ELECTRODYNAMIC CONFINEMENT

Abstract: Electrodynamic confinement of extremely energetic, charged plasmas for use in energy production and energy storage is achieved by exploiting nonlinearities in the electrodynamic equations to effect an oscillatory motion of the charges in the plasma, whereby the charges repetitiously "bounce" against the electric field and thereby instantaneously reverse their direction of motion, thus composing a dynamic state in which there is a net electric field and acceleration, and yet no net expansion.

Description: ELECTRODYNAMIC CONFINEMENT FIELD OF THE INVENTION The present invention relates to a method for electrodynamic confinement of charged plasmas, or ensembles of charged particles in general, and apphcations 5. thereof in energy production and energy storage, and potentially also as building blocks for new types of materials. The invention comprises but is not limited to a method for electrodynamic self-confinement, whereby the ensemble of charges is being confined by its own forces only and without external means. BRIEF DESCRIPTION OF PRIOR ART 10. Electrodynamic self-confinement was first suggested in 1973 as a conceivable mechanism for strong interactions, possibly manifesting itself on a macroscopic scale in ball lightning (A Bergstrδm, Phys. Rev. D 8, 4394 (1973)). Although the basic equations are essentially equivalent to those used below, the calculations in the cited article involved considerable simplifications, and the peculiar confinement mechanism 15. ofthe present invention was not understood at the time. The cited article also does not consider how to circumvent fundamental theoretical objections ofthe type studied below in the discussion ofthe present invention. Thus, despite the fact that a connection between electromagnetic and weak interactions has since been established, the proposed electrodynamic origin of strong interactions is far from being generally 20. accepted. Nevertheless, the cited article influenced experimental work, most prominently by K Shoulders who in 1989 filed patents for an experimental apparatus which produces entities which can be interpreted as microscopic ball lightnings (US Patent 5,018,180, US Patent 5,054,047). A type of electromagnetic self-confinement somewhat similar to the above work from 1973 but involving a self-generated rotating 25. magnetic field in the confinement mechanism has been proposed by G ArnhofF (European Transactions on Electrical Power Engineering 2, 137 (May/June 1992)) as an explanation of ball Hghtning. SUMMARY OF THE INVENTION The confinement mechanism ofthe present invention is based on the electrodynamic properties of charged, gaseous configurations with extreme energy contents, and involves primarily the electron population. The mechanism is governed 5. only by electric fields, and it should be emphasized that no magnetic fields are necessarily involved in the mechanism. Indeed, in the following essentially only the case of spherical symmetry will for simplicity be considered, in which case Maxwell's equations do not allow any magnetic field. One objective ofthe present invention is thus to provide a method of plasma confinement not requiring the bulky and 10. expensive paraphernalia of normal magnetic confinement, which constitutes a tremendous structural overhead in any magnetic confinement device. In a tokamak, for example, which is the most conceivable candidate for a commercial, magnetic confinement device for thermonuclear power production (cf R W Conn, Scientific American Oct 1983, p 44), a typical weight ofthe magnets and supporting structure in 15. the magnetic container is ofthe order of hundreds of tons compared to hectograms for the contained gas producing the energy. Another advantage of electrodynamic confinement versus magnetic confinement is that electrodynamic confinement involves only short-range motion ofthe charges, in contrast to the long-range motion (typically meters) ofthe charges required in 20. magnetic confinement. A second objective ofthe invention is thus to employ electrodynamic confinement instead of magnetic in order to construct devices with very small over-all dimensions, in addition to the minimal structural overhead. In contrast to magnetic fields, electric fields are easily produced within a gaseous medium itself by charge separation. A third objective of the invention is thus to 25. provide a method of electrodynamic self-confinement, i e a state in which a charge configuration becomes stable as a result of its own internal forces without requiring external fields for its subsistence. The energy involved in the chemical bonds in molecules is typically ofthe order of eV, whereas the total mass ofthe accompanying atoms is typically ofthe order of GeV 30. or more. This means that if we are Umited to the materials nature provides us with for energy storage and structural materials, then less than one part in a billion of the total mass is actually used for the purpose in question, the rest is just dead weight. All the heavier elements in nature, such as aluminum, iron, titanium or lead, are slag left over from supernova explosions and not necessarily optimal for using as structural 35. materials or energy storage as we do. A further, long-term objective ofthe invention is thus to provide a method for producing a self-confined, gaseous state of matter with high energy density and structural stability, and in which the energy involved in the confinement mechanism consitutes a considerable fraction ofthe total mass, thus providing a potential for creating radically new, Ught-weight materials for energy storage and mechanical structures. According to the invention therefore there is provided a method and/or device for 5. electromagnetic confinement of an ensemble of highly energetic, charged particles, and/or for extraction of energy from such an ensemble, characterized in that fundamental nonUnearities inherent in the electrodynamics of said ensemble, and/or the spacetime dynamics of said ensemble, with respect to accelerations and deceleration of said particles in said ensemble are utiUzed to confine said ensemble 10. and/or extract energy from said ensemble. Preferably, a nonlinearity in the mutual electrodynamic interactions between the electromagnetic field and said accelerating charged particles in said ensemble at strong fields is utilized to achieve confinement of said ensemble by producing a violent, radially osciUating motion of said particles in which, due to a repetitive discontinuity 15. in the velocity of said particles when - analogously to bouncing - their direction of motion is instantaneously reversed, the average spatial displacement of each particle is essentially zero even though its average acceleration is not zero. According to the invention there is provided a method and/or device characterized in that said electrodynamic confinement is utiUzed to store electric energy, thus 20. providing extremely Ught-weight energy storage. Preferably also the energy content per volume of said energy storage is increased by compartmentalization of the confinement structure into a large number of subunits, and said compartmentalization ofthe confinement structure is used to create extremely light-weight, mechanical structure elements. 