Stephenson SPESIF-10-96 Manuscript Draft 6Oct09a_2

EDITORIAL REVIEW DRAFT – 10/06/09

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A Linear Force from an Array of Gravitomagnetic London Moment Generators

G. V. Stephenson a

a Seculine Consulting 425-443-9651; [email protected]

Abstract. The generation of a gravitomagnetic London moment due to the circulation of cryogenic superfluids may have been indirectly observed, most notably by Tajmar (2007). Also known as the frame-dragging effect or the Lense-Thirring effect, a gravitomagnetic moment results only in rotational force or angular acceleration, and is therefore not useful as a linear propellantless drive. In this paper a topological argument is made for a method to use an array of gravitomagnetic London moment generators (GLMGs) to create a small but useful linear force from the geometric sum of rotational gravitomagnetic forces. A number of geometries are compared and contrasted, geometric predictions of aggregated gravitational field gradients are analyzed, and experimental test configurations are proposed, including the circulation of a superfluid through a spiral tubing array.

Keywords: Gravity, Gravitational, Gravitomagnetic, Effect, Control, Amplification, Acceleration, Generator, Linearized, Lense-Thirring, Frame-dragging, Superfluid, Vortex, Vortices, Aharonov-Bohm , Magnus, Iordanskii, Force PACS: 04.20.Gz, 04.60Pp, 04.80.-y, 04.80Cc

INTRODUCTION

When rotated, a superconductor produces a magnetic field with respect to the frame in which it is being rotated. The moment of this magnetic field, which is aligned with the spin axis, is known as the London Moment. By analogy, Tajmar et al. have named a field of gravitomagnetic acceleration observed around rotating superconductors a “gravitomagnetic London moment,” (Tajmar et al. 2007a and 2007b; Tajmar and Hense 2007c and 2007d; Tajmar , Plesescu, and Seifert 2008). Regardless of the root cause of this effect, the notation of GLMG, for Gravitomagnetic London Moment Generators, will be used here to describe a mechanism that creates this effect. In the aforementioned set of experiments, the GLMGs were always unitary in nature, i.e. for simplicity’s sake there was always only one rotating element creating only one rotational acceleration field. The thrust of the present paper is to investigate other possible experimental topologies on the basis of the results already presented to date, and possible ways of combining multiple numbers of GLMG elements to create a useful linear force out of a summation of rotational forces. We begin with a background section that summarizes the experiments of Tajmar et al. and provides an overview of relevant results, and also explores the notion that the gravitomagnetic London moment (GLM) effect may be linked to superfluid motion rather than superconductor motion, first introduced by Tajmar and de Matos (2005). This is important because if superfluid motion is the root cause of effect, then it could be magnified by increasing velocity of superfluid motion and volume of superfluid in motion. Next we introduce the geometric argument that a rotational force can be converted to a linear force via an arrangement of rotational acceleration components, and explore some alternate geometries. Some of these geometries are valid regardless of the cause of the GLM effect, and some will work only if superfluid circulation is the cause. Finally a number of suggested experimental configurations are presented, including in particular possible ways in which the superfluid behavior may be better quantified.


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BACKGROUND

It has been firmly established from a wide range of experiments by Tajmar et al. that the GLM effect is a real and repeatable effect, (Tajmar et al. 2007a and 2007b; Tajmar and Hense 2007c and 2007d; Tajmar , Plesescu, and Seifert 2008.) However, the root cause of the effect, presumed for years to be caused by the superconductor rotation, has yet to be firmly established. During the course of the experiments a number of anomalous observations have continued to accumulate which point to more than just purely superconductors as the responsible mechanism:

1) the effect is not observed with “high temperature (LN2 class) superconductors, only with low temperature (LHe class) superconductors

2) the temperature of the onset of the effect is not the critical temperature of the superconductor in question, i.e it does not appear to align with the onset of the superconducting regime

3) the type of superconducting material does not seem to play a substantial role in the strength or onset of the effect

4) there often appears to be a rotational asymmetry, in which the effect is much stronger when the superconductor is spun in one direction preferentially over the opposite direction, but this is not fully repeatable and appears to vary depending upon the experimental setup.

