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«PACS-classification: 84.60.-h, 89.30.-g, 98.62.En, 12.20.-m, 12.20.Ds, 12.20.Fv Summary of a Scientfic Work by Claus Wilhelm Turtur Germany, ...»

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5.1. Magnetic analogue with the electrostatic rotor With regard to the similarities between the circulation of energy of the electric field and the circulation of energy of the magnetic field, as demonstrated in section 2.3, it is expected, that it should be possible to build a magnetic rotor for the conversion of vacuum-energy in analogy with the electrostatic rotor for the conversion of vacuum-energy [e15]. A suggestion for an appropriate setup is conceived in section 5.1. The considerations also contain exemplary calculations of the forces being expected (in comparison with the force being expected from the electrostatic rotor).

In order to understand the rotation of the electrostatic rotor, the Coulomb-force of an electric field acting onto a rotor of electrically conducting material was calculated with the imagecharge method [Bec 73]. One central fundament for the applicability of this method is the fact, that the electric flux coming from outside onto the surface of the material rearranges the electrical charge distribution on the surface in such a way, that the flux-lines are always exactly perpendicular to the conducting surface [Jac 81] and the field does not penetrate into the inside of the material. The force between the charge and the image-charge explains the rotation of the rotor-blades and thus it shows the instrument to get some energy out of the cycle of energy between electrostatic energy and vacuum-energy.

If this principle of energy conversion shall be adopted to the energy cycle between the magnetic field energy and the vacuum-energy, a rotor driven by magnetic forces should be constructed, which can be understood in analogy to the rotor driven by electrostatic forces.

The analogue to the image-charge method is to be found in the Meissner-Ochsenfeld-effect occurring on the surface of a superconductor in a magnetic field [Tip 03]. Similar as the image-charge method is based on the appearance of electrostatic charges on the surface, the Meissner-Ochsenfeld-effect is based on the appearance of superconducting currents on the surface of a superconductor in a magnetic field. These currents evoke magnetic fields, which exactly compensate the external magnetic field, so that in the inside of the superconductor the total magnetic field is zero. (In the inside of the electrical conductor the electrical field is also zero.) In this sense, the superconductor displays ideal diamagnetic behavior with a susceptibility of   1 [Ber 05].

In order to calculate the forces which superconducting rotor-blades take up in a magnetic field, the field strength at each point on the surface of the rotor-blades have to be taken into account and their interaction with the field strength of the same absolute value but of the opposite orientation has to be determined (finally going back to the associated electric currents). An exemplary setup of an imaginable rotor is show in fig.26 with a permanent magnet in the above part of the sketch and a rotor consisting of four superconducting blades in the bottom part of the sketch. The geometrical dimensions noted there serve as input parameters of an exemplary calculation, which has the purpose to give a feeling of concretely

5.1. Magnetic analogue with the electrostatic rotor 69 achievable forces and torques. The forces are repulsive (not attractive), because the flux-lines can not penetrate into the ideal diamagnetic material, independently from the orientation of the external magnetic field produced by the permanent magnet. It is generally known that the Meissner-Ochsenfeld-effect is independent from the polarity of the flat permanent magnet.

Thus, the direction of the rotation of the rotor in fig.26 is counterclockwise (other than the direction of rotation of a similar electrostatic rotor). The electric forces between charges and image-charges are attractive, but the magnetic forces between currents and “image-currents” are repulsive.

–  –  –

be orientated parallel to the z-axis. Thus, the vector of the magnetic field is the same on all positions on the surface of the rotor-blades. Consequently, the magnetic field produced by the Meissner-Ochsenfeld-effect (which compensates the external field) is orientated exactly into the negative z-direction for all positions of the rotor-blades (and has the absolute value of  H  1 m ). But the position-vectors from all individual points of the field source to all A individual points on the surface of the rotor-blades are going into individually different directions. And each rotor-blade is not symmetric with regard to the z-axis. Consequently, the total force acting onto each rotor-blade, which is the sum of all forces acting between each individual part of the rotor-blade and each individual part of the field source, contains a tangential component, which is not orientated into the z-direction. This consideration implies a subdivision of the field source and the rotor-blade into finite elements.

