(c)2000 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. A1AA 2000-3338 Magnetic Surfing : Reformulation of Lenz's and Applications to Spacecraft Propulsion G. L. Matloff New york University and Pace University and L. Johnson NASA Marshal! Spacefiight Center 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference 17-19 July 2000 Huntsville, Alabama For permission to copy or to republish, contact the American Institute of Aeronautics and Astronautics, 1801 Alexander Bell Drive, Suite 500, Reston, VA, 20191-4344.
Transcript
(c)2000 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.
A1AA 2000-3338Magnetic Surfing : Reformulation of Lenz's
and Applications to Spacecraft Propulsion
G. L. MatloffNew york University and Pace University
For permission to copy or to republish, contact the American Institute of Aeronautics and Astronautics,1801 Alexander Bell Drive, Suite 500, Reston, VA, 20191-4344.
(c)2000 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.
MAGNETIC SURFING
AIAA-2000-3338
REFORMULATION OF LENZ'S LAW AND APPLICATIONS TOSPACECRAFT PROPULSION
Gregory L MatloffSummer 1999 and 2000 ASEE/ UAHFacuity Fellow,
NASA Marshall Spaceflight Center, Huntsviile, ALand
New York University and Pace University, New York, NY417 Greene Avenue, Brooklyn, NY 11216
andLes Johnson*
NASA Marshall Spaceflight Center, Huntsville, AL
AbstractThe treatment of the induced EMF
in a conductor moving through a magneticfield is incomplete in most physics textswhere the conductor moves through astationary magnetic field. As confirmed byexperiments performed at NASA / MSFCin Summer 1999), an induced EMF willalso be produced in a stationaryconductor in a moving magnetic field. Inboth cases, work done by the inducedcurrent will be at the expense ofconductor kinetic energy relative to themagnetic field. If work is done by themotionally-induced current in a low-velocity conductor in a rapidly movingmagnetic field, the conductor will speedup from the point of view of a "stationary"observer to match velocity with the fieldlines. This effect may have applications tofuefless spacecraft propulsion.
A number of constrants limit theperformance of various suggested modesof deep-space propulsion. Fission mayremain environmentally unacceptable tothe voting public, fusion may behampered by the lack of easily-obtainableaneutronic isotopes (especially He-3),antimatter may remain economically out-of-reach for large scale applications, evenperforated solar sails may be limited tovelocities less than 0.01 c and laser-sailsmay have problems with long-term beamalignment.
A new approach to magneticpropulsion, however, may haveinterplanetary and interstellar application.It derives from the fact that Lenz's Law isincompletely stated in most physicstextbooks and should be reformulated toaccount for relative rather than absolutemotion. Both electrodynamic tethers andsuperconducting colis or solenoids couldexploit this fact to accelerate in very-highearth orbit, the magnetosphere of Jupiter,the interplanetary magnetic field, andpossibly the interstellar magnetic field.
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Consider Figure 1 A, which isbased upon the discussion of inducedcurrents in a conductor moving through astationary magnetic found in everyundergraduate physics text examined bythe authors .1 As stated by Lenz's Law,the induced EMF in the moving conductorwill counter the motion of the conductorthrough the magnetic field. Essentially, ifwe attempt to get useful work (say forpropulsion) out of a conductor movingthrough a stationary magnetic field, at!work obtained is at the expense of theconductor's kinetic energy relative to themagnetic field.
But what happens in the morecosmically common (and interesting) caseof a slow-moving conductor (from ourpoint of view) and a rapidly movingmagnetic field, as shown in Fig. 1B? In
Figure 1. Current (I) Produced in aConducting rod in Relative Motionto a Magnetic Field. (Field tines aredenoted by 'X' and into page).
X
X X
X
X
X-
(A) Conductor inMotion
(B) Field inMotion
considering this problem during the earlysummer of 1999, our contention was thata current would still be generated in theconductor by its motion relative to the
magnetic field. If this induced current isused to perform useful work, theconductor will slow down relative to themoving Sines of magnetic flux. From aterrestrial point of view, high accelerationsand velocities may be acheived for little orno propulsive cost.
Figure 2. A Double-Pendulum Deviceto Demonstrate Currents Induced byConductor Motion Relative to aMagnetic Field. (Constructed at NASAMSFC in Summer 1999).
To demonstrate the currentsinduced by a conductor's relative motionto a magnetic field, a simple double-pendulum was constructed at MSFCduring the summer of 1999 with the
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assistance of NASA technician BruceMcCoy and ASEE accompanyingstudents Russei! Lee and Alkesh Mehta,both of New York City Technical College.This device, which is shown schematicallyin Fig. 2, allows one to move conductorand magnets independently andconvincingly demonstrates the relativenature of motionally-induced currents.