Collected together these features tend to point away from the superconductor (SC) as the root cause of the GLM effect, and towards the cryogen, in particular the LHe, as a possible source of the effect. This would account for observations (1) through (3) in that it would be the presence and temperature of the cryogen that would be the critical feature of the experiment, and the hidden variable, not the superconductors. Additionally, if the experimental apparatus where inducing cryogen flow, such as a rotation of cryogen, this may account for observation (4), where the direction of the superconductor acceleration does not always change the direction of the effect. In this case the hidden variable would be the change in the flow rate of the cryogen, in particular the LHe. The hypothesis that the LHe cryogen is the principal actor in the GLM effect is represented in figure 1. In figure 1a the arrangement of the LHe cryogen in a typical experimental test setup (Tajmar et al. 2007b) is shown with the induced cryogenic rotation superimposed to clarify this hypothesis, and in figure 1b rotating cryogen is idealized to represent an elemental GLMG. This symbol will be used elsewhere in the paper to represent a GLMG in the generic sense. FIGURE 1. Superfluid circulation acceleration as a possible source of Gravitomagnetic London Moment Generators (GLMGs)

(a), a typical Tajmar experimental configuration (Tajmar 2007b) and (b), superfluid motion as the elemental source of a space-time “twist” or rotational acceleration.

Symbolic representation of elemental unit of

coherent superfluidmotion: “GLMGs,”

Or space-time twistors

Rotational force…

…spun a super-conductor..

…and also causedSuperfluid circulation...

…causing qravitomagnitic(twist) force in apace-time.


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Why would LHe cryogen rotational (angular) acceleration cause the GLM effect? The answer is not currently fully understood and experimental research currently underway should soon bring additional detail to light. While the root cause of the effect is beyond the scope of the present paper, it is important to consider possible mechanisms if for no other reason than to bound the art of the possible in terms of how the effect could be exploited by geometric means. In particular, it may be significant to consider the possibility that at least a small portion of the LHe cryogen may have been in the He-II state for the experiments exhibiting the GLM effect. This could have been possible if the internal temperature within the LHe dropped from 4.2K, where He boils, to below the lambda point of 2.17K, where LHe transitions to the superfluid state of He-II. This could have been caused via evaporative cooling, by relieving the vapor pressure through an exhaust tube or in some cases even through a fill tube, (Rellergert, 2008). The possibility that the root cause of the GLM effect is due to the rotation (angular acceleration) of superfluid helium is significant for a number of reasons. When a superfluid (SF) is rotated it spawns the nucleation of persistent quantized vortices within the superfluid. This is the source of quantized angular momentum in SF. These vortices have been verified experimentally for both naturally occurring isotopes, 4He and 3He, (Lounasmaa and Thuneberg, 1998). Given the temperatures at which the experiments in question were operating, the portion of the LHe in a superfluid state would have to be 4He. When a portion of the LHe is SF and a portion is not, it is said to be in a “two-fluid” state. Two-fluid hydrodynamics exhibit 3 different topological forces on the vortices setup by SF rotation (Volovik, 1998, and Wexler, 1997):

1) the Magnus Force, a relative vortex drift force due to vortex motion with respect to the “SF vacuum” (outside the vortex)

2) the Axial Anomaly, a.k.a. the Chiral anomaly, due to the interaction of EW (electro-weak) fields with fermions (only relevant for 3He)

3) the Iordanskii Force, an angular force due to the vortex motion (velocity field) with respect to the “heat bath” of quasi-particle excitations in the SF, such as phonons.

The Iordanskii force is of particular interest. Phonons in SF in the presence of a velocity field act like photons in the presence of a gravitational field, and can therefore be described by the same metric, (Volovik, 1998.) This interaction with space-time gives rise to a time delay for an arbitrary particle traveling in a closed circle outside the rotating vortex but in the opposite direction, which is otherwise known as the gravitational Aharonov-Bohm (AB) effect. One result of this effect is that a spinning vortex generates a non-zero angular momentum density outside the vortex, giving rise to the Iordanskii force. Whether this force extends beyond the bounds of the superfluid remains an open question, but if it does this would certainly qualify as one possible cause of the GLM effect. The metric implications of the gravitational AB effect would certainly seem to imply this. Regardless of the mechanisms at work, if the root cause of the GLM effect is superfluid acceleration, a new class of experiments may be proposed to more fully determine how best to exploit the effect, and may also bring additional insight into physical properties of the effect. In the following sections generic solutions for magnifying and linearizing the GLM effect will be expanded on for the special case where the SF motion is the cause.

