PERFORMANCE ANALYSIS OF AN ELECTRON POSITRON ANNIHILATION ROCKET

Transcription

1 PERFORMANCE ANALYSIS OF AN ELECTRON POSITRON ANNIHILATION ROCKET Date of Submission: 25 May 2004 Jonathan A. Webb Brandon Tripp Thomas Stopa Submitted to Dr. Darrel Smith Department of Physics College of Arts and Sciences Embry-Riddle Aeronautical University Prescott, Arizona

2 APD Performance TABLE OF CONTENTS Table of Contents...i List of Tables...Error! Bookmark not defined. List of Figures... ii 1 Introduction Performance Velocity Profile Interplanetary Mission Analysis Conclusions and Recommendations References...11 Rev C i 12 April 2004

3 APD Performance LIST OF FIGURES Figure 1: Photon Absorbing and Reflecting Shields...1 Figure 2: Isp vs. <cos θ>....3 Figure 3: Isp For Low <cos θ>....3 Figure 4: Thrust vs. <cos θ > and Isp (dm/dt = 50 mg/s)...4 Figure 5: Burnout Velocity (%c) vs. <cos θ >....5 Figure 6: Burnout Velocity (km/s) vs. Small < cos θ>....6 Figure 7. Interplanetary Transfer Times for Low Isp, Low Cosine Average S/C of 5000 kg....7 Figure 8. Propellant Mass Fraction for Interplanetary Transfers, Low Isp, Low Cosine Average with S/C of 5000 kg....8 Figure 9. Interplanetary Transfer Times for High Isp, High Cosine Averages with a S/C of kg....8 Figure 10. Propellant Mass Fractions for High Isp, High Cosine Averages for a S/C of kg...8 Figure 11. Earth-Lunar Transfer Time vs. <cos(θ)> and Propellant Mass...9 Figure 12. Hohman Transfer Parameters for an Absorbing/Reflecting APD and Chemical Engine. 10 Rev C ii 12 April 2004

4 APD Performance Page 1 of 11 1 INTRODUCTION In recent studies it has been shown that a spacecraft engine utilizing the annihilation of electrons and positrons could produce incredible space-flight velocities and specific impulses (1). A positron-electron ( e + e! ) engine would annihilate electrons and positrons to produce gamma rays that would be absorbed into a momentum transfer shield at the extreme end of a rocket system. Two momentum-capturing shield configurations have been considered to capture the momentum from the resultant photons as shown in Figure 1 (1). IT! 9/10/04 1:18 PM Comment: a) In this paper? For this paper? What is the purpose of this paper? Is it to describe/evaluate/construct a model for such a system? TRIPP/STOPA: Do we discuss both configurations or stick with the possible one? Figure may have to be changed to reflect this. b) Two Configurations? It looks like we have only one. Are we modeling both? Testing both? If so, where is the other one. TRIPP/STOPA: Need to break this figure up into two figures to show the difference between reflecting shield and absorbing shield.. ((Figure 1): Photon Absorbing and Reflecting Shields.) (Note: Dashed line represents reflecting shield.) IT! 9/2/04 10:36 PM Comment: Double Captions. Is this correct? For the first configuration, separate beams of electrons and positrons would be directed!! toward the center of a hemispherical dish extending from to ", where e + e! 2 2 annihilation would occur. At this point, the annihilated e + e! pairs would produce two 511 kev gamma rays (! -rays) that would travel away from the annihilation point at 180 from each other (back-to-back). Half of the resultant photons would collide with the perfectly absorbing shield, while the other half would be ejected into space. The annihilation process is isotropic which would produce a uniform distribution of photon collisions across the surface of the dish. Each! -ray collision with the shield would produce a transfer of momentum to the spacecraft and one of these momentum transfers would boost the spacecraft from some initial velocity to a higher velocity. The incident photons would cause a scattering effect inside of the shield. The photons would collide with atoms of the shield material, causing a spray of electrons and lower energy photons to be ejected in random directions. Some of these photons and electrons would therefore be ejected opposite to the direction of motion, causing some momentum to be lost and thereby decreasing the specific impulse

