Drag and Propulsion of Large Satellites in the Ionosphere: An ...

3OURNAL OF GEOPHYSICAL RESEARCH VOL. 70, NO. ]3 3ULY 1, 1965Drag and Propulsion of Large Satellites in the Ionosphere'An Alfv(n Propulsion Engine in SpaceS. D. DRELL, 1 H. M. FOLEY, 2 AND M. A. RUDERMAN 3Jason Division, Institute/or De/ense AnalysesAbstract. There is a motionally induced charge separation in a conductor moving acrossmagnetic field lines. This charge may be conducted away, resulting in adc current flowthrough the conductor if it moves through a plasma. The generation of Alfv•n waves is amechanism particularly effective for circulating the charge for very large conductors movingin or above the earth's ionosphere. This mechanism is studied in this paper and when appliedto the analysis of the orbit of the Echo satellite is found to give rise to a significant dampingof the motion as mechanical energy is converted to that of Alfv•n radiation. The calculateddrag is comparable to that observed for the orbit of Echo I and attributed in earlier studiesentirely to the mechanical drag of considerable nonionized atmospheric density. Perturbationsin electron density associated with this current flow may in appropriate circumstances bedetectable even thousands of kilometers away from such a high altitude satellite. The dragcan be changed to a propulsion mechanism when a source of electrical power is available onthe satellite. Up to fifty per cent of the expended power is available for pushing a spacevehicle across an ambient magnetic field.1. INTRODUCTIONA conductor moving across a magnetic fieldB0 in a vacuum will have an induced chargeseparation sufficient to cancel the electric fieldE = (v X B0)/c seen by a co-moving observer.When the surrounding medium is a plasma, thereexist possible mechanisms for charge to be conductedaway, resulting in adc current flowingthrough the conductor. In this paper we considerthe circulation of charge by means of the generationof Alfv•n waves, a mechanism which isparticularly effective for very large conductorsmoving in or above the earth's ionosphere. Whenapplied to a study of the Echo satellite it givesrise to a significant damping of the orbit asmechanical energy is converted to that of Alfv•nradiation. The calculated drag is equal to thatobserved for the orbit of Echo 1 and attributedin earlier studies entirely to the mechanical dragof considerable nonionized atmospheric density.In an appropriately designed satellite the dragforce can be altered by variations of an internalresistance, or the associated dc current flow canx Stanford Linear Accelerator Center, StanfordUniversity, Stanford, California.2 Physics Department, Columbia University,New York, New York.a Physics Department, New York University,New York, New York.3131be tapped as a battery. With a source of electricalpower the drag force can be converted to apropulsion mechanism: the satellite pushes onthe earth's magnetic field without any emissionof propellant.We exploit the qualitative analogy between acollisionless plasma in a magnetic field and aseries of transmission lines parallel to the magneticfield. The moving conductor with itsmotionally induced charge separation is, in asense, in successive contact with different transmissionlines as it moves. It induces an impulse(Alfv•n wave) traveling along the magnetic fieldwhich carries a charge separation and essentiallycompletes the circuit in which the movingconductor is adc battery.Initially we shall idealize the conductor sothat it not only has no internal resistance butalso no work function to prevent the outwardflow of electrons in response to an appropriatelydirected electric field normal to its surface. Theproposed mechanism is appropriately modifiedfor real conductors for which the work functionis significant.Alfv•n waves, magnetohydrodynamic disturbancesof frequency much less than the ioncyclotron frequency 9i = eBo/Mic, propagateone-dimensionally along the direction B0. Asmall disturbance persists with constant amplitudeor until damped by collisions among elec-

3132 DRELL, FOLEY, AND RUDERMANFig. 1. Conductor moving with velocity vc in the x direction perpendicular to magnetic fieldlines Bo along the z direction leading to a charge separation and mottonal electric field E inthe y direction.trons and ions in the plasma. We have notfound the solution offered here in earlier studiesof related problems; these have been twodimensional,or involved only motion parallelto B0, or posed boundary conditions that theplasma was not disturbed at large distancesfrom the conductor, none of which are valid forour solution. Moreover, we find in the restframe of the moving conductor a steady dccurrent rather than a static situation.2. IDEAL CONDUCTOR IN A LOSSLESS PLASMAFor the idealized conductor (see section 1)moving through a collisionless plasma in adirection perpendicular to the field lines (Figure1), the Alfv•n disturbance extends out in wingsmaking an angle a with the field lines such thattanwhere v• = speed of the conductor, and Va ------Alfv•n speed. The motional electric