TOPOLOGICAL FORCE GEOMETRY CONVERSION

For the present section let us take as a given that an elemental GLMG will create a the rotational acceleration, which when applied to a test mass will result in a rotational force in the free space surrounding the GLMG element. How then could this type of rotational force be converted to a useful linear force, suitable for instance for thrust? Consider the simple nut and bolt mechanism as depicted in figure 2a.This is essentially the same device as a common screw – a device that converts a rotational force into a linear motion or translation. In machinery this is known as a one degree of freedom screw joint kinematic pair (Norton, 2008). Note that half of the kinematic pair is the hole through which the screw can thread. In topology this represents pairing a S0 surface (bolt/screw) with an S1 (nut/hole) type surface. The same technique can be used with the GLMG. If one uses a ring of GLMGs oriented so that the flows are aligned as shown in figure 2b, the rotational forces generated during superfluid acceleration will constructively add in the center so that any test masses in this area will experience an upward force. Likewise around the outside parameter test masses would experience downward accelerations. In this case the ring of GLMGs is the equivalent of the nut, and the bolt is spacetime itself.


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FIGURE 2. Two methods for the topological conversion of a twist (rotational acceleration) into a push (linear acceleration). (a), a nut and bolt pair as the archetype of the kinematic pair (b), an array of GLMGs acting on ST as a kinematic pair equivalent.

LINEARIZATION ARRAY OPTIONS

Let us now consider a variety of options for how to arrange arrays of GLMGs to create a linear force. The minimum set would appear to be only one pair of counter-rotating GLMGs. In this case they would be counter rotating so that the vectors of accelerations add where they meet. This would be inefficient, and the field would not be uniform, but it would be a very simple configuration to test. With three GLMGs, all rotating inward, the field would be slightly more uniform and would have additional planar control stability. The use of four GLMGs, two matched counter-rotating sets, as shown in figure 3, would be still better, but is still creating a field that is far from uniform.

FIGURE 3. Two matched sets of GLMGs in a circular array for the linearization of rotational gravitomagnetic forces.

net linear force up in center (twist up)

exhaust forces on outside edges (twist down)

Rotational force…

…results in a net linear force..

…via an S1 surface.

Rotational force…(twist)


…results in a net linear force (in center)..all forces twist up center

Rotational force…

…results in a net linear force..


Rotational force…(twist)


…results in a net linear force (in center)..all forces twist up center


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The most uniform inner acceleration field would be created by a spiral of GLMGs with the inner acceleration fields all pointing up. If superfluid flow is responsible for the GLM effect this would be very straightforward to implement, as standard cryogenically cooled piping or tubing could be used. Figure 4 depicts this situation, which has a geometry similar to that suggested by Forward (1962) as that which generates a dipole gravitational field. The advantageous features of the spiral configuration are that it is easy to construct - a spiral of tubing can be used - and it is easy to magnify forces by adding more spirals and more SF He-II. Constraints and disadvantages of the superfluid spiral design:

- Velocity constraints: superfluid must be pumped (or rotated) above a critical velocity before the superfluid will react (the velocity of the superfluid is quantized)

- Pumping / stirring constraints: it is difficult to pump without disturbing coherent flow – a circulation pump must maintain flow with little or no turbulence. It is not obvious how such a pump would be designed, especially if higher velocity flow are desired.

- Temperature must be maintained below the lambda point: Superfluidity in 4He only occurs at temperatures below 2.17 K

FIGURE 4. Schematic of a spiral array of GLMGs for a more uniform generation of gravitomagnetic forces, (Forward, 1962).

FIELD DISTRIBUTION PREDICTIONS

Detailed field predictions have not yet been performed by this author, and are the subject of ongoing research, however some field strength predictions can be made based on extrapolations using historical measurements from Tajmar et al., (Tajmar et al. 2007a and 2007b; Tajmar and Hense 2007c and 2007d; Tajmar , Plesescu, and Seifert 2008). For the purposes of scaling the GLM field effect we assume here that the effect is based not on superconductor related effects but on superfluid related effects. It is therefore instructive to quantify the angular momentum of the LHe cryogen in terms of the He-II quantized superfluid circulation. For instance, if the effect is related to the Iordanskii effect the impact on the metric will scale according to the quantized rotational angular momentum, (Volovik 1998). The quantum circulation of superfluid velocity is given by (Lounasmaa and Thuneberg 1998):

