the static polarizability is α 0=(2a0)3, where a0 is Bohr's radius. If the atom is in a Rydberg state, that is, in an excited state with relatively large principal quantum number n> >1, the atomic radius can be replaced by an=a 0n2. On the strength of this argument alone, the atomic polarizability of a Rydberg state appears proportional to n6 . In fact, if one accounts for all states with different orbital quantum number l, the static polarizability of a Rydberg atom results proportional to n7. For instance, the atomic radius of atoms in one-electron Rydberg states with n˜102, which are routinely created in the laboratory and are present in interstellar space, is ˜104a0—similar to the size of an Ebola virus! Under these circumstances, the static polarizability is a stunning ˜1014 times larger than its static value [19, 30, and Refs. therein].
[0113] From the practical standpoint, it is important to notice that Rydberg atoms gases have already been “ frozen” and trapped in order to study, among others, the very dipole-dipole interactions we discussed at the very beginning of this disclosure [31]. The atoms themselves are prepared by causing them to absorb laser light of wavelength appropriate to induce a radiative transition to the desired excited state. Noticeably, the radiative lifetime of Rydberg atoms can be quite long, even compared to the relatively short crossing time within the propulsive system. The choice of atoms in states other than the ground state, such as Rydberg atoms, imposes an additional constraint upon the interatomic distance, since the radius of these atoms can be macroscopic. It is therefore important to require that the interatomic distance be much larger than the Rydberg atom radius, which in turn affects the size of the entire propulsive system.
[0114] It is appropriate at this time to again stress the difference between the atom-atom force, which is related to the dependence of the dispersion energy on the interatomic distance and is a central force, and the vertical lifting force acting upon all atoms as a consequence of the modification of their interaction potential in an accelerated reference frame. For instance, let us again consider the potential energy of a pair of atoms (Eq. (12)) and let us rewrite it to highlight the close similarity to the gravitational case: TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE where the equivalent quantum-electro-dynamical “gravitational constant” is, by definition:TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE and the dynamic polarizabilities play the role of the “ gravitational mass.” The total potential energy can then be written as usual: TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE where the summation is meant over all pairs and Rij is the magnitude of the interparticle distance vector, Rij.
[0115] Every atom in the gas is acted upon by a gravitational-like self-force and thus undergoes an acceleration gQED towards the center of the cloud (assumed approximately spherical) similar to a typical gravitational acceleration. This is in complete analogy to the collapse of a “cold” gas sphere taking place whenever the gravitational pressure is vastly larger than any opposing gas pressure gradient. The order of magnitude of the time required for the entire cloud to collapse to its center is an important characteristic time in stellar evolution and in stellar dynamics, and it is referred to as the free-fall time [32-33]. In order to generalize this quantity to our case, let us consider the equation of motion of a particle (atom) in the above potential at a distance r from the center of the cloud with αA(kL)=αB(kL) and NA>>1. In this case it is well-known from elementary mechanics that Gauss' Theorem allows us to only consider the force exerted by the atoms inside a sphere of radius equal to r and we find: TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE Since we are only estimating an order of magnitude, let us assume, as done typically, that the acceleration is approximately constant during the free-fall process. Thus: TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE which yields, for r˜D TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE Finally, by substituting Eq. (15) into this result, we obtain:TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE The importance of this result lies with the fact that the physics of the system after such free-fall time must be expected to be substantially different than in its initial state. For instance, in the case of atoms in their Rydberg states, a drastic evolution of the system towards a higher density configuration can be expected to result in the transformation of the gas into a neutral plasma, with consequent complete loss of thrust.
[0116] The condition to be required so that the atoms do not have the time to evolve into an extremely different, and technologically useless, state is that the free-fall time above be much longer than the time the atoms spend in the trap before the lifting force causes them to be ejected, ΔtA. Evidently, if the gas evolves into, for instance, a plasma upon ejection, that is of no consequence to the momentum it will transfer to the vehicle. By using the result below at Eq. (40), we can write this requirement as: TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE If the lift acceleration is much larger than g, the term in square brackets in the denominator of the right-hand-side will become much larger than unity so that term can be neglected and we easily find the limiting condition:TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE This condition, which of course results also by requiring that a umlaut over (r), can be satisfied by realistic values of the geometry of the propulsive system, although it clearly points to the usefulness of employing larger traps, for which NA ..1.