fieldr =xin the conductor is cancelled by a charge separationas illustrated in Figure 1. In the collisionlessplasma, with infinite conductivity along the B0,or z, direction, but with zero conductivity perpendicularto B0, current wings as shown inFigure 2 are created along with a charge separationas required to maintain a constant • fieldalong the wing equal to that at the conductor.Anomalous radar echoes obtained from ionosphericdisturbances associated with Echo I mayalso be related to these predicted Alfv•n 'wings,'although further studies are desirable to confirmtheir presence. We comment more on this insection 5.Let us first analyze the fields produced by themotion of an ideal conductor through a plasmawith an impressed magnetic field B0 in order toestablish the appropriate regime of parametersand the nature of the Alfv•n disturbance. Wemake the following approximations:1. The conductor moving through the plasmais 'ideal'--i.e., it has zero internal resistanceand work function; it maintains the chargeseparation required to produce the fieldr = --(vc X B0)/½ (1)In the opposite case of a conductor with internalresistance moving through a medium of higherconductivity, the charges would be 'bled' fromTopBottomt 4 - z + + ++---m,..YlFig. 2. Alfv•n wings generated by an ideal conductorin a collisionless plasma.vc

3134DRELL, FOLEY, AND RUDERMANiooo900800700E',' 600i /Day sunspot maximum i • ,!--.--Night sunspot maximum-----Night .... Daysunspotminimumßß • 5004OO•002OO.•..•.•;.•'•ßII:, ii•.'•'1Fig. 4.I0010 -15 I 0-12 10- II I 0-10 I 0 -9 I 0-8Specific electrical conductivity %, abmho/cmSpecific electrical conductivity of the ionosphere (zero field conductivity) versusaltitude; taken from Johnson [1961].where4•rn M ;c 2Bo 2I + 4•rpic2 -- I + c•'/va(8)•--Bo 2(•oV•.,,),• -•defines the Alfv•n velocity in terms of the magneticfield strength B0 and the ionic massdensity pi ---- nMi. Numerically the plasma frequencyvaries from c% • 6 X 107 cps at altitudesof a few hundred km correspondingto electron densities of up to 106/cm 3, tow• • 4 X 106 cps at altitudes of 1600 km andelectron densities of .--5 X 103/cm s. The Alfv•nvelocities rise from values of va • 2 X 107cm/sec at 300-kin altitude to v• • 10 • cm/secat 1600-km altitude. The value at 1600 km isnot accurately known, owing to uncertainties inthe ionic composition at the high altitudes. Wereturn to this point later. The ratio of parallelto transverse components of e is very large forthe parameters of interest to us,[e,,/•_[ > 10 • (9)Essentially the electrons are wrapped aroundthe magnetic field lines, free to move only alongthe Bo direction, as are the ions. This large ratioreflects propagation only in the direction parallelto B0.We want now to solve the Maxwell equationsV x r = -V X B = i)/c d- 4•-j,/c (10)V.D = 4•rp.V.B=0with D and E related by (5) and (6) and withj. and p, representing the current and chargesource provided by the moving conductor. Thecurrent in the moving conductor of Figure 1flows mainly in the y direction to maintain thecharge separation. We work in a linearizedapproximation in the field strengths E andh = B-- B0;f• = 1].Fourier transforming (10) we havek x •(•., •,,,o) = o•_h (•_,•,,,o)(•)k X h = •oD 4•ri j,(k_L, k,,)•(•0 -- k.vc)cceilkllEll Ji- ezkz' E• = 4•rp.(lib)(11c)Taking the curl of (11a), inserting (lib) and(11c), and defining Ez = Ez • -t- Ez", where

DRAG AND PROPULSION IN THE IONOSPHERE 3135k. ß E• • k.E. • and kx X E• • k. X E•' r, givesez k, -- kz 2 Eza medium at speeds greater than the lightvelocity in the medium.In this lossless plasma approximation, theequations for E and h read4srkip.•-- k.k2)E.k t"(12a)4•-i= • ',o•e -- •','c) I• X •_•/a (•,)½• ell - k•_ -- kll eñ] "-0 (12c)n. = •(• x r)•/(•.•c) (•)hi' = c(ki (k' X v•) Ex 'r)General features of the solution can be identi-(12e)fied in (12). For a plasma with low transverseconductivity which approaches the behavior ofa lossless medium satisfying (9), (12a) reducesto a one-dimensional wave equation for atransverse electric field propagating along theB0 direction with velocity c/eJ/'. •' Va accordingto (8) and with frequencyand longitudinal wavelengtho• -- k'vc (13)xll-- •1-•1=va• - k.v•Va (14)4•r 0c 2 OtVñ'js(x -- Vct, y, z) (15a)at 0 • v•)(V• x r•)4;r 0c 20t•_ x •(:• - ,,ct, y, •) (1,•,)fi• = -c(V x r)•fi, -- --c(Vx X rx)(•)(15d)with Ell = 0. Equation 15b describes the netradiation of energy into a magnetoionic wavewith velocity va only if vc > va. As we noted,this radiation is analogous to the Ccrenkovradiation, or sonic boom. Equation 15a radiatesenergy out along the direction of B0 for allvalues of vc if the idealized conductor movesacross the magnetic field lines and plucks themlike violin strings. This solution satisfies theequationBo.