Theoretical Considerations
Devices to apply this in spaceinclude electrodynamic tethers (Fig. 3A)and superconducting, partially-sheathedsolenoids or loops as shown in Fig. 3B. InEarth orbit, an electrodynamic tether(EOT) produces electricity and thrust atthe expense of orbital energy - a situationthat is not necessarily true in other parts ofour solar system, as will be explainedlater. An EOT generates and forms part ofa unique type of electrical circuit, whichhas been successfully demonstrated inspace. 2 The tethered system extractselectrons from the ionospheric plasma atone end (upper or lower) and thencarries the electrons through the tether tothe other end, where it returns them to theplasma. The circuit is completed bycurrents in the plasma. The net forcecaused by a uniform magnetic field actingon a current-bearing closed loop of wire(i.e., a normal circuit) would be zero, asthe force on one length of wire would becanceled by that on another in which thecurrent was flowing in the oppositedirection. However, since there is nomechanical attachment of the tetheredsystem to the plasma (which is just therarefied medium through the system istraveling), magnetic forces on the plasmacurrents do not affect the tether motion. In
other words, there is a length of wire witha unidirectional current flowing in it, andthis wire is accelerated by Earth'smagnetic field.
The bias voltage of a verticallydeployed metal tether, which results justfrom its orbital motion through Earth'smagnetic field, is positive with respect tothe ambient plasma at the top andnegative at the bottom, thus, the "natural"current flow is the result of negativeelectrons being attracted to the upper endand then returned to the plasma at thelower end. for an eastward movingsystem, such as most Earth-orbitingspacecraft the field is such that theelectrical potential decreases withincreasing altitude (at a rate of« 100 V/kmfor a 400-km circular orbitO. The magneticforce, in this case, has a componentopposite the direction of motion, and thusleads to a lowering of the orbit andeventually to reentry.
The motion of the system throughthe Earth's magnetic field induces avoltage emf = L • (v x B) between the twoends of the conductive tether, where L isthe vector parallel to the tether whosemagnitude is the length of the conductivetether, v is the velocity of the systemthrough the ionosphere, and B is the localvalue of the Earth's magnetic field vector.
The current in the tether variesalong its length, since collected electronsaccumulate in an increasing downwardstream in the wire. Denoting the current ina segment of tether Al at a distance I fromthe lower end of the tether by I (I), wehave for the drag force on this tethersegment F^ (I) = /(I) M x B, where A/points in the direction of the current flow.The total drag force on the system is then
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the sum of the F<y (I) over the full tetherlength.
To get an orbit-raising thrust, acurrent in the opposite direction must beobtained. This requires a reversal of thenatural electrical bias (i.e., that due to themotion through the magnetic field) bymeans of an electrical power supply,which can, of course, use solar energy.The Plasma Motor Generator (PMG) flightexperiment successfully demonstratedthis mode of operation using batteries,though no thrust measurements weremade.3
One of the most important featuresof EOT thrust is that no on-board powersource is required to drive the electricaicurrent flow in either the orbit-raising ororbit-towering mode. Sources inherent toEarth orbit are used. To raise the orbit, thenatural energy of the Sun can beconverted to the electrical energyrequired to drive the tether current. Tolower the orbit, the orbital energy itself(supplied by the Earth-to-orbit launcherwhen it raises the system into orbit) is theenergy source of the tether current.
In LEO, it is important to note thatthe spacecraft loses orbital energy since itis moving faster than the Earth's magneticfield lines. Assuming that the Earth'smagnetic field lines move with the Earth'srotation in higher orbits, the spacecraft wiligain orbital energy at altitudes aboveGeosynchronous Earth Orbit (GEO) sincethe field lines are moving faster than thespacecraft. Of course, electrodynamic-tether operation above GEO may be lesseffective than in LEO because of the lowerion density above the Earth's ionosphere.The superconducting solenoid or loop(referred to below as the "flux surfer"),which is derived from the
Figure 3. Two Methods of GeneratingUnidirectional Current in Space
(A) Electrodynamic Tether in LowEarth Orbit
directionbfJcJOTU? <A
motion
of ^ft — *%ijiiij) spacecraft
electron
tether
electron emitter
Earth
(B) A Superconducting Solenoid orLoop in which a SuperconductingLayer Shields Current return frominterstellar Magnetic Field
supercurrentdirection
spacecraftvelocity
sheath
superconducting interstellar ion scooporiginally discussed by Matloff andFenneliy in 19744 and the Andrews /Zubrin magsail^, may be less limited
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above LEO than the eiectrodynamictether. The interplanetary or interstellarmagnetic field lines see a unidirectionalsupercurrent because the current return issheathed by an additional layer ofsuperconductor.
