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Pressure Balance Between Solar Wind and Magnetosphere

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Pressure Balance Between Solar Wind and Magnetosphere •OURNALOF GEOPHYSICALRESEARCH, SPACE PHYSICS VOL. ?4, NO. 5, MARCH 1, 1959 Pressure Balance between Solar Wind and Magnetosphere M. A. SCHIELD 2 Department of Space Science Rice University, Houston, Texas 77001 An evaluationof the subsolarpressure balance between the solarwind and the geomagnetic field showsthat the average proton density of the quiet-day solar wind (300-400 km/sec) shouldbe between6 and 10 p/cma. Even duringstorm times the protondensity should always be between2 p/cm3 and 70 p/cm3. The relation betweenthe interplanetarysolar-wind param- eters and the stagnationpressure is reviewed.The subsolargeomagnetic field, including the quiet-dayring currentfield, is evaluatedas a functionof subsolardistance. The quiet-dayring current is based on the dipole gradient-drift motion of the low-energyprotons observedby Davis and Williamson and by Frank. This quiet-day ring current has a magneticmoment of 0,?6 MB and producesa 41-? decreaseat the earth'ssurface. A geomagneticfield normalization of observedboundary distancesis also proposedto remove the effectsof the dipole tilt to the solar wind. INTRODUCTION man-Ferraro theory, which assumesthat the The size of the magnetosphereand the pres- solar plasmais noninteractingand field-freeand sureof the solarwind are relatedby the pressure assumesthat the geomagneticfield is free of in- balanceequation p + B2/2/• -- constant.For a ternal plasma. Observationsof the solar wind field-freesolar wind and a plasma-freegeomag- [Wilcoxet al.,1967], of plasmaenergy densities neticfield this equationreduces to po--- B,2/2/•o. within the magnetosphere[Davis and William. The subsolarsolar-wind pressure po was first son, 1963; Frank, 1967], and of the geomag- calculatedby assumingspecular reflection of the netic field [Mead and Cahill, 1967] indicate noninteractingions and electronsand was given theseassumptions are not satisfied.The purpose by po = 2 pv• wherep is the massdensity and v of this paper is to evaluatethe pressurebalance is the solarwind velocity.The subsolargeomag- between the shockedsolar wind and the mag- netic field Bg was first assumedto be twice the netospherewith its internal plasma. The solar tangentialcomponent of the subsolardipole field wind pressure necessaryto confine the mag- in analogywith the confinementof a dipolefield netosphereto a given subsolardistance is cal- by a plane boundary. A self-consistentsolution culated.The proton number density of the solar of the Chapman-Ferraro problem [Mead and wind is deduced from observations of the size Beard, 1964] indicated that the geomagnetic of the magnetosphereand the velocity and com- field was actually 2.44 times the dipole field at positionof the solarwind and is comparedwith the subsolar point [Mead, 1964]. See Beard observations. [1964] for a review. On these bases a 400- SOLAR WIND PRESSURE km/sec solar wind containingabout 2.4 p/cm• would confinethe geomagneticfield to a subsolar The body pressure po of the shockedsolar distance of 11 RB. wind on the subsolarpoint of the magnetosphere However, this conclusionis based on Chap- may be related to the interplanetary solar wind momentumflux pv• at 1 AU by a solar wind pressurecoefficient K definedby K = po/pV•. x Based on thesis submitted in partial fulfillment The value of K dependsupon the modelof the of the requirements for the Ph.D. at Rice Univer- solar wind. See Spreiter et al. [1966] for a re- sity. view. In the steady-state condition the zero- 2 Present address:Physics Research Center, Uni- temperature, field-free solar wind has a K of 2 versity of Iowa, Iowa City, Iowa 52240. appropriate to an elastic collision.In the gas- Copyright ¸ 1969 by the American Geophysical Union. dynamic approximation(B = 0) for a blunt- 1275 1276 M. A. SCHIELD nosed obstaclein a hypersonicstream, K is +18 • I i I I I I 0.844 for y = 2 and 0.881 for y = 5/3. When the solarwind passesa magneticfield in alignedflow the stagnationpressure is givenby pm,,•/(pv•) = 1 -- (%)e [1 + 2/(( 7 -- 1)M•)] •-,o • • .