[0117] That the physical state of the gas can in fact be extreme after a few free-fall times if this is not accomplished, can be seen by writing the condition that the gas be in equilibrium under the action of this gravity-like interaction. As well-known, gravitationally bound systems do not display what can be properly referred to as equilibrium configurations in the thermodynamic sense. This is well illustrated by an appropriate similitude between the cold gas in the propulsive system of this invention and a globular star cluster—a spherical system in which thousands to hundreds of thousands of stars are bound by their mutual gravitational interaction—or, alternatively, a star [ 22].
[0118] In a globular cluster (or in a star), the distribution of velocities of the constituent particles “ relaxes” to a quasi-Maxwellian velocity distribution after a time properly referred to as the “relaxation” time of the object. However, a Maxwellian velocity distribution contemplates a finite number of particles whose speeds at any given time are higher than the escape velocity from the system. Therefore there occurs a process of constant evaporation, which clearly forbids the existence of any equilibrium configuration [32-35].
[0119] However, it is possible to define a condition of quasi-equilibrium, in which a gravitationally bound system does not change drastically over many relaxation times. Under these conditions, the object obeys a general theorem referred to as the virial theorem, which links its total average kinetic and potential energies. This connection is very powerful, as it allows one to obtain estimates of the average speeds of its particles, whether they be stars or atoms [35-36]. For the purposes of our estimates here, this very general theorem can be written as
2Kgas+Ugas =0, (23) where Kgas is the total kinetic energy and the triangular brackets indicate the time-average. By writing the total kinetic energy as TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLEand by approximating 1/D>=1/D, the virial theorem yields:TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE The physical significance of these equations can be found by imposing the condition that the average kinetic energy be equal to the ionization potential of the atoms EI in the gas so that the atoms may become ionized as they collide, in analogy to the Saha and Boltzmann equations of stellar astrophysics [33]: TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE where the right-hand-side of the above equation contains the ionization potential of a hydrogen atom in its n-th state and E0 is the ionization energy of the ground state. By using Eq. (24), this yields:TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE which can be expressed in even more fundamental terms in the case of Rydberg atoms as:TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE In the near-resonance case we can instead write:TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE Replacing the numerical values we shall produce below in a few realistic examples, it is immediate to conclude that the almost immediate ionization of the entire atomic population is highly likely in all technologically meaningful cases, and that, as already pointed out in this section, it is imperative to choose parameters that ensure the expulsion of the gas from the trap well before this process is completed. 4.1.2 Validity of the Present Approach
[0120] In this subsection we concern ourselves with the possible limitations of our treatment. Let us first of all notice that we have so far dealt with atoms in the trap as “ classical” objects, that is, as material particles whose positions and velocities can be likened to those of stars in a cluster, for instance. This is approximately correct only if the de Broglie wavelength λA of the atoms is much smaller than the interatomic distance, that is, if: TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE where pA is the momentum of the atoms and the middle step is warranted for non-relativistic speeds. This condition may be violated for extremely low temperatures and for high densities, such as those of artificial “white dwarfs,” and in these cases the gas must be treated as a quantum gas of the appropriate statistics as is the case, for instance, in white dwarf stars [22, 33]. Although such extreme conditions are only marginally important to the present work, a well-established theoretical framework exists in the literature to describe them.
[0121] Secondly, the basic result at Eq. (12) is rigorously valid only within fourth-order perturbation theory [ 21]. An order of magnitude of the regime within which our results are certainly warranted can thus be found by requiring that the energy shift per atom due to the total intermolecular force of the gas cloud be much smaller than the energy of the n-th unperturbed state occupied by the atoms, that is:
|En|NA |ΔE|, (31) or, for hydrogen atoms: TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE where the relationship between total power and intensity at Eq. (48) was used. Let us consider only the s-state polarizability as α n(λL)=αnr(2an) 3 and let us write the average intermolecular distance in terms of the atomic radius as {overscore (R)=overscore (r)a n. Finally, by recalling that an=a0 n2, we find:TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE The dynamical consequences of this constraint can be seen by recalling our basic Eq. (14) written by making use of the first two terms of Eq. (32):TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE In order to extract a physical meaning from this requirement, let us consider the problem of bringing the gas cloud to a hover from a different standpoint. The condition of balance between weight and lift of one atom is given by Eq. (14) above:TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE By using the expression for the potential of one pair at Eq. (12), we can express this condition by introducing the total intermolecular energy of one atom due to all the others, NAΔE:TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE With the usual strong caveats of using our non-quantum “ intuition” to interpret results in the realm of quantum-electro-dynamics (QED) in curved space-time, a possible qualitative view of this hovering condition is that this requirement corresponds to having the total (negative) intermolecular potential of the gas cloud cancel its total gravitational mass, thus resulting in atoms which are, for all practical purposes, “weightless.” By going further, it is possible to consider intermolecular potentials which are negative and larger in magnitude than the gravitational mass of the atoms, thus causing the total energy of the cloud to become effectively negative. According to Newton's Law of Gravitation, this would require the atoms to be “repelled by gravity,” instead of being attracted. Although this is an interesting and useful image—which has in fact been pursued by Boyer in the past [16]—one has to be extremely careful to adopt it as an “explanation.”