5 APD Performance Page 2 of 11 and thrust of the engine. Unfortunately, this method would absorb all of the incident electromagnetic radiation, which in turn would cause a significant temperature increase of the shield (2). Currently, Monte Carlo simulations are being developed to determine the loss of efficiency due to the scattering of electrons and photons. The second configuration involves the use of a parabolic shield that extends to some arbitrary point. In this case the shield is assumed to be capable of perfectly reflecting the 511 kev photons. This reflection process would create a significant increase in the resulting momentum vector of the incident photons. This concept would yield a much larger I sp and thrust than the photon-absorbing shield. Although this is by far the more efficient of the two cases, current technology lacks the ability to reflect 511 kev photons. Even though the reflecting shield configuration is technically the more difficult of the two, it offers the largest cosine average and specific impulse (I sp). I sp values determined for this type of propulsion ranges from 1000 to 30.0 x 10 6 seconds. As this paper will show, the performance of this engine is highly dependant on the cosine average obtained from the momentum transfer of the photons. The efficiency at which the shield could capture the momentum from the incident photons is measured by using a cosine averaging technique. The cosine average is written mathematically as Equation 1: # 2 1 cos # =!( 1+ cos # ) d # (1) "# # 1 The maximum theoretical value for the cosine average that can be obtained is 2. The engine s burnout velocity and specific impulse both increase as the cosine average approaches 2. Figure 2 and Figure 3 show this relationship. IT! 9/10/04 1:13 PM Comment: Currently? As in This paper??? As part of an ordinary project? By you? By others??? TRIPP/STOPA: By other members of the Hyperion Team along with Dr. Smith at ERAU. The results of those simulations will be discussed in another paper. IT! 9/10/04 1:10 PM Comment: What is this term? Undefined. TRIPP/STOPA: We could define this here or we could have a list of symbols at the beginning of the paper, such as in the Smith/Webb AIAA paper. IT! 9/1/04 10:15 PM Comment: It is defined here, but defined too late. May need to redesign much of the paper. IT! 9/10/04 1:19 PM Comment: Being that these two paragraphs describe things on the next page, we should probably put them on the next page in section 2. TRIPP/STOPA: talk to Dr. Smith about how to incorporate these last paragraphs into the next section. IT! 9/10/04 1:12 PM Comment: How do we know this? TRIPP/STOPA: Based on calculations, maybe we should show this calculation. IT! 9/10/04 1:20 PM Comment: Before you move on, how about an overview of the contents/organization of the forthcoming sections?? TRIPP/STOPA: Write another paragraph to do this and to end this section.

6 APD Performance Page 3 of 11 2 PERFORMANCE For the electron-positron annihilation engine, thrust, specific impulse, and cosine average are all related. The manner in which they are related is best shown in the specific impulse and thrust equations shown below in Equations 2 and 3 and in Figure 2: cos! F = ( m& c) (2) 2 cos! c I sp = (3) 2g IT! 9/2/04 10:37 PM Comment: Double Captions. Need to replot this graph and delete the header. ((Figure 2): Isp vs. <cos θ>.) Figure 3 shows that very high specific impulses can be achieved at low cosine averages. IT! 9/1/04 10:22 PM Comment: Data Dumping. Don t just show the Figure now describe the relationship. IT! 9/2/04 10:37 PM Comment: Double Captions. Ditto. Replot and delete the header ((Figure 3): Isp For Low <cos θ>.)

7 APD Performance Page 4 of 11 According to Figure 3, a cosine average of only , which represents an engine propulsive efficiency of only 0.005%, still yields an I sp of 1500 seconds. This specific impulse is larger than even Nuclear Thermal Rockets can offer. Using Equation 2 in conjunction with a 50 mg/s propellant mass flow rate, the thrust vs. specific impulse and cosine average were graphed and are shown in Figure 4. Thrusts on the order of thousands of Newtons (kn) require cosine averages of 0.2 or higher. Cosine averages lower than 0.2 would most likely be best utilized for low mass spacecraft applications due to the lower achievable thrust. Higher thrusts than those shown here can be achieved with larger propellant mass flow rates. IT! 9/10/04 1:27 PM Comment: Data commentary comes after the Figure to avoid dumping. TRIPP/STOPA: Talk to Angela about whether commentary about figures should go before or after. IT! 9/10/04 1:29 PM Comment: Separate Captions Needed. These also need to be re-graphed still and then labeled as separate figures. Maybe only one of these is needed to get the point across, ask Dr. Smith. Figure 4: Thrust Vs. <cos θ > and Isp (dm/dt = 50 mg/s). Doesn t Match up with Webb s charts I believe. IT! 9/10/04 1:33 PM Comment: My thoughts we need to get this to match. TRIPP/STOPA: This has a lower slope than Webb s charts do.

