4. The energy balance of the Brown - Ecklin generator
Normally, regarding energy energy balances in electrodynamics every physicist assumes that this problem is solved already in physics by the equation of energy conservation in an electromagnetic field. But if we have a more precise look at the derivation of this equation we recognize that this imagination only holds for the special case if moving charge interacts with moving charge. But if we have a coupling of the field to spins in a collective (thermodynamic) system of a hard ferromagnet (not to a charge) then we have a situation which differs physically from the situation described by the usual Maxwell theory as well as by standard theory of special and general relativity which is build around electrodynamics. Then we have to realize that Ampere's idea of molecular currents gets incompatible with reality if we leave magnetostatics. For example a perfectly hard ferromagnet cannot be influenced by a changing B-field - contrary to a current loop in a coil. There exists no Lenz Law for it. However, the law of induction (i.e. the Lenz law) is used to derive the equation of energy conservation. Therefore this equation must fail if it is applied to the time dependent coupling of a field to the spins of a hard permanent magnet. Exactly this situation is exploited technologically by Brown's flux switching generator. Therefore, we have to look for an energy balance elsewhere. We realize that
1) our machine works periodically according our simulation,
2) every state of the generator can be simulated quasi-stationary,
3) the magnetic field of the coil is a potential field, and
4) the generator exchanges heat with the environment because the generator runs cool !
From 1)-3) we conclude that the energy balance has a potential
character and because of (4) we make a thermodynamic ansatz for the free
energy with S:=entropy
If we integrate this potential over a closed cycle we get the energy
is the heat energy exchanged with the heat bath of environment, understood
in the widest sense as possible. Perhaps this last two equations can be
derived from the quantum dynamic Dirac equation which adds a tensor to
the Maxwell stress tensor due to the spin. If this equation is applied
to a many particle system a transition into thermodynamics should be possible
by averaging out the many partikel coordinates and reducing the system
to the thermodynamic coordinates.
However, we should note that equation (7) and (8) do not hold for every electromechanic system because it is possible to generate stationary non-conservative magnetic fields which are mathematically uncompatible with a potential formalism like thermodynamics. To give an example I will propose here a brushless magnetic D.C. motor with a non-conservative force field indepent from time. Maxwell  showed that the circular field lines of the B-field around a conducting file can not produce a permanent torque on a constant magnetic dipol because of the 1/r dependence of the field. Therefore, in order to get a motor, all what we require is a circular non-1/r radial B-field dependence. This can be generated by the following geometry which is analogous to that of an electrical bowl capacitor of radius r0, comp. fig.12: One or more magnet rods the magnetic north poles pointing radially circulate in an orbit in the equatorial plane of a bowl which is made of conducting material. On this bowl a current is flowing in the direction from the upper pole to the lower pole. In order to have a broken current loop the inner wall of the volume of the bowl is shielded by mu-metal and the inner volume of the bowl contains the current sources. The current density on the surface is (roughly) maintained constant by adding current at appropriate locations on the surface preventing the field of the cables in the inner of the bowl by the inner mu metal shield layer of the bowl. In order to calculate the field we solve again the Poisson equation for the magnetic vector potential A. We use polar coordinates this time. Because the problem is independent from the coordinates of the angles the Poisson equation reduces to
Solving this equation we get
Now, according standard electrodynamics we calculate the magnetic B-field using the formula of the vector potential A:
Calculating the curl we get the B-field. Using this geometry and calculating the curl, a 1-dependence of the circular B-field can be calculated in the equatorial plane of the orbit. This leads to a constant torque around the upper-lower-pole axis exerted on both the rods by the magnetic charges +/- g(r) at radiuses in the field:
Remembering that B = C (C is a constant) in the equatorial plane we get a non-vanishing net torque of
Therefore, a circular constant magnetic B - field motor is feasible. But the energy balance for this motor still has to be established.
5. Technological outlook
The principle standing behind the Ecklin generator I call mechnical flux switching. In electromechanics this principle has been applied in generators proposed and build by
1) Kromrey  comp. fig.13
The Kromrey generator is a precursor of the Ecklin-generator. It contained already a closed flux which is switched periodically by rotation. The rotor coil still has windings on it like a normal generator. The generator had already anti-Lenz behaviour, i.e. lower torque with increasing current from the generator. The efficiency was about 1.
2) Bedini 
In a Bedini generator of 1985 the rotor consists of two parallel rotating opposite faced permanent artificial horseshoe magnets (made by two cylindical permanent magnets bound by a soft iron) whose common circuit of magnetic flux is closed periodically by two stationary iron cores which are wound around by coils each which deliver the energy of the generator. The oscillogram shown by Bedini confirms qualitatively our calculated diagram. It contains a positive and a negative pair of spikes because the direction of the flux through the coils alterates every half rotation. Bedini restored already the energy from the generator back into a battery by use of a switching power electronic. The energy of the battery delivered enough power to drive the motor of the generator and, because of the overunity efficiency of the generator, a further battery could be charged additionally.
