Space Plasma Physics The Study of Solar-System Plasmas (1978) / Chapter Skim
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Plasma Processes in the Earth's Radiation Belt
Plasma Processes in the Earth's Radiation Belt
Pages 220-260
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PLASMA PROCESSES IN THE EARTH'S RADIATION BELT by L
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Readers are referred to the comprehensive treatment of the radiation belts by Schulz OQ and Lanzerotti for earlier research . Trapped particles execute quasi-periodic motion which can be divided into three components, each component associated with an adiabatic invariant.
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The loss cone is <1° wide in equatorial pitch angle in the outer regions of the radiation belts, and increases to a few tens of degrees wide at L<2.) Pitch angle diffusion into the loss cone is often an important loss process for radiation belt particles, while diffusion in energy can be an important particle energization process.
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'x-B) , In addition to diffusive particle sources and losses, direct energetic particle injection and loss results from processes such as energetic neutron decay and charge exchange with cold neutrals, and particles can be injected directly into the radiation belts from the geomagnetic tail and cusps by electric fields normal to 13 and from the ionosphere by electric fields parallel to IS.
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Within the plasmasphere, well-defined plasma processes proceed essentially continually for periods of weeks to months uninterupted by direct injections. This region is thus ideal for comparing radiation belt particle measurements with theoretical discriptions of plasma processes, and fortunately good measurement of the plasma energetic particle distribution function are available from the Explorer 45 satellite.
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The simple picture in Figure 3 is modified somewhat in the radiation belts because the geomagnetic field is not homogeneous, and wave energy is generally distributed over some range of geomagnetic latitudes.
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Given a proposed distribution of wave energy in the 20 radiation belts, quasi-linear diffusion theory can be applied to 23 24 obtain pitch angle and energy diffusion coefficients " . These diffusion coefficients can then be used to calculate the distribution of 19 22 trapped particles as a function of pitch angle ' , and these calculations can be directly compared with particle measurements.
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. Given radial diffusion coefficients and loss rates calculated from pitch angle diffusion coefficients, and including other processes such as those listed in Section I when relevant, radiation belt fluxes as a function of radial distance can be calculated.
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Using the calculated diffusion coefficients, prediction of electron pitch angle distributions and loss rates from diffusion into the loss cone were obtained. Examples of the calculated pitch-angle diffusion coefficients and equatorial pitch-angle distributions at L=4 are shown in Figure 4 for 20 keV, 200 keV, and 2 MeV electrons.
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This slow diffusion manifests itself in the equatorial pitch-angle distributions as a region of large slope. Thus the equatorial distributions develop bumps surrounding 90° pitch angles, and this bump decreases in size and pitch angle extent with increasing electron energy.
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Radial diffusion was assumed to be driven by fluctuations of the magnetospheric po2 tential electric field as modeled by Cornwall The resulting particle distribution function f for equatorially mirroring electrons as a function of L at constant first adiabatic invariant M is shown in the left-hand panel of Figure 6. Curves for the various values of M were all normalized to the same value at the plasmapause, here taken to be L=5.5.
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During large geomagnetic storms, electrons are injected within the quiet time location of the plasmapause, and the equilibrium pitch angle distributions and radial structure are destroyed. However, Explorer 45 observations have shown that the pitch angle distribution and radial profiles gradually return to their pre-storm 30 structure over a period of a few weeks " .
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He followed the approach of Cornwall and balanced radial 2 diffusion as modelled by Cornwall with proton losses from charge exchange with the ambient neutral hydrogen geocorona and Coulomb collisions. The outer boundary condition was taken from the observed ion fluxes from ATS-6 at L=6.6.
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It is unfortunate that valid measurements are not available below 100 keV, since Spjeldvik's calculations imply that any significant ion fluxes below 100 keV may not be dominated by protons. This range of energies at L~4 is discussed in more detail in the following section on the decay of the stormtime ring current.
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Enhanced ion fluxes are observed from VL keV to ^200 keV during storms, and fortunately these fluxes are above the Explorer 45 background levels so the valid measurements of equatorial pitch angle distributions and energy spectra are available over most of this energy range from L=2.5 to 5. Figure 9 shows Explorer 45 observations of the distribution function f of equatorially mirroring ions throughout the period of the large storm on Dec.
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From page 235... ...
On the other hand, the observed increase in f at the lower energies represents a net increase in the trapped ion population, and this increase is a significant part of the stormtime ring current. Two processes are believed to be important in the decay of the 9 stormtime ring current: charge exchange with neutral hydrogen and resonant interactions with ion-cyclotron waves .
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The isotropic distributions show significant flux decreases whenever the pitch angle scan of a measurement reaches the loss cone, implying the loss cones are nearly empty of particles. Such isotropic distributions with empty loss cones indicate a stably trapped particle populations undergoing negligible pitch angle diffusion into the loss cone.
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from regions of rounded distributions at higher values of E... In order for an E., , to be evident in the observed pitch I I,min angle distributions, pitch angle diffusion driven by resonant wave-particle interactions must have been the dominant loss process responsible for the rounding of the distributions.