(Vx X r•) = 0 (16)so that a two-dimensional slice perpendicular toB0 gives the electric field from a two-dimensionalcharge distribution (Vx' Ex). According to (15a),the Alfv•n fields are functions only of thevariablesThis is the Alfv•n wave. According to (13), for thedominant transverse wave numbers k. •' l/L,Vawhere L is the dimension of the current sourceand propagate as described earlier in Figuresalong the direction of motion, the frequency is 1 and 2. The wings move out from the conductorco •, vc/L, as was claimed earlier in (3). There is, with Va along B0 and form an angle a such thatin addition, according to (12b) an isotropicdistu-'rbance which is a solution of the ordinaryd'Alcmbcrtian wave equation, also with Alfv•n as illustratedtan a =there.velocity va. For a steady source current generatedFor the magnitudes of the fields, we knowby a moving conductor with v• < va, the solutionfrom the first of (10) that the tangential comisa localized disturbance falling off as 1/r'. atponent of • is continuous across the conductorlarge distances from the source; this is the casesurface and is fixed by the motional electricapplying here. When, however, v• > va, a radiafieldin the conductor according to (1):tion pattern is created that is the analog of theCerenkov radiation for a charge passing throughE = --(v• X Bo)/C (17)

3136 DRELL, FOLEY, AND RUDERMAN¾i/M--'v', vFig. 5.An/-bar conductor idealized as two fiat rectangular plates with indicated dimensionscharged to maintain the potential difference V.Since we are dealing with long wavelength modesof field excitation and by (14)1/kll >> 1/k•_ • Lthe detailed three-dimensional geometric shapeof the moving conductor is of no relevance. Wecan write an exact solution for an /-bar con-ductor described as in Figure 5 by two fiatrectangular plates of dimensions L and N,separated by a distance M, and charged tomaintain a potential difference in the y directionofv = =The solution consists of growing parallel wingswith a charge sufficient to keep the difference inpotential between the wings always V. Thecurless part of Ex, which is the solution of (15a),has the functional form_,ct_,_ z ,and is the solution of the two-dimensiOnal problemcorresponding to Figure 5, i.e. two platesof width L and separation M making an anglea = tan -• (Vc/V,,) with B0. A constant potentialdifference V is maintained between the wings,so that Ell -- 0, and a constant current j8 flowsthrough the I bar in the y direction. Only outalong the horizontal arms of the I bar in the xdirection does the current j8 decrease (i.e.,•'x'jx.• • 0) as current flows into the wings.The vertical current in the source must beexactly sufficient to supply the charge neededfor the two growing wings tips, i.e.E •_ Lc 2v cc LI., --'• - Bo2•'v • 2,rv •We note that the field Ex that moves downthe tube in the B0 direction is not particularlydifferent if the moving source is the I bar or asolid plate of the same dimensions. Only thefringing fields near the vertical edges are different,as is indicated in Figure 6. In particular thepower radiated into the Alfv•n-type waves isessentially the same in both cases; the effectiveradiating area need not be filled with conductor.For the magnetic field, (15c) and (17) give= (between the plates plus correction terms nearthe edges from the fringing fields plus correctionsvanishing as one moves out into the radiationzone far from the body due to local currents.A small ratio of the Alfv•n field [hi to the earth'sfield B0 is a necessary criterion for the linearapproximation we have made. For satellites inearth orbit, we have• 4 X 10 -2 at 200-km altitude10 -a at 1600-km altitudealways very small next to unity.The sufficiency condition for the validity ofthe neglect of higher-order terms depends on theinterval over which we need to be sure of anaccurate solution. For computations of thecurrent flow through the moving satellite, itsdrag, and the power radiated into the Alfv•nwaves, the solution should be valid out to adistance of about 1 wavclcngth/2•r --• Va/00away from the conductor. Over this interval hxmay cause a change in direction for the flow ofcharge away from the z axis by an angle •'•h_t./Boand a resultant transverse displacement of(hzv•)/(Bow). For this not to exceed the transversedimension of the Alfv•n wave, we needh•_v, • Bow/kx =Bov,

DRAG AND PROPULSION IN THE IONOSPHERE 3137Fig. 6. Fringing fields differing for I bar or solid plate conductors.orstant z) of the Alfv•n tube (wing) moves as ifhj_/B 0 • •)c/•a (20)through an incompressible fluid. In the comovingframe the electric field vc X Bo/COnly for an ideal conductor with no internalresistance moving in a collisionless plasma intogether with that of an infinitesimally thincharge distribution looks like that in Figure 7.which the inertia of the electrons is negligible The drift velocity v of ions in the crossed electriccan the left-hand side of (20) gain even equality and magnetic fields iswith the right-hand side.For an irregularly shaped three-dimensionalideal conductor for which v•/va