8 APD Performance Page 5 of 11 3 VELOCITY PROFILE The velocity profile for the Antimatter Photon Drive (APD) derived by Smith and Webb (1) is written as Equation 4: & x ' 1# v = c$! (4) % x + 1" IT! 9/10/04 1:33 PM Comment: Introduce this in section 1; at the beginning not middle. TRIPP/STOPA: Good point. The APD should be introduced in the very beginning. where cos! cos! ( % & M i ( 1 % x = # = & #$ (5) ' M f $ ' 1) " The mass fraction was set equal to 100 assuming that 100% of the spacecraft s total mass is comprised of fuel; the maximum flight velocity was determined as a function of cos!. Figure 5 shows maximum burnout velocity as a percentage of the speed of light vs. cosine average and Figure 6 on the next page shows maximum burnout velocity in km/s vs. cosine average: Figure 5: Burnout Velocity (%c) vs. <cos θ >.

9 APD Performance Page 6 of 11 Figure 6: Burnout Velocity (km/s) vs. Small < cos θ>. ***Need to graph Isp(y) vs. burnout velocity(x) Figure 5 shows a dramatic increase in burnout velocity as a function of cosine average. As expected, the maximum burnout velocity approaches the speed of light as the cosine average approaches 2. In theory, spacecraft with cosine averages of 0.30 or greater can reach significant fractions of the speed of light. ***Explain significant fractions of the speed of light (i.e. relativistic effects are noticeable at 20% of c). IT! 9/2/04 10:42 PM Comment: Another graph. IT! 9/1/04 10:32 PM Comment: Notice the lack of an explanation for Figure 5 IT! 9/10/04 1:37 PM Comment: Just how signicant? How fast? TRIPP/STOPA: Need to write in an order of magnitude and probably compare that with something else. TRIPP/STOPA: Need to compare in tabular form or graphical form, this engine with other engines. IT! 9/1/04 10:31 PM Comment: I don t know where to start here; my guess is that we need an explanation and a plot.

10 APD Performance Page 7 of 11 4 INTERPLANETARY MISSION ANALYSIS In order to demonstrate the use of the APD, minimum one-way rendezvous times to the other eight planets in the solar system were calculated and graphed as a function of cosine average and I sp using an all propulsive trajectory code. It was assumed that all spacecraft started with the exact same position and velocity vector of earth, i.e., a C3 = 0 orbit which is a parabolic orbit that has just enough energy to escape the influence of Earth s gravity. They were also assumed to have the exact same orbit in reference to their target planets. IT! 9/10/04 1:39 PM Comment: Figure out and explain what this is. All calculations were made assuming that launch would occur when the planetary alignment brought the two bodies (earth and the target planet) to their closest approach. The time needed for plane changes and orbit insertions were not considered within this analysis and are negligible compared to the transfer time. Equation 6 (3) was used to describe the one-way time of flight for the various spacecraft: 2D Dm f! = + 2 (6) I g F sp Due to the fact that the lower I sp engines would produce smaller thrusts, the calculations were separated into two categories. The lower thrust engines are assumed to propel an unmanned satellite of 5000 kg dry mass. The higher I sp engines are assumed to propel a manned spacecraft of 50,000 kg dry mass. The propellant mass flow rate assumed in the calculations for all transfer times was 50 mg/s. IT! 9/10/04 1:40 PM Comment: Get rid of headers in all these graphs. In addition, we need to separate these figures. TRIPP/STOPA: These Excel graphs need to be redone, and explained. Figure 7. Interplanetary Transfer Times for Low Isp, Low Cosine Average S/C of 5000 kg. IT! 9/1/04 10:33 PM Comment: I had to change this from 5 to 7; make sure intro is AOK.

11 APD Performance Page 8 of 11 Figure 8. Propellant Mass Fraction for Interplanetary Transfers, Low Isp, Low Cosine Average with S/C of 5000 kg. Figure 9. Interplanetary Transfer Times for High Isp, High Cosine Averages with a S/C of kg. IT! 9/1/04 10:37 PM Comment: Dr. Beck circles the Saturn through Pluto. Figure 10. Propellant Mass fractions for high Isp, high cosine averages for a S/C of kg.