-,o whereß = (7 -- 1)/(7 + 1) andp• = p + B•/2•o [Lees,1964; Hayes and Probstein,1959, p. 14]. For hypersonicflow (M' >> 1) this rela- • -•o- {190e• tion reducesto 5/6 (0.832)for 7 = 2 andto 7/8 _401• •EQUATORIALFIELDOFQUIET- DAY •--•0 (0.875) for 7 = 5/3. If the interplanetary field has a component • 50• I I I I I I I I I [ I I/• - 50 perpendicularto the free stream velocity vector, I 2 5 4 5 6 7 8 9 I0 II 12 R/R E the gasdynamicapproximation breaks down at the stagnationpoint [Alksne, 1967]. When the •i•. •. •qu•[oriM field of eurren• obtained as the •um of [he fie]d• pro- interplanetaryfield is antiparallelto the subsolar ducedb• •he hi•h- •nd ]o•-ener• component• geomagneticfield, the total stagnationpressure Lhe ma•neLo•pheric plasma. Inclusion of proto• is (2/3)pv • for 7 = 2 [Lees, 1964]. No coefti- be[•een 50 •nd 100 key •hould smoo[h ou• eient is presently available for the parallel or bump • • = 5. perpendicularcases. sphericmodels and will be designatedby 2] GEOMAGNETIC FmLD PaESSUaE [Ferraro, 1960]. In an image dipole magneto- The geomagneticfield is the sum of the earth's sphere] equals 1, while for a two-dimensional internal field, the magnetospheric surface- line dipoleconfined by a streamingplasma ] is currentfield, and the field producedby plasmas less than I [Chapman, 1963]. In the Mead- within the magnetosphereof which the quiet-day Beardmagnetosphere, which contains no internal and storm-timering currentsare examples.The plasmaand no neutral sheet,Bg/B• equals2.44 ratio of the subsolargeomagnetic field B, to so that ] equals1.22 [Mead, 1964]. the subsolardipole field B• is nearly independent The field of the quiet-day ring current is of the subsolardistance in simple magneto- derived and discussedin the Appendix. This ring current is based on low-energy proton energy densitiesmeasured by Davis and Wil- ,o-6 . ..• liamson[1963]andby Frank [1967].These I '..'--:I,•!:!??•i•i'!17•i? I I12øøenergy densities, illustrated inFigure 1,are I '' e.'-",,".'' "•"('"'• •. v'__•F'•'• •ve)x=•ol-I'øø I0 10-7•-- "," ,J....... fittn dntn I--I50.) I /oE=i38kev/cm.......... I ,ooo- - r, . ..";i---- _t< .... ,o_.[.,,,,,,; , .,,,,,fi, r•9ioo /d - •o-*I , I, I :",,,,,,,,,,,,t: • 50 20 Fig. 1. Radial distribution of plasma energy densitiesobserved by Davisand Williamson [1963]and by Frank[1967]. The parameters and the resultant functional forms used to describe theseenergy densities are also illustrated. Future observationof protons between 50 and 100 key Fig. 3. Sum of the quiet-day ring currentfield shouldfill in the gap in energy density around and the earth'sdipole field versusequatorial dia- L = 5. rance. MAGNETOSPHERE PRESSURE BALANCE 1277 assumed to be symmetric and moving in a sistent with the external field statistically de- dipolar magneticfield. The equatorialquiet-day rived from ground-basedobservations [Cain, ring current field, illustrated in Figure 2, pro- 1966]. The quiet-day ring current has a total ducesa 41-7 decreaseat the earth'ssurface and magnetic moment of 0.26 M•. Between 10 and a maximum decreaseof 58 7 at 3.5 R,. The 12 R•, the ring current field enhances the equatorial ring-current field changessign at 9 equatorial dipole field by 25% to 35%, whereas R, and enhancesthe dipole field by 8 to 10 7 alongthe polar axis, the dipolefield is enhanced between 10 and 11.5 R,. The sum of the dipole by 15% to 17% over the sameradial region. field and quiet-dayring current field is shownin To calculate the subsolargeomagnetic field Figure 3. This quiet-day ring current field is while including internal plasmas, the entire consistentwith satellite observations[Mead and problem should be reworked self-consistently. Cahill, 1967], illustrated in Figure 4. The net However, the zeroth-ordereffect of this ring external field caused by the ring current and current field is to enhancethe earth's dipole magnetopausecurrents is shown to be con- moment by 26% beyond 10 R•. By neglecting AUGUST 28, 1961 INBOUND EXPLORER 12 , . ! I I ! I I I I I 407 ß0 ß ßßß ß0ß _ ß ß ßß ß AB 207 ßß% ßß0 ß ß ß _ ßø ß 0000ßß ß ß 07 ....•_***** ** ß *'0• '00 *% 4** ß ß ß -20.7 30 ø .0 - oOOOoooOoo o o(•pøøø•ø o o I 0 ø __ "'""'O•Ooo oßcoOß øOoooOoooOOOoø•o øøøøøøø•øø•o __ -30 ø o 30 ø - Boundary-/ _ D 0 ø eeøoee%oeeOøeeeeeOeoooeeeaeeea•eaeo.__e .ee•,.___.- Jensen and Cain -30 ø •-J. and Co plusboundary currents I I I I I I I I ,•,t 1'* R/RE; 4 5 6 7 8 9 10 11 12 km 4 ø -4 ø - 9 ø - l l ø - 9 ø zSEP 37 ø 24 ø 17 ø 15 ø 18 ø / SED 90 ø 91 o 91 o 89 ø 82 o L.T. 14:30 13:35 13:05 12:40 12:20 U.T. 6:30 5:25 4:05 2:l0 23:l0 Bj. &C. 510y 150Y 65Y 337 197 Fig. 4. Difference between the observedgeomagnetic field within 30ø of the subsolaraxis for DST _• 10 ,• and the theoretically predicted geomagneticfield [Mead, 1964] assuming no internal plasma[Mead and Cahill, 1'967].The field of the quiet-dayring current (Figure 2) is capableof explaining this difference. 1278 M.A. SCHIELD higher-ordereffects, the shape of the magneto- solar distanceby about 20%. However, the dis- sphere remainsunchanged from that obtained turbance field at the earth can be enhancedby by Mead and Beard. In this case,the subsolar up to a 100 ¾ if the magnetopauseexpands from geomagneticfield continuesto be 2.44 timesthe 6 to 10 R• [Mead, 1964]. internal field, which now includes both the Large subsolardistances often occur during dipole and ring current fields.The ratio Bg/B• the recovery phases of geomagneticstorms is now 26% greater than 2.44 so that in the [Freeman, 1964].
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