MAGNETIC GAS ENGINE AND METHOD OF EXTRACTING WORK

Abstract

The present subject matter overcomes the deficiencies in the prior art by introducing or generating charged particles in an air stream and manipulating the air stream with magnetic fields operating on the charged particles. Embodiments of the present subject mater compress the air stream by accelerating charged particles with a moving magnetic field, where the magnetic field has a velocity perpendicular to its flux lines. The increased velocity of the charged particles increases the statistical mean particle velocity and thereby increases the pressure in the air stream. The compressed air stream is then heated and expanded through a second magnetic field. The expansion of the air stream substantially increases the velocity of the air stream and the charged particles therein. The interaction of the high velocity charged particles and the magnetic field imparts a force perpendicular to the flux lines, this force powers the movement of the magnetic field.

Claims

1.-8. (canceled)

9. A jet engine for providing thrust across the subsonic to supersonic regimes comprising: a duct having an inlet and an exit; a magnetic field device for providing a rotating magnetic field about an axis, said magnetic field defined by a first set of magnetic flux lines proximate to said inlet and a second set of magnetic flux lines proximate to the exit; a combustion chamber within said duct and between said inlet and said exist; wherein an ionized gas stream having a net charge enters said duct via said inlet through the first set of magnetic flux lines, passes into the combustion chamber and exits said duct through the second set of magnetic flux lines and said exit; further comprising an ionized gas generator, wherein said generator is turned off above a predetermined Mach no.

10. A jet engine for providing thrust across the subsonic to supersonic regimes comprising: a duct having an inlet and an exit; a magnetic field device for providing a rotating magnetic field about an axis, said magnetic field defined by a first set of magnetic flux lines proximate to said inlet and a second set of magnetic flux lines proximate to the exit; a combustion chamber within said duct and between said inlet and said exist; wherein an ionized gas stream having a net charge enters said duct via said inlet through the first set of magnetic flux lines, passes into the combustion chamber and exits said duct through the second set of magnetic flux lines and said exit; further comprising a charge separator, said charge separator directing gas with a net charge into the duct by separating part of the ionized gas into positive and negative charged gas ion, wherein said separator is turned off above a predetermined Mach no.

11. The jet engine according to claim 9, wherein said first set of magnetic flux lines having a radial component in one direction normal to the axis proximate to said inlet; and the second set of magnetic flux lines having a radial component anti-parallel to said first set of magnetic flux lines proximate to the exit.

12. The jet engine according to claim 9, wherein the rotation of said first set of magnetic flux lines about said axis is coupled to the rotation of said second set of magnetic flux lines about said axis.

13. The jet engine of claim 9, wherein said first set of magnetic flux lines of the rotating magnetic field devices has a velocity substantially normal to the ionized gas stream.

Description

[0073] These and many other objects and advantages of the present subject matter will be readily apparent to one skilled in the art to which the invention pertains from a perusal of the claims, the appended drawings, and the following detailed description of preferred embodiments.

[0074] FIG. 1 is a representation of a generalized thrust producing device.

[0075] FIG. 2 is schematic diagram of a prior art ramjet engine.

[0076] FIG. 3 is a representation of the thermodynamic path of fluid in an ideal ramjet.

[0077] FIG. 4 is a performance chart of three ideal ramjets.

[0078] FIG. 5 is a representation of thrust per unit airflow for three ideal ramjets.

[0079] FIG. 6 is schematic diagram of a prior art turbojet engine.

[0080] FIG. 7 is a T-s diagram for afterburning and non-afterburning ideal turbojet engines.

[0081] FIG. 8 is a T-s diagram for prior art real turbojet engine.

[0082] FIG. 9 is Maxwell velocity distribution, showing most probable, arithmetic mean, and root-mean-square velocities.

[0083] FIG. 10 is a schematic diagram of an embodiment of the present subject matter.

[0084] FIG. 11 is a representation of an embodiment of the present subject matter.

[0085] FIG. 12 is a schematic diagram of another embodiment of the present subject matter.

[0086] FIG. 13 is a representation of another embodiment of the present subject matter, having inner and outer chambers.

[0087] FIG. 14A is a representation of the interaction between the rotating magnetic field and a charged particle in an inertia frame.

[0088] FIG. 14B is a representation of the interaction between the rotating magnetic field and a charged particle in a frame fixed in the magnetic field.

