# Which theoretical propulsion system has the highest specific impulse?

I know that NERVA physically demonstrated 811 seconds, and the theoretical range for Orion was around 10,000.

After stipulating that we can't really know for sure until it's built, given plausible systems, which one is most efficient with respect to Isp?

For the sake of scope limiting, let's say a TRL of 2, where at least some basic research had been done to validate the concept.

• A great resource for theoretical propulsion systems is Project Rho. – Russell Borogove Oct 25 '20 at 18:59
• Project Rho is good times for sure, but is it reliable? – Chris B. Behrens Oct 25 '20 at 19:29
• What's your minimum acceleration? – SE - stop firing the good guys Oct 25 '20 at 19:46
• @ChrisB.Behrens Project Rho tries to stick to the physically plausible, but it's on you to read between the lines, investigate the sources, and decide how "theoretical" a propulsion system you're willing to accept. – Russell Borogove Oct 25 '20 at 20:37
• TRL 2 captures... an awful lot of stuff. As far as ISP -- it is very important to understand that ISP, thrust, and available energy sources (for electrical thrusters) all tightly tie into each other in an interdependent way and it almost never makes sense to simply endlessly optimize ISP. – ikrase Oct 26 '20 at 10:52

With respect to specific impulse and nothing else? Simple, the photon drive, $$c\over g_0$$ or $$3.057×10^7$$ seconds (almost a year). It's pretty damn simple though - any kind of directional light source, like a halogen bulb with a reflector works just fine, you can also go with photons in other spectra - hard gamma from antimatter acceleration (providing you can reflect it; currently not doable) would make a very good one, microwaves, gamma decay of radioactives, LED lights, laser, pretty much everything that emits photons. The practical barrier is puny thrust - currently scarce piconewtons of thrust from normally maintainable photon sources, which makes it practically useless; anything that could produce and reflect enough to produce some meaningful thrust will have enough losses in form of heat absorbed by the craft to make it inoperable - or require so much cooling capacity (and as result mass of radiators) all benefits of increased thrust are eaten up by the increased dry mass that must be accelerated. As result there are no practical photon drives in sight - if we manage to find the unobtainium to reflect photons from annihilation of anti-matter, it would be probably the second best theoretical propulsion after the Alcubierre drive. So far it's not even on the horizon of being practically usable - nothing known to current material engineering even approaches remotely sufficient for the task.

If you want something that is in the realm of "achievable within foreseeable future provided fantastic funding" AKA "We know the theory how to make it, just need to develop the engineering part", muon-catalyzed fusion drive is more practical. Specific impulse up to roughly a month, and thrust approaching something practically usable.

• Do we have any idea how to actually make muon catalyzed fusion viable let alone fusion in general? – ikrase Oct 26 '20 at 6:22
• @ikrase: Yes. Of course as far as all "cold fusions" go it seems like yet another dud that costs more energy to achieve than it produces, useless for the energy industry. In this scenario the main difference being most of the energy put into it is spent on Earth (imaking antimatter), and released in space (as propulsion), so if you think of the process as a form of (lossy) energy storage, not energy source, this deficiency isn't crucial. Think electrolyzing and cryocooling hydrogen and oxygen for chemical engines. – SF. Oct 26 '20 at 6:42
• Energy-storing muon catalyzed fusion is a new thing to me -- I was not aware that is possible (is it different from antimatter catalyzed fusion?) – ikrase Oct 26 '20 at 10:48
• Your radiators work as photon thrusters, too. en.wikipedia.org/wiki/Pioneer_anomaly – John Doty Oct 26 '20 at 18:11
• @SF. It doesn't scale well to large spacecraft. But at nanoscale, a square micrometer of radiator at 350 W/m^2 makes ~an attonewton of thrust. If your spacecraft is a cubic micrometer of density 1 g/cm^3, massing a picogram, you may achieve your 1 mm/s^2 using nothing but your radiator as a thruster. – John Doty Oct 27 '20 at 12:30

Optimising for Isp only is problematic, as it's simply:

$$I_{sp} = \frac{v_e}{g}$$

Which is the same as optimising for exhaust velocity.

With no constraints on thrust, particle accelerations can achieve velocities arbitrarily close to the speed of light (The LHC is 3 m/s close). That's an Isp 30.6 million seconds, which can't be directly used in the usual rocket equations since you will have to account for relativistic effects.