[0122] In the scheme of the present invention, the upward lifting force does not result from such view, but from the well-understood distortion of the Coulomb potential due to the presence of the gravitational field. Although Boyer's work proved these two points of view to be equivalent [16], his study dealt with completely classical dipoles within the realm of special relativity and very weak gravity, and not with fully quantized atoms with the framework of QED in curved space-time. Since one possible interpretation of dispersion forces between molecules involves a modification of the zero-point-energy of the quantum vacuum [ 37], such simple “semi-classical” explanations should be looked at only as useful mental pictures, since the “ system” under consideration is actually an open system.
[0123] In this context, two possible objections must be addressed. The first is whether it is at all correct to use perturbation theory in this case. After all, in order to bring a cloud of hydrogen atoms to a hover, the intermolecular potential must contribute an energy approximately equal to the rest-mass of a hydrogen atoms, or ≈1 GeV, whereas the ionization potential of a hydrogen atom is 13.59 eV if the atom is in its ground state and much less if it is in a Rydberg state. The intermolecular potential will be vastly larger if we want to achieve an upward acceleration. The answer rests with the key fact that, in our case, the processes we are studying take place on relatively “short” time-scales. At some time after the cloud of atoms has been cooled and trapped, a very intense beam of radiation is turned on within a total time that will be assumed to be much shorter than that of any possible atomic transition. For instance, the radiative lifetimes of very high n Rydberg atoms can be even fractions of a second, whereas lasers can be turned on in fractions of a nanosecond (10−9 s) and that radiation will require a similar time to cross the entire trap at the speed of light.
[0124] A well-known feature of the perturbation theory of “sudden” interactions is that the perturbation does not have to be small for theory to be used, unlike most other applications of perturbation theory, as stated, for instance in [38] (see also [39-41]): “The transition probabilities in instantaneous perturbations can also be found in cases where the perturbation is not small . . . If the change in the Hamiltonian occurs instantaneously (i.e. in a time short compared with the periods 1ωif of transitions from the given state i to other states), then the wave function of the system is “unable” to vary and remains the same as before the perturbation. It will no longer, however, be an eigenfunction of the new Hamiltonian Ĥ of the system . . . ”
[0125] By making further use of this same mental picture, we can say that in the description of the fundamental physical process at the basis of the present invention we assume that the phase of upward acceleration of the atoms takes place in the very early stages immediately following the application of the laser radiation field and before the eventual modification of the wave functions intervenes. In other words, there exists a relatively brief time span immediately following the laser turn-on time, during which the atomic dipoles still behave as such, although, eventually, the gas evolves towards a very different state, such as a plasma for instance. Part of the refining work of the present invention will be to consider in detail the dynamics of the evolution of the atoms in the intense radiation field. However, the references quoted show that there is a solid logical foundation in the use of perturbation theory in the present case due to the instantaneous application of the radiation field.
[0126] The second objection to consider is whether it is against any fundamental law of physics to even consider the existence of a volume of space where the total energy is negative, as appears to be necessary in order to obtain a gravitational “ repulsion” of the atoms. We have already provided a first hint above that one answer to this objection is that it is not at all necessary to look at this process as being due to a “ negative” energy. In fact, one alternative and much more satisfactory way to explain the upward motion of the atoms is to appeal to the distortion of the dipole-dipole field due to the acceleration in the presence of a gravitational field. The distortion of the field lines due to the presence of gravitational appears to be a much firmer concept than that of a “negative” energy.