DETAILED DESCRIPTION

[0089] The present subject matter overcomes the deficiencies in the prior art by introducing or generating charged particles within an air stream and manipulating the air stream with magnetic fields operating on the charged particles. For the purposes of this disclosure charged particles and ionized particles are used synonymously. Embodiments of the present subject matter compress the air stream by accelerating charged particles with a moving magnetic field, where the magnetic field possesses a velocity perpendicular to its flux lines. The increased velocity of the charged particles increases the statistical mean particle velocity and thereby, as discussed previously, increases the pressure of the air stream. The compressed air stream is then heated and expanded through a second magnetic field. The expansion of the air stream substantially increases the velocity of the air stream and the charged particles therein. The interaction of the high velocity charged particles impart a force perpendicular to the flux lines of the second magnetic field and the velocity of the charged particles. This force powers the movement of the magnetic field and can also be extracted in the form of mechanical work.

[0090] The advantages of the present subject matter over the prior art should be clearly evident. The restraint on turbine inlet temperature T.sub.04 as a result of material limitations is substantially lifted, the viscous losses due to interaction between the compressor and turbine blades are eliminated and the operating velocity range can extend from the low end of turbojets to the top end of ramjets without the problems associated with each. In fact, embodiments of the present subject matter can switch between operations as a turbo jet to operation as a ramjet with the proverbial flick of a switch.

[0091] FIG. 10 is a schematic diagramF of an embodiment of the present subject matter. An ionized air stream having a net negative charge is provided at the inlet (a), the air stream may also have a net positive charge but for clarity the embodiment in FIG. 10 is discussed using an air stream having a net negative charge. The net negative charge can be a result of ionizing the air, an introduction of negatively charged particles, or a reduction of positively charged particles. Pressure is recovered from the air stream by the diffuser 1003 at (1) and then is compressed by the flux compressor 1005 between stations (2) and (3). The interaction of the ionized particles in the air stream with the rotation or relative movement of the magnetic field 1100 is responsible for the increase in pressure from the flux compressor 1005. Ionized particles with a negative charge are exposed to the portion of the moving magnetic field 1110 emanating out of the magnetic core 1101. The magnetic field is defined by a plurality of magnetic flux lines which collectively define the magnetic field intensity vector, or magnetic flux density. The flux field as shown in FIG. 10 has a component 1110 in the outward radial direction and since the magnetic field is rotating about the core's axes it has a velocity of r{circumflex over ()} where is the angular velocity of the rotating magnetic core 1101 and r is the radial distance from the center of the magnetic core 1001. The relative velocity between the magnetic flux lines and the charged particle is |r|{circumflex over ()}; therefore, an examination of the interaction of a negatively charged particle with the magnetic flux density can be viewed using the flux lines as the reference, in which case the particle has a velocity of r{circumflex over ()}. Thus, it follows that the force exerted on the negatively charged particle is qrB{circumflex over (z)}, where {circumflex over (z)}={circumflex over ()}x r, in a cylindrical coordinate system. Therefore the negatively charged particle is accelerated in the z direction, resulting in an increase in pressure as governed by equation (24). Thus, the increase in pressure for the air stream is largely a function of charge density, magnetic field density and angular velocity, between r and r.

[0092] The work exerted on the air stream is therefore a function of volume charge density .sub.q, magnetic field density and angular velocity and may be expressed as

[00016]${}_{r^1}^r.Math.2.Math..Math..Math..Math.r^3\left({}_q\right).Math..Math..Math..Math.B.Math..Math.\mathrm{dr}.Math..Math.\mathrm{or}.Math..Math.\mathrm{generally}.Math..Math.\mathrm{as}.Math..Math.f\left({}_q,B,,r\right).$

[0093] The power consumed by the rotating magnetic flux lines in compressing the air stream, i.e. the flux compressor 1005, is supplied by expanding the air stream through a second set of magnetic flux lines or flux turbine 1009. The compressed air stream, prior to expansion is heated by mixing and burning of fuel in the air in combustion chamber 1007 or heater. The air is then expanded through the flux turbine 1009 to obtain power to drive the flux compressor 1005 and extract additional work if so configured. It is the interaction of the charged particles through the magnetic flux lines of the flux turbine 1009 which generate the force and thus it is the movement of the flux turbine 1009 which allows work to be extracted. The expansion of the air stream increases the velocity of the air stream and thus the individually charged particles. Whereas the interaction between the particles and the flux compressor 1005 is driven primarily as a result of the rotation of the magnetic flux lines 1110, thus creating a relative velocity between the particle and the flux lines in the {circumflex over ()} direction. The interaction between the charged particles and the flux turbine 1009 are driven primarily as a result of the relative velocity between the charged particles and the magnetic flux lines 1120 of the flux turbine 1009 in the z direction. The force exerted on the magnetic field 1120 of the flux turbine 1009 F=qu x B=qu.sub.z{circumflex over (z)}b{circumflex over (r)}=qu.sub.zB{circumflex over ()} and the work provided can be expressed generally as:

f(.sub.q, B, u.sub.z). (38)

