VOL. 82, NO. 4 JOURNAL OF GEOPHYSICAL RESEARCH FEBRUARY 1, 1977 Radiation Belt Electrons: Structure of the Loss Cone WALTHER N. SPJELDVIK Space Environment Laboratory, NOAA/ERL, Boulder, Colorado 80302 A criticalanalysis of existing theories for the structure of the atmospheric loss coneof energetic radiation belt electrons is presented. Emphasis is put on inadequacies andlimitations of these theories. Some of the important errorsources characteristic of experimental studies of the electron loss cone are also discussed and their effects assessed. Observations of energetic loss coneelectrons obtainedon board the satellite OVl-14 are presented and compared to theoretical predictions. The need [or independent approaches is emphasized. 1. INTRODUCTION The gross features of the structure of trapped radiation belt electronfluxes at geomagnetically quiet times may be under- stood'in terms of a simultaneous inward radial diffusive trans- port and losses to the atmosphere driven by wave-particle and particle-particle interactions. Important theoreticalwork has beendone by Dungey[1963], Cornwall[1964], Roberts [1969], Lyonset al. [1971, 1972], Lyonsand Thorne [1973], and many others. Electronsthat precipitatefrom the radiation belts re- side within the atmospheric bounce losscone definedby pitch angles so srfiall that the mirror points encounter the denser parts of the earth's atmosphere. An early attempt to theoreti- cally predictthe angulardistribution of loss cone electrons was made by Theodoridis and Paolini [1967] using the mathemati- cal framework suggested by Kennel and Petschek [1966]. Their calculations neglected the angularredistribution and backscat- tering provided by Coulomb collisons with nuclei of atmo- spheric particles as well as energydegradation. The work of Sp. jeldt)ik and Thorne [1975a] emphasizes the importance of theseprocesses in the control of the interior of the losscone. The theory by Spjeldt)ik and Thorne [1975a]and the numerical approach by Dat)idson and Wait [1975, 1976, 1977] are criti- cally reviewed in section 2 with particular emphasison the shortcomings of both methods. The ultimate test of any phys- ical theory is its comparison with experimental observation of high quality. Experimentalinformation on energetic loss cone electron fluxes is, however,rather sparse, either because avail- able satellite instrumentation does not permit accurate mea- rate corresponding to the quarter bounceperiod and that no interaction between radiation belt electron fluxes and atmo- spheric particles takes place outside the nominal loss cone. This impliesthat a fraction 1/e of the nominally precipitated flux is returned from the atmosphere without change in pitch angle. More realistic calculations using Monte Carlo and Fok- ker-Planck methods generallyindicate backscattered electron fluxes to be in excess of 20% of the incident flux, somewhat dependent on the incident pitch angle distributionand energy spectrum [e.g., Wedde, 1970; Spjeldvik and Thorne, 1975a; W. Francis, personalcommunication, 1973]. Such backscattered ratios are not necessarily grossly different from the simple fraction l/e; the important point is rather that the backscat- tered flux, having undergone strong scatteringin the atmo- sphere,tends to become isotropized. To modelthe equilibrium loss cone pitch angle distribution, Spjeldvik and Thorne [1975a] introducedthe rate of atmo- spheric scattering into the diffusion coefficient for those ele.c- tronswhose trajectories encountered the atmosphere. An aver- agerate of angularscattering integrated over the zeroth-order (unperturbed) electron trajectorywas addedto the scattering rates because of wave-particle interactions. The averagewas taken as a quarterbounce average for electrons whose mirror pointswere sufficiently abovethe denser parts of the earth's atmosphere; for electrons with low mirror points, energy deg- radation was computed togetherwith the scattering rates. If the electron energy wasfoundto be reduced to 1/e of its initial value, the electron wasdeclared 'lost' and its path terminated. surements of the angular distribution within the loss cone or This procedure has the following drawbacks. (1,) The contri- because satellite orbits have been unfavorable. A discussion of bution from energy degradation of higher-energy electron fluxes to the lower-energy electronpopulationis disregarded. some of the pitfalls in the analysis of loss conedata is givenin section 3. Observations, of loss cone electrons from the satellite OVI-14, which had suitable instrumentation and proper orbit but whose electron experiment wasvery shortlived(48 hours), are presented in section 4. A summ/•ry with suggestions for future work is given is section5. 2. THEORETICAL STUDIES OF THE Loss CONE Electrons scattered into the loss cone are lost to the atmo- sphere on a time scale comparable to the quarter bounce time, generally a fraction of a second at radiation belt energies. Followingthe approach of Kennel andPetschek [1966], Theod- oridis and Paolini [1967] computed theoretical loss conedistri- butions by assuming that electronswithin the nominal loss cone (i.e., with mirror points below 100 kin, independent of electron energy)are lost to the atmosphere at an exponential Copyright ¸ 1977by the AmericanGeophysical Union. This limits the validity of the approach to cases where the trapped electron energy spectrumfalls off steeply toward higherenergies. Fortunately, this condition is often well satis- fied for energetic radiation belt electrons. (2) Use of the unper- turbed electron orbits to calculateaverage scattering rates is only an approximation to a stochastic average over real elec- tron trajectories. When the atmospheric scattering rate is high, the zeroth-order path approximation will certainly be invalid. Fortunately, however,one finds that the error in scattering rate becomes significant only when the precipitating electrons are subject to locallystrong atmospheric scattering, and in this limit the electron angulardistribution becomes independent of the precise scattering rate. The greatestasset of the method of Spjeldt•ik and Thorne [1975a]liesin its simplicity in application and the fact that the loss cone distribution can be calculated with great angular resolution, typically 500-1000 angulargrid pointsin the criti- Paper number6A0818. 709