25. As will be further discussed below, there exists a relativistic Carnot process in which it is not quite clear that energy in its normal definition is conserved. This relativistic Carnot process involves accelerations and decelerations which are simultaneous in different frames of reference, resulting in a possible excess energy after each cycle in the process which may be due to extraction of energy from vacuum 30. fluctuations. The possibility of extracting energy from the zero-point fluctuations of the vacuum field has recently been seriously considered in the scientific Uterature (R L Forward, Phys. Rev. B 30, 1700 (1984), D C Cole and H E Puthoff, Phys. Rev. E 48, 1562 (1993)). The confinement mechanism ofthe present invention involves accelerations and decelerations of the type required in the above-mentioned Carnot 35. process. Indeed, an excess energy production has actually been reported (K R Shoulders, PCT/US90/02368), albeit on a microscopic scale. A further feature of the invention is thus to provide macroscopic conditions where it is possible to test experimentaUy whether excess energy can be extracted from a relativistic Carnot process ofthe type disclosed below, and if so, extract such energy. BRIEF DESCRIPTION OF THE DRAWINGS Fig 1 shows the velocity as a function of time for a nonsymmetric, periodic 5. motion, and illustrates the fact that it is impossible to achieve self-confinement by tailoring an osciUatory motion so that there is zero average displacement but still a nonzero average acceleration, and with the velocity and acceleration assumed to be continuous functions of time. Fig 2 depicts the acceleration (Fig 2A), velocity (Fig 2B), and displacement (Fig 10. 2C) as functions of time in a harmonic oscillator with two identical particles bouncing against each other, and where each particle has a zero average displacement even though its average acceleration is nonzero, this being possible due to a discontinuity in the velocity caused by the bounces as shown in Fig 2B. Fig 3 depicts a complete solution ofthe electrodynamic equations in the case of 15. extremely high fields when the mutual interactions between the field and the moving charges dominate over colUsional effects. Shown are the acceleration (Fig 3A), velocity (Fig 3B), and displacement (Fig 3C) as functions of time for a charge configuration with extreme excess charge, illustrating that there exist solutions which exhibit the type of bouncing osciUations which is the characteristic of self-confinement. 20. Fig 4 depicts the deformation, as observed from a stationary spacetime frame xt and calculated by the Lorentz transformation, of a frame x't' which is accelerating with respect to frame xt by a constant acceleration simultaneous in x't' (i e a constant acceleration as observed from an inertial frame which momentarily coincides with x't'). The x't' frame exhibits the hyperboUc form expected from a frame in constant 25. acceleration, but closer scrutiny reveals that the time t' is observed from the xt frame to go in different directions for positive and negative times t. The inserted perspective figure which displays a picture ofthe x't' frame in xtx'-space clearly iUustrates the topology involved. DISCUSSION OF THE INVENTION 30. Intuitively, the idea of attaining electrodynamic self-confinement of, say, a cloud of electrons would seem out ofthe question. To be more specific, the following very fundamental theoretical objections can be raised against the idea of electrodynamic self-confinement. Suppose first that we have a static, sphericaUy symmetric charge configuration 35. with a density of excess charge given as a function q(r) ofthe distance r to the centre of symmetry. For simpUcity, and also because electrons are more mobile than ions, we consider the excess charge to consist of an excess or deficit of electrons against a background of positive ions. The static excess charge density q(r) in the assumed charge configuration may be negative (indicating an excess of electrons) in some spherical sheUs, and positive (deficit of electrons) in others. As a result, the entire charge configuration may have a total charge ≠ 0. 5. Regardless ofthe distribution of sheUs with different charge, there must always be some innermost sphere, extending from radius r = 0 to some radius r = a, within which the charge density has only one sign, say positive, and a total charge ≠ 0. Any possible stability ofthe entire charge configuration rests on the possibility ofthe charges in this innermost sphere being stable and not blowing apart due to their own 10. mutual Coulomb repulsion. In a medium with electric permittivity ε, the relationship (or definition) ofthe charge density q(r) to the electric field E(r) is given by the Maxwell equation V-E(r) = q(r)/ε. (1) Using Gauss' theorem, the radial component ofthe electric field at radius r then 15. becomes in the case of spherical symmetry E(r) = Q(r)/(4πεr2), (2) where Q(r) is the total charge inside radius r, i e According to Newton's second law, the acceleration a(r) of a charged particle with 20. charge-to-mass ratio e/m (positive for positive charges, negative for negative charges) due to the electrostatic Coulomb field in Eq (2) then becomes a(r) = e/m E(r) = e/m Q(r)/(4πεr 2 ). (4) In the case studied with an assumed deficit of electrons in the innermost sphere, all quantities in Eq (4) are positive. Thus the acceleration a(r) must also be positive, i 25. e directed outwards. If we had, instead, a negative excess charge in the innermost sphere, then e/m and Q(r) would both be negative but their product and thus the acceleration a(r) would again be positive, and thus again directed outwards. From these very fundamental considerations there seems no way for anything but an outward motion ofthe charges in the innermost sphere, and thus eventually for the 30. entire charge configuration. The case for self-confinement becomes more promising, at least at first sight, if we consider a dynamic instead of static charge configuration. In this case, a special kind of motion could perhaps be achieved in which the average spatial displacement is zero even though the average acceleration as discussed above is not zero. Specifically, we 35. here study quasi-stationary motion such as, e g, radial oscillations of an electron gas with respect to a background of heavy positive ions, which can be regarded as essentiaUy stationary due to their much higher mass. Considering such radial oscillations ofthe innermost sphere discussed above, we would have a charge density which is negative everywhere inside the sphere during one half-period and positive 5. everywhere inside the sphere during the next half-period (both states being due to minute radial displacements of each electron to the inside of or to the outside of the radius vector). This means that an electron in the innermost sphere would experience an outward acceleration during the first half-period and an inward acceleration during the second half-period. Conceivably, this acceleration might then be tailored so that 10. the time-averaged displacement of the electron due to the acceleration is zero even though the time-averaged acceleration at radius r (and thus the average charge inside r) is not, as will be attempted below. Also in the case of a dynamic charge configuration there is, however, a very fundamental theretical objection to the possibiUty of attaining