3) Dorman  comp. fig.14
Dorman has announced a book about the design of LIAG - generators (low inertia armature generator). In a short mail he mentions his design form:
"A LIAG has a rotating perforated magnetic shield that spins between a stationary magnetic field (for our purposes, and for greatest efficiency, made up of permanent rare earth supermagnets) and stationary coils (wound upon laminated soft iron cores). This shield alternately passes and blocks the magnetic field and thereby induces an electric current in the coils." Dorman emphasizes that the construction of LIAG - generators would be quite cheap because the rotating armatures are quite light reducing the costs of bearing and armatures.
For the Brown-Ecklin design upscaling is possible if the flux switching iron pieces are mounted on a cylindrical cage or tube which rotates, comp fig.15. They close and open periodically the stationary magnetic circuit which are mounted stationary in the outer or even inner periphery of the cage. The cage or tube construction must prevent any inductive eddy currents contrary to an asyncronous cage induction motor/generator. Therefore, the material of the cage has to be an insulator - or the possible circuits in the cage/tube have to be broken by isolating parts.
For all known mechanical flux switching generators the difficulty
exists that for every form of load impedance connected to the concerned
generators the waveform changes because the differential equation changes
as well. The power produced by these generators contains many A.C. overtones
which are surely not compatible with today technology of D.C. and A.C.
current. Therefore, to make this generators useful the form of energy released
has to be changed.
Bedini has done this using power electronics which restores back the energy released in batteries which act as well as capacitive buffers. Acc. to a open mail  the rpm of the generator is chosed to be in the resonance state optimizing to get energy at high voltage but with low current and low back torque. For the author this is difficult to believe because the preliminary numeric experiments with additional capacities in the circuit show that they reduce the output power. Flux gate generators are more efficient at higher ohmic load. Therefore, perhaps a transformer stage between flux gate generator and battery could be responsible for that. A further step would be to connect an alternating current shaper to this setup or to the mechanical flux switching generators directly to produce alternating current for external consumption.
Perhaps upscaling in number of flux switches pro length and number of flux switches pro circuit of all these different types of flux generators allows to get off the many harmonics problem to certain extent. If n magnets and n stator generator coils of different wounding numbers and in appropriate distance from each other stator coil are taken then, a purer alternate current can be produced by connecting the coils of appropriate wounding numbers (i.e. voltages) and distances(i.e. phase differences) which deliver the appropriate A.C. voltage in combination if they are connected or swiched in series by the electronics or commutators at the right moment. The adding of the coils could be controled by a microprocessor which reacts to load situation and tries to optimize the output to a sinus signal.
Therefore, the initial weakness of this type of generators could be overcame and their capability of overunity efficiency -which allows a gain feedback of energy into a motor driving the generator again- promises a purely economic end of atomic and oil-driven power technologies soon.
Thanks for some critical remarks regarding the first version of this article especially to Larry Wharton (firstname.lastname@example.org), Greg Watson (email@example.com), Robert Dorman (firstname.lastname@example.org) and Stefan Hartmann (email@example.com). They helped to improve the second version.
1) Brown, Paul The magnetic distributor generator 1982
copy of a report, 1982
entry: Dr. Nieper Gravity Folder
was available from "list of shielding theory of gravity papers" at
Admiral Ruge Archives of biophysics and future science
Keith Brewer Library, Richland Center, Wisc. 53581 USA
2) John Bedinis
homepage at http://rand.nidlink.com/~john1/index.html
look in the Kromrey section
3) Dorman, Robert short message from firstname.lastname@example.org
from mailing list email@example.com at www.eskimo.com/~billb
4) Bauer, W.D.
Incompatibility of Planck's Version of the Second Law with Thermodynamics Regarding Mixtures in Fields 29.5.96 see my homepage at www.overunity.com/theory.htm
5) Ecklin, John W. US-patent No.3,879,622 Apr. 22, 1975
6)Kromrey, Raymond US-patent No. 3,374,376
German patent No. 1,463,899
French patent No. 911,348 Okt. 4,1962
7)Engeln-Müllges G., Reutter F.
Formelsammlung zur numerischen Mathematik
mit C-Programmen B.I.Wissenschaftsverlag Mannheim 1990
source code of the Runge-Kutta routine is available at
Prof. G. Engeln-Müllges Kesselstr.88 52076 Aachen-Lichtenbusch
8)Jackson,J.D. Classical Electrodynamics second edition Wiley New York 1975
9)Hielscher, Gottfried Energie im Überfluß- Ergebnisse unkonventionellen
Adolf Sponholtz Verlag Hameln 1981
10)Maxwell J.D. Treatise on Electricity and Magnetism Vol.I
(Dover publishing edition) should be available in book shops
11)Magnetismus - Dauermagnete Werkstoffe und System
Catalog by IBS Magnet Ing.K.H.Schroeter Kurfuerstenstr.92 D-12105 Berlin
12) The idea of the non-conservative force field has been posted already by me at 9th May 1995 under pseudonym by firstname.lastname@example.org (now email@example.com) in the forum SCI.PHYSICS, ALT.SCI.NEW-THEORIES, SCI.ENERGY,SCI.ENVIRONMENT CL.ENERGIE.ALTERNATIVEN, ALT.ENERGY.RENEWABLE and ALT.PARANET.SCIENCE under the thread "Burn's critique of PM_Square! free energy !"
13) Wesley Crosiar (firstname.lastname@example.org) An open letter to all working
Source lost, probably freenrg-l.@eskimo.com or email@example.com