NASA TECHNICAL NASA TR R-177 ". ". REPORT LUA Kt R i THE EFFECT OF A RING CURRENT ON'THE BOUNDARY OF THE GEOMAGNETIC FIELD IN ASTEADY SOLAR WIND by John R. Spreiter and Alberta Y. AZksne Ames Research Center / Moffett FieZd Cali$ THEEFFECTOFARINGCURRENTONTHEBOUNDARY OF THE GEOMAGNETIC FIELD IN A STEADY SOLAR WIND By John R. Spreiter and Alberta Y. Alksne Ames Research Center MoffettField, Calif. NATIONAL AERONAUTICS AND SPACE ADMINISTRATION ~ . For sale by the Office of Technical Services, Department of Commerce, Washington, D. C. 20230 -- Price $1.25 NATIONAL AERONAUTICS AND SPACEADMTNISTRATION OF THE GEOMAGNETIC FELD IN A S'IIEADY SOLAR WIND By John R. Spreiter and Alberta Y. Alksne SUMMARY Approximatesolutions are givenfor the shape of theboundary separating a steady neutral stream of ionized solar corpuscles from the combinedmagnetic fieldsof a three-dimensionaldipole and an equatorial ring current. Results are presented for the traces of theboundary in the geomagnetic meridian plane containing the sun-earth line for several orientations of the latter relative to thedipole axis, and for the trace of the boundary in the geomagnetic equatorial planefor the case in which the dipole axis is normal tothe sun-earth line. It is found that the presence of a ring current having values for the diameter and strength of the order proposed to explain the magnetometer data from Pioneer I andPioneer V has the effect of greatly increasing the size, as well as altering the form,of the region within which the geomagnetic field is confined. INTRODUCTION The present paper reports the results of anextension of the theoretical study reported in references 1, 2, and 3 in whichapproximate results are deter- mined forthe traces, in the geomagnetic equatorial plane and in the geomagnetic meridianplane containing the sun-earth line, of the cavity carved out of a steady neutral ionized solar corpuscular stream by interaction with a magnetic dipolerepresenting the geomagnetic field. The novelfeature of this extension is the inclusion of the effect of an equatorial ring current having properties similar to those of the modelproposed by Smith, Coleman, Judge, and Sonett in reference 4 to represent the magnetometer data from Pioneer V and Explorer VI. These properties are that there exists, duringquiet times, a westwardflowing current of about 5x106 amperes distributed over a large volume havingthe form of a toroidal ring 3 earth radii in cross-sectional radius with its center line situated in the geomagnetic equatorial plane at a distance ofapproximately 8 to 10 earth radii. The magnetic moment ofsuch a current system is ofthe same signand order of magnitude as thatof the rain dipole field. Although the con- cept of a ring current is of long standing in the explanation of the decrease of the horizontal component of the magnetic field in the mainphase of a magnetic storm, and values for the strength and radius similar to those stated abovehave also been deduced recently from cosmic-ray data by Kellogg and Winckler (ref. 5), magnetometer and other data from more recent space experiments with Explorer X (ref. 6) andExplorer XI1 (ref. 7) have failed to detect the presence of such substantialring-current effects. As a result, the entiresubject of theprop- erties and even the existence of a significant ring current mustbe regarded as an open question at the present time. It is evident that the presence of a ring current having a magnetic moment comparable to that of thepermanent magnetic field of the earth should have the effect of greatly increasing the size, as well as altering the form,of the cav- ity. It is thepurpose of this paper to present the results of a number of calculations undertaken to determine in a more quantitative manner the nature of theeffects of such a ringcurrent. A preliminaryaccount of the present inves- tigationincluding plots of the results for the case in which the dipole axis is normal to the direction of the incident stream hasbeen given in reference 8. Those results are presentedin greater detail in the present paper. Also pre- sented are additional results for the traces of the boundary in the above specified meridian plane for other orientations of the dipole axis relative to the stream direction. It shouldbe recognized that the concept of a toroidal ring current with protonsand electrons circulating round the geomagnetic axis at differentspeeds, althoughsimple and of long standing, is, at best, not particularly precise. Singerhas proposed a different concept in reference 9 in whichthe observed mag- netic variations and the associated ring current are explainedin terms of the spiraling and drifting motion of trapped particles similar to those discovered shortly thereafter by satellite experimentsby Van Allen and his