[0127] However, even if one wants to engage in the widespread debate concerning the existence of negative energy, it is interesting to point out that dispersion forces in general and Casimir forces in particular are in fact commonly used as examples to the affirmative. In other words, whereas there exist strict quantum limits, similar to the uncertainty principle, as to the length of time a very negative energy density can be imposed upon a volume of space, dispersion forces clearly afford an example where the energy density can remain negative indefinitely (although the same limitations apply if one attempts to decrease the energy even further). The important point to the present invention is that there is no fundamental physical reason that dispersion forces cannot be made negative for the brief time needed to accelerate the atoms upward as required to provide thrust. On the other hand, much more exotic and fantastic applications of negative energy to “warp-drives,” “time-machines,” and “faster-than-light” travel, which now appear forbidden by fundamental laws of quantum mechanics in curved space-time [42-45] are not involved in the physical processes of this invention. 4.1.3 Thrust
[0128] By using Eq. (13) above, we can write the total lifting force on the trapped atoms in the case that αA (kL)=αB(kL), by assuming that the average of the interatomic distance between any given atom and all others is ˜D, as: TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE Let us now consider the total momentum acquired by the gas as it flows out of the atomic trap. Without getting into the details of the dynamics of such process, which certainly deserve further consideration, let us consider the acceleration of the atoms under the action of the lifting force, Fgas. In an inertial reference frame, the total acceleration undergone by the atoms would be Fgas/NAmA, but, in this non-inertial frame, the acceleration will be (Fgas−NAm Ag)/NAmA=(Fgas/NA mA)−g. For instance, if the lifting force is exactly equal to NAmAg, the atoms will not accelerate with respect to the vehicle, but only hover, as we have seen in the above theoretical treatment. Therefore: TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE At this rate, the average final velocity of the atoms will be v A,fin=√square root over (2aA(D/2)): TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE where, of course, the application considered in this invention considers only circumstances in which the radical is real.
[0129] It is also of interest to find an order of magnitude for the time required to leave the atomic trap defined as TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE which sets a lower minimum to the “reload” time of the thrust cycle:TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE From Eq. (39) we can immediately write the total momentum of the gas, ΔPgas, for each cycle at it approaches the shock absorber:TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE Finally, let us estimate the total momentum transferred to the vehicle in the assumption that the impact of the gas against it is dissipative, that is, by assuming the complete conservation of momentum. In this case, the final speed change of the (gas+ craft) system at the end of the n-th cycle will be given by m gasvA,fin=(mgas+Mcraft )Δvn. That is, by solving for Δvn, TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE Although the acceleration of the vehicle varies over time during the cycle, it is useful to introduce an average acceleration over the cycle itself, we the understanding that the acceleration experienced by the atoms during their phase of acceleration may be different, and usually higher, than this value because of the cycle synchronization we discussed earlier. We write: TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE where ΔtReload is the time required to prepare the new atomic cloud in the trap for the following cycle. This definition allows us to also define a nominal thrust for the engine as:
Fengine=(NAm A+Mcraft)acraft. (45)
[0130] In the limit in which the reload time vanishes (ΔtReload→0), of course we find, as expected: TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE In this ideal limit, the hovering condition becomes that F gas=(NAmA+Mcraft)g, that is, the total force on the atomic cloud must be equal to the weight of the entire vehicle. This is also the thrust that could be obtained if the atomic cloud could be trapped permanently within the chamber even as it acts on the vehicle via the action-reaction law. 4.1.4 Energy Considerations and Thruster Efficiency
[0131] The total radiation power utilized will be estimated as W=18ID2, which corresponds to six laser triads (this is an upper estimate of the power needed as it is possible to induce gravitation-like behavior in a particular direction by using less power than this maximum). This yields:
W=18INA2/3{overscore (R)}2. (48) By solving this expression for the radiation flux I, we find: TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE This result allows us to obtain a realistic estimate of the relationship between the dynamics of the process and the total amount of energy needed. For instance, by substituting it into Eq. (38), we obtain the following useful expression: TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE which exposes the interesting fact that, in the present approximation, the atomic acceleration as a function of the total laser power irradiated is independent of the number of atoms in the trap. By means of this equation, it is possible to write the total power needed to be focused onto the trap to achieve a hover, that is, a vanishing acceleration of the atoms with respect to the vehicle. This corresponds to: TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE independently of g. For practical reasons, let us rewrite this result in units of Megawatts (MW) in terms of the wavelength in micrometers, λ(μm), of the average interatomic distance in units of Bohr radii, {overscore (R)/a0, and by involving the dimensionless polarizability factor as αA(kL )=αnr(kL)α0: TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE Of course this result should be interpreted as allowing the atoms to be brought to a hover for a time no longer than the free-fall time given at Eq. (19) above unless an independent trapping approach is employed to hold the atoms at constant intermolecular distances, such as in an optical crystal.
