have been like the submarines, destroyers and aircraft carriers of today. 200-1000 ton spaceships would have been the small versions and 1,500 to 100,000-ton military nuclear ships would have been possible. Propulsion would have used shaped nuclear explosions. The blast of nuclear bombs can be shaped. This has been researched by the USA over the decades. Narrowing the shaped explosions further would have enabled single shot super-powerful plasma blasts.
The Casaba Howitzer was a project to develop shaped nuclear blasts as plasma weapons.
In the 1960s, Project Orion was a major effort to use nuclear bombs to propel a massive spaceship. Researchers had found that a massive metal plate could survive a nuclear blast and the plate could be accelerated to very high speeds.
Exploding a bomb 25 meters away would only use 1% of the energy of the explosion.
If the nuclear device is encased in a radiation case of x-ray opaque material (uranium) with a hole in the top. This forces the x-rays to to exit only from the hole. Whereupon they run full tilt into a large mass of beryllium oxide (channel filler).
The beryllium transforms the nuclear fury of x-rays into a nuclear fury of heat. Perched on top of the beryllium is the propellant: a thick plate of tungsten. The nuclear fury of heat turns the tungsten plate into a star-core-hot spindle-shaped-plume of ionized tungsten plasma. The x-ray opaque material and the beryllium oxide also vaporize a few microseconds later.
The tungsten plasma jet hits square on the Orion drive pusher plate. The plate is designed to be large enough to catch all of the plasma. With the reference design of nuclear pulse unit, the plume is confined to a cone of about 22.5 degrees. About 85% of the nuclear device’s energy is directed into the desired direction instead of 1%.
Each charge accelerates the spacecraft by roughly 12 m/s. A 4,000 ton spacecraft would use 5 kiloton charges, and a 10,000 ton spacecraft would use 15 kiloton charges. For blast-off, smaller charges of 0.15 kt and 0.35 kt respectively would be used while within the Terra’s atmosphere. The air between the charge and the pusher plate amplifies the impulse delivered, so if you are not in airless space you can get away with a smaller kt yield.
More focused nuclear charge is a plasma beam weapon – Casaba Howitzer
The Casaba Howitzer was the result of research into reducing the spread of the particles produced by a nuclear pulse unit. Make the cone narrow enough and it becomes a destructive beam.
A Casaba Howitzer charge is about 115 kg and 0.14 m3, with a probable yield of 5 kilotons.
The original nuclear shaped charge design called for the use of a tungsten plate. The particles would be relatively slow (between 10 and 100km/s depending on thrust requirements) and rather cool (14000°C in transit, 67000°C after hitting the plate).
Using lighter elements, such as plastics or even hydrogen, in a thick and narrow instead of wide and flat shape, you can achieve a very narrow cone and very high particle velocities.