3138 DRELL, FOLEY, AND RUDERMANP = (1/47r)h22(ML)va (21)- Bø2 vc• (ML)2•rwhere 2MLv• is the volume filled per second byan energy density h2/4•r; the factor 2 takes intoaccount the existence of wings extending in bothdirections along B0. Combining with (18) for thepotential difference between the top and bottomwing, we compute the current flow:The effective impedance of the plasma for thiscurrent flow is then defined asVz - -In terms of these familiar quantities of electricalcircuit theory, the Alfv•n wings can be interpretedas one-dimensional open-ended transmissionlines of impedance Z across which apotential V is applied. In this ideal limit of alossless medium, there is an infinite resistancebetween the upper and lower line (or Alfv6nwing) and zero resistance along them. Correctionsdue to collisions leading to a finite transverseionic conductivity are computed in the nextsection.The l•rge electronic surface charge density•rises from the enormous dielectric constantsex • 1 + c:/vd (•th v•lues between 10a •nd10•). The totM charge density given by div. E issmaller by (v•/c):; i.e., •lmost •11 the electroniccharge density is c•ncelled by the ions. Thisl•rge pol•fiz•bility of the heavy pl•sm• ions•11 always result in •n ionic displacement muchsmaller th•n the wing separation •s long as theverficM dimension of the body, M, satisfiesv•/M

DRAG AND PROPULSION IN THE IONOSPHERE3139for •0 < 103 cps and for 1/k•, • M > 10 meters.This means that the wings cannot be consideredto have zero thickness, but will spreadto a thickness of perhaps ten meters. Theimaginary (damping) correction from electroncollisions is also small for these conditions when1/kj. •> 10 meters according to Figure 3.For higher altitude orbits above 1000 km, thedamping term i/oor• in (28) is < 1 in magnitudefor •0 •> 10 eps, corresponding to conductordimensions no larger than L • 1000 meters (forthe Echo 1 with L • 30 meters at an altitude of1600 km, the correction is less than a few percent). The real factor in (28), however, leads toa major change in the radiated Alfv•n waveunless 1/ki •> 75 meters; the simple Alfv•nsolution propagating in one dimension onlyapplies only to the modes with ki •< 1/75 metersand with frequency •0 •> 10 eps, and we restrictour attention to these. Thus the wing thicknessfor these parameters will, if geometrically possible,spread to more than 75 meters in order tocarry the required currents, despite the electroninertia and the reduced density of electronsabove 1000 km.For an object such as Echo 1 with effectivedimensions of L • M • 30 meters for thecurrent source as defined in Figure 5, this meansa reduction in the field strength, since only themodes with kx < 1/75 meters • L-•/2.5 canbe described by the Alfv•n solution discussedhere. Since the power spectrum is flat in theZ = Z 1 + IZ12+ 2ZlZ 2•- 2Z 1 + Z 2 for Zl/Z 2 > 1.The finite transverse ionic conductivity betweenthe top and bottom layers of the Alfv•n wingsin Figures i and 2 allows the damping andtermination of the disturbance. Viewing thesewings as a simple transmission line, these termsare, respectively, the resistance cc (ax•)-• andthe capacitance cc (k_•o'_•5/O'o) -• between thelines, i.e. the impedance Z•. in Figure 8 in additionto the inductance Z• o: Va/C • along the linethrough which the current flows.Even if the moving conductor has dimensionssuch that inertial term of (27) is smaller than 1,the fact that it is nonzero means that in thedispersion law+ (28')the second term on the right-hand side plays arole at large z: the Alfv•n pattern spreads in thexy plane as it propagates in the z direction.For subsequent calculations of currents and dragthrough the conductor, it is sufficient thatthe proposed solution be adequate out totransverse wave number kx = (k•, k•.) out toHi/L, the power radiated in the Alfv•n disturbancemust be reduced by a factor • (30/75)•'•z •-• v•/oo • (v•/v•) L. (In the transmission line1/6 from the value computed in (21).analogy, the moving conductor remains inWe have presented these numbers in somecontact with a given transmission line for adetail in order to make clear the very approxi- time L/v, during which the signal has traveledmate and qualitative nature of our numerical a distance v• L/v• in the z direction. What hapresultsand to show their sensitivity to the pens after that does not affect the forces andvarious atmospheric parameters, variable in currents in the conductor.) From (28') thetime and imperfectly known, that have been used. perpendicular spreading of E. is such that forA useful analogy that may help provide a • = •k•physic91 picture of this behavior is suggested inthe low frequency limit such that •0r• --* 0 andc IZOO• v•jz •< 1wr, --* O. Then (28) can be rewritten asTherefore the Alfv•n wave spreads ultimately(M2 ito a lateral dimension d which increases as z TM.= -•----•-ax -- ki 2 (29)t/a ½ 0' 0 For ki ,• lfd, v• • 10 • cmfsec, v, • 10 • cm/sec,and •%•' --• 10 •3 sec -•., corresponding to n, •5 ) 10•/Sz •/• cm (30)