[0132] Similarly for Eqs. (17), (18), (20), and (21): TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE with the same restrictions on the duration of the impulse.
[0133] The ratio of thrust to radiation pressure: This dimensionless quantity compares the thrust obtained from the present thrust mechanism to the radiation pressure one would obtain by simply radiating away the power used instead to alter the intermolecular potential. Clearly one expects this quantity to be much larger than unity in order for the approach of this invention to be of practical use. Should that not be so, the case could be made that focusing the radiation onto an appropriately large sail would be a more efficient use of that energy. We have, in the ideal case in which the reload time vanishes, TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE In the limit in which aAg, we have, simply:TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE Typical estimates of this quantity in interesting cases indeed indicate values much larger than unity for this quantity.
[0134] As in any other system that does not make use of the traditional expulsion of high speed gases to generate momentum (e.g. light sails), one must introduce new figures of merit. For instance, the typical concept of the specific impulse (the ratio of engine thrust to the weight of the material ejected in the unit time) [29], requires special attention in this case. Let us consider the case of a thrust system in which all radiation emitted by the high power lasers is permanently lost and radiated away from the spacecraft. Because of the mass-energy equivalency, this will correspond to a net mass-loss of the vehicle at a rate M craft=−W/c2. In the literature, the “photon rocket,” which annihilates matter and antimatter to eject the corresponding radiation in a particular direction, is defined by theoreticians as the “perfect” rocket engine, because it yields the highest terminal speed at burnout for the same final to initial mass ratio [46]. However, whereas in that case the thrust is directly due to the reaction to the emitted photons, in our case the presence of the radiation in the chamber where the atoms are trapped is only a catalyst to create the thrust upon the vehicle. Thus, since the origin of the thrust in our case is not the lost radiation one could just as convincingly argue that the specific impulse becomes undefined in this case.
[0135] From the quantitative standpoint, therein lies the great interest of the approach of the present invention. That is, for the same amount of energy expended, the thrust derived is much higher than that obtainable in the photon rocket [46]. At the same time, this high thrust does not come at the price of an impulsive propulsive system as in chemical engines, but one that can actually provide high accelerations over almost indefinite periods of time [47].
[0136] Thruster efficiency: This is the ratio of the kinetic energy of the atomic cloud as it emerges from the trap to the total energy used during the acceleration of the gas. By using the above expression for the final velocity of the atoms, this quantity can be written as: TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE In the same limit aAg we find: TABULAR OR GRAPHIC MATERIAL SET FORTH AT THIS POINT IS NOT DISPLAYABLE Special care must be exercised in interpreting the results obtained by extrapolating this equation to values of the efficiency that exceed unity, since this may be an indication that other phenomena are becoming important. Furthermore, we have here neglected other forms of energy that are also required, such as, for instance, the radiation required to excite the atoms if Rydberg states are used and the energy used for the initial trapping. As shall become clear in the examples below, the present invention represents a useful and revolutionary technological innovation even in regimes where the thruster efficiency is below unity. 4.2 Start-Up, Maneuvers, Cruise, and Turn-Off
[0137] The fundamental, basic physics principle of this invention is the distortion of the field of a dipole in an accelerated reference frame and the resulting “lifting” dipole-dipole force. In order for this principle to operate, an acceleration must be induced upon the dipole system before the thrust on it can appear. In other words, it is not possible to turn on the thrusting system of this invention from a cruise phase (approximately at constant speed). Because of the Principle of Equivalence, such initial acceleration can be provided by means of any combination of two different, but equivalent mechanisms. In the former, the acceleration is due to gravitation, which provided the initial motivation for the present invention.
