I've frequently mentioned a type of electrostatic fusion reactor (and associated rocket systems), designed by Robert Bussard and detailed in the papers listed below. In it the fusion fuel is confined by a spherical voltage potential well of order 100,000 volts. When the fuel reacts, the particles are ejected with energy of order 2 MeV, so escape the potential well of the voltage confinement area. The standard reactor design discused used p+11B (hydrogen and Boron-11) as fuel, since it fuses without releasing any of its energy as radiation or neutrons. All the energy of the reaction is contained in the kinetic energy of released charged particals. If the fusion reaction is surrounded with voltage gradiants or other systems to convert the kinetic energy of high speed charged particals directly to electricity. Virtually all their energy (about 98%) directly to electricity. Making a ridiculously compact and simple electrical generator.
For example: Bussard fusion reactor with a radius of about 2.5-3 meters burning P+11B (hydrogen and Boron-11) produces 4500-8000 megawatts (4.5-8 E9 watts) of electricity and weighs about 14 tons (.00174 kg per KWe (575 KWe/Kg)). That's enough electricity per reactor to power a couple of big cities, and will be the standard power plant of most of our support craft. This isn't nearly enough power for the drive systems of one of the Explorer ships of course, but the system can be scaled up and retain its efficency.
This design is Bussard's variation of the Farnsworth/Hirsch electrostatic confinement fusion technology. Whats important to us is that it makes such a fantasticly small light power plant, that it can be used as part of a high thrust to weight ration propulsion system for space craft and aircraft. Bussard and associates have designed propulsion versions with a specific impulse of between 1500 and 6000 sec. (Best chemical specific impulse is 450.) I'll discus the rocket applications below.
As I mentioned above certain fusion fuels release all the energy of their fusion reaction in the kinetic energy of the released particals. The table below lists the various fuels with this charicteristic, and the power they release per kilogram of fuel.
|Fuel --> Exhaust||Power / Reaction||Number of Particals||Joule / kg|
|p + 11B --> 3 4He||8.68 MeV||12||6.926 E13|
|De + 3He --> 4He + p||18.3 MeV||5||3.505 E14||*|
|p + 6Li --> 4He + 3He||4.00 MeV||7||5.472 E13||**|
|3He + 6Li --> 2 4He + p||16. MeV||12||1.277 E14||**|
|6Li + 6Li --> 3 4He |
|20 MeV||12||1.596 E14||**|
|3He + 3He --> 4He + 2 p||12.9 MeV||6||2.059 E14||***|
* De +3He reactors would have at least some De + De reactions, which produce neutrons. Possibly 2% of the energy will be released this way. This Neutron bombardment could not be directed like the charged particals. So the energy would impact the rear of the ship. Neutron bombardment is a very toxic form of radiation for people and metal, and would cause tremendous heat load on the rear of the ship.
To avoid shielding mass, we could put the reactor behind a shielding wall at the back of the ship, and make the reactor out of open mesh to limit its exposure.
** Since p can be reused in the two stage p + 6Li --> 4He + 3He &;3He + 6Li --> 2 4He + p reaction, its mass isn't counted as consumed in the reaction. This two staged reaction effectivly combines into 6Li + 6Li --> 3 4He with 20 MeV of total output.
*** 3He + 3He reactions are difficult to convert into electricity in a Bussard reactor, but can be used as a direct plasma thrust.
Power is given in Million electron volts (MeV). An electron volt is equal to 1.60219 E-19 Joule, and a Joule / sec is equal to a Watt. Mass in this case is the number of Protons and neutrons involved in the reaction. They each weigh about 1.673 E-27 kg. So since p + 11B has 12 P's and N's per 8.68 MeV reaction. (Note I'm ignoring electrons. Life's to short, they're too light).
8.7 MeV = 8.7 E6 eV per 12 * 1.673 E-27 kg = 4.324 E32 eV per / kg = 6.926 E13 watts / kg (1 ev/second = 1.60219 E-19 Joule / sec) 1 j/s = Watt
Since the fusion reactions listed above, release all their energy in the kinetic energy of their exaust particals; the most direct way to power a rocket is to use these particals directly as a fusion rocket exaust stream. This can be done by placing an uncontained fusion reactor (without any electrical power conversion equipment), in the focus of a paraboloidal shell. The shell then reflects the fusion particles to the rear in a narrow beam (20-30 degree width), making a high efficency plasma rocket.
The efficency of such a rocket depends on the exaust velocity of the fuel, and the energy released per pound of fuel. This is decribed in the table below.
QED Direct plasma thrusters
|Fuel --> Exhaust||Power / Reaction||(f) Mass conversion fraction||Joules / kg||Exhaust speed m/s|
|p + 11B --> 3 4He||8.68 MeV||1287||6.926 E13||11,800,000 m/s|
|p + 6Li --> 4He + 3He||4.00 MeV||1645||5.472 E13|
|3He + 6Li --> 2 4He + p||16.0 MeV||704||1.277 E14|
|6Li + 6Li --> 3 4He |
|20.0 MeV||564||1.596 E14||17,800,000 m/s|
|3He + 3He --> 4He + 2 p||12.9 MeV||437||2.059 E14||20,300,000 M/s|
|De + 3He --> 4He + p||18.3 MeV||257||3.505 E14||26,500,000 m/s|
watts are Joules per second.
F is the fraction of the fuel mass converted to energy. I.E. An f of 257, means 1/257th of the fuel mass is converted to energy.