self-confinement by 15. tailoring an oscillatory motion as was proposed above. This objection will now be discussed in some detail. Suppose that the acceleration of an electron in the charge configuration at time t can be described by a function a(t), assumed to be continuous and periodic (with period T) in t. If we assume the initial velocity ofthe electrons at time t=0 to be zero, then 20. from the definition of acceleration their velocity at a later time t is given as t v(t) = J a(t)dt, (5) o where v(t) is also continuous and periodic (with period T) in t, and obviously has a continuous first derivative. Fig 1 gives an example of what the function v(t) may look Uke in a typical 25. situation where an assumed osculating field has produced an osciUating, periodic velocity ofthe electrons ofthe type given in Eq (5). The asymmetric osciUation in Fig 1 is the sum of two harmonic osciUations with angular frequencies ω and 2ω, respectively, and in phase with one another. We will now investigate whether it is possible to tailor the asymmetry ofthe osciUation in such a way that there is an 30. average acceleration ≠ 0 and still no net displacement. The velocity in Eq (5) results in a radial displacement s(t) of the electrons, which after a period is T sCr vtødt, (6) o corresponding to the area between the curve and the horisontal axis, with positive sign above the axis and negative sign below. In the example in Fig 1, the integral in Eq (6) is constant (=0), so that there is no net radial displacement and the required state of quasi-stationary motion is thus at hand. 5. We now address the question ofthe time-averaged charge inside radius r corresponding to the assumed acceleration a(t). As discussed above we have, due to Newton's second law and Gauss' theorem, a proportionaUty between electric field, acceleration and charge, i e for the charge inside r averaged over a period we have T <Q(r)> J a (t)dt /T = MT) - v(0)]/T. (7) o 10. In order for (Q(r)) to be compatible with an assumed excess charge, we must thus require that v(T) ≠ v(0). On the other hand, in order for the motion to be quasi- stationary, we must require that it return to its initial state after a period, i e that v(T) = v(0). Since an excess charge (Q(r)) ≠ 0 is thus possible only if the velocity averaged over a period is nonvanishing, (v) ≠ 0, this is incompatible with a quasi- 15. stationary motion ofthe type assumed above. A crucial part ofthe invention is thus how to find a way around the theoretical objections just discussed, and this can be achieved by observing that the above objection to dynamic stabiUty is based on the assumption that v(t) is a continuous function oft. For motions containing cusps at which the function v(t) is discontinuous 20. (Uke, e g, the common cycloid or the bouncing harmonic osciUator discussed below), the above objection is circumvented. Now cusps are typically a nonlinear effect, and fortunately - from this point of view - the electrodynamical equations form a nonlinear system. The invention exploits nonlinearities inherent in the electrodynamic interaction between the field and the moving charges to circumvent the above 25. objection to dynamical stabiUty by effecting a motion which contains discontinuities in v(t). In fact, precisely the common cycloid appears as a solution to the nonUnear electrodynamic equations. In the disclosure ofthe invention below, we wiU first iUustrate confinement according to the invention in a different context - a bouncing harmonic oscillator - 30. which will be shown to exhibit a type of confinement in which the above theoretical objections are circumvented. With this in mind, we then give a complete analytical solution for the case of extremely high fields when the interactions back on the field from the velocities and accelerations ofthe charges caused by the field completely dominate over collisional effects. Indeed, this case turns out to exhibit the same type of confinement - and with the bouncing harmonic osciUator reappearing as a close approximation. DISCLOSURE OF THE INVENTION - 'BOUNCING HARMONIC OSCILLATOR" Consider an adiabatic, harmonic oscUlator with two identical particles moving in 5. response to an attractive force proportional to the distance δ to their common center- of-mass (as if they were connected by a rubber band), and with their common center- of-mass δ=0 at rest. When the particles meet at δ=0, we can either assume that they bounce against each other in a perfectly elastic coUision, or pass through each other without frictional loss, depending on whether we choose to define the particle going 10. outwards after the coUision to be the same as the one going inwards or not. We here assume the particles to bounce against each other so that Fig 2C describes the trajectory of particle 1. The trajectory of particle 2 is then described by a mirror image above the t-axis ofthe trajectory of particle 1 in Fig 2C. Since the time-dependent restoring force T(t) and acceleration a(t) in a harmonic 15. osciUator is assumed to be proportional to the displacement δ(t), we can (with suitable scaling oft) express the equation of motion for particle 1 ofthe harmonic osciUator in the form d2T(t)/dt2 = - i T t) I , (8) which (with suitable scaling of T(t) and choice of t=0) has the solution 20. T(t) = I cos(t) I , (9) and the first derivative dT(t)/dt = ± (l-T(t)2), (10) which is discontinuous when T(t) = 0. Obviously, the net displacement of particle 1 (and particle 2) after a period is zero, 25. and it experiences an average acceleration outwards as depicted in Fig 2A. This is thus a case where we have indeed achieved a state of motion with a net acceleration but with zero net displacement - a situation which seemed to be ruled out from the discussion above. Why this is possible at all is because the assumption above of v(t) being a continuous function oft is no longer vaUd in the motion we are now discussing; 30. there is a discountinuity in v(t) at the time of colhsion, when v(t) instantaneously retums to its starting value by reversing direction, as is shown in Fig 2B. Suppose now for iUustration that the particles are separated from each other at δ=0 by a large, rigid sphere which transfers momentum between the particles (so that the motion of particles looks somewhat like two balls bouncing against the surface of 35. the earth at two antipodes). Then obviously both particles have net accelerations outwards (or both inwards depending which one we put where) and at the same time zero net displacements. As was discussed above, these are the requirements for quasistationary motion of the charges in a stable configuration with an excess charge. Summarizing the results so far, Fig 2 thus depicts the acceleration (Fig 2A), 5. velocity (Fig 2B), and displacement (Fig 2C) as functions of time for a bouncing harmonic ostillator, for which the velocity of one particle is repetitiously and instantaneously reflected inwards by colUsion with something, and where the recoil momentum at each colUsion with this 'something' is somehow taken up by a similar reflection ofthe velocity inwards of a second particle opposite with respect to the 10. center of symmetry of the system. For this type of oscillatory motion with a discontinuity in v(t) (in this case a reflection ofthe direction ofthe velocity), it would thus be possible to have a quasistationary