[0138] Because of the Principle of Equivalence, the effect of a gravitational field is indistinguishable from that a uniformly accelerated reference frame (if we neglect the Linet term mentioned in our comment of Eq. (3) and in Ref. [9] and quantitatively unimportant to this invention). Therefore, the trigger acceleration can be provided by the gravitational field as a supported (not freely falling system) rests, for instance on the ground. Because of the Principle of Equivalence, if the spacecraft is freely falling its acceleration exactly cancels that of the gravitational field and it becomes indistinguishable from a laboratory at a large distance from any other mass, to the extent that its size is relatively small.
[0139] Because of the mechanism of this invention, if the spacecraft is resting on the ground, upon laser turn-on, the intermolecular forces will be distorted in such a way as to cause an upward acceleration of the atoms, which can be made, for instance, as large as needed for the spacecraft to hover. On the other hand, if the spacecraft is in outer space at a large distance from any other celestial objects, such as in interplanetary flight, the initial acceleration must be provided by independent means. This can be achieved in a variety of ways. For instance: (1) an initial forward acceleration can be produced by a traditional thrusting system until the first few cycles of the present engine are produced—in this case the traditional thruster becomes an “ignition system” for the present invention; (2) the entire craft can be put into rotation around an appropriate axis, thus reproducing Einstein's rotating disk [46]; (3) on re-entry, a spacecraft undergoes an aerodynamic deceleration that can be used as the trigger.
[0140] The same above sample triggers can be also used for maneuvering, that is, to create an initial acceleration in a direction different than that of the present motion. This can be very useful to transform the present invention in a vehicle for motion near the surface of the earth. A slight acceleration parallel to the ground could be maintained with relatively little radiative energy while a larger amount of radiation would keep the vehicle hovering safely. A slow decrease in the power of the lasers, or any other change in the parameters determining the thrust, such as intermolecular distance or total atom number, would result in a decreased acceleration of the atoms and, thus, of the vehicle. In order to bring the vehicle to a cruise (constant speed) the only necessary action is to turn off the high power lasers, or, alternatively, to empty the atomic trap system of atoms. The acceleration upon the vehicle would then immediately stop along with the dipole-dipole field distortion, thus bringing the craft to constant velocity. Finally, a trigger acceleration can be exercised in a direction opposite to the instantaneous velocity to start an opposite thrust that brings the vehicle to a deceleration and to a new hover.
[0141] Although the notion of flying by exploiting an initial acceleration may appear counterintuitive, it must be said that a similar transition also challenges some pilots at the beginning of their training. In fact, flying through air requires speed to create lift from the airfoils and a slower and slower aircraft is unable to keep altitude. This concept requires constant training in beginning pilots today to fight the instinct to “ pitch-up” to regain lost altitude on landing, as that can result in a stall. Similarly, the lifting mechanism of this invention requires the user to become sensitive to acceleration—as opposed to speed—and to the notion that an accelerating vehicle can maintain thrust, whereas one at constant speed will loose thrust. 4.3 Numerical Examples
[0142] The following numerical examples were generated by making use of a Mathematica notebook [13] which encoded the equations discussed in this document. The design of any of the missions below could (and does) take many years of study, but the goal of this section is to provide the information necessary to appreciate the fact that the physics of this invention leads to realistic engineering demands. In other words, whereas relativistic travel is usually assumed to require harnessing absolutely fantastic amounts of energy, the method below yields numbers that can be realistically contemplated to be put into feasible design with presently existing technologies.
[0143] Any space mission must start with some requirements, which are to some extent arbitrary or descend from other constraints. In the examples below, we assumed that all travel takes place at a given spacecraft acceleration a/g<1. This is to contrast the approach to space travel of this invention with typical designs, which either impose high (several g) accelerations for a short periods of time (chemical rockets) or provide very low thrust over very long periods of time, such in the case of ion propulsion, in which the author of this invention has been directly involved [47]. Let us recall that the present method requires that the intermolecular potential be distorted by the acceleration of the vehicle (or by gravitation if the vehicle is held at rest, as required by the Principle of Equivalence). Therefore, the acceleration of the vehicle due to the impact of a gas cloud into the plate determines the efficiency of the atomic acceleration in the following cycle.