However, as reported by Vulpetti 6,all superconducting space devices maybe limited to operation in the outer solarsystem or beyond. Even new high-temperature superconductors may havethe annoying habit of "going normal" andlosing superconductivity when operatedcloser to the Sun than Mars, unless verymassive thermal shielding is employed.
Superconducting solenoids andloops will'be most useful, therefore, in theouter solar system or in interstellar space.Andrews and Zubrin § estimate thatsupercurrents in excess of 105 ampscould be maintained in a supercurrentloop far from the Sun, whuch is close toCassenti's estimate for supercurrentscarried by linear superconductors ininterstellar space.7
The first interplanetary applicationof propulsion by a conductor in a rapidlymoving magnetic field is likely to be atJupiter, which has a complex and intensemagnetic field that probably arises fromelectrical currents in the rapidly spinningmetallic-hydrogen interior. Jupiter'smagnetic field is much more intense thanthe Earth's and the ion density in Jupiter'svicinity is high.8 The rapid rotation rate ofJupiter is one of the unique properties ofthe Jovian system that broadens thepotential applications of eiectrodynamictethers for Jovian missions. For example,in a posigrade orbit the direction of thetether propulsive force can vary by asmuch as 180 degrees depending on the
altitude of the orbit. At high altitudes therotational velocity of the magnetic fielddominates the relative velocity andconversely at Sow altitudes the spacecraftvelocity dominates the relative velocity.
The forces resulting from theeiectrodynamic tether can be exploited forpropulsion. The orbital maneuvercapabilities of a 4.75 km tether areillustrated in Figures 4 and 5. In thesefigures, a 90-degree inclinationcorresponds to a polar orbit; a 180-degree inclination corresponds to anequatorial orbit. Figure 4 shows the rate ofapojove change predicted as a function oforbit inclination.
Fig. 4. Tether Orbital ManeuveringCapability for Changing Apojove(Maximum Apojove Change Rate is in Rjper Orbit, Tether Length is 4.75 km, in 5-Day Retrograde Orbit at 1.01 Rj).
A maximum rate of 1.15 Rj per orbit ispredicted for the case of a retrogradeequatorial orbit. The peak power
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generation rate corresponding to thismaneuvering rate is 895 kW. Figure 5shows the piane change rate generatedby the 4.75 km tether on a 340 kgspacecraft. A maximum plane change rateof 0.041 degrees per orbit is possible.
Fig. 5. Tether Orbital ManeuveringCapability for Changing Orbital Plane(Maximum Orbital Plane Change Rate isin Degrees per Orbit, Tether Length is4.75 km, in 5-Day Retrograde Orbit at 1.01Rj).
Preliminary analysis indicates thata megawatt of power can theoretically begenerated by a 10-km tether in near-Jovian space. Specifically, such a tetheroperating near the planet wouldexperience induced voltages greater than50, 000 volts, currents in excess of 20Amperes, generate approximately 1megawatt of power and experience morethan 50 N of thrust! This poses enormousengineering challenges that must beovercome before it is implemented, but itclearly demonstrates the importance of re-
examining Lenz's Law in the context of aconductor that is stationary relative to amagnetic field in rapid motion.
Both devices shown in Fig. 3 mayhave the potential to reach high velocitiesby "surfing" on magnetic flux Sinesassociated with the Sun or the solar wind.But the most exciting possibleapplications are to interstellar travel, if thelocal interstellar magnetic field is rapidlymoving.
It must be emphasized that themotion of the focal interstellar flux linesrelative to the Sun is unknown. If the localinterstellar magnetic field is entrained inthe large-scale motions of ionizedhydrogen gas, the interstellar flux linesmove at only a few hundred kilometersper second or less relative to the Earth. Inthat case, the proposed method ofmagnetic flux-Sine "surfing" will have verylimited interstellar application.
However, what if the localinterstellar magnetic field has acomponent due to highly collapsedneutron stars, or "magnetars?" Suchcompact, evolved stellar objects havediameters of about 15 km and rotationrates 50-1000 revolutions per second.The magnetic field at the surface of such astar is estimated to be about 1012 Gauss,about 1 tritton times that at the surface ofthe Earth.1® Perhaps most importantly forour proposal, the magnetic flux linesmight move around the collapsedmagnetar at relativistic velocities.