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satisfy the condition for cyclotron I I,min resonance with ion-cyclotron wave when realistic cold plasma densities are assumed for the outer region of the plasmasphere during •I Q C 1 CO a storm recovery phase ' ' ' t Landau resonant diffusion of the ions is probably of little importance for these waves, since wave energy at large wave normal angles is needed for such diffusion and such wave energy is probably damped by low energy electrons . 51 52 Williams and Lyons ''"" concluded that the ion-cyclotron waves were amplified by the ring current particles as proposed by Cornwall et al.
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Thus their calculations imply that E., , should continually decrease as is observed. lI,min 3.2 Inconsistency with proton charge exchange 47 Tinsley has noted that the charge exchange lifetimes for equatorially mirroring protons at energies -30 keV should be on the order of hours.
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These lifetimes were obtained from a recent neutral hydrogen density model using parameters for Dec., 1971. At both L-values, the charge exchange calculations predict that the pitch angle distributions for 2 and 10 keV protons will become greatly anisotropic in <8 hours.
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Some form of pitch angle diffusion cannot account for the discrepancy in the shapes of the pitch angle distributions, since this would imply total loss rates even greater than those from charge exchange alone. 25 Lyons and Evans concluded that neither a strong, continual proton source between L=3 and 4 during the storm recovery nor a large error in the neutral hydrogen densities were a reasonable explanation for the observed discrepancy between the observations and the charge exchange predictions.
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IV. Summary and Future Directions ' While the dominant particle source and loss processes have yet to be understood throughout most of the magnetosphere, significant quantitative understanding of the quiet-time structure of radiation belt electrons O30 keVl and equatorially-mirroring protons CVLOO keV)
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Most of these observations have come from the equatorially orbiting Explorer 45 satellite, with some useful observations also obtained from OGO-5. Electrons with energies <30 keV have not yet been adequately studied, and the suggestion that harmonic waves from ground power distribution networks may affect these electrons needs to be evaluated, The Explorer 45 equatorial pitch angle distributions of ions, in conjunction with some low altitude observations of precipitating ions, have also given us significant information on the post-storm decay of ring current ions.
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However, identification and quantitative evaluation of the dominant source and loss processes outside the plasmapause will be impossible until equatorial pitch angle distributions as a function of particle energy and radial distance become available. Hopefully, some of the concepts that have been successfully applied to the inner region of the radiation belts, particularly
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. Until pitch angle distributions and good energy spectra become available from Jupiter, we will be unable to definitively identify which processes govern the distribution of Jovian trapped particles and to quantitatively analyze these processes.
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999 CUSP MAGNETOPAUSE GEOMAGNETIC TAIL FIGURE 1 Schematic illustration of the three components of trapped particle motion and relevant magnetospheric regions.
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by 35-70 I03 75-125 I02 120-240 10' 240-560 10° 35-70 10s 75-125 I02 120-240 10' 240-560 10° 35-70 I03 75-125 I02 120-240 10' 240-560 10° 35-70 I03 75-125 I02 120-240 10' 240-560 10° FIGURE 2 Fluxes of equatorially mirroring electrons versus universal time for the period Dec.
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For each energy, the line coding used for the Landau resonant diffusion coeff1cients corresponds to that for the sum of the cyclotronharmonic resonances, where the particle energy is indicated. Equatorial pitch-angle distributions, calculated using the diffusion coefficients shown in the f1gure, are displayed on the right-hand side (from Lyons et al., 1972)
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. FIGURE 6 Equilibrium distribution function f of equatorially mirroring electrons versus L at constant first adiabatic invariant M, with each curve normalized to the same value at L=5.5 (left panel)
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and quiet time observations of Pfitzer et al.
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382599~ CONSTANT ENERGY J I I I I II IT II 19 ? 0 21 22 23 IT II 19 20 21 22 23 II IT II II 20 21 22 23 100' -200r 16 IT II 19 20 21 22 December 1971 23 II IT II 19 20 21 December 1971 22 23 II IT II 19 20 21 22 tl December 1971 FIGURE 9 Distribution function, multiplied by 2 times the ion mass, for equatorially mirroring ions as a function of time throughout the period of the December 17, 1971 storm for 8 Explorer 45 energy channels.
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1H H lI'n ' ' 'r.' FIGURE 10 Equatorial ion pitch-angle distributions observed on Explorer 45 orbit 103 inbound, ~16 h after the minimum Dst of the December 17, 1971 storm main phase. Distributions are shown every 0.4 in L from L=3 to L=5, and selected ion energy channels are stacked vertically at each L
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FIGURE 11 Same as Figure 10, except for Explorer 45 orbit 104 inbound, ~24 h after the minimum Dst of the storm main phase (from Joselyn and Lyons, 1976)
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FIGURE 12 Equatorial pitch angle distributions at L=3 observed during the recovery phase of the Dec. 17, 1971 storm are compared with those expected to evolve from proton charge exchange with neutral hydrogen.
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1 jj jj- j 1 If II In III W 99 ft Ifl II r n H In Ii ) 0 90 I8 0 0 90 I80 0 90 18 OBSERVED lOkeV PREDICTED OBSERVED 2 keV PREDICTED Pitch Angle (Degrees)
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M., On the role of charge exchange in generating unstable waves