[0144] According to the present method, space travel is most efficient when it is significantly accelerated. This is not a drawback, since, for instance, it is now understood that the dangers to human health of very long periods of weightlessness are significant. The data presented herein were thus produced by assuming a spacecraft acceleration a=g and then by demanding self-consistency, that is, by requiring that the spacecraft acceleration produced by any given gas cloud also be equal to g. Even with this requirement, the choices shows below represent only one of many possibilities chosen for their being realistic from the engineering standpoint or for their being representative of a contrast between the present invention and present-day technology. For simplicity, the reload time was everywhere assumed to be negligible. 4.2.1 A Robotic Low-Thrust Delivery System to the planet Mars Propulsive System Specifications W=35.0 MW=3.5x1014 erg/s αnr=1x106 (quasi-resonant
response) n=1 (ground state) {overscore (R)=5a0 λL=1000 Å (quasi-Lyman-α transition) Mcraft=107 g=10 metric tons NA=4.66x1026 mgas=7.86x103 g=0.786 kg Chamber Size D=20.3 cm Whover (acraft=1 g)=2.7 kW aA=1.28x 105 cm/s2 vA,fin=2.29x 103 cm/s ΔtA=1.79x10−2 s tff=60.6x10 s Efficiency=3.3x10−4 Δvcraft/cycle=2.62 cm/s acraft=10 cm/s2 (self-consistent) Thrust=10.0 kN (Thrust/Total Radiation Pressure)=8.57x104 Earth-Mars distance at opposition (Aug. 27, 2003) 55.758x10
11 cm [48] Total Travel time=1.52x106 s=17 d 13 h
17 min 46.7 s Maximum Speed (reached after=6x105 s)=
6.0x106 cm/s=60 km/s Maximum Kinetic Energy (reached after 6x105 s)=
1.8x1020 erg Total Energy Radiated (up to maximum speed)=2.1x1020
erg Time to Mach 1 (Speed of Sound vsound<<congruent331 m/s)=
3.31x103 s Time to Clear Low-Earth-Orbit (400 km)=2.8x103
s=47.1 min Time to Clear the Earth-Moon System (4x105 km)=
8.94x104 s=1 d 50.7 min Comments
[0172] In order to obtain the above estimates for the transfer to Mars, we greatly simplified the problem by neglecting the gravitational force of all objects involved, including the Sun, the Earth, and Mars. Of course, the gravitational force of the Earth is actually an integral part of the engine start-up mechanism of the present invention and in that sense its effect is accounted for here. However, since the gravitational field of all near-by objects is cleared in a matter of minutes, its influence on the dynamics of flight was neglected in these order-of-magnitude calculations.
[0173] It is useful to make come comparisons between the specifications of the system above and present-day delivery systems, since that helps elucidate the great technological relevance of the present invention. A typical choice for such recent space missions to Mars as the ones of Spirit and Opportunity is the Boeing Delta II 7925 or 7925H (the letter H indicates the more powerful high performance version) [49]. In its common configuration, the RS-27A engine of the Delta II first stage, along with the additional nine strap-on solid rocket motors, generates approximately 8.9x 105 Newtons of thrust, which are necessary to lift the total “wet” (fueled up) vehicle mass of 285, 228 kg off the launch pad. This thrust is almost one order of magnitude larger than that of the engine described in this document until the Main Engine Cut Off (MECO), approximately 265 s after lift-off. The thrust of the following stages is smaller, with the thrust of the third stage at approximately 6.6x104 N.
[0174] Since the initial phase of ascent takes place under the thrust of a chemical rocket, not surprisingly we see that both in the case of Spirit and Opportunity the Delta II vehicle passes through Mach 1 in a much shorter time than the one propelled by the engine of this invention (32.4 s and 29.6 s, respectively) [ 50]. However, very importantly, by a very good approximation, the entire launch mass of 10 metric tons (104 kg) is propelled towards Mars in the present case whereas, in the traditional approach, only 1.070x103 kg out of the initial 285, 228 kg represent the useful remaining payload. Of this surviving mass, only 533 kg actually lands on Mars in the traditional case, since approximately 250 kg are allocated to the cruise stage alone.
[0175] Finally, the entire vehicle propelled by the engine of this invention arrives at Mars in a matter of less than twenty days, whereas both Spirit and Opportunity, extremely reduced in mass, arrive approximately six months later. It is very significant that the gravitational field of Mars, added to the deceleration of the spacecraft, makes the process of landing much slower and completely safe, in contrast with what NASA/JPL itself defines as the “six minutes of terror,” during which the vehicle must be slowed down from 12,000 miles/hr to 0 miles/hr corresponding to average accelerations acraft˜1.5 g, although during the last drop the acceleration can reach ˜40 g [51] In contrast, since the present vehicle is approaching Mars decelerating at acraft=10 cm/s2, the same process can be executed within over a week-long time and distributed over a path at uniform acceleration that concludes with the entire vehicle safely hovering at a desired height above the ground of the planet.