For example: the fusion plasma from a P + 11B reaction has an exaust velocity of 11,800,000 meters per second. This translates to a specific impulse of approximately a *million* seconds. I.E. a pound of fuel consumed would provide a million pounds of thrust for a secound. For higher thrust, thou less effecient, rocket. We can use the fusion plasma to heat a working fluid. If you dilute the plasma with 100 times its weight in the following propellents (assuming I figured out the right equations), the direct QED plasma drive generates the following specific impulses:
|Fluid||Specific Impulse (Isp) in seconds|
For an externally fueled reaction, or for a short range craft, the high thrust to weigh reactions in the mixed plasma table would be desirable. But for the deceleration into the target starsystem using only fuel and reaction mass stored in the ship. Only the high efficency (high specific impulse), low fuel mass, pure fusion plasma reaction would be usable. It is those reactions we will consider in our fuel load calculations below.
The classic rocket equation gives the fuel to ship mass ratio, needed to get a given change in speed, with a fuel that has a given exaust velocity.
dv = Desired change (or delta) in the ships speed.
Vexh = Exaust velocity of the material
M = The fuel mass ratio =Exp(dV/Vexh)
The specific impulse of a fuel (The pounds of thrust, a pound of fuel will give, when burned in a second) is determined by dividing the fuels exaust velocity by 9.8 m/s^2.
The following table shows the fuel mass ratios nessisary to get a ship fueled with various fuels up to the listed speeds. For example, to accelerate a ship up to 1/4the the speed of light (.25 c or 75,000,000 m/s) a ship fueled with hydrogen and boron-11 (p + 11B) would need to start out with 576 times its own weight in fuel. To get the same ship to half the speed of light, it would need to carry over 300,000 times its weight of fuel! Fuel the same ship with duterium and helium-3 (De + 3He) and you'ld only need 17 and 287 times the ships weight of fuel.
|Fuel --> Exhaust||Vexh||75E6m/s|
( .25c )
|100 E6 m/s|
|p + 11B --> |
|6Li + 6Li --> |
|3He + 3He --> |
4He + 2 p
|De + 3He --> |
4He + p
Note: that the fuel ratios listed are only enough to accelerate the ship to, OR decelerate the ship from the listed speed. Carrying enough fuel to do both, would require squaring the ratio. In our case that would mean that the amount of fuel that could get you to 1/2 light speed, would only be enough to get you up to and down from 1/4th of light speed.
One thing the table illistrates clearly is why engineers want high exaust speeds and high energy fuels. Doubling the exaust speed can cut over 70%-80% out of the fuel mass needed to get to a speed. It also, all other things beings equal, allows a small lighter engine system and theirfor ship. This is an especially great advantage when the desired maximum speeds are several times greater than the exaust speeds.
So historically most starship design studies have gravitated toward the higher exaust speed fuels like 3He + 3He or De + 3He. However these fuels have a couple of serious practical problems not normally considered. First Helium-3 (3He) and Deuterium (De) are extremly rare isotopes, virtually unknown on Earth. Starship Design studies that used these fuels, were forced to also assume masive mining operations, scooping the materials out of Jupiters atmosphere. Also these fuels are extreamly light gases. Unless these gases are kept liquid at cryogenic temperatores in sealed tanks, they will boil away into space. In our case where deceleration fuel will need to be stored for a decade or more, this is highly questionable at best. Also the tanks themselves are very bulky and therefore heavy. A tank could probably not carry much more then 20-30 times its own weight in fuel. Which in our case would require a much bigger heavyer ship, and one that drops its empty tanks along route. This becomes absurdly impractical.
An under considered fuel is Lithium-6 (6Li). As you can see from the table it still has fairly good performance as a fuel. But it also has two very large practical advantages. At room temperature it is a solid structural metal requireing half the volume of Helium-3, and not requireing any tanks or structural supports. It could even be used as part of the engine. Allowing the ship to consume part of its engine structure toward the end of the flight. Its secound advantage is that it is a cheap plentiful material on earth. So we can get access to virtually any amount of it we want, cheaply; and we can carry it in space for years without any tanks or leakage problems. This means we can easily carry far greater amounts of it on the ship. So even though it doesn't seem that efficent on paper. It has critical design advantages for a starship, and is the baseline fuel chosen for our fusion driven starship designs.
Fusion/Electric/Thermal-rocket motor configuration.
The QED reactor can be used to produce electricity. That electric power can be efficently converted to heat in a reaction mass such as hydrogen or water. Which makes for a good drive system assumed for secoundary thrusters on the starship, and all the primary rocket thrusters on support ships and shuttles.
Again a Bussard fusion reactor with a radius of about 2.5-3 meters burning P+11B produces 4500-8000 mega watts (4.5-8 E9 watts) of electricity and weighs about 14 tons (.00174 kg per KWe (575 KWe/Kg)). Bussard and co-authors in his various papers have designed rocket systems using these reactors to heat a reaction mass (usually with relativistic electron beams). Giving a specific impulse of between 1500 and 6000 sec, and thrust to weight ratios of 1.5 - 6. (Best chemical specific impulse is 450.) For example, in the Support_craft web document, I have worked up two classes of support ships using these engines. These are a high speed aerospace shuttle, and a simpler vacume rocket craft.
(This is an introduction to the application of Bussard's version of the Farnsworth/Hirsch electrostatic confinement fusion technology to propulsion. Which gives specific impulses of between 1500 and 5000 secounds. Farnsworth/Hirsch demonstrated a 10**10 neutron flux with their device back in 1969 but it was dropped when panic ensued over the surprising stability of the Soviet Tokamak. Hirsch, responsible for the panic, has recently recanted and is back working on QED. -- Jim Bowery)