[0094] When used as a power plant, the air stream is more fully expanded as it passes through the flux turbine 1009 in order to extract the most work via the flux turbine 1009; however, in the case of a propulsion device, the air stream is expanded only enough such that the work supplied by the flux turbine 1009 is substantially equal to the work required by the flux compressor 1005. The air stream is further expanded downstream of the flux turbine 1009 in a nozzle 1013 which has the effect of generating thrust for propulsion.

[0095] The steady state operating point occurs where the turbine power, governed by equation 38, is equal to the power required to drive the flux compressor 1005, governed by equation 37, or in the case of power generation equal to the power required to drive the flux compressor 1005 and the extracted power.

f(.sub.q, B, u.sub.z)dr=f(, B, , r)dr+extracted work. (39)

[0096] The expansion of the gas prior to exiting through the portion of the magnetic field 1120 can be altered (or controlled) to regulate the turbine power. The more the gas is expanded, the larger the velocity of the ions, and thus an increase in the power extracted from the air flow and vice versa, as can be seen by inspection of Equation 39.

[0097] Hereto for, the interactions have been described with relative velocities perpendicular to the magnetic flux lines. This was done for clarity only; it is very likely that the relative velocity will not be perpendicular to the magnetic flux lines, such eccentricities do not diminish the operation of the engine as described. For the description of the present subject matter only components of the relative velocity perpendicular to the flux lines are discussed for simplicity purposes. Furthermore, the inlet velocity of the air stream is assumed to be negligible with respect to the rotation speed of the flux compressor and will not be included in the discussion.

[0098] FIG. 11 shows an embodiment of the present subject matter. The ionized air stream enters through the diffuser 1003 through the flux compressor 1005, becomes heated in the combustion chamber 1007 and expands out through the flux turbine 1009 and further expands through the nozzle 1013. The rotating magnetic field defined by flux lines 1110 at the inlet and flux lines 1120 at the outlet is generated, in this embodiment, by a permanent bar magnetic 1101 rotating at an angular velocity, however other mechanisms for generating the rotating magnetic field are equally envisioned. The outer casing 1070 is preferably constructed with a magnetically conducting material, such as a ferrous metal. The magnetically conducting material further allows the flux lines to effectively complete the magnetic circuit from the inlet to the outlet and further serves to concentrate the magnetic field and shield the objects in the vicinity of the engine from the magnetic field. The selection of the magnetic conducting material will also involve other considerations, such as material strength, weight and temperature tolerance and other well-known engineering principles. The embodiment shown in FIG. 11 requires an ionized air stream with a net charge.

[0099] As noted earlier, an advantage of this embodiment as well as others, is that as the Mach number of the air stream is increased, the diffuser 1003, combustion chamber 1007 and nozzle 1013 can effectively operate as a ramjet, independent of the flux compressor 1005 and flux turbine 1009, and thus, the requirement for an ionized field can be lifted. However, this embodiment is preferably, but not exclusively, used in a closed system, since the ionized stream can be recycled, and thus power losses from generating the ionized stream can be minimized.

[0100] FIG. 12 shows a schematic of another embodiment of the present subject matter. The embodiment in FIG. 12 divides the ionized stream into a positive 1260 and negative 1261 stream and operates on each stream independently. The embodiment of FIG. 12 recognizes that an ambient gas, such as air, is comprised of generally neutral particles that can be ionized or separated into two streams of equal and opposite charges, so that while, on a macro level, the total stream is generally neutral, the individual streams can each have a net and opposite charge and may be operated on as discussed above.

[0101] An air stream separator is preferable for operation in a neutral gas environment and is discussed at a later time. In the schematic diagram the stations are the same as discussed throughout. The gas stream is compressed in diffuser 1203 and divided into an outer stream with, for exemplary purposes, a net negative charge and an inter stream with a net positive charge. In the embodiment shown an outer duct concentric with an inner duct are divided by a magnetic cylinder 1202 and preferably a conductive casing. The outer duct and the inner duct each comprise an inlet and an exit represented generally by stations (2) and (5) respectively. The rotating magnetic field can be generated by a magnetic cylinder 1202 rotating about an axis. Additionally, a center bar 1201 can be made of magnetically conductive material or an oppositely disposed bar magnetic. The magnetic field is described by a first set of magnetic flux lines 1210 with a radial component in a positive direction normal to the axis and located generally between the boundary and a periphery of the outer chamber near the inlet at station (2) and a second set of magnetic flux lines 1220 with a radial component in a negative radial direction normal to the axis and between the boundary and the periphery of the outer chamber proximate to the outlet generally at station (5).