The calculation of the sum of all finite force elements is done as following: Each finite element of the field source produces a field at each finite element of the rotor (this field element produced by the magnet shall be numbered with the index no.1). And the finite element of the rotor itself reacts to the total field with its orientation into the opposite direction (the finite field reaction element of the superconductor shall be numbered with the index no.2). The magnetic forces between all these pairs of field elements are determined as usual on the basis of Biot-Savart’s law and the law of the Lorentz-force. But here these formulae are written in a way, that we directly see the forces between the two field strengths  

of the particular field element pairs ( H1 and H 2 ). This is the following formula:

70 5. Outlook to the future    2    F12  40  r12  e12  H1  H 2, Vs  with 0  4  107 Am, r12  vector connecting the field-elements (1.69)  e12  unit-vector between the field-elements.

and Because the field strength has been chosen to be homogeneous in our example (absolute values H1   H 2  1 m ), the total force onto a rotor-blade can be determined by a rather A simple integration over the surfaces of the field source and the blade (keeping in mind the double vector-product for each field-element-pair). For the given example, this was carried out by a subdivision of the blade as well as the field source into finite elements and summation of all these force-elements. If the subdivision is refined more an more (with growing number of elements), the result (on the basis of the given numerical parameters) converges to a force values of FR  4.2  108 N for the radial component of the force and FT  3.1  1010 N for the tangential component of the force per each single rotor blade. The radial component of the force is compensated by the mechanical axis of the rotor, whereas the tangential component of the force should make the rotor spin. A rotor consisting of four blades takes up four times the tangential force, this is FT  1.2  109 N. The torque onto the rotor was calculated by summing up the torque of each finite element pair of the rotor with its individual radius of rotation, which leads to the result of M  4.8  1011 Nm.

Please be aware, that the radial component absorbed by the bearing of the axis of rotation is the dominant part of the force. This leads to the consequence that the experimental setup has to be built with extreme mechanical precision, otherwise a small part of the radial force component could already disturb the rotation. Additionally the homogeneity of the magnetic field has to be very good (better than a single pair of permanent magnets can do) and the mechanical adjustment has to be done with an adequate precision. Otherwise the rotor would not spin.

The calculated value of the torque is too small for an experimental verification, but the field strength can be enhanced remarkably and with it the forces and the torque. They increase quadratically with the field strength according to (1.69), following the proportionality of the    absolute values M  H 2  H1. The limit of the field strength is given by the critical field strength Bc of the Meissner-Ochsenfeld-effect, which depends on the temperature. For instance, a superconductor type 1 can have Bc  0.080 T for Pb or Bc  0.01T for Al (with temperature extrapolated T  0 K ). In order to have some safety distance from the critical field, and in order to respect that the fact the temperature in a real experiment is different from zero, we can allow a magnetic induction B of few milli Tesla, corresponding with a field strength of about H1  103 m. This lets us expect a the tangential component of the force A in the order of magnitude of FT  1.2  109 N  106  1.2  103 N, providing a driving torque of about M  4.8  105 Nm. This should be sufficient for a measurement, namely to surmount the friction of a real existing bearing as said in (1.65), (1.66), or (1.67).

If cooling should be made as easy as possible by using liquid nitrogen, it could be interesting to work with a high-temperature superconductor, as for instance Y Ba2 Cu3 O7, which is known to be a superconductor type 2. It only behaves ideal diamagnetic as long as the

5.1. Magnetic analogue with the electrostatic rotor 71 Shubnikov-phase is avoided. Nevertheless the field strength and with it the maximum of the reachable forces and the torque should be expected to be even larger than with the superconductor type 1 as mentioned above. In this sense, a conversion of vacuum-energy via magnetic field energy into classical mechanical energy should be detectable even under liquid nitrogen.

Continuative remarks regarding an experiment Another question is, whether the practical performance of the experiment really needs ideal diamagnetic rotor-blades made from superconductor material. Also conventional dia-, para-, and ferro- magnetic materials experience forces when they are exposed to magnetic fields even at room temperature. This question can not be answered here, but it is possible to develop some thoughts about forces and torques.

If a rotor would be made from classical diamagnetic metal (at room temperature), for instance such as copper (   1  105 ) or bismuth (   1.5  104 ) (see [Stö 07]), it would be H 2     H1. With the same strength of the external field, the forces and the torque would be about 4 or 5 orders of magnitude smaller compared to a superconducting rotor, but the field strength could be enhanced perhaps to 1 Tesla of even more rather easily, so that finally the torque might be enhanced to a value even a bit larger than with a superconducting rotor. The mentioned values lead us to a torque in the order of magnitude of about 105... 104 Nm.

Instead of using a diamagnetic rotor, it might be discussed to build up a paramagnetic rotor, for instance of platinum (   1.9  106 ) or aluminium (   2.5  104 ) (see [Ger 95]). The forces will be attractive in this case so that the rotor spins with opposite direction than a diamagnetic rotor (if it spins), but the absolute values of the torque should be of the same order of magnitude as those of diamagnetic rotor.

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