charge configuration despite an excess electric charge. What wUl be shown in the following is that a motion of this type can indeed be achieved in a charge configuration by the field itself, and with the field 15. playing the role of the 'something' mentioned above with which the particles collide and which transfers momentum between them. The algebra in the derivation below is with necessity extensive. For this reason the algebraic calculations have been performed using a computer program for symbolic mathematics (Maple V.2, see B W Char et al, First Leaves: A Tutorial Introduction to 20. Maple V (Springer, 1992)). In the text below only a summary ofthe algebraic calculations is given. For the detaUed derivation the reader is referred to the output from the computer program in Appendices A-C in the priority application. A method and/or device according to the invention thus preferably incorporates an ensemble of charges which is essentiaUy spherically-symmetric, and the 25. electromagnetic field is an essentiaUy sphericaUy-symmetric electric field. In one embodiment external electric fields are used to produce the periodic, radiaUy- osciUating motion ofthe charged particles and preferably then said electric field is created by a central, preferentially spherical electrode supplied by an external high- frequency source connected to said electrode by a shielded connector. 30. DISCLOSURE OF THE INVENTION - ELECTRODYNAMIC BOUNCING We define extremely high electric fields as a field regime where the interactions of the field on the charges - and the corresponding interactions back on the field from the accelerations and velocities ofthe charges - completely dominate over effects of coUisions between the charges or with the background medium. To be more specific, it 35. wiU be shown that under special circumstances the charges wUl experience "bouncing" against the field due to nonlinearities in the electrodynamic equations. In extremely high fields this "bouncing" wiU be the dominant effect for changing the velocities of the charges, and appear on a time-scale which is much shorter than the coUisional relaxation time, so that velocity changes due to colUsion effects are negUgible in comparison. In this case, energy losses due to Ohmic heating can also be assumed to be negUgible in comparison with the energies involved in the mutual interactions 5. between the charges and the field, and the particle dynamics thus be assumed to be essentially adiabatic. In the extremely high electric fields discussed here, the inertial mass corresponding to the electric field energy may become comparable with or higher than the mass ofthe charges themselves which take part in the mechanism. Thus the 10. conditions described here may enter into the regime within the "classical particle radius" r c = Q 2 / (4 π ε 0 M c 2 ), (11) where Q and M are, respectively, the total charge and mass of the particles constituting the excess charge (normaUy electrons). The "classical particle radius" is 15. normaUy regarded to be ofthe order of fermis (IO"* 3 cm) or less, and to be a regime where classical electrodynamics breaks down and has to be replaced by a quantum description. However, conditions corresponding to those within the "classical particle radius" as defined by Eq (12) can be realized on a macroscopic scale at comparatively modest fields, voltages and excess charges, and it is not quite clear why or what 20. quantum description should be used for a system with "classical particle radius" of the order of decimeters. Assume, for instance, that the molecules in a sphere of air at normal density become sUghtiy deformed by a radial electric field so that all electrons (approx. 4 IO 23 electrons/dm 3 ) are being slightly displaced radiaUy inwards in the sphere relative to their unperturbed positions by 10" 12 m (i e = 1/100 ofthe radius of 25. the atom), and that this displacement ofthe electron population relative to the background nuclei constitutes the charge configuration in the present study. For a sphere with radius 1 dm we then have an excess charge Q equal to the electron charge times the number of atoms in a 10" 12 m shell with radius 1 dm, i e Q = 0.8 10"5 As. With Q/Mc 2 = electron charge/electron mass-energy = 2 IO" 6 V" 1 , Eq (11) then gives r c 30. = 1.5 dm for the "classical particle radius" for this system. The voltage is = 500 kV and the electric field at the surface ofthe sphere is = 5 IO 6 V/m, i e ofthe order ofthe breakdown field strength in air. The charges, voltages and electric fields at macroscopic "classical particle radii" ofthe order of decimeters are thus far from exotic, and in a range easUy attainable in the laboratory. 35. The electric field E(r,t) is derived from the basic electrodynamic equations (Maxwell's equations plus conservation of charge, mass/energy and momentum): 1) Relationship between electric field E, electric permittivity ε, and charge density q as described by MaxweU's equation V-E = q/ε, Eq (1), which in spherical symmetry becomes q = ε [2 E/r + 3E/3r]. . (12) 5. 2J Relationship between electric field E, electric permittivity ε, and current density j as described by MaxweU's equation c 2 V xB = j/ε + 3E/3t, which with j = q v and in spherical symmetry, when the magnetic field B ≡ 0, becomes 0 = q v /ε + BE/dt. (13) 2) Continuity equation for charge density q, i e 3q/3t + Vj = 0, which with j = q v 10. and in spherical symmetry becomes 3q/3t + 1/r 2 3(r 2 qv)/3r = 0. (14) 4) Continuity equation for mass/energy density p, i e dp/3t + p v = 0, which in spherical symmetry becomes dp/dt + 1/r 2 3(r 2 pv)/3r = 0. (15) 15. 5 Relationship between electric field E, charge density q, mass density p, and "convective derivative" dv/dt = dv/dt + (v«V)v as described by Newton's second law dv/dt = qE/p, which in spherical symmetry, when dv/dt = dv/dt + v 9v/3r, becomes 3v/3t + v dv/dr = q E/p. (16) In addition to the 'physical' assumptions Eqs (12) through (16), the foUowing 20. 'mathematical' assumption is necessary in order to be able to solve the equations: fi) The electric field E(r,t) is assumed to be separable into one factor R(r) which is a function of radius r alone, and one factor T(t) which is a function of time t alone, E(r,t) = R(r) T(t). (17) The general solution ofthe coupled electrodynamic equations Eqs (12) - (17) is 25. performed using the symboUc mathematics program Maple V.2. It is interesting to note that the electrodynamic equations in spherical symmetry is one ofthe rare cases where nonlinear partial differential equations possess exact analytical solutions, viz E(r,t) = Q(r,t) / (4 πε 0 r 2 ), (18) v(r,t) = - y_ r C sinτ /( η ( cos τ + ) 2 ), (19) 30. q(r,t) = - QCr.t) η / (4 πr 3 ), (20) p(r,t) = Q(r,t) 2 η 3 ( ι 2 cos τ + _ )3 / (8 π 2 εo C 2 r 6 ), (21) where the time-dependence is impUcit through the variable τ, defined through t = η ( ι / fc sinτ + 2 τ ) I C, (22) C and η being constants, and where Q(r,t) is the total charge inside radius r at time t, given by the expression (A is positive or negative real-valued scaling constant) 5. Q(r,t) = 4 π ε 0 A rfl rn ( _ cos τ + \/_ ) (23) The solutions in Eqs (18) through (22) can be verified by back substitution into the basic electrodynamical equations, Eqs (12)-(16). The most important characteristic ofthe solutions is that (for η>0 when τ is real) they exhibit a recurring