[0102] The negatively charged gas stream enters the inlet of the outer chamber, through the first set of magnetic flux lines 1210 of the flux compressor 1205 where it is compressed by its interaction with the magnetic field. The compressed gas stream is mixed with fuel and combusted in a combustion chamber 1207, expanded out through the second set of magnetic lines 1220 of the flux turbine 1209 and exhausted through the nozzle 1213.

[0103] The inner chamber includes a third set of magnetic flux lines 1211 with a radial component in the negative direction normal to the axis and between the magnetic cylinder 1201 and the bar 1201 proximate to the inlet at station (2) and a fourth set of magnetic flux lines 1221 with a radial component in the positive direction normal to the axis and between the magnetic cylinder 1202 boundary and the bar 1201 at the axis proximate to the outlet at station (5).

[0104] The positively charged gas stream enters the inlet of the inner chamber, through the third set of magnetic flux lines 1211 of the flux compressor 1205 where it is compressed by its interaction with the magnetic field. The compressed gas stream is mixed with fuel and combusted in a combustion chamber 1207, expanded out through the fourth set of magnetic lines 1221 of the flux turbine 1209 and exhausted through the nozzle 1213.

[0105] The combustion chamber 1207 is compartmentalized within each of the outer chamber and the inter chamber and preferably each chamber is separated from the other. The rotation of the first set of magnetic flux lines 1210 about the axis is coupled to the rotation of the second set of magnetic flux lines 1220 about the axis.

[0106] Alternatively the center bar 1201 can be made of a dielectric or non magnetic conducting material thereby substantially eliminating the third and fourth set of magnetic flux lines. In such a case, the inner gas stream is not operated on by the magnetic field. Alternatively, as well, the outer casing can be made of a dielectric or non magnetic conducting material. Thus, the first and second sets of magnetic flux lines are substantially eliminated resulting in the outer gas stream not being operated on by the magnetic field. The engine in these alternatives simply bypasses the gas streams in the non operable chambers or with the addition of traditional compressor blades or fans, the engine can extract some of the work from the flux turbine and act as a traditional high bypass turbofan with respect to the magnetically disabled chamber.

[0107] FIG. 13 is a representative illustration of an embodiment of the schematic shown in FIG. 12. The air stream is separated into positive and negative streams. Each stream is compressed, heated and expanded through respective concentric ducts. For the embodiment illustrated in FIG. 13, the negative air stream passes through the outer chamber 1372 while the positively charged air stream passes through the inner chamber 1373.

[0108] The outer chamber 1372 is formed between an outer casing 1370 and an inner casing 1371. As noted earlier, the casings are made with magnetically conductive materials. The negatively charged air stream enters through the diffuser 1003 through a set of magnetic flux lines 1310 radiating out of rotating cylindrical magnet 1302. The magnetic flux lines 1310 have a component in the outward radial connection and flow into the outer casing 1370 and periphery of the flux compressor 1205. The reaction between the negative particles in the negative air stream and the rotating magnetic field defined by the set of flux lines 1310 compresses the negatively charged air stream. Fuel is injected into the compressed negatively charge air stream, and combustion is maintained by flame holder 1350a in the combustion chamber 1370a. The heated air stream is then expanded through the set of magnetic flux lines 1320 radiating out of the periphery of the flux turbine 1209 at the outer casing 1370 and into the rotating magnetic cylinder 1302. This second set of magnetic flux lines 1320 have a component in the opposite radial direction as the first set of magnetic flux lines 1310. The expanded air stream is then further expanded through the nozzle 1313. This additional expansion, along with the force generated by the flux compressor 1205 on the air stream, generates the engine's thrust.

