Potential Fusion Drive system calculation issue

I will start off by saying that this is an entirely hypothetical drive system with plenty of handwaving and optimistic physics. My question I think is fairly simple and may just be something that needs clarification.

This is a hypothetical fusion fuel in the far future, around 500 years into the future, where they use a fusion pellet for a torchdrive. The basic premise is that a powerful laser will shoot the pellet at a certain distance behind the ship, then magnetic fields created at the thruster will catch the useful energy and propel the ship forward while the rest will be waste heat energy.

Fusion Fuel:

• Fusion fuel mass per pellet: 100g
• Fuel Stored Energy: 942.42 TJ/kg
• Net Pellet mass: 2,399.715g
• Fusion fuel Exhaust Velocity: 3,794,355 m/s
• Pellet Efficiency: 97.25% Thermal, 0.125% Neutrons, 2.625% X-Ray, etc Radiation

Thruster

• Pulse rate of 14Hz
• 200m detonation range

Calculations and End Results

Through various efficiencies the end result of the energy harnessed by the thruster (Thrust Power) is 1,026.49TW. But when I do the other calculations I get a Thrust Power of 241.83TW. That is using the Thrust at 127,471.96kN and an exhaust velocity of 3,794,355 m/s, and a mass flow rate (mDot) of 33.596kg/s. The Mass Flow Rate is obtained by 14Hz*2.399715kg.

The main question I have is if my method for obtaining the Mass Flow Rate is correct, or if I need to account for some other things in the mass flow rate since the engine harnessed charge particles and the explosion of the fusion rather than the propellent/fuel sent out the back of the thruster? When I do a calculation based off the Thrust Power attained by the fusion pellet, I get a much higher mDot value.

As a note, I am open to any criticism for the propulsion system as the more I know the better I can make it and perhaps the more realistic the story will be.

Fuel Stored Energy: 942.42 TJ/kg

This seems implausibly high. Are you sure of your numbers here? It seems at least 50% higher than optimistic approximations of D-3He fusion, which seem to assume a rather optimistic burnup fraction.

Working backwards from your thrust figures gives a more plausible energy density (eg. ~170TJ/kg assuming the whole pellet mass contributes to useful thrust and everything except the 100g of fusion fuel is inert and fuel burnup is 100%, etc), so I can't quite tell where this figure is coming from.

Pellet Efficiency: 97.25% Thermal, 0.125% Neutrons, 2.625% X-Ray, etc Radiation

Your exhaust velocity figures seem to imply a fairly low propellant density, but a low density propellant (or hohlraum or whatever) and a comparatively small pellet is going to have a hard time absorbing all the neutrons and x-rays from whatever fusion reaction you're using. The chances of it doing so and thermalising nicely to get the figures you're quoting here are slim, to say the least.

Thrust at 127,471.96kN and an exhaust velocity of 3,794,355 m/s, and a mass flow rate (mDot) of 33.596kg/s.

Those numbers all seem to be basically OK, other than your slightly high exhaust velocity (though there are no efficiency figures anywhere here... presumably you're hiding them behind your exhaust velocity?). It also matches the ~240TW power figure.

What is missing are the workings you used to compute your 1000TW figure, and without those it is hard to say where you went wrong with that. Maybe you could include your working in your question?

I am open to any criticism for the propulsion system

It is hard to criticise when you give us so little to go with ;-)

Aside from the issues above though, this seems odd:

200m detonation range

This is a little confusing... what do you actually have in mind here?

I see figures of this magnitude appearing in the Medusa rocket idea, but you say "shoot the pellet at a certain distance behind the ship" which isn't compatible with the Medusa design at all. When I look at ICF rocket designs like the Hyde D-D, you have a reaction chamber which is several metres across with the nuclear blast in the middle. For other things like Orion, I see talk of standoff distances measured in maybe 10s of metres, and a quite different thruster design with much lower exhaust velocities. It is very hard to tell what your rocket is based on, or how you're expecting it to work!

Stack exchange doesn't really lend itself very well to critique, but you should include a bit more detail in future questions.

• Thank you for the answer. I have adjusted the stored energy to be lower, my initial thought was that after a few hundred years of fusion use in drives, they have found ways to alter the composition of the elements and therefore increase the power and decrease the radiation created. I will also add some more calculations to this maybe later today. As for the detonation range, I was using a similar design to the Epstein drive as broken down at Project Rho. The detonation range is at a distance where the heat from the explosion can be successfully absorbed without melting anything Mar 22 at 15:34
• As for the larger thrust power number. That was derived by taking the stored energy per detonation and using the thermal energy output per second of all the pellets. Then an efficiency of the magnetic nozzle was added in to allow for a reasonably high amount of energy absorption. Mar 22 at 15:37
• @Markitect I suggest you direct further questions to Worldbuilding.SE which is a better place for soft scifi stuff; this site is slightly more grounded in reality. Trying to make a magnetic nozzle that can usefully generate large amounts of thrust from a nuclear explosion 200m away is going to be somewhere between challenging and infeasible (Consider that it is going to have a radius of a similar size, and will need to be made of superconductors, and will need to be cooled and shielded and and and...) Mar 22 at 16:33