∫∫ ⋅=⋅= ns vdrvdrκ (1)

GG

G

P

P

Spiral array of GLMGs

Integrated inner acceleration field generated

GG

G

P

P

GG

G

P

P


Integrated inner acceleration field generated


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where vs is the velocity of the superfluid and can be expressed in terms of vn, the quantized vortex count. When evaluated for a cylindrical of radius R, the total vortex count is:

02 /2 κπ Ω= RN where 42/ mho =κ

(2) where Ω is the rotational rate, and κ0 is the circulation quantum, which has been confirmed experimentally, (Lounasmaa and Thuneberg 1998), and is related to Planck’s constant and the mass of the helium isotope in question, in this case the 4He mass. Based on the experiments of Tajmar et al.(2007a), equation (2) can be used to calculate scaling approximations to predict the integrated effects of GLMG arrays as described in equation (3), which describes the scaling with volume and angular acceleration, with numerical results in captured in Table 1.

}/{* 000 ΩΩ= VVNN (3)

Table 1. Predicted GLMG Array Parameters

(assuming scaling based on superfluid flows ).

Number of GLMGs /

circulation loops

Total LHe Flow Volume

(m^3)

Average LHe Flow Velocity

(m/s)

Predicted Force Developed

(m/s^2) 4 .08 568 1.2E-3

20 .08 568 5.9E-3 20 .8 568 5.9E-2 100 .8 568 .294

1000 8 56800 29.4 (3G) These are the predicted peak accelerations as observed just to the inside of the spiral array of GLMGs. Figure 5 is a representation of the rough field distribution in the proximity of a spiral array of GLMGs.

FIGURE 5. Gravitational field prediction of a spiral array of GLMGs.


Integrated acceleration field generated






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SUGGESTED EXPERIMENTAL CONFIGURATIONS

The following experiments are recommended for determining to what extent superfluids are responsible for the GLM effect:

1) Vary the superfluid rotational rate, vary the quantity of superfluid, and vary the temperature to compare performance above and below the lambda point, all while attempting to measure the GLM effect 2) As shown in figure 6, create two counter-rotating GLMG elements, place them in proximity, and attempt to measure the aggregated acceleration 3) To the extent possible measure the dynamics at work in the superfluid while performing the GLM effect experimental regime, to characterize and quantify the flows and turbulence conditions present.

FIGURE 6. Ground testing with pair of counter-rotating GLMGs. In addressing item (3), one way to track SF dynamics is through the use of laser induced florescence (LIF). Exposing SF He-II to ionizing radiation will create He molecules which can undergo scintillation and florescence when stimulated with 910nm and 930nm wavelengths of laser light, (Rellergert 2008). This method could be used to create a 3D flow map within the SF, even down to the Kolmogorov length scale to characterize turbulence. Another potentially relevant feature of 4He superfluids is that of quantum evaporation. In an analogy with the photoelectric effect, just as a photon of energy is needed to eject an electron, in SF a “roton” with a quantum of kinetic energy is needed to eject one atom of He, (Balibar 2006, Dalfovo 1995). This amount of energy is equivalent to the amount stored in one vortex. As a rotating SF is accelerated or decelerated vortices are nucleated or annihilated, altering roton densities within the SF. Roton densities can be studied via inelastic neutron scattering to better understand SF quantum dynamics and interactions with the surrounding metric. Finally, there is an inherent constraint for earth bound applications – the Earth’s gravitational field itself – that creates a preferential direction to superfluid flow, and may disallow certain dimensionalities of experiment. For example, the spiral configuration around a toroid as indicated in figures 4 and 5 may be difficult to maintain in an external gravitational field. It is therefore recommended that if ground laboratory testing of simple geometries provide promising results, that zero-g to micro-gravity testing of the more complex geometries be performed to extend research in these areas. This would of course require packaging and launching a test article designed for use in space, or at the very least designed for use in a space-borne laboratory environment.

CONCLUSIONS

A topological argument is made for a method to use an array of gravitomagnetic London moment generators (GLMGs) to create a small but useful linear force from the geometric sum of rotational gravitomagnetic forces. A

Force adds in center


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number of different geometries would function to create a linear force, possibly including a spiral toroid geometry of circulating superfluid. Predictions of aggregated gravitational field gradients were made based on the supposition that the GLM effect is due to superfluid circulation. Experimental test configurations have been proposed, including both ground and space based configurations.

