Nuclear Fusion Rocket Engine

But first, let's all welcome Rush Limbaugh to Hell. If ever anyone distilled the acid bile of white supremacy, bigotry and chauvinism, bottled it in victim-size personal containers, it's Rush. People will say he was being funny, kidding, joking around. No, our soft round boy was never kidding and everyone knew it. He was just a mean feral pest.

Hopefully, Rush is being passed around like an underage Dominican pajama boy from demon to demon, contracting every possible venereal disease in existence. 

Anyway, let's talk nuclear fusion rocket engines. You would think a rocket engine would be easier to build than a reactor, seeing as you don't need a sustained and contained reaction, but you always have that squishy spurts at the magnetic pinch that kablooeys the plasma burn. Fusion has been produced since 1932 with a cyclotron by Marc Oliphant at Cambridge's Cavendish laboratory. Fusion is easy to do. Why, a high school science fair student could (has) produce nuclear fusion by constructing a Farnsworth Fusor. The problem is producing a big enough reaction to propel spaceships.

My guess is a successful fusion rocket will, well, first of all it s all magnets. But my guess is a fusion rocket will require a little machine learning AI to cuddle and tickle the plasma to create an exhaust. An AI that we will find composed of algorithms we cannot understand. The fusion rocket will be an alien organ, and part of a larger animal called your spacecraft. You can read all sorts of technical things on fusion engine but I would prefer to work it as a Fermi question from three assumptions. 

First, that the engine fuses regular old hydrogen. No fancy lithium deuteride fuel like Project Daedalus used. Let's assume a boron nitride consumable along with the liquid hydrogen fuel, utilizing a cominaion of laser driven intertial confinement and magnetic compression powering a magnetic pulse plasma, and leave it at that. 

The second assumption is that whatever the engine looks like, it is about the size and weight (8400kg)of a Rocketdyne F1 engine.I choose the F1 as still the most powerful rocket engine built (late 50s) and its performance characteristics are well known. 1.5 million pounds of thrust. Managed by pumps that could drain an Olympic size pool in seconds.

The third assumption is we are using an Orion spacecraft as payload which is about 22,700kg in mass, and a rocket configuration similar to the first stage of a Saturn 1B, which gives us a rocket dry mass of about 42,000kg, for a total mass of 64,700kg. 

Ready to be bored with math? Here we go. A B11-proton fusion reaction produces about 8.9 million electron volts per reaction.

Treating the boron nitride component as part of the engine allows us to use only the mass of the hydrogen fuel for energy density which works out to about 107 trillion joules per kilogram.

So our ideal exhaust velocity from momentum equation, E=1/2 *m * V^2, converts to V = sqrt(2* E/m), plug in the 107 in E/m, gives us V = sqrt(214tj/kg) = 14,629 km/sec.

That's not bad considering. Okay, lets' go to Mars. Or Mars and back.

Accelerating at 1 g to go halfway to Mars, flip over and decelerate at 1 g to Mars, gives us a very comfy ride that takes, in total depending on the distance, about 8 days 9 hours round trip (assuming average distance of 2 AU). This is about 7128.6 km/sec total speed for the trip

So, using the idealized Tsiolkovsky rocket equation of  propellant mass is U = 1 - 1/exp(total speed/exhaust velocity) = 1 - exp(7128.6/14629) = .245 of total mass.

Given that our rocket is 66,700kg gives is a total liquid hydrogen weight of 66,770 * .245 = 16,345kg. Liquid hydrogen has a density of 71 kg per cubic meter meaning the fuel tank is about 21 meters x 21 meters which is just about the size of the fuel tanks of our Saturn 1B first stage.

For comparison purposes, a Saturn 1B equipped with an Orion spacecraft payload and using an F1 engine would use 399,400kg of fuel.

Wait, you say, I thought a ton of deuterium fusion fuel is equal to 29 billion tons of coal, and our propellant mass from crude chemical to fusion rocket is only .04 which is 4/100s. Not very impressive.

Fine. This was a crude estimation problem* and besides I'm getting you to Mars in 4 days versus 9 months. Sure we can do better on the approximation but would you rather fly my fusion rocket or end up a tumor-ridden cripple on one of Elon Musk's Starships?