discontinuity in the velocity at times corresponding to τ = π, 3π, 5π, etc, when the velocity abruptly 10. changes direction. This behaviour is a crucial characteristic ofthe nonlinear electrodynamic equations for sufficiently steep charge distributions (viz η>0), and is the essence ofthe confinement mechanism according to the invention as discussed above in connection with the analysis ofthe "bouncing harmonic ostillator". As seen from Eqs (18), (22) and (23) the time-dependence ofthe electric field E(r,t) 15. for η>0 is of a general cycloid form, which when η approaches 0 becomes broader and broader around the peak, and eventually approaches a rectangular shape with E(t) constant, interrupted by narrow spikes when E(t) dips down to zero. In the asymptotic case η → 0, the solution to the electrodynamic equations thus reduces to the simple static solution 20. E(r,t) = const /r 2 . (24) Thus the Coulomb field <*= 1/r 2 is singled out as a pecuUar case when there is a static solution to the electrodynamic equations. Isolated, however, there is no clue why the Coulomb field should correspond to a static charge configuration, nor how a static solution could exist at aU in view ofthe discussion above of theoretical obstacles to 25. stability. It is only when considered as a Umiting case of "bouncing" fields as depicted in Fig 3 and explained in terms ofthe confinement mechanism ofthe invention that des Pudels Kern of its static nature reveals itself. Furthermore, the Coulomb field also has the following "boot-strapping" property. If we calculate the charge density q(r) from the Maxwell equation Eq (12), we find that 30. a Coulomb field corresponds to a charge density q(r) ≡ 0. Or stated in an alternative way: Any infinitesimal charge density of a form approaching that which gives a Coulomb field wiU produce an arbitrarily large field. For exemplification, consider a charge density q(r) ofthe form q(r) = A (25) 35. where η is a smaU number «1 (for simplicity here assumed to be positive). In accordance with Eq (3), the charge Q(r) within a sphere of radius r is then Q(r) = 4π (A/η) rη, (26) which according to Eq (2) corresponds to an electric field E(r) at radius r, E(r) = (A/η) r 1 !" 2 / ε = (r^l/η) A / (ε r 2 ). (27) 5. When η → 0, the electric field E(r) approaches the Coulomb field A /(ε r 2) but with a factor rΗ/η which tends to infinity as η -→ 0, so that no matter how small the factor A may be in the charge density in Eq (25), a finite field may still result from Eq (27). The Coulomb field is thus an asymptotic Umit when an arbitrarily large field can be produced by an infinitesimaUy small charge distribution ofthe form in Eq (25). 10. In a method and/or device according to the invention thus the electric field is preferentiaUy created internally by the electrodynamics ofthe ensemble of charges itself, thus producing an electrodynamic self-confinement of said ensemble. Preferably, also said self-confined ensemble of charges is created from an initially cyUndrical discharge, which is caused to pinch due to the magnetic field ofthe 15. discharge current, characterized in that said pinched discharge is aUowed to deform by inherent instabilities, preferentially of 'sausage' type, leaving - after the current is switched off- at least one highly energetic, essentially spherically symmetric charge configuration which is arranged through the current distribution in the initial cyUndrical discharge to get a radial charge density distribution proportional to 1/rN. 20. where r is the distance from the center of symmetry and with N greater than 3 (or approaching 3 infinetely close from above), corresponding to a radial electric field distribution in said charge configuration which is (possibly only infinitesimaUy) steeper than a Coulomb field, i e proportional to l/r n with n greater than 2 (or approaching 2 from above). 25. ONE MODE FOR CARRYING OUT THE INVENTION - NUCLEAR FUSION The confinement mechanism ofthe invention involves high-frequency oscillations of an electron population with respect to a background of positive ions. In order to conserve momentum the ions must also osciUate, and with typical velocities depending on their mass. With a sufficient excess charge in the charge configuration, extremely 30. high energies may be involved in the osciUations. This is also necessary in order to overcome losses and recombinations, and for the system to be in the field regime where confinement according to the invention can take place. Extrapolating from estimates of energy contents in ball Ughtnings (which as discussed above are considered to be natural embodiments ofthe confinement mechanism ofthe invention) 35. energies of the order of tens to perhaps hundreds of keV per particle can be assumed to be attainable in a confinement according to the invention. With a plasma containing a mixture of ions with different mass, say hydrogen and deuterium, the proton population would osciUate with higher velocities than the deuteron population. This constitutes an ideal situation for thermonuclear fusion both because thermonuclear energies are easUy attained but also because the proton and deuteron 5. populations osciUate relative to each other. This means that thermonuclear reactions between the populations are greatly enhanced relative to reactions within each population. In the case discussed with a mixture of hydrogen and deuterium, the reaction D 2 + H* → He 3 + γ + 5.5 MeV, 10. which involves ions with different mass would thus be greatly enhanced compared to the competing reactions D 2 +D 2 → He 3 +n+3.3MeV, D 2 +D 2 → T 3 +H 1 +4.0MeV, H 1 +H 1 → D 2 +e++v e + 1.4MeV-0.3MeV, 15. which involve particles with the same mass. Here the two branches ofthe D-D reaction occur with about equal probabiUty, and the negative energy contribution in the last formula represents energy which is being carried away by the neutrino. The D-H reaction is the main energy source in medium-sized stars. The cross section for the D-H reaction is much lower than for the D-D reaction, for which reason 20. it is the D-D reaction (and to some extent the deuterium-tritium reaction D-T) that is being utiUzed both in nuclear fusion weapons and proposed fusion reactor designs. However, in any viable long-term scheme for power production from nuclear fusion, it is probably necessary to suppress the D-D reaction (and the D-T reaction) since this reaction is a heavy polluter: One branch produces neutrons which penetrate 25. exponentially deep into materials and easUy cause induced radioactivity, as is all too apparent in ordinary nuclear fission reactors. The other branch produces tritium which is a serious health hazard due to its beta radiation. In contrast to this, the charged He 3 particles from the enhanced H-D reaction discussed above can be completely stopped even by very thin radiation shields from which power is easily 30. converted by conventional methods or directly into usable form, and helium-3 is also a stable, inert and completely harmless substance. A further reduction ofthe poUuting D-D reaction can be obtained by lowering the deuterium/hydrogen ratio ofthe mixture. SimUarly, in a mixture of D 2 and He 3 the following reaction would be enhanced 35. since it involves nuclei with different mass D + He 3 → He 4 + H + 18.3 MeV, in comparison to the competing reactions D2 + D 2 → He 3 + n + 3.3 MeV, D 2 + D 2 → T 3 + Hi + 4.0 MeV, He 3 + He 3 → He 4 + 2 H* + 12.9 MeV, which involve nuclei with the same mass. This embodiment of the invention thus 5. provides a promising candidate for future clean nuclear power. According to the invention there is thus provided a method and/or device characterized in that violent, high-frequency osciUations of the positive background ions in response to osciUations ofthe electron population in the confined ensemble of charges are employed to produce energy through nuclear fusion reactions. Preferably 10. also said oscUlations of said background ions, due to differences in their mass, enhance such nuclear fusion reactions which produce essentially only charged particles and no neutrons as end products. Preferably also said background ions are protons (H 1 ) with a small fraction of deuterons (D 2 ), and which produce fusion energy through the reaction D 2 + H 1 with a 15. negligible proportion ofthe reaction D 2 + D 2 , or altematively, said background ions are heUum-3 ions (He 3 ) with a small fraction of deuterons (D 2 ), and which produce fusion energy through the reaction D 2 + He 3 with a negligible proportion of the reaction D 2 + D 2 . FURTHER MODE OF THE INVENTION - EXTRACTION OF ZERO-POINT ENERGY 20. As mentioned above in the summary ofthe invention, there has recently been serious discussions in the scientific Uterature on the possibility of extracting energy from the zero-point fluctuations ofthe vacuum field. One example where the zero- point fluctuations are observable is the Casimir effect, in which parallel plates placed close together are attracted towards one another by a (normally minute) force caused 25. by the zero-point fluctuations (cf, e g, P W MUonni and M-L Shih, Contemporary Physics 33, 313 (1992)). Reference is also made to the experiments by K Shoulders, documented in PCT US90/02368 as cited above in the summary. A further, independent indication is the remarkable efficiency in conversion of pulsar rotational energy to synchrotron radiation which occurs in some supernova remnants, notably 30. the Crab nebula, and which might possibly be indicative of a natural occurrence of energy extraction in accordance with the ring-shaped electron accelerator method described below. Considering the paramount importance of these indications - frail though they are - both from the theoretical and practical point of view, an analysis wiU here be made ofthe feasibUity of using the confinement mechanism according to 35. the invention as a test-bed to test whether energy could possibly be extracted from the vacuum fluctuations in a sustained manner in accordance with the conjecture of the relativistic Carnot process disclosed below, and if so, extract such energy on a useful scale. Zero-point energy should not be understood as a new physical concept providing an easy, alternative source of energy. Rather, zero-point energy has been an accepted 5. concept in physics, in particular quantum mechanics, for a long time but previously regarded essentiaUy as a mathematical entity without physical relevance. First the Lamb shift, then other effects Uke spontaneous emission and the Casimir effect eventuaUy drew the attention to the physical reaUty ofthe zero-point fluctuations. Zero-point fluctuations can be regarded as an enormous heat bath permeating the 10. entire universe, and with which normal physical objects are in thermal equiUbrium at absolute temperature T=0. Vacuum fluctuations provide an alternative, and in some respect more comprehensive description of many phenomena in nature like inertia and gravitation (H E Puthoff, Phys. Rev. A 39, 2333 (1989); B Haisch, A Rueda and H E Puthoff, Phys. Rev. A 49, 678 (1994)). It should be emphasized, however, that it is an 15. alternative description, not an alternative theory (somewhat analogously to the kinetic theory of gases being an alternative description ofthe classical, phenomenological gas laws). Thus, if energy is to be extracted from the vacuum field, this must be in obeyance with the basic laws in physics, and it is against this background that the case for energy extraction from the vacuum field wiU be analysed 20. in the following. Ofthe thermodynamical laws, the second law (the total entropy never decreases) was early put on a firm theoretical foundation by Clausius, Carnot and others, and connected to irreversibiUty. Stephen Hawking (S W Hawking, A Brief History of Time, Bantam Press (1988), Ch 9) considers the second law as an almost tautological 25. consequence of our awareness of time with a past which is ordered into our memories and a future which then becomes more disordered. Except in some elementary and simple processes, the total entropy is always increasing. In most macroscopic systems, the behaviour ofthe system is infinitely sensitive to the initial conditions and any attempt to produce a reversible process wiU only result in a new, less ordered state 30. and a higher total entropy (R P Feynman, The Character of Physical Law, MIT Press (1967), Ch 5). Even a MaxweUian demon is expected to have to wait infinitely long time between the rare situations when he could extract work from heat in violation of the second law (C M Caves, Phys Rev Lett 64, 2111 (1990)). Concerning the first law of thermodynamics (conservation of energy), the original, 35. empirical nature of this law has now been supplemented with a firm theoretical foundation based on the understanding that conservation laws are connected to symmetries according to Noether's theorem (Emmy Noether, Nachrichten Gesell. Wissenschaft. Gδttingen 2, 235 (1918), cf also H Goldstein, Classical Mechanics, 2 Ed (Addison-Wesley, 1980), Sect 12-7). Thus symmetry with respect to a translation in space impUes conservation of momentum. Symmetry with respect to a rotation in space impUes conservation of angular momentum. Similarly, symmetry with respect 5. to a translation in time implies conservation of energy and thus leads to the first law of thermodynamics. (It should be emphasized that Noether's theorem states that symmetry impUes conservation laws. The inverse is, however, not true. Lack of symmetry does not necessarily imply lack of conservation; there may be conservation laws without corresponding symmetry). 10. Ofthe three conservation laws for momentum, angular momentum, and energy, the last one has a somewhat different character than the other two since it is based on symmetry with respect to time. As discussed above, we know that - save for some very simple phenomena - time is not symmetrical, there is always an increase in total entropy with time. For this reason it does not seem necessarily true that a symmetry 15. with respect to a time translation is always maintained. Viewed in this way, the second law of thermodynamics thus erodes the foundation for the first law. On the other hand, there is a symmetry which is not included in the list above, viz symmetry with respect to Lorentz transformations. This symmetry requires conserved quantities to be Lorentz invariant. Specifically, if momentum and energy 20. form a four-vector, then conservation of momentum also impUes conservation of energy. In this way we have thus retrieved the first law of thermodynamics without having to invoke time symmetry. The above rederivation ofthe first law of thermodynamics from symmetry with respect to the Lorentz transformation is, however, valid only if momentum and energy 25. transform Uke components of a four-vector. Now, it is known that in some extended systems this requirement is not fulfiUed (cf C Møller, Mat. Fys. Medd. Dan. Vid. Selsk. 