[0109] The inner chamber 1373 is formed between a second inner casing 1374 and a magnetic bar 1301 having a magnetic orientation opposite of the magnetic cylinder 1302. The rotation of the magnetic bar 1301 is coupled to the rotation of the magnetic cylinder 1302. The positively charged air stream enters through the diffuser 1203 through a third set of magnetic flux lines 1311 radiating out of the rotating cylindrical magnet 1302. The magnetic flux lines 1311 have a component in the inward radial direction and flow into the center magnetic bar 1301 in the center of the flux compressor 1205. The reaction between the positive particles in the positive air stream and the rotating magnetic field defined by the third set of flux lines 1311 compresses the positively charged air stream. As in the outer chamber, fuel is injected and combustion is maintained by flame holder 1350b in the combustion chamber 1307b. The heated air stream is then expanded through a fourth set of magnetic flux lines 1321 radiating out of the center magnetic bar 1301 and into the rotating magnetic cylinder 1302 at the outlet of the chamber. The fourth set of magnetic flux lines 1321 have a component in the opposite radial direction as the third set of magnetic flux lines 1311. The expanded air stream is then further expanded through the nozzle 1313.

[0110] The rotating magnetic cylinder 1302 rotates at an angular velocity as illustrated in FIG. 13. The initial rotation of the magnetic cylinder 1302 can be electrically or mechanically initiated similar to the startup of conventional turbojet engines and thus is not discussed further.

Sources of Charged Particles

[0111] While not the emphasis of this disclosure, several methods of injecting charged particles or ionizing a gas stream are discussed. The following methods are exemplary only and are not exhaustive.

[0112] The electron structure of an atom consists of a number of shells, each containing specified number of electrons. The removal of one of these electrons to create a positive ion requires a quantity of energy called the ionization potential. As might be expected, those atoms containing single electrons in unfilled outer shells are easily ionized (i.e., they have relatively low ionization potentials. The alkali metal elements-lithium, sodium, potassium, rubidium, and cesium-have particularly low ionization potentials). Table I lists first and second ionization potentials (pertaining to the removal of the first and second electrons, respectively) for these elements, along with others for reference purposes. Note the relatively high ionization potentials of the inert elements, reflecting the fact that electrons must be extracted from a stable outer shell which is completely filled. The second electron extracted from an alkali metal must also come from a full shell accounting for the high ratio of second to first ionization potentials of these materials. Mercury, often considered as a propellant because of its high atomic mass and relatively easy handling characteristics, normally contains two electrons in its outermost shell. Hence its first two ionization potentials are relatively close together.

TABLE-US-00001 TABLE 1 First ionization Second ionization Element Atomic Number potential, eV potential, eV Alkali metals Li 3 5.4 75 Na 11 5.1 47 K 19 4.3 31 Rb 37 4.2 27 Cs 55 3.9 23 Inert elements He 2 24.5 54 Ne 10 21.5 41 A 18 15.7 28 H 1 13.5 C 6 11.2 24 Hg 80 10.4 19

[0113] Two ionization processes are of importance for ion rockets: electron-bombardment ionization, occurring as a result of direct collision between an energetic electron and a single propellant atom in the gaseous phase, and contact ionization, occurring as an interaction between a single propellant atom and a suitable solid surface. In the former, low ionization potential favors low charging power, but it is not absolutely essential. In the latter it is essential that the ionization potential be quite low.

[0114] As a gas stream (air stream) with a net charge is required for operation of the gas engine described in this disclosure, the creation of the charged gas stream is necessarily important. The charged gas stream can be created by injecting charged particles into the gas stream, the air stream can be ionized and separated; or other known methods can be used.

[0115] Charge insertion and ionization is well known in the aerospace field. In a typical ion rocket, neutral propellant is pumped to an ion production chamber from which ions and electrons are withdrawn in separate streams. The exact method of generating and separating ion streams is immaterial. The subject matter of this disclosure needs only the result of these methods.

[0116] While embodiments of the present subject matter have been presented as air breathing engines with air as the working gas, such should not be construed as a limitation of the subject matter. Working gases of all types may be employed and various methods of applying heat are equally envisioned. It is only limitations of the basic cycle that limits the selection of the working gas and heating method.

[0117] Alternatively, while not discussed explicitly in this disclosure, the magnetic field can be replaced with an electric field and in turn, the ionized or charged particle stream can be substituted with a magnetically charged stream of magnetic charged particles to achieve a similar result. Changes to the described system and method to operate in the aforementioned manner are well within the ability of one skilled in the art given the teachings of this disclosure.

[0118] It is also envisioned that the gas engine described herein may utilize a regenerator extracting heat form the engine exhaust, an intercooler which reduces the stagnation temperature of the air stream after compression or a re-heater, such as an afterburner, or a combination thereof. It is also envisioned that the present subject matter may be used in combined cycle power systems.

