Regarding matter antimatter reactor powered manned interstellar space craft or perhaps manned matter antimatter rocket space craft, we will first assume an M0/M1 value of 10. Using the relativistic rocket equation delta V = C tanh [(Isp/C) ln (Mo/M1)] = 0.98 C. For M0/M1 = 100, we have delta V = C tanh [(Isp/C) ln (100)] = 0.9998 C.
The gamma factor of 0.98 C is 1/{1 – [(v/c) EXP 2]} EXP (1/2) = 1/{1 – [(.98C/C) EXP 2]} EXP (1/2) = 5.0252. For v = 0.9998 C, the gamma factor is 1/{1 – [(.9998 C/C) EXP 2]} EXP (1/2) = 50.0025.
These above examples assume that both the matter and antimatter portions of the fuel are carried along from the start of the mission and that the efficiency of the system is very close to 100 percent, perhaps a tall order with current state of the art matter antimatter rocket concepts.
I will go one further extreme on the relativistic rocket themes by suggesting that one can imagine antimatter rockets that derive their normal matter reactants from the interstellar medium wherein the propulsion system effeciency would approach 100 percent, exactly, and wherein the effective Isp therefor equals 2C.
For such as system wherein the effective Isp = 2C, first we will assume an M0/M1 value of 10. Using the relativistic rocket equation delta V = C tanh [(Isp/C) ln (Mo/M1)] = C tanh [(2C/C) ln (10)] = 0.999866 C. For M0/M1 = 100, we have delta V = C tanh [(Isp/C) ln (100)] = C tanh [(2C/C) ln (100)] = 0.99999998 C.
For v = 0.9998 C, the gamma factor is 1/{1 – [(.9998 C/C) EXP 2]} EXP (1/2) = 50.0025. For v = .99999998, the gamma factor is 1/{1 – [(.99999998C/C) EXP 2]} EXP (1/2) = 5,000.
However, if we could deploy in orbit around the Sun, 100 million membranous solar concentrators wherein each solar concentrator has a capture area of 10,000 square meters, at 1AU from the Sun, we would collect about 10 EXP 15 Watts. Each of these concentrators could have a high energy density PV cell that may be as much as 40 or more percent efficient if the claims of researchers in cutting edge PV materials R&D pan out. This could result in say 400 TW of power. In one year, (4 x 10 EXP 14)(3 x 10 EXP 7) Joules of electrical power may be produced or the equivalent of 120 metric toms of matter converted into energy. If antimatter can be produced with 10 percent efficiency, we could produce 12 metric tons per year; at nearly 100 percent efficiency, 120 metric tons per year.
If 1,000 such stations could be set up, we could generate at 10 percent efficiency, 12,000 metric tons of antimatter per year; at nearly 100 percent efficiency 120,000 metric tons per year.
Providing we develope a workable system, the antimatter generation infrastructure could be amped up several more orders of magnitude to produce millions if not hundreds of millions of tons of antimatter per year. In 100 years, this would amout to tens of billions of tons per year.
One caveat is producing very low cost and durable reflectors with current technology and cheap abundant materials.
My brother John and I have patented inventive material which involves but is not limited to very low cost, high mass specific power output inflatable reflectors, made of durable high modulus reflective membranous materials. We managed to produce reflectors that have a mass specific power output on Earth’’s surface of up to 10 kW/kilogram using 0.5 mil metalized mylar or 0.5 mil metalized nylon. The method of manufacture simply involves efficient flat sheet manufacturing patterns using mainly 4, 6, or 8 sheets of thermally bonded, adhesively bonded or otherwise bonded materials. For our first prototypes, we used a clothes iron to thermally bond Mylar toy balloons cut-outs of various inner and outer radii and were more than able to cook hot dogs to a char even in intermittent sunlight using the devices.
As thin film materials of greater strength are developed, the mass specific power yield of our reflectors will only increase.
Some potential exotic super high strength materials might consist of carbon nanotube membranous sheets anywhere from a few nanometers thick to tens of nanometers thick thus increasing the mass specific power yield of the reflectors themselves by 4 orders of magnitude.
