# What would be the specific impulse of a continuous nuclear fusion drive?

Let's assume problems of running sustained nuclear fusion are overcome (be it by making the mechanism highly energy-positive, or just supplying all the energy deficit externally, like beamed power.) Let's also assume we managed to direct all products (and none of the substrates) of the fusion in one direction (through the nozzle). Plus matters of cooling, safety etc, all the engineering trivia.

Essentially, the drive reacts Deuterium and Tritium, converting them into Helium through nuclear fusion, and the newly created extremely hot helium is ejected through the nozzle, as reaction mass.

What would be the exhaust speed of such a drive - speed at which the atoms of helium would be ejected; the specific impulse of such a drive?

I tried to ballpark typical temperatures of fusion plasma into average speeds of particles, and got nowhere, as the gas equations don't really work with plasma. Could you give me a ballpark value?

• That's not how fusion works. You are confusing released energy (photons) with the randomly-directed motion of 'hot' atoms. You can't focus those particles any more than you could focus the emissions from the sun. At least, not without typical Sci-Fi use of unobtanium containers and uncompilium software. – Carl Witthoft Oct 19 '18 at 13:53
• Many such questions are addressed at Project Rho: projectrho.com/public_html/rocket/enginelist.php#modes – Russell Borogove Oct 19 '18 at 14:10
• @CarlWitthoft: Ionized particles can be guided quite well using magnetic field - that's how a stellator works. Momentum from the photons will be much smaller than from the ions due to mass difference, so I'm not so worried about reflecting them. And Project Orion somehow deals with them... – SF. Oct 19 '18 at 15:37

So we get that $$1/2 mv^2 = 1/250 mc^2$$ From which we can quickly find $$v$$ to be about $$c/11$$.
Specific impulse is exhaust velocity divided by $$g$$, so we get about 2.7 million seconds as the $$I_{sp}$$.