[0119] FIG. 14A is a more rigorous representation of the interaction between the charged particles and the rotating magnetic field. A single flux line 1401 is shown for clarity. The rotating magnetic field, as described in this disclosure, is comprised of an infinite collection of these conceptual flux lines. The flux line 1401 radiates from the z axis at an opening 1490 then curves back to the periphery of the opening 1490. At the opening 1491 the flux line 1401 curves back around into the z axis at the origin of the opening 1491 thus completing the magnetic circuit. The flux line 1401 rotates around the z axis with an angular velocity of S2 . The local velocity of the flux line 1401 is r{circumflex over ()} and is represented in FIG. 14a as V.sub.(r).

[0120] A charged particle 1410a enters the opening 1490 with an approximate velocity of V.sub.1 {circumflex over (z)}. In this depiction the charge has a negative charge. The magnitude of the charged particle's velocity is preferably less than that of the local velocity of the flux line 1401. In FIG. 14A, the particle velocity is much less than the average local velocity |V.sub.1{circumflex over (z)}<|V.sub.0(r)|. The charged particle 1410a follows the air stream path 1420. The air stream path 1420 is a conceptualized generalized path, the actual path for each particle will of course differ greatly and be more chaotic.

[0121] The negatively charged particle, 1410a upon interacting with the flux line 1401 at opening 1490, experiences an acceleration along the z axis. The acceleration, =(V.sub.8(r)B {circumflex over (z)}+V.sub.1B{circumflex over ()})q/m, can be simplified since |V.sub.1{circumflex over (z)}|<|V.sub.(r)| to =V.sub.(r)qB{circumflex over (z)}/m. As noted above, the collective effect on the air stream because of the increased velocity of the charged particles is an increase in pressure. The air stream and the charged particles therein, as a result of being heated and expanded, experience a significant increase in velocity. The charged particle 1410a, prior to interaction with the flux line 1401 and the opening 1491, has increased its velocity to V.sub.2{circumflex over (z)} where V.sub.2>>V.sub.1 as a result of the expansion. Due to the increased particle velocity, V.sub.2>>V.sub.(r), the particle now experiences an acceleration of:

=(V.sub.(r)B{circumflex over (z)}V.sub.2B{circumflex over ()})q/m

Since V.sub.2>>V.sub.(r), the acceleration can be generalized by:

=V.sub.2qB{circumflex over ()}/m.

The force exerted on the charged particle to develop the acceleration results in an equal and opposite force on the flux line 1401. This force is generalized as =V.sub.2qB{circumflex over ()} which results in a torque ==rV.sub.2qB{circumflex over (z)} on the flux line1401 and thus the magnetic device. A similar result occurs if the charged particle 1410a is directed through the flux line 1401 along path 1421. From the perspective of the charged particle, these interactions would be indifferent.

[0122] FIG. 14B is a representation of same interaction between the charged particle 1410b and the magnetic flux line 1401 as shown in FIG. 14A but from a frame fixed in the in the magnetic field. The magnetic flux line 1401 remains fixed and its relative rotation is now expressed on the charged particle 1410. The charged particle now, upon entering the opening 1490, has a velocity =V.sub.lz{circumflex over (z)}V.sub.(r){circumflex over ()}, where |V.sub.1{circumflex over (z)}|<V.sub.(r)|.

[0123] The charged particle 1410 upon interacting with the flux line 1401 at opening 1490, experiences an acceleration along with the z axis. The acceleration as above is simplified to =V.sub.(r)qB {circumflex over (z)}m. The charged particle 1410b prior to interaction with the flux line 1401 and the opening 1491, has increased its velocity to V.sub.2{circumflex over (z)} where V.sub.2>>V.sub.1 and V.sub.2>>V.sub.(r) as a result of the expansion. The particle now experiences an acceleration of:

=V.sub.2qB{circumflex over ()}/m.

The force exerted on the charged particle to develop the acceleration results in an equal and opposite force on the flux line 1401. This force is gernalized as =V.sub.2qB{circumflex over (z)} which results in a torque =rF=r V.sub.2 q B.sub.{circumflex over (2)} on the flux line 1401 and thus the magnetic device. From a fixed frame, the path 1420 of the particle looks like an expanding spiral. Again from the perspective of the charged particle, these interactions and paths are generally the same.

[0124] While preferred embodiments of the present invention have been described, it is to be understood that the embodiments described are illustrative only and that the scope of the invention is to be defined solely by the appended claims when accorded a full range of equivalence, many variations and modifications naturally occurring to those of skill in the art from a perusal hereof.