12 APD Performance Page 9 of 11 Figure 11. Earth-Lunar Transfer Time Vs. <cos(θ)> and Propellant Mass. Figures 5 through 9 show very rapid transfer times to all eight planets using very little propellant mass even for engines with low cosine averages. Figure 7 and 8 shows that engines with low cosine averages should only be used to propel low mass spacecraft due to the low thrust-to-weight ratio. Even with a lower thrust, spacecraft of 5000 kg or less can be delivered to the inner planets within 9 weeks or to the outer planets within 12 months. Engines with cosine averages larger than 0.1 are well suited to drive high mass spacecraft as shown in the Figures 9 an 10. Spacecraft can be delivered to any point in the solar system within a few days to weeks with a propellant mass fraction of less than 6 percent. A spacecraft using an engine with a cosine average of 1.9 can deliver a 10 metric ton spacecraft to the moon in less than 7 hours using 1.11 kg of propellant Figures 7-11 are assuming direct trajectory calculations and do not take into account the thrust-to-weight ratio. In each of these figures the time of flight will increase above the calculated times for lower cosine averages. The flight times will deviate from the graphed times at cosine averages below 0.3 for the figure 7 trajectories and for the Figure 7 trajectories. This is because the acceleration of each spacecraft will not be enough to compete with the acceleration due to the suns gravity. This will not allow the spacecraft to fly a direct trajectory and will more than likely require the spacecraft to either spiral out of the solar gravity towards its desired burnout velocity or fly a propulsive conic trajectory. Figures 7 through 11 show the maximum performance capabilities of an antimatter engine for interplanetary propulsion applications. The above figures show the fastest transit times and the most propellant consuming trajectories. This engine could also be used on conventional Hohman transfers with extreme savings in propellant mass. The propellant requirements for both the absorbing shield at a cosine average of 2/π and the reflecting shield with a cosine average of are shown in figure 10 compared to that of a chemical engine with a specific impulse of 450 seconds.

13 APD Performance Page 10 of 11 All Hohman transfers assume the spacecraft is in an initial earth parking orbit of 400 km with an eccentricity of The plane change for each transfer is assumed to occur at a true anomaly of 90 degrees. It is also assumed that the spacecraft enters into a 0.95 eccentricity orbit with a perigee altitude of 300 km around the target planet. Figure 12. Hohman Transfer Parameters for an Absorbing/Reflecting APD and Chemical Engine. As is seen in Figure 12 both forms of electron positron annihilation engines offer extreme savings in propellant mass over chemical engines. In every interplanetary transfer the chemical engine at 450 seconds of specific impulse requires hundreds of kilograms of propellant where the antimatter concepts only need a few grams of propellant. It should also be noted that 450 seconds of specific impulse is currently the highest I sp achievable with any type of chemical propellants, namely liquid hydrogen and liquid oxygen. 5 CONLCLUSIONS AND RECOMMENDATIONS The performance of an antimatter engine relying on electron positron annihilations is highly dependant on the cosine average. This is a performance characteristic highly dependant on advances in the engineering materials field. In order to obtain high cosine averages a reflecting shield is needed. Unfortunately no shield is currently capable of reflecting MeV photons. High specific impulse engines can still be obtained with an absorbing shield concept. Unfortunately the thrust would have to be limited to incredibly low levels in order to prevent the shield from melting under the extreme conditions (2). IT! 9/1/04 10:46 PM Comment: New Section, start on new page. IT! 9/10/04 1:41 PM Comment: 511 kev photons or MeV, page 1 used 511 kev TRIPP/STOPA: Need to be consistent with this number throughout the paper. The results of this study show that even at low cosine averages and specific impulses an antimatter engine offers performance well above that of any other known propulsion systems and can allow for extremely rapid interplanetary travel. Due to the potential of this engine further study is warranted to push the envelope of space exploration. In order for an antimatter engine to become a reality advances in the storage and production of antimatter are required as are advances in reflecting shield materials.

14 APD Performance Page 11 of 11 6 REFERENCES 1 Smith, D., Webb, J., (2001) The Antimatter Propulsion Drive A Relativistic Propulsion System, AIAA Paper Webb, Jonathan, (2002) Thermal Analysis of a Tungsten Radiation Shield for Beamed Core Antimatter Rocketry, Embry Riddle Aeronautical University 3 Kammash, Terry, (1995) Fusion Energy in Space Propulsion, Washington D.C., American Institute of Aeronautics and Astronautics 4 Gaidos, G., Lewis, R.A., Meyer, K., Schmidt, T., Smith, G.A. (1998), AIMStar: Antimatter Initiated Microfusion for Pre-cursor Interstellar Missions. Conference on Applications of Thermophysics on Microgravity and Breakthrough Propulsion Physics. STAIF-99 Albuquerque, NM. January 31-February 4, Chakabarti, S., Dundore, B., Gaidos, G., Lewis, R.A., Smith, G.A. (1998). Antiproton- Catalyzed Microfission/fusion Propulsion Systems for Exploration of the Outer Solar System and Beyond. The 34 th Joint Propulsion Conference, AIAA Paper , Cleveland, OH. July 13-15, IT! 9/1/04 10:48 PM Comment: Not mentioned in paper. Need to reference or delete. What shall it be?