36, 1 (1967); N G van Kampen, Phys. Rev. 173, 295 (1968)). Thus, if energy can be extracted from the vacuum field in seeming violation ofthe first law, then the above argument indicates that the only allowed regime for such occurrences would be 30. relativistic phenomena involving accelerations of extended systems. A closely related observation is that there is - surprisingly enough - no uniquely defined relativistic transformation of temperature such as there is for, e g, velocity, energy, pressure etc ("the Planck-Ott imbroglio", cf W Israel and J M Stewart, Progress in Relativistic Thermodynamics and Electrodynamics of Continuous Media, in 35. A Held (Ed), General Relativity and Gravitation (Plenum 1980), Vol 2, p 508. Cf also J Shaffer, U Nuovo Cimento 103B, 259 (1989)). Defining temperature as usual by a Carnot process, an acceleration to a specific relativistic velocity leads to a temperature of the system which is different if, say, the acceleration has taken place simultaneously in the stationary or in the moving frame of reference. The above observations, and the fact that vacuum fluctuations are Lorentz invariant and only manifest themselves at accelerations, lend support to the conjecture disclosed below 5. that a relativistic Carnot process involving accelerations and decelerations which are simultaneous in different frames of reference might be a way to extract energy from the vacuum field in a sustained manner, and which is not in conflict with basic thermodynamical or conservation laws. In contradistinction to the case of accelerations at classical velocities, and due to 10. the difference in simultaneity in systems at relativistic velocities, accelerations at relativistic velocities are not unique. For relativistic accelerations of extended objects, it is necessary to specify in which frame the acceleration is simultaneous, i e constant over the object. If we have a stationary frame xt and a second frame x't' corresponding to an extended object in accelerated motion with respect to frame xt, we must specify 15. if the acceleration is simultaneous in the frame xt, or in the frame x't', or in any other frame. For accelerations due to a constant force and simultaneous in the xt frame, such as due to a static field, the x't' frame forms a family of hyperbolas in the xt frame, as is weU known from the literature. For accelerations due to a constant force and simultaneous in the x't' frame, such as corresponding to a rigid object, which case 20. does not seem to have been studied in detaU before, we can derive the foUowing differential equation for the relative velocity v(t') between the xt and x't' frames. From the relativistic addition of velocities we get (with velocity of Ught c = 1) for the increase in relative velocity between the xt and x't' frames due to a constant acceleration a in the x't' frame during a short time dt' 25. dv(t') = (v(t') + a dt')/(l+v(t') a dt") - v(t'), (28) which for dt' → 0 gives the ordinary differential equation dv(t')/df = a (1 - v(t') 2 ). (29) With suitable choice of t'=0, Eq (29) has the solution v(t') = tanh (t'a), which inserted in the Lorentz transformation connecting the xt and x't' frames, gives 3 0. x = x' cosh(a t') + t' sinh(a t'), (30) t = x' sinh(a t') + t' cosh(a f). (31) In Fig 4 the x't' frame is plotted in the xt frame. Superficially, the x't' frame also in this case forms a famUy of hyperbolas. Closer scrutiny, however, reveals the fact, as seen most clearly by the inserted 3D separation ofthe Unes, that the time t' in the 35. accelerating system wUl be observed from the stationary system xt to go forwards for t > 0 and backwards t < 0. This remarkable fact could thus make it possible to design a Carnot process in which in principle, say, a heat engine/pump employed by the observer in the x't' frame whose time goes backwards, as observed by a stationary observer in the xt frame, is used by the observer in the xt frame to extract energy. The 5. osciUations described above in an apparatus ' according to the invention alternate between acceleration phases due to a field, i e involving accelerations with are simultaneous in the stationary frame, and deceleration phases at the bouncing, involving decelerations which are simultaneous in the moving frame. The confinement mechanism according to the invention thus provides an apparatus to implement on a 10. macroscopical scale a Carnot process as described above, involving extraction of energy from vacuum fluctations, or whatever other source may supply the energy in the Carnot process described. More specifically, in accordance with the invention an asymmetry in the spacetime dynamics of an extended system with respect to relativistic accelerations 15. and decelerations which are essentiaUy simultaneous in different frames of reference is utUized in a relativistic Carnot process to extract energy. Preferably, said extended system is a device as mentioned above, in which phases of relativistic accelerations which are essentially simultaneous in the stationary frame alternate with phases of relativistic decelerations which are essentially simultaneous in the co-moving frame of 20. the charges. Preferably, also said violent, radially oscillating motion includes expansion phases in which the mass/energy in a subsystem of said extended system is negative, corresponding to a thermal energy ofthe zero-point energy fluctuations ofthe vacuum in said subsystem which is lower than the ambient thermal energy ofthe vacuum 25. fluctuations, resulting in a flow of energy from the ambient zero-point field into said subsystem, and which energy during the compression phases ofthe oscillation is dissipated to the immediate surroundings of said subsystem, thus providing a pumping of energy from the ir-iϊnetely-extending vacuum field to said immediate surroundings of said subsystem for purposes of power generation. 30. Preferably, also said dissipation of energy from said subsystem to its immediate surroundings is achieved by slight inhomogeneities in said subsystem, which are arranged so that the dissipation of energy during the compression phases matches the energy inflow from the ambient vacuum field during the expansion phases, resulting in a steady-state power generation. Preferably, also said extended system is a ring- 35. shaped electron accelerator in which electron bunches are cyclicly accelerated and decelerated by separate processes such that the acceleration and deceleration processes are simultaneous in different frames of reference, and from which energy is extracted in the of form synchrotron radiation. In summary, the confinement method ofthe invention thus uses a reflection ofthe direction ofthe velocity in order to achieve a state of motion in which the average spatial displacement is essentially zero even though the average acceleration may not be zero. Although discussed above in relation to electrodynamic confinement or self- confinement, the confinement method is not limited to those cases, but may also find use in other types of confinement, such as magnetic confinement. 10. 15. 20. 25. 30. 35.