We can examine the performanceof a superconducting "flux surfer" in aninterstellar magnetic field moving at amoderate, sub-relativistic velocity relativeto the spacecraft. We adopt the estimateof Pikel'ner for the local strength of theambient interstellar magnetic field, Bin = 5
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X 10'10 Tesia11 from p.568 of Searset a/.,1 the work W done on a charge qmoving along a conductor with length Lmeters with an angle (j> between shipvelocity V m / sec and the interstellarmagnetic field lines can be written:
W=VBinqLsin(t) J0uies. o>The power P imparted to the supercurrentisu amps by interaction with theinterstellar magnetic flux can beimmediately written:
Watts. (2)In a real design, some of the power wouldbe utilized to operate on-board thrusters.here, we conservatively assume that it isall simply radiated as waste heat. Thesuperconducting 'flux suffer" must bethermally shielded or separated by agreat distance from the heat radiator sothat it does not go normal
For an angle <j> of 45 degrees, avalue of V of O.OSc (107 m/sec), asupercurrent of 5 X 10§ amps and alength L for the path of the supercurrentexposed to the interstellar magnetic fieldlines, P « 2 X1010 Watts. Spacecraftacceleration towards the velocity of theinterstellar magnetic flux lines can beestimated in the Newtonian frame byrecalling that the power obtained from theinteraction with interstellar magnetic fluxlines is at the expense of spacecraftkinetic energy relative to the flux lines:
(3)
where m is spacecraft mass, and AV is thevelocity increase (from Earth's point ofview) within time increment At. Thus,spacecraft acceleration is approximatelyequal to P / (mV).
For the case of a million-kg shipnearly at rest (from a terrestrial viewpoint)in an interstellar magnetic field moving atO.OSc and P « 2 X1010 Watts, thespacecraft will accelerate at about 0.002m/sec2, or 0.0002g. From the terrestrialviewpoint, the ship will increase itsvelocity by about 0.0002 c / year, reaching0.02c in about 100 years. And, onceagain, this acceleration requires noon-board propulsion.
Certain trajectory directions willmaximize acceleration by interstellar flux-line surfing. After concluding itsacceleration by the moving interstellarmagnetic flux lines, the spacecraft's"magnetic surfer" should be reconfiguredso that the craft can adjust its trajectory bythrustless electrodynamic turning in theinterstellar magnetic field ,12
Conclusions
It is too early to ascertain whetherNature cooperates and supplies a rapidlymoving local interstellar magnetic field.So astronomers should learn what theycan about thelocal interstellar magneticfield remotely. Our first generationheliopause probes, which hopefully canbe launched within the next decade,could carry a tether-based magnetometer
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to help determine the magnetic-fluxvelocity of the local interstellar medium.Using "conventional" tether technology,the concept can be tested locally bydispatching an electrodynamic-tetherequipped robotic probe to the jovianmagnetosphere.
References
1. See, for example, H. C. Ohanin,Physics, 2nd ed., Norton, NY (1989), pp789-791 and F. W. Sears, M. W.Zemansky, and H, D. Young, CollegePhysics, 5th ed., Addison-Wesley,Reading, MA(1980), pp. 567-570.2. N. H. Stone, K. Wright, J. D.Winningham, C. Gurgiolo, U. Smair, C.Bonifazi, B. Gilchrist, and M. Dobrowoint,"identification of Charge Carriers in theIonospheric Branch of the TSS-1 TetherGenerated Current System," Proceedingsof the Fourth international Conference onTethers in Space, Smithsonian Institution,Washington, D.C., 1995, pp. 359-371.3. J. E. McCoy, M. D. Grossi, and M.DobrowoSny," Plasma Motor Generator(PMG) Flight Experimental Results,"Proceedings of the Fourth internationalConference on Tethers in Space,Smithsonian Institution, Washington, D.C.,1995, pp. 57-82.4. G. L Matloff and A. J. Fennelly, "ASuperconducting Ion Scoop and itsApplication to Interstellar Flight," JBIS, 27,663-673 (1974).5. R. Zubrin and D. Andrews, "MagneticSails and Interplanetary Transport," AlAA89-2441.6. G. Vulpetti, "A Critical Review on theViability of a Space Propulsion Based onthe Solar wind Momentum Flux," ActaAstronautica, 32, 641-642(1994).7. B. N. Cassenti, "Design Concepts for
the Interstellar Ramjet," JBIS, 46, 151-160(1993).8. E. Chaisson and S. McMillan,Astronomy Today, 2nd ed., Prentice Hall,Upper Saddle River, NJ (1995), Chap.11.9. D. L Galiager, L. Johnson, J. Mooreand F. Bagenal, "Electrodynamic TetherPropulsion and Power Generation atJupiter," NASA Technical Publication TP-1998-208475, June 1998.10. J. N. Winn, "The Life and Death of aNeutron Star," Sky and Telescope, 98,No. 1, 30-38 (July, 1998).11. S. B. Pikel'Ner, "Structure andDynamics of the Interstellar Medium,"Annual Review of Astronomy andAstrophysics, 6, 165-194 (1968).12. G. L. Matloff, E. H. Walker, and K.Parks, "Interstellar Solar Sailing:Application of Electrodynamic Turning,"AIAA-91-2538.
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