NOMENCLATURE

h = Planck’s constant κ0 = circulation quantum κ = quantum circulation (of superfluid velocity)

m4 = mass of the helium-4 isotope (kg) N = total vortex (quantum circulation) count Ω = angular rotation rate (rad/sec) R = radius (m) vn = angular velocity, in numerical vortex counts vs = superfluid angular velocity

ACRONYMS

3He - Heium 3 isotope 4He - Helium 4 isotope AB - Aharonov-Bohm GLM - gravitomagnetic London moment (effect) GLMG - gravitomagnetic London moment generator(s) He - helium He-II - superfluid helium LHe - liquid helium LIF - laser induced florescence LN2 - liquid nitrogen S0 - topological equivalent of a sphere S1 - topological equivalent of a torus SC - superconductor SF - superfluid

ACKNOWLEDGMENTS

The author wishes to acknowledge Dr Martin Tajmar and his research team: without their dedicated research this paper would not have been possible. The support of Seculine Consulting is also gratefully acknowledged.


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REFERENCES

Balibar, S., “Rotons, Superfluidity, and Helium Crystals,” 24th International Conference on Low Temperature Physics, AIP Conference Proceedings 850, Melville, New York, (2006).

Dalfovo, et al., “Rotons and Quantum Evaporation from Superfluid 4He” (1995). http://arxiv.org/abs/cond-mat/9505121v1 Forward, R., “Guidelines to Antigravity,” Proceedings of the Gravity Research Foundation, (1962). Lounasmaa, O.V. and Thuneberg, E. “Vortices in Rotating Superfluid 3He,” Proc. Natl. Acad. Sci. USA, Vol. 96, Physics, (1999),

pp. 7760–7767. Rellergert , W.G., “Detecting and Imaging He2 Molecules in Superfluid Helium by Laser-Induced Fluorescence,” PhD

Dissertation presented to Yale University (2008). http://mckinseygroup.physics.yale.edu/publications/RellergertDissertationV5.pdf

Norton, Robert L. Design of Machinery (4th ed.). McGraw Hill, Boston, MA, (2008). Tajmar, M. Plesescu, F. Seifert, B. “Anomalous Fiber Optic Gyroscope Signals Observed above Spinning Rings at Low

Temperature,” 25th Low Temperature Physics Conference, Amsterdam, J.Phys.Conf.Ser.150:032101(2008). http://arxiv.org/abs/0806.2271

Tajmar, M., Plesescu, F., Seifert, B., Schnitzer, R and Vasiljevich, I., “Search for Frame-Dragging-Like Signals Close to Spinning Superconductors, ” Proceedings of the 2nd International Conference on Time and Matter, University of Nova Gorica Press, Nova Gorica, (2007), pp. 49-74. http://arxiv.org/abs/0707.3806

Tajmar, M., Plesescu, F., Seifert, B., and Marhold, K., “Measurement of Gravitomagnetic and Acceleration Fields Around Rotating Superconductors,” Proceedings of the Space Technology and Applications International Forum (STAIF-07), edited by M. S. El-Genk, AIP Conference Proceedings 880, Melville, New York, (2007)

Tajmar, M., Hense, K., “Possible Gravitational Anomalies in Quantum Materials, Phase I: Experiment Definition and Design,” Air Force Research Laboratory Report AFRL-MN-EG-TR-2007-7012, Final Report, (2007).

Tajmar, M., Hense, K., “Possible Gravitational Anomalies in Quantum Materials, Phase II: Experiment Assembly, Qualification and Test Results,” Air Force Research Laboratory Report AFRL-MN-EG-TR-2007-7013, Final Report, (2007).

Tajmar, M., and de Matos, C.J., "Extended Analysis of Gravitomagnetic Fields in Rotating Superconductors and Superfluids", Physica C 420(1-2), 56 (2005).

Volovik, G.E., “Vortex vs. Spinning String: Iordanskii Force and Gravitational Aharonov-Bohm Effect,” Pis’ma v ZhETF 76, issue 11, (1998), pp841-846.

Wexler, C., “Magnus and Iordanskii Forces in Superfluids,” Phys. Rev. Lett., 79, no. 11, (1997), pp1321-1324.

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Stephenson SPESIF-10-96 Manuscript Draft 6Oct09a_2