colleagues (see, e.g., ref. 10). As is now familiar, thetrapped particles spiral rapidly to and fro along the local magnetic lines between mirror points in the northern and southernhemispheres. At the same time thetrapped particles drift roundthe earth,the protons to the west, theelectrons to the east, thus setting up a westward electriccurrent. This current is identifiedwith the ring current. There is, in addition, a diamagnetic effect producedby the gyration of the par- ticlesabout the line of force. Superposition of these two effectsgives the total magneticinfluence, although Singer states in reference 11 thatunder cer- tainconditions, the diamagnetic effects are notimportant. It is assumed in the present investigation that the simple ring current model proposedby Smith, Coleman, Judge,and Sonett in reference 4 canbe used to obtainan adequate representation of the basic geomagnetic field. It shouldbe recognized that the values indicated for the strength and position of the ring current may be at considerablevariance with those of theequivalent diamagnetic ring current which could also be used to represent the measured field, but which wouldbe more consistent with the concept of the magnetic field arising from the motion of trappedparticles. It is notnecessary, however, for the determination of theterminal shape of the geomagnetic field to duplicate the properties of the ringcurrent in all details. It is important,though, that a consistentsystem beemployed so thatthe approximations introduced in proceeding from the measured values to an equivalent current system are removed when the process is repeated in reverse orderto calculate the magnetic field. This has been done in the 2 present analysis, and all results presented herein are based on the consistent use of the model andassociated numerical values proposed by Smith, Coleman, Judge,and Sonett. The onlydeviation is thatthe ring current of finite cross section is replacedby an idealized oneof infinitesimalcross section. This change simplifies the computations considerably and should lead to little differ- ence in the results, provided the boundaryof the cavity is farther than about 2 or 3 earth radii from the idealized ring current. PRINCIPAL SYMBOLS a radius of ringcurrent, em (seefig. 1) ae radius of earth, ern B - totalmagnetic field, gauss B’ magnetic field due tocurrents in boundary, gauss intensity ofgeomagnetic field at equator =: 0.31-2 gauss BpO E i current , e.m. u. K complete elliptic integral of the first kind k modulus of ellipticintegrals dipole moment of earth = ae3B MP PO Ml dipole moment of ring current = na2i m mass of proton = 1.67~10-~~gm n number of protonsper cm3 n unit vector in the direction of theoutward normal to the boundary sphericalcoordinates (see fig. 1) n r unit vector in radial direction 3 rO unit lengthof defined byequation (8), cm v plasma,velocity of cm/sec x, Y, z rectangularcoordinates (geomagnetic, see fig. 1) x!, y', z' rectangularcoordinates (geographic) h 0 unitvector in direction of increasing 0 A anglebetween direction undisturbedof plasma stream andthegeo- magneticequatorial plane (see fig. 1) P 4J anglebetween direction of undisturbedplasma stream andtheout- wardnormal tothe boundary (see fig. 1) Subscripts front pertaining to ring current lower neutral point pertainingto permanent, or dipole,field rear upper component inthe direction of increasing 0 component inthe direction of increasing p FLTNDAMENTAL ASSUMPTIONS AND EQUATIONS The basic concepts of the present study are classical and stem from a long series of investigations by Chapman, Ferraro, Dungey, andothers (see refs. 12 and 4 13 for a rksumd) undertaken to explain the connection between solar flares and geomagneticstorms. The fundamentalassumption is that there exists a rarefied neutralionized corpuscular stream, the solar wind, consisting principally of protons and electrons in equal numbers, which flows past the earth at hypersonic speeds. The particles are presumed to beof solar origin,and to be of uniform velocityin the undisturbed incident stream. The directionof the incident stream will be referred to for convenienceof discussion as though it were coming directlyfrom the sun. It shouldbe understood, however, that the directionof the sun is actually immaterial in the analysis, and that only the direction of theundisturbed incident stream relative to the dipole axis is significant. Interaction between the solar windand the permanentgeomagnetic field is such that a cavity,bounded by a thin current sheath, is carvedout of the stream. The solar wind is thus confined to the exterior, and the geomagnetic field to the interior, of thecavity. The latter region,dominated by the geomagnetic field, is now generally referred to as themagnetosphere. The particles