Worse yet, photon thrusters can achieve thrust without expanding mass at all, achieving a force of $$F = \frac{P}{c}$$ (3.3 Newtons per gigawatt). At that point, Isp as a useful measure is utterly broken.

These are both possible to build. Particle accelerators have been with us for decades, and photon thrusters ("lightbulbes") for two centuries.

Some minimum acceleration is therefore required

Tier 1, able to lift off from the ground.

Chemical propulsion is unrivalled for thrust, and top out at around 450-460s for LH2/LOX. Exotic Lithium-Hydrogen-Fluorine Tripropellant systems have been demonstrated up to 542s, but those are highly impractical.

Generalising thermal rockets, current materials can withstand temperatures enabling an Isp of around 1,500s. This is lower in practice, as the proposed power source is usually a reactor. RD-0410 demonstrated a specific impulse of 910s.

Tier 2, interplanetary speeds within years.

Ion thrusters have been experimentally tested up to 10,000s, and used in space up to 3,100s

Improving the first category requires materials standing more heat, as heated gasses is the only propellant dense enough to achieve enough thrust. Alternatively, confinement of the exhaust must be done with something other than solid materials.

Improving the second category requires propellants that can achieve higher velocities than ionized atoms. No realistic systems are capable of producing a great enough amount of subatomic particles to achieve enough thrust.

• Yeah, it seems to be coming down to materials science these days. – Chris B. Behrens Oct 25 '20 at 20:49
• "without expanding mass at all" *expending? – Acccumulation Oct 26 '20 at 3:14
• of course, there are big practical problems with using anything measured in "Newtons per gigawatt" – user253751 Oct 26 '20 at 11:48
• Photon thrusters expend mass. Einstein arrived at his famous mass-energy equivalence by reasoning about the thrust of light: en.wikipedia.org/wiki/… – John Doty Oct 26 '20 at 18:09
• -1 for unsourced, authoritative-sounding yet wrong statement. How should mass specific impulse calculated for relativistic exhaust? – uhoh Oct 27 '20 at 2:29

JUST ISP optimization, using near-future tech.

Photon drive: ISP = ∞ (ok, actually about 30 500 000) Has ludicrously bad energy-to-thrust ratio though. We do not have realistic power sources for this yet, or soon. But it exists. Just flick on your pocket flashlight. Expect to be disappointed at the thrust levels though.

Monatomic Hydrogen Ion Drive: ISP = 200 000 - 15 000 000.. It wastes a lot of power for the ionization, and produces very little thrust per power input. This is the very best Ion drive possible. It is not energy-efficient but makes best use of reaction mass. At the extreme top end this is basically an open-ended relativistic particle accelerator firing Hydrogen Ions and Electrons.

Sensible Ion drive, using a heavy noble gas: ISP = 2000 - 30000 This is almost off-the shelf by now.

Nuclear Thermal: ISP = 800-1200

Chemical rocket: ISP = 0 - 550

Nuclear Pulse propulsion: Orion - style: ISP = 6000-ish This is a very workable model, easy enough to build. Has the slight disadvantage of declaring WWIII on the ground it gets launched from. Rains down radioactive hellfire.

Medusa - style: ISP = 50 000 - 100 000 ish Works only in deep space. Also rains radioactive hellfire all around it, but it's in deep space so no, ahem, less problem

And then there is the really weird stuff, that is definitely not at the required tech readiness level: Antimatter-catalyzed fusion drive, etc..

• Photon doesn't really work that way -- like chemical, it's an engine where the power source is the rocket. Anything less than antimatter, and no sane planner would use photon. And it definitely has a very distinct and finite ISP. – ikrase Oct 26 '20 at 10:46
• There's no "almost" to the ion drive's "off the shelf". SpaceX has an assembly line making thrusters fast enough to build three Starlink satellites a day. – Mark Oct 26 '20 at 20:22
• The Orion Drive nuclear pulse rocket doesn't "raid down radioactive hellfire". Nuclear fallout is caused by objects being sucked into the fireball and vaporized, and when you're flying through the air, there's no objects to be vaporized other than the casings of the propellant-bombs. During takeoff, you can either minimize fallout by using a specially-designed launchpad (a giant, graphite-coated steel plate) or use another propulsion method to reach an altitude where the bombs won't touch the ground (about 500m up, so take your pick). – nick012000 Oct 27 '20 at 6:58