3140 DRELL, FOLEY, AND RUDERMANAt a distance of z ,-• l0 s km, d •> 200 meters,which is an increase in size of less than a factorof 10 for a conductorsuch as Echo 1 of size•,30 meters. By conservation of energy, thereis a corresponding reduction by a factor •10in the field strengths E x and hx of the Alfv6nwave at these distances. This result suggeststhat, for very high altitude satellites wherecollisions are not dominating, the wings may bedetectable out to very great distances. Further,as the Alfv6n wave penetrates to lower altitudeswhere the ion density increases and Va decreases,energy conservation implies that in the WKBapproximation D•_E•_Va remains approximatelyconstant. Therefore the charge separation associatedwith the wave increases as (Va) -•"'. In thisestimate we have neglected the possible growthof the transverse dimension of the Alfv6n wavebecause of the neglect of higher-order terms in(•).Effect o/ finite work/unction limiting the currentflow through the sur/ace o/ a conductor. In theupper wing of the Alfv•n disturbance in Figure 2,a negative current flows out from the conductor,while in the lower wing the negative flow istoward the conductor. In our solution we assumethis flow is maintained indefinitely withoutchange in charge density. The plasma electronsare drawn into the conductor surface, neutralizingthe electric field of the ions. In order tomaintain the charge separation producing theelectric field E = --(v•/c) B o, the electrons atthe top surface of the conductor must be emittedinto the wings and a current must exist throughthe electrically neutral conductor in the steadystate. The problem is that of overcoming thework function at the conductor surface so thatthe electron current can flow. The alternativeto this is for the current to be carried by theions into the surface of the conductor at the top,and the corresponding reduction of the con-ductivity •0 by the mass ratio m/M; •< 5 X 10 -4would mean the failure of our simple Alfv•nsolution for the scale of sizes that we haveconsidered and the dominance of the resistiveand capacitive corrections discussed in thepreceding section.The proposed solution is valid only if thecurrent can be maintained by electrons. Sincecold emission is totally negligible, we turn tothe sun's radiation and calculate the possibleelectron current which could be maintained byconsidering the Alfv•n wave emission togetherwith the photoelectric emission during the daylighthours only. The flux of photons from thesun deposits 0.140 watt/cm •' as the total irra-diance above the atmosphere at the earth's meandistance from the sun. This corresponds to thetotal radiation [Johnson, 1961] from a blackbodyat a temperature of 5800øK (although thespectrum is close to that of a blackbody at6000øK). The numbers of incident photons percm •' with energies above 2, 3, and 4 electronvolts are 1.2 X 10 •7, 3 X 10 •6, and 3.5 X 10 •5,respectively. The corresponding maximum photoelectriccurrents for these work functions are20•, 5•, and 0.6• milliampere/cm% respectively,where • is the efficiency defined as the numberof electrons emitted per incident photon.For the physical parameters of interest hereand with readily achieved efficiencies •, thesephotoelectric currents are large enough to maintainthe Alfv•n disturbance and are nowherenear the space charge limit of Child's Law[Hamwell, 1949]. If we consider Echo 1, forexample, in a 1600-km orbit where va •'" 109cm/sec, with effective dimensions of L • M • 30meters, we obtain the following values from(19)-(24) for the voltage, power, current,impedance, and surface charge density associatedwith the radiation of the Alfv•n wings:P = 3 wattsV ,-• 3 voltsI • 1/2 amp in each wing (31)Z • 6 ohms in each wingY• • 8 X 105 electrons/cm 2An average value of 0.2 gauss at this altitudefor the perpendicular component of the earth'smagnetic field was assumed in writing thesenumbers. Since 1//•x • 75 meters for the Alfv•nsolution to be valid according to (28), for• ,-• 4 X 106 cps, the power of 3 watts mustbe reduced by a factor of (30/75)•' • 1/6 toP = 1/2 watt. The current is correspondinglyreduced by a factor of •1/2.5, according to(22), to a total value of I • 0.2 amp.The Echo 1 balloon has a good conductingsurface consisting of a few microns of aluminumevaporated on to a mylar base, and, if we takea very conservative (i.e. high) value of 4 voltsfor the work function and an effective emittingsurface area for electrons of LSM, where L isthe width and •M • M the thickness of a

DRAG AND PROPULSION IN THE IONOSPHERE 3141¾XFig. 9. Alfv•n wings of separation M and thickness •M.wing in the notation of Figure 9, we find thatthe incident flux of 3.5 X 10 •5 photons/cm •- withenergies _>4 ev produces the required 0.2-ampcurrent if the efficiency • is not less thanf = 1.2 X 10-3/•M(meters)flow before being limited by space chargeaccording to Child's law.In (31) we compute a surface charge densityof •cn - 8 X 105 electrons/cm •' in the wing.For a wing thickness of bM • 15 meters, thecorresponding volume density isFor a wing thickness of •M •< M/2 • 15 meters,the required efficiency of f • 10 -4 is even lessthan expected. Since work functions and photoelectricefficiencies are relatively sensitive t(; the'history' of a surface, we do not probe thisquestion here in further detail.Electrons can also be removed from the surfaceby collisions with positive ions that areneutralized at the surface. These ions collidewith the