I'm a newbie so this might be obvious to others but....if the specific impulse of an ion engine is limited by it's fuel load then why not accelerate singular fuel (krypton) ions to relativistic speeds before exhausting them out of the engine. Does Newton's law apply? Does the increased mass of the ion give an equal and opposite reaction whilst still within the engines accelerator?
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1$\begingroup$ Newton does not strictly apply since it is a relativistic case, but things work the same. Conservation of momentum: what you want is to eject the ions with as much momentum you can, since that will impart equal momentum to the craft. $\endgroup$– Anders SandbergCommented Aug 12, 2018 at 10:10
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2 Answers
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Theoretically, greater exhaust velocity is better for conservation of fuel.
Suppose your spacecraft has mass $m_s$ and you need to change its speed by $v_s$ by shooting your fuel at speed $v_f$, and the mass of the fuel $m_f$ is negligible. Then $m_s*v_s=m_f*v_f$. This is great - fuel mass is inversely proportional to exhaust speed, and with little fuel you can change your speed a lot! This doesn't even require relativistic speeds.
However, consider the following:
- Accelerating fuel requires energy. Using the designations above, the kinetic energy of the fuel will be $m_f*{v_f}^2/2$, or $m_s*v_s*v_f/2$. That is, for the same delta-V of your spaceship, the energy your engine consumes is proportional to exhaust velocity. That is, saving some krypton/xenon fuel has energy cost - it becomes impractical for speeds much lower than relativistic.
- All these ions flying at high speeds are not friendly to materials. If an ion hits any structural element of the engine, it can do damage. Greater exhaust speeds do greater damage. See also here.
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$\begingroup$ Thank you for your answer, do I deduce from that that, provided the energy source was abundant (nuclear) and the engineering was sufficiently advanced that damage was not done, limited fuel capacity would not be a limitation on long journeys, ie. Interstellar? $\endgroup$– EricCommented Aug 12, 2018 at 15:22
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$\begingroup$ Mostly yes, but in saying "energy source is abundant", you also imply "reaction mass is unlimited", which makes it rather meaningless: If your spaceship burns 1 kg of antimatter per second, and because of that its "fuel" (reaction mass) consumption is reduced to 0.1 kg per second, it's not a technologically wise design. $\endgroup$ Commented Aug 12, 2018 at 15:26
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$\begingroup$ Maybe that's what some of those ultra-high energy cosmic rays are - exhaust particles from spaceships. $\endgroup$ Commented Jul 24, 2020 at 4:28
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why not accelerate singular fuel (krypton) ions to relativistic speeds before exhausting them out of the engine.
This isn't practical today. A real spacecraft engine has mass, volume, and reliability limits. We can't put the equivalent of the LHC onto a rocket. So with modern designs, ions can only be accelerated so fast, and that's a long way from relativistic. There are designs for engines that can reach $v_e$ of about 0.0006c.
answered Aug 13, 2018 at 23:29