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Works like a slingshot, the slingshot is inside the ship and the released projectile imparts its momentum onto the ship, moving it forward. The projectile is then picked up again and it repeats.

There is no exhaust and the fuel is reused endlessly, take the nautilus shell where using electrical energy the spiral acts as a chamber to impart momentum in a circular motion onto the projectile free floating, not connected to the ship, at some amount of momentum the projectile goes from circular motion to linear motion where it strikes the ship imparting its force and moving the ship forward. The projectile is then sent back to the chamber to endow it again with momentum, and the process repeats.

The LHC uses electrical power to accelerate particles, the slingshot launch system also uses electricity to propel a projectile. This differs as this accelerator is inside the ship, with the projectile being inside the ship but not attached to the ship.

The more elegant design has a nuclear power plant that magnetizes the fuel and turns it into a state that is not a particle such as plasma, the fuel is contained in a magnetic wall and the fuel in momentum is directed magnetically so it does not damage the material parts of the ship, the plasma is magnetized opposite of the pusher plate and magnetically repels the fuel pushing the ship forward. As the plasma loses momentum, it is again directed to the circular chamber to have momentum endowed to it.