surface by virtue of the motion of theconductor (see Figure 7). The maximum currentdensity so obtained at 1600 kmis • n+evc,•' 10 -•/•amp, much less than the currents maintainedby photoelectrons in daylight. The possibleelectron ejection from impacts of the ions(sputtering) and of the more copious neutralatoms will also increase the electron emission.The current of 0.2 amp/4 X 10 ø cm •- < 0.1/•amp/cm 2 is well below the space charge limit.To show this, we compute the thickness of theion sheath surrounding the conducting surfaceof the Echo 1 in order to neutralize the electricfield in the plasma. It is, by Gauss' law,l -- E -- vcB • 10_•cm2 >( 47rnion•e 87reCnion•where we used nio=s • ne• .... • 5 X 10•/cm •at 1600 km altitude. Thus we have a potentialdrop of 3 volts occurring in a distance of 0.1cm from the surface of Echo, and through thisdrop a current of hundreds of microamperes can8 >( 10•/1.5 >( 103 -- 530 electrons/cm • (32)which adds •10% to the ambient density.There is thus a sizeable perturbation in theionosphere which can be observable by radar.Effect of finite inter•al resistance in the conductor.According to (22), the electric field--(v•/c) B o of the moving conductor causes acurrent flow of magnitude=This current flow and the electric field aremaintained if the conductivity of the conductoritself (so far assumed to be a perfect conductorwith a•. = •o) is high enough. By Ohm's law theflow of current in the conductor in the y directionin Figure 5 ish = =The criterion for there to be no reduction ofpower or current flow due to internal resistanceis obtained by combining (33) and (34) to getcvcBo/va' 2w) L> c2/2rNv•For Echo 1, with v• • 10 • cm/sec and N • 30meters, the requirement is• > 6 X 10 • esu • 6 X 10 -• abmho/cm

3142 DRELL, FOLEY, AND RUDERMANSince this is well below the specific conductivityof an aluminum layer a few microns thick, nosignificant correction need be made. For conductorsat lower altitude orbits, the criterion(35) become somewhat more severe as va dropsto •2 X 107 cm/sec' at 160-500 km altitude.As is clear from the Maxwell equations, thecurrent flow is reduced by a factor1 + Nac)(36)due to internal resistance of the conductor if itis appreciable. In simple terms of Ohm's law,(36) says merely that the effective resistanceincreased from the value given in (23) becauseof adding the internal and plasma resistancesin series.5. DAMPING OF ECHO 10RmT4M• (for He +) and --•10 -2ø gm/cc if the ionsare H +. Thus there can be, at most, a few percent ionization at these altitudes if all the Echo 1damping comes from neutral atoms as in (37).However, the Alfv•n mode damping whichrequires no neutral atoms may be sufficient togive the needed damping from the observedelectron (ion) density n+ • 5 X 10S/cc.We need a dissipation of • « watt to replacePatna-drag in the analysis of the Echo 1 orbit.In (31) and the subsequent discussion, we founda magnetohydrodynamic breaking from radiationinto the Alfv•n mode of P • -} watt, veryclose to the required damping. Since we mustrely on the sun to provide the energy leading tophotoelectric emission and to maintain thecurrent, we should further reduce P by anotherfactor of 2 to a time averaged value ofwatt, as Echo 1 is in the daytime sky only onehalfof the time. What we have achieved here,then, is a new drag mechanism which is of theright order of magnitude to explain the observedorbit parameters of Echo 1 without the requirementof a high value of the ionospheric massThe detailed orbit of the Echo 1 satellite showsa complicated variation of perigee, apogee, andeccentricity values with time due to a combinationof factors. This problem has been studiedby Jastrow and Pearse [1957] and by Shapiro and density relative to ion density.Jones [1960], who include effects of electrostaticAs we follow Echo 1 to lower altitude orbits,charging of the body in orbit (negligible), solarthe frictional drag increases in proportion to thepressure, and atmospheric drag. This lattermass density and dominates the Alfv•n drag byfactor plays a significant role even at tiny the time we are down to altitudes •< 1000 km.densities above 1000 km, because of the veryabnormally large ratio of surface area to massof Echo 1 (,rR 2 --• 6 X l06 cm2; weight • 150Direct experimental confirmation of the ideaspresented here is highly desirable, particularly inview of the very qualitative nature of our resultspounds). In fact the detailed analysis of Echo'sas applied to Echo l, which is somewhat tooorbit has yielded a 'measurement' of the masssmall to meet the criteria for the Alfv•n regimedensity in the upper ionosphere. To account forof parameters. This confirmation could bethe observed drag, after allowance for otherachieved by observation of the Alfv•n wings bycalculable factors such as solar pressure, thespecular reflection of radar from the surfaceneeded mass density [Shapiro and Jones, 1960]charge layer computed in (32).is given as p .... = 1.2 >( l0 -•s gm/cm s at 1600As we saw in (30), an ionospheric disturbancekm. The corresponding power dissipation (inis