All that would be required from the reflector material standpoint to collect 10 EXP 15 watts with our current technology would be 100 billion kilograms of material or 100 million metric tons; 100 billion metric tons for 1,000 such stations. Perhaps building and deploying such reflectors would be an excellent way to sequesture carbon to manufucture the required carbonacious high strength polymer materials.
For reflectors made of carbon nanotube materials or perhaps the theoretically even stronger carbon hexane, the mass required for the reflector portions of 1,000 conjectured stations is only 10 million metric tons.
We achieved full stable deployment of our devices which were only about one meter in diameter with a relative Delta Pressure of about 0.1 PSI or less. The larger the device, the less the required relative Delta P.
Another ceveat is actually launching the stuff. I think the problem is tractable this very centurry if we can get the hardware in orbit at 1 AU. At 0.1 AU, the required mass of the reflective materials drops by 100 fold. However we need low cost and efficient access to low Earth orbit so that we can launch and deploy the systems at 1 AU.
What could we do with 120,000 metric tons of antimatter antimatter fuel that would somehow be utilized with almost 100 percent efficiency? If we assume that we have a space craft with a final payload mass of 12,000 metric tons, using the relativistic rocket equation, delta V = C tanh [(Isp/C) ln (Mo/M1)] = 0.98 C, where Mo/M1 is the ratio of the fully fueled rest mass to final payload or dry rest mass of the vehicle. This corresponds to a relativistic gamma factor of 5.
For M0/M1 = 100, e.g. a fully fueled mass to dry wieght of the vehicle of (120,000 metric tons)/(1,200 metric tons), we have delta V = C tanh [(Isp/C) ln (100)] = 0.9998 C. This corresponds to a relativistic gamma factor of 50.
For the case where only the antimatter fuel component is taken along from the start, perhaps in the form of shielding antihydrogen ice, we have for such as system wherein the effective Isp = 2C for systems that operate at near 100 percent efficiency wherein the matter fuel is collected in route.
For M0/M1 = 100, we have delta V = C tanh [(Isp/C) ln (100)] = C tanh [(2C/C) ln (100)] = 0.99999998 C. For v = .99999998, the gamma factor is 1/{1 – [(.99999998C/C) EXP 2]} EXP (1/2) = 5,000.
Assumming that the human life expectancy can be augmented to 1,100 years in duration, a gamma factor 5 would permit roughly 5,000 lightyear trips for the original living crew; a gamma factor of 50, 50,000 light year trips; a gamma factor of 500, 500,000 lightyear trips; a gamma factor of 5,000, 5 million light year trips.
I am convinced that we could launch such missions within the next two centuries in droves, and for missions that are limited to terminal gamma factors of say between 5 and 500, this very century within the life times of some persons who are young children today.
To arrive at the destination, we need not use rocket thrust with the need to carry extra fuel. We can use electrodynamic breaking such as magnetic breaking, electrodynamic-hydrodynamic-plasma breaking, or magnetic sail based breaking. Magnetic breaking could be accomplished by deploying a large superconducting coil which would build up extremely high current as it sliced through the interstellar or intergalactic magnetic fields thus producing a magnetic field to react against the space based fields in a drag inducing manner. Electrodynamic-hydrodynamic-plasma breaking could be accomplished by a reverse interstellar ramjet type of mechanism. Magnetic sail based breaking could be accomplished through the deployment of a magnetic bottle consisting of plasma deployed around the ship and held fixed by electrodynamic fields.
I think of the meager infrastructure that the New World settlers had here in what would become the U.S. and know we have super highways, 100 story buildings, hundreds of airports, an over 300 ship advanced Navy, dozens of large cities and the list goes on and on.
I have a gut feeling that we can produce vast quantities of antimatter from the Sun. And we still do not know what the qualities of bulk quantities of antimatter are due to CPT violation in certain particle pair creations. We have not yet determined whether antimatter possesses antigravity according to Frank Close’s recent book entitled “Antimatter” or even “partial antigravatic” effects.
One way or another, I feel that antimatter sequestration from natural sources such as within the magnetosphere within the gas giant planets within our solar system, and/or it production in bulk quantities, will prove extremely useful to our manned interstellar travel missions, within the next two centuries and even bolder missions beyond.
Regards;
Jim