[0176] An obvious question when carrying out a comparison between traditional propulsion technology and the mechanism described in this document concerns the feasibility of generating ˜10 −3-10−2 s laser pulses requiring over 30 MWe (that is, MW of electric power) on board of a space vehicle. Is this possible? Has this possibility ever been carefully considered in the past? The answer to such legitimate question is that the study of high power, high efficiency, low-mass nuclear reactors for use in space applications is actually extremely advanced, although political and public opinion considerations tend to hide the enormous amount of available information away from the non-technical readership. A small selection of such literature, which cannot be cited here even partially because of its sheer size, can be found at [52] and References therein. General historic motivations behind this technical effort are to be found in the large energy needs of any hypothetical “Star Wars” defense system, in research into the possibility of interstellar travel, and, finally, in the recently renewed commitment to the human colonization of space made by the President of the United States and NASA. What is important to the evaluation of the engineering feasibility of the present invention is that, typically, reactor power densities in the order of ˜1-5 kW/kg are surely possible, with very wide variations in either direction of that estimate depending on the specifics of design and shielding requirements. However, the figure above is sufficient to make the case that, by means of presently existing technology, it is absolutely appropriate to consider a 10 ton-vehicle carrying a reactor able to produce pulses in the 30 MWe range in space.
[0177] The implications for human flight to Mars by means of the present invention are very significant as well. At present, the delivery of several tens of tons of payload to Mars is contemplated to take approximately 180 days, with a typical mission duration for the crew of 2-3 years. The overwhelming majority of the mission duration would be spent in complete weightless conditions during transit and possibly under exposure from harmful radiation. In addition, the prospects of recovery in case of an even minor malfunction are dire not to speak of a major accident of the type that occurred on Apollo 13. Being able to reduce the travel time to a matter of days, while transporting the crew under at least partial gravitational conditions completely changes the prospects for successful colonization of the Red Planet as well as the potential for a rescue mission should that be necessary [53]. 4.2.4 A Thrust System for Safe, Low-Speed, Near-Earth Human Transportation Propulsive System Specifications aA=6.29x106 cm/s2 vA,fin=1.61x104 cm/s ΔtA=2.55x103 s tff=60.6x10 s Efficiency=11.2% Δvcraft/cycle=18.35 cm/s acraft=g/2 (self-consistent) Thrust=0.491 MN (Thrust/Total Radiation Pressure)=4.20x106 Earth-to-LEO distance=4x107 cm Total Travel time=4.97x102 s=8 min 17.5
s Maximum Speed (reached at midpoint)=1.22x105
cm/s=1.22 km/s Maximum Kinetic Energy (reached at midpoint)=7.44x10
16 erg Total Energy Radiated (at midpoint)=1.74x1017
erg Time to Mach 1 (Speed of Sound vsound congruent 331 m/s)=
67.5 s Note: The quantities not repeated are unchanged with respect to the
previous example. Comments
[0194] The interest of this particular case lies not in the acceleration, which is less favorable than by means of already available technology, but in its ability to deliver the entire payload to high altitude at rest. This allows us to consider an entirely new philosophy or air transportation and space travel around the Earth (or other planets). Whereas the key objective to reach extreme altitudes with ordinary technologies must be the achievement of high speeds, as that is the only strategy which allows the vehicle to be injected into a permanent orbit, in the case of the present invention it is possible to deliver a payload to a high hovering altitude without requiring orbital speeds.
[0195] Similarly, the descent maneuver of our vehicle does not require the fiery but unavoidable re-entry of typical deorbiting, thus avoiding the accompanying extreme heating and grave dangers to the crew, as in the recent Columbia tragedy. In fact, the vehicle of this example would not reach speeds higher than Mach 4 before decelerating to its hovering point, as opposed to the orbital re-entry speed of the Shuttle of approximately Mach 24. This achievement would represent nothing less than a revolution in aerospace technology. Interestingly, the present approach also lends itself to being phased-in as it replaces traditional propulsion technologies. In other words, it is conceivable that a system of lower thrust, unable by itself to attain a complete hover, could be placed into service for the only purpose to provide additional breaking in an emergency at those speeds that make parachute deployment am impossible option.
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