predicted extending perhaps many hundredsthe approximation that vc = 7 )• l05 cm/sec isof kilometers along field lines in both directionslarge compared with molecular and ion velocities;from Echo 1. This may explain why Echo 1transits were seen in instances when the radarwith T ø • 1500øK and effective molecular massof M • 8Mp, the average molecular velocity iscross section of the body itself was too small tov•--" 2 X 105 cm/sec) isbe seen above the instrumental noise [Tiuri andKraus, 1963]. In these same measurements iono-Patna-drag = (71'R2) P .... •½3• « watt (37)spheric disturbances of duration -1-20 minutesBackscatter radar measurements made at Lima, before and after transit of Echo 1 above thePeru, in 1962 have found •5 >( l0 s electrons/cm s radar sighting were often recorded. To explainat the 1600 km altitude [Bowles, 1964; Bowles this in the present context, the Alfv•n wingset al., 1962]. The corresponding ion mass density would need to extend as a detectable chargeis •-•3 X 10 -20 gm/c ms for a molecular mass of separation along a magnetic field line in one

DRAG AND PROPULSION IN THE IONOSPHERE3143direction for a distance between 5000 and 10,000kilometers.Passive detectionat sea level is not feasiblebecause of critical reflection at the D level.AlfvlSn waves generated by a source whosegeometrical size is not • 1 km will not give adetectable magnetic anomaly at sea level (Drell,Foley, and Ruderman, to be published).6. SPECULATIONS ON ORBIT MANEUVERABILITYAND POWER STORAGE USING AN ALrV•NPROPULSION ENGINEIN SPACEFor Echo I the power level generated in theAlfv•n disturbance was measured in watts.From (21) it is evident that large conductors(L--• M --• 100 meters) at lower altitudes(•160-500 km with va • 2 X 107 cm/sec andB0--• 0.4 gauss) can dissipate power at thelevel of kilowatts when crossing field lines; forexample,L • M -- 100 metersVa = 2 X 107 cm/secB0 = 0.4 gausslead, by (19), (21), (22), and (23), toPAlfv•n = 8(L/100 m)(M/100 m) kw = 8 kwV = (vc/c)BoM = 30(M/100 m) volts= 30 voltsI = 130(L/100 m) amp= 130 amp in each wing (38)Z = 0.23M/Lohm= 0.23ohmAccording to (28), we are comfortably withinthe Alfv•n regime with this choice of parameters.The surface charge density in a wing is, by (24),2•a • 2 esu = 4 X 109 electrons/cm"For a wing thickness of --•10 meters, this givesa volume density of--•4 X 10 • electrons/cc, orabout 10 times ambient at these altitudes. Thecorresponding current flow through the conductingsurface of area 10 X 100 m • = 107 cm"into each wing is 13 /zamp/cma = 8 X 101•electrons/cm". Since metallic conducting surfaceswith work functions in the range 3-4 voltsand with photoelectric efficiencies of --•1% arewell within the range of comfortable technology,there is no difficulty maintaining this currentflow with the sun as the source of photoelectrons.(For 24-hour operation, we could resort to hotwire filaments or some other active device.)Once again, this current of •13 /zamp/cm'. iswell below the Child's law limit for emissionthrough a potential drop of 30 volts occurringin a fraction of a centimeter.The high level of power generated by theAlfv•n disturbance invites speculation on waysof making practical use of it. If used passivelyas a controllable drag mechanism it can serve(1) as a means of converting satellite kineticenergy to electrical power, (2) as a way ofbringing satellites to lower altitudes withoutpropellant, and (3) to adjust satellite attitudesby exploiting torques. If used in conjunctionwith an on-board source of electrical power (viz,solar panels or small nuclear reactors), it canserve (4) to counteract atmospheric drag effectson satellites and even propel them to higheraltitudes, (5) as a means of storing energy byconverting it temporarily to satellite kineticenergy, and (6) to maneuver the position andattitude of a spacecraft (without propellant) bypushing on the earth's magnetic field.Most simple is the question of utilizing thepower flowing in the current producing theAlfvdn fields. A low impedance motor withinternal resistance, of --•0.23 ohm could tap• •X 8 kw - 2 kw of power for use in a satelliteat the expense of its kinetic energy. This mightbe generated by flying a 'kite,' as illustrated inFigure 10, consisting of two 100-meter-longconducting slabs each of •5- to 10-meterdiameter, connected by a conducting rod of100-meter length oriented perpendicular to B0through which the current flows. The surface ofthis conducting rod is insulated from the outsideworld, and in series with it is connected the lowimpedance motor delivering the power. Figure10 shows a schematic design. The rigidity mustbe sufficient to withstand some tens of poundsof force distributed over 100-meter rods andsurfaces. A number of photosensitive slabs mightbe desirable to minimize effects of rotation aboutthe vertical conductor. For short time powerneeds, we must compare with a very efficientsmall gasoline engine which can deliver •1 kwof power for an hour by burning •1 pound offuel. For more sustained use, 500 pounds ofsolar cells would give an equivalent power.

