How feasible is it to use a cyclotron in this manner for space propulsion?

Inject small amounts (aliquots) of ionized matter into cyclotron at some high integer multiple n of the cyclotron frequency $\omega=qB/m$ so that there are n aliquots at each radius in the cyclotron. Since the time it takes to complete one revolution is the same for all of these aliquots, one could use the frequency $2n\omega$ of the alternating electric field to accelerate all these aliquots in a synchronous manner. This would give essentially a continuous stream of very high speed plasma or material to accelerate spacecraft. Of course, the aliquots could move at relativistic speeds which would affect the cyclotron frequency by $\gamma$. But one could design a magnetic field that gets stronger with increasing radius especially toward outer portions where relativistic effects would be more prominent. There would also be electrostatic repulsions between aliquots that would need to be taken into account. The spacecraft would likely need nuclear power source. Is this a feasible idea? Has this been thought of already?

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    $\begingroup$ aaaand we have a very efficient propulsion for an orbital torus-shaped station, to keep it spinning. The problem with cyclotrons is that they eject the particles far off center. You'd need two, or one working with bidirectional streams, or some way to turn the stream 90 degrees. Plus energy requirements and mass. So far we use just linear accelerators AKA ion engines. $\endgroup$ – SF. Dec 7 '15 at 7:31
  • $\begingroup$ Nah, you just need to install it with its thrust line going through the CoG. You end up with an asymmetry (the entire cyclotron on one side of the ship) but if the ship is large enough you can install enough mass on the other side to balance things. $\endgroup$ – Hobbes Dec 7 '15 at 11:31
  • $\begingroup$ @Hobbes: It won't be sufficient. The force of propulsion in this case isn't applied the moment the propellant leaves the nozzle, at the point of the nozzle - it's applied along the whole route of acceleration, tangent to the acceleration trajectory at all its points - in this case generating a genuine torque with the center in the middle of the cyclotron, completely regardless of what and where you attach to its circumference. Even my suggestion ("turn the stream 90 degrees") wouldn't suffice. $\endgroup$ – SF. Dec 7 '15 at 14:04
  • $\begingroup$ Ah, I see what you mean now. $\endgroup$ – Hobbes Dec 7 '15 at 16:01
  • $\begingroup$ This would work very well for something that lived at the pace of the continents. The ISP (assuming solar power) would be phenomenal. The flight time would also be phenomenal, though. $\endgroup$ – Loren Pechtel Apr 19 '17 at 22:49

A cyclotron is a type of Ion engine. Cyclotrons (in the classical sense of the word) haven't been used because they have a very low power-to-weight ratio (tons of magnet to accelerate tiny amounts of matter).

There are ion engines that use the Electron cyclotron Resonance principle; these use the cyclotron princple at a tiny scale to create ions that are then accelerated in a linear accelerator.

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Eject the particles at relativistic speeds, into a magnetic decelerator to generating a vector force in the opposite direction. Matter at that speed will increase in mass, to infinity actually, so a small particle could have substantial force through the deceleration cycle, relative to the energy input. Seal the entire unit, then move the particles back to the cyclotron at lower mass/velocity for recycling into the process.

The net effect would be particles at very high speed and mass moving in one direction for some period of time, then moving back the same distance, at low speed, in the opposite direction into the cyclotron for reacceleration with a 0 net force until they enter the decelerating field again. Eventually the particles would be exhausted then reused in a pulsating manner, over and over again forever. A self contained force generating device that could accelerate great mass to relativistic speeds with no matter input or loss, just energy, leveraging the ability of matter to increase in mass as it accelerates.

To over come the torque effects, just use to counter rotating cyclotrons, vary the particles to each in the beginning after each pulse cycle to correct for any imbalances. One could even use four cyclotrons, two counter rotating in the y axis and two in the x axis to control pitch, yaw and roll. Six in three axis would give you the ability to move in any direction, pulse cycles permitting.

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    $\begingroup$ The force exerted by accelerating the particles will be equal to the force exerted by decelerating the particles. When both actions happen aboard the spaceship, the net force is 0. $\endgroup$ – Hobbes Apr 18 '17 at 19:52
  • $\begingroup$ @Hobbes is correct, although conceivably the increased gravity from outside influences experienced by particles at higher mass would allow you to make a reaction-mass-less drive by effectively "pumping" that gravity back. Unfortunately, I ran the numbers some time ago, and it looks like it's highly impractical to make it even as power-efficient as a simple photon drive, so it's essentially useless. $\endgroup$ – Nathan Tuggy Apr 18 '17 at 21:29
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    $\begingroup$ This answer makes use of "magical" (impossible) physics. Worse than failing to contribute, it actively misinforms. $\endgroup$ – Kengineer Apr 18 '17 at 21:36

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