Claims: CLAIMS 1. A method and/or device for electromagnetic confinement of an ensemble of highly energetic, charged particles, and/or for extraction of energy from such an ensemble, characterized in that fundamental honUnearities inherent in the 5. electrodynamics of said ensemble, and/or the spacetime dynamics of said ensemble, with respect to accelerations and deceleration of said particles in said ensemble are utUized to confine said ensemble and/or extract energy from said ensemble. 2. A method and/or device according to claim 1, characterized in that a nonUnearity in the mutual electrodynamic interactions between the electromagnetic 10. field and said accelerating charged particles in said ensemble at strong fields is utilized to achieve confinement of said ensemble by producing a violent, radially osciUating motion of said particles in which, due to a repetitive discontinuity in the velocity of said particles when - analogously to bouncing - their direction of motion is instantaneously reversed, the average spatial displacement of each particle is 15. essentially zero even though its average acceleration is not zero. 3. A method and/or device according to claim 1, characterized in that an asymmetry in the spacetime dynamics of an extended system with respect to relativistic accelerations and decelerations which are essentially simultaneous in different frames of reference is utiUzed in a relativistic Carnot process to extract 20. energy. 4. A method and/or device according to claim 3, characterized in that said extended system is a device according to claim 2, in which phases of relativistic accelerations which are essentially simultaneous in the stationary frame alternate with phases of relativistic decelerations which are essentially simultaneous in the co- 25. moving frame of the charges. 5. A method and/or device according to claims 1 and 2, characterized in that said violent, radially oscillating motion includes expansion phases in which the mass/energy in a subsystem of said extended system is negative, corresponding to a thermal energy ofthe zero-point energy fluctuations ofthe vacuum in said subsystem 30. which is lower than the ambient thermal energy ofthe vacuum fluctuations, resulting in a flow of energy from the ambient zero-point field into said subsystem, and which energy during the compression phases of the osciUation is dissipated to the immediate surroundings of said subsystem, thus providing a pumping of energy from the infinetely-extending vacuum field to said immediate surroundings of said subsystem 35. for purposes of power generation. 6. A method and/or device according to claims 1 and 2, characterized in that said dissipation of energy from said subsystem to its immediate surroundings is achieved by sUght inhomogeneities in said subsystem, which are arranged so that the dissipation of energy during the compression phases matches the energy inflow from 5. the ambient vacuum field during the expansion phases, resulting in a steady-state power generation. 7. A device according to claim 3, characterized in that said extended system is a ring-shaped electron accelerator in which electron bunches are cyclicly accelerated and decelerated by separate processes such that the acceleration and deceleration 10. processes are simultaneous in different frames of reference, and from which energy is extracted in the of form synchrotron radiation. 8. A method and/or device according to claim 2, characterized in that said ensemble of charges is essentiaUy sphericaUy-symmetric, and said electromagnetic field is an essentially sphericaUy-symmetric electric field. 15. 9. A method and/or device according to claim 2, characterized in that external electric fields are used to produce said periodic, radiaUy-osciUating motion ofthe charged particles. 10. A device according to claim 9, characterized in that said electric field is created by a central, preferentially spherical electrode supplied by an external high-frequency 20. source connected to said electrode by a shielded connector. 11. A method and/or device according to claim 8, characterized in that said electric field is created internaUy by the electrodynamics of said ensemble of charges itself, thus producing an electrodynamic self-confinement of said ensemble. 12. A method and/or device according to claim 11, in which said self-confined 25. ensemble of charges is created from an initiaUy cyUndrical discharge, which is caused to pinch due to the magnetic field ofthe discharge current, characterized in that said pinched discharge is aUowed to deform by inherent instabihties, preferentially of 'sausage' type, leaving - after the current is switched off - at least one highly energetic, essentiaUy sphericaUy symmetric charge configuration which is arranged through the 30. current distribution in the initial cyUndrical discharge to get a radial charge density distribution proportional to l/r N , where r is the distance from the center of symmetry and with N greater than 3 (or approaching 3 infinetely close from above), corresponding to a radial electric field distribution in said charge configuration which is (possibly only infinitesimaUy) steeper than a Coulomb field, i e proportional to l/r n 35. with n greater than 2 (or approaching 2 from above). 13. A method and/or device according to claim 2, characterized in that violent, high-frequency oscUlations ofthe positive background ions in response to said osciUations ofthe electron population in the confined ensemble of charges are employed to produce energy through nuclear fusion reactions. 14. A method and/or device according to claim 13, characterized in that said osciUations of said background ions, due to differences in their mass, enhance such 5. nuclear fusion reactions which produce essentiaUy only charged particles and no neutrons as end products. 15. A method and/or device according to claim 14, characterized in that said background ions are protons (H 1 ) with a small fraction of deuterons (D 2 ), and which produce fusion energy through the reaction D 2 + H 1 with a negligible proportion ofthe 10. reaction D 2 + D 2 . 16. A method and/or device according to claim 14, characterized in that said background ions are heUum-3 ions (He 3 ) with a small fraction of deuterons (D 2 ), and which produce fusion energy through the reaction D 2 + He 3 with a negUgible proportion of the reaction D 2 + D 2 . 15. 17. A method and/or device according to claim 2, characterized in that said electrodynamic confinement is utilized to store electric energy, thus providing extremely Ught-weight energy storage. 18. A method and/or device according to claim 17, characterized in that the energy content per volume of said energy storage is increased by compartmentalization of the 20. confinement structure into a large number of subunits. 19. A method and/or device according to claims 2 and 18, characterized in that said compartmentalization ofthe confinement structure is used to create extremely light-weight, mechanical structure elements. 25. 30. 35.

Inventors: BERGSTROEM ARNE, BERGSTROEM, ARNE
Applicants: BERGSTROEM ARNE, BERGSTROEM, ARNE
Application year: 1996
Main classification: H05H1
IPC codes: H05H1