3144 DRELL, FOLEY, AND RUDERMANI t 6M ~ 5 - 10 metersL ~ 100 metersM + M 1 •' 100 metersestimated that the drag will lower the orbit of a20,000-pound manned orbiting laboratory atthis altitude by •15 km/day. This representsdrag force ofSatellite / vcB odp_ 1dh/dtdt -- • mg• (39)where h is the altitude and dh/dt = 15 km/day •15 cm/sec, and a power dissipation1 dhPdrag -- 2 mg -• • 7 kw (40)Fig. 10. A schematic arrangement for theAlfv•n propulsion engine.Short-circuiting the junction between M and M'of Figure 10 maximizes the drag (equivalent to8 kw of power or a drop of 40 km per day for a104-pound satellite.) Opening the junctionbetween M and M ' reduces the drag by anorder of magnitude, since the effective areafor Alfv•n wave radiation is reduced from(M -5- M•)L to 2(AM)L. Changing the relativesizes of M and M • gives a torque about theearth's magnetic field direction and thus rotatesthe satellite about B0. Rotations about thevertical occur if the center of mass of the satelliteis slightly displaced from the vertical line currentM -- M •. Other geometries offer a variety ofsimilar possibilities.If a source of electrical power is available onthe satellite, the direction of the drag currentscan be reversed and the drag converted to apush. The advantage of the Alfv•n propulsionengine over a small rocket engine lies in thosecircumstances in which the source of power doesnot involve the consumption of a heavy fuel (asin the case of a gasoline engine) which could justas well be used as a propellant. Rather, theAlfv•n engine as a propulsion mechanism wouldbe most useful for power which originates fromsolar panels or a nuclear generator.Among the problems in using a mannedorbiting laboratory is that the atmospheric dragis a major source of power dissipation, setting alower limit of 100 miles on the altitude. It isTo compensate for this drag, we propose flyingthe 'kite,' but with a power source aboard todrive the current backward, thereby gaining the5-10 kw power required to neutralize the dragloss and to maintain the altitude of the satellitewith a small increase of total weight in orbit.Higher power levels could also be utilized tomake the satellite sail to higher altitudes, the.gain being •2 kin/day for each steady input of•2 kw (available, for example, from about 500pounds of solar cells).When the current flow through the conductoris reversed by an impressed voltage, the dragforce I X B reverses its direction, leading to anacceleration. The normal Alfv•n wave gave apower dissipation (drag)__ ---.P•u,• Bo • Vc ( ML) I2•' V a• MBov•where I is the current flow driven by the potentialdifference v• BM/c. An impressed voltage V• inthe opposite direction (say between M and M'of Figure 9) gives a rate of increase of satellitekinetic energyP•c = Palfv•n l'r- (vc/c)BoM (41)A sufficiency condition for the validity of ourapproximations (in this case, that of linearityover a distance X from the conductor) restrictsVz to 2vc BoM/c. It is not yet clear whether theregion of nonlinearity increases or decreases thelinear drag or propulsion. Thus a power sourceof 60 volts and 16 kw can give half its power togenerating Alfv•n waves and half to increasingthe kinetic energy of the system described in(38). This is sufficient to lift the manned orbitinglaboratory about 15 km per day. Clearly this isalso a way to store electrical or solar panel energyC

DRAG AND PROPULSION IN THE IONOSPHERE 3145by using it to lift a satellite, but the storage andsubsequent reconversion are at most each 50%efficient.We may speculate on this kind of mechanismas a propulsion engine for flight to furtherreaches of space. For interplanetary travel,typical parameters are B0 • 10 -5 gauss anddensities •10 -2a g/cm a, leading to Alfv•n speedsofv• • 10 • cm/sec = 10 km/secTo be in the Alfv•n regime we requirew< i2• = eB/ M•c• 10 -1 cps for B• 10 -5 gaussThe corresponding conductor dimension isL •, Vc/W > 107 cm = 100 kmFor our solution we have the presumed requirementThen for vc • v•= = ø om/eo < 1- (1.6 X 10 --11) X (106)(1010)ß (ML/km 2) X 10 -7 watt (42)• O.02(ML/km 2) watt < } kweither for the conversion of electrical energy tosatellite kinetic energy or vice versa.The conversion of energy from gravitationalattractionear another planeto electrical energyis a reasonable possibility if both a reasonablemagnetic field and ionospheric plasma arepresent.The phenomenon discussed in this paper canbe used to determine ionic mass densities inregions of known field strength, as both theAlfv•n field strength and the power dissipationare proportional toPAlœv{n cc (Bo2/)a) ccAcknowledqment. We wish to thank Drs. C.Longmire, M. Rosenbluth, and H. Lewis for theirlearned and useful remarks.Additional note. M. J. Lighthill has discussedthe theory of Alfv6n radiation from objects ofsmaller dimension, for which the unidirectionalmode discussed here (the vorticity wave, in histerminology) is not radiated [Liqhthill, 1960a, b].We wish to thank Professor Lighthill for a veryfriendly and illuminating letter discussing thesequestions.P•EFERENCESBowles, K. L., Advances in Electronic and ElectronPhysics, Vol. 19, page 55, Academic Press,New York, 1964.Bowles, K. L., G. R. Ochs, and J. L. Green, On theabsolute intensity of incoherent scatter echoesfrom the ionosphere, J. Res. NBS, 66D, 395,1962.Hamwell, G. P., Principles of Electricity andMagnetism, McGraw-Hill Book Company, NewYork, 1949.Jastrow, R., and C. A. Pearse, Atmospheric dragon the satellite, J. Geophys. Res., 62, 413, 1957.Johnson, Francis S., Editor, Satellite EnvironmentHandbook, pp. 40, 41, 42, and 78, Stanford UniversityPress, Stanford, 1961.Lighthill, M. J., Studies in magneto-hydrodynamicwaves and other anisotropic wave motions,Phil. Trans. Roy. Soc. London, A, 252, 397,1960a.Lighthill, M. J., Note on waves through gases atpressures small compared with the magneticpressure, with applications to upper atmosphere,Fluid Mech., 9, 465, 1960b.Shapiro, I. I., and H. M. Jones, Perturbations ofthe orbit of the echo balloon, Science, 132, 1484,1960.Tiuri, M. E., and J. D. Kraus, Ionospheric disturbancesassociated with Echo I as studiedwith 19-megacycle-per-second radar, J. Geo-phys. Res., 68, 5371, 1963.(Manuscript received December 21, 1964;revised April 12, 1965.)