Ricky Tang

What makes a problem GP-hard? validating a hypothesis of structural causes

This paper provides an empirical test of a hypothesis, which describes the effects of structural mechanisms in genetic programming. In doing so, the paper offers a test problem anticipated by this hypothesis. The problem is tunably difficult, but has this property because tuning is accomplished through changes in structure. Content is not involved in tuning. The results support a prediction of the hypothesis - that GP search space is significantly constrained as an outcome of structural mechanisms.

Propulsive Capability of an Asymmetric GDM Propulsion System

*† The role of the ambipolar potential in the propulsive capability of the Gasdynamic Mirror (GDM) has been studied previously. The electrostatic potential arises as a result of the initial rapid escape of the electrons due to their small mass, leaving behind an excess of ions and creating a positive electric potential that slows down the electron escape while speeding up the ions until their respective axial diffusion are equalized. As a result, the ion confinement time is reduced while the ion escape energy is increased by an amount equal to the potential, translating into increased thrust and specific impulse. Previous studies, however, have only considered a GDM configuration with equal mirror ratios at both ends such that on average half of the ions escape through either end of the GDM. For a thruster it is desirable to bias the direction of ion escape to the thrusting end of the GDM. This can be achieved by properly controlling the mirror ratio at both ends such that on average a specified fraction of ions escape through the thrusting end. Due to this asymmetry, the magnitude of the ambipolar potential is changed, and as a result, the ion confinement time and escape energy are affected resulting in different propulsive capabilities compared to the case of a symmetric system.

Phase Transitions in Genetic Programming Search

Phase transitions occur in computational, as well as thermodynamic systems. Of particular interest is the possibility that phase transitions occur as a consequence of GP search. If this were so, it would allow for a statistical mechanics approach and quantitative comparisons of GP with a broad variety of rigorously described systems. This chapter summarizes our research group’s work in this area and describes a case study that illustrates what is involved in establishing the existence of phase transitions in GP search.

Muon-Boosted Fusion Propulsion System

[Abstract] Several years ago a great deal of excitement was generated by muon-catalyzed fusion due to the experimentally verified multiplicity – 100 per muon – of fusion reactions in deuterium (D) and tritium (T) resulting from this process. This excitement was somewhat tempered, however, in its application to power-producing reactors due to the large amounts of energy expended in the production of muons and the need for the presence of muonproducing accelerators in the proximity of the fusion reactor. It was found that the combination of these factors rendered the power balance for the system unfavorable. These problems can now be significantly alleviated by utilizing the pions that are generated by the “at rest” annihilation of antiprotons in U 238 targets. Upon decay, these pions give rise to the muons needed to catalyze DT fusion reactions, and prior to their decay they, along with the fission fragments, can contribute to additional fusion reactions through the plasma heating they provide. Catalysis takes place because a negative muon, when slowing down, forms a meso atom with tritium, and during a certain time this meso atom collides with a deuterium to form a mesomolecular ion. It takes a very short time, subsequently, for an exothermic fusion reaction to take place. It can be shown that the number of cycles which a muon has time to catalyze is about 100, i.e. a single muon can give rise, during its lifetime, to a hundred fusion reactions releasing about 2 GeV of energy. We apply this to a fusion propulsion system consisting of a Gasdynamic Mirror (GDM) attached to an antiproton trap where “at rest” annihilation of antiprotons on U 238 targets is employed for driving the system. We find for a mission of interest, such as a Mars mission, the number of antiprotons required to achieve the mission is substantially reduced due to muon catalysis.

Fusion -Fission Hybrid Revisited - Potential for Space Applications

In several recent papers, we addressed the case of fusion propulsion by focusing on the gasdyna mic mirror (GDM) as a magnetic device in which fusion plasmas are heated to ignition by the reaction products resulting from the “at rest” annihilation of antiprotons in U 238 targets. Unlike terrestrial fusion power systems where large Q (ratio of fusion power to injected power) values are required, only modest Q-values were shown to be adequate for space applications. In this paper, we focus on a bi -modal fusion propulsion system in which Q-values of about unity or less are needed since the GDM will serv e mainly as a neutron source. It is well known that fusion reactions are neutron rich but energy poor, while fission reactions are energy rich but neutron poor. We make use of this fact by considering a system in which the GDM device serves as a fast neu tron source surrounded by a blanket of Th 232 , which we utilize to breed U 233 and simultaneously burn it to produce energy. For a reasonable size blanket and a D -T plasma density, size and temperature, we find that the proposed hybrid system is capable of producing tens of gigawatts of thermal power per centimeter. If we use this power to heat a hydrogen propellant, we find that a seven meter long engine can generate a specific impulse of about 59,000 secon ds at a thrust of about 8 mega -newtons at a propel lant flow rate of about 130 kg/sec. Such a propulsion capability would allow many meaningful space missions to be carried out in relatively short times. Furthermore, such a hybrid system can generate large amounts of electric power for surface power appl ications once destination is reached .

Alpha particle dynamics in muon-boosted fusion propulsion system

In a previous paper, we demonstrated that negative muons resulting from antiproton annihilation in a relatively cold deuterium-tritium (DT) plasma confined in a gasdynamic mirror (GDM) can result in catalyzing on average over 100 fusion reactions. The alpha particles produced by these reactions could contribute significantly to heating the background plasma toward ignition. In fact, it was pointed out that on the basis of energetics only, muon-catalyzed fusion would reduce the amount of antiprotons required to achieve thermonuclear burn by about 60%. This scenario, however, does not address the issue of alpha particle confinement in the GDM, and thereby leaves open the question of their true effectiveness in providing the heating noted above. In this paper, we address this problem by noting that, as they slow down, these alpha particles can escape from the system. We deduce explicit expressions for alpha particle density as a function of energy, and calculate the mean energy of these particles allowing simultaneously for slowing down and escape as reflected by the confinement time. Assuming that the alpha particles slow down primarily on the electrons, as is the case in relatively cold plasmas, we find that muon catalyzed fusion is indeed effective in heating the plasma in a GDM device.

Antiproton-Driven Fusion Propulsion System for OTV Applications

[Abstract] It has often been argued that fusion propulsion systems are strictly suitable for deep space missions such as those to the outer planets or interstellar space due to the large specific impulses they are capable of producing. It is intriguing however to find out how suitable they may be for near Earth missions such as orbit transfers from low Earth orbits (LEO) to geosynchronous orbits (GEO). We examine these cases using an antiprotondriven fusion system consisting of a Gasdynamic Mirror (GDM) magnetic confinement chamber connected to an antiproton “trap”. Taking LEO to be at an altitude of 200 km and GEO to be at approximately 36,000 km, we follow Cassenti’s analysis 1 of Hohmann transfers to establish the required ∆v for a basic mission of transferring a vehicle from LEO to GEO and back. It is found that ∆v = 5.5 km/sec. The vehicle in question is the DT burning fusion propulsion system noted above where plasma heating in the device is achieved by the fission fragments and annihilation products resulting from the “at rest” annihilation of antiprotons in U 238 targets. It is found that such a system will produce an Isp of 2×10 5 seconds and a thrust of 1.2×10 6 Newtons for a total mass of approximately 23×10 3 mT. Assuming a continuous burn acceleration/deceleration type of trajectory, we find that the orbital transfer noted above can be undertaken in about 8 hours, and the amount of antiprotons needed is about 4 µg. The propulsion system will have a specific power of about 40 and a thrust to weight ratio of about 5×10 -3 .

The Role of Ambipolar Potential in the Propulsive Performance of the GDM Thruster

Many of the studies assessing the capability of the Gasdynamic Mirror (GDM) fusion propulsion system used analyses that ignored the ambipolar potential. The electrostatic potential arises as a result of the fast escape of the electrons due to their small mass. As they escape they leave behind an excess of positive charge which manifests itself as a positive electric potential that slows down the electron escape while speeding up the ions until their respective axial diffusions are equalized. The indirect effect on the ions is that their confinement time is reduced, and to compensate for that, the length must increase, relative to that of zero potential, in order to allow for recovery of an equal amount of fusion power. But as they emerge from the thruster mirror, the ions acquire an added energy equal to the potential, and that manifests itself in increased specific impulse and thrust. We examine in this paper the underlying theory of this effect and evaluate its impact on the GDM propulsion capability. Nomenclature Ac = area of plasma core A0 = mirror area D = axial diffusion coefficient E = electric field Ee = electron energy EL = escape energy e = electron charge k = density scale length L = length of plasma

Transportation and Power Requirements for He3 Mining of the Jovian Planets

A bi‐modal fusion propulsion system that can be used for transportation to and the mining of He3 from the Jovian planets is proposed. It consists of the Gasdynamic Mirror (GDM) fusion reactor which is analyzed for utilization as a propulsion device, as well as for use as a surface power system. The fusion reactions in the device are initiated by the heating provided by the fission fragments and the annihilation products produced by the “at rest” annihilation of antiprotons in uranium U238 target nuclei. The energetic pions and muons of the antiproton‐proton (or neutron) annihilation in the U238 nucleus can heat a suitable fusion fuel to several keV temperature during their short lifetime, while the remaining heating to ignition is provided by the fission fragments. We examine the use of such a system to travel to Jupiter, for instance, to mine the He3 which is known to exist to the tune of 350 trillion tons in its atmosphere. Such a rich source of this isotope can readily meet the needs of a fusion‐powere...

Fusion Driven Fission System for Space Surface Power Application

It is well known that fission reactors are energy rich and neutron poor, while fusion reactors are neutron rich and energy poor. As a result, it may be desirable to use the neutrons produced by a fusion reactor operating at a multiplication factor Q ~ 1 to breed fissile material in a blanket, which can also undergo fission reactions with the fast neutrons to produce power. We examine this approach in conjunction with a bi-modal fusion propulsion system which, upon reaching destination, is operated primarily as a neutron source. The neutrons produced by the DT reactions are allowed to impinge on a blanket containing thorium-232, thereby producing uranium-233. This uranium isotope has a fast neutron fission cross reaction of about 2 barns, which we employ to calculate the power density produced in a steady-state operating system. We consider a cylindrical system whose length is significantly larger than its diameter, thereby invoking a one-dimensional approximation for the neutron flux equation which we solve in conjunction with the U production rate equation. For reasonable blanket dimensions consistent with the fusion plasma parameters, we calculate the power density in the fission system and find that it is about 70 times larger than would have been the case in a pure fusion reactor. Hence, such a hybrid system may be viewed as equivalent to a fusion reactor with a Q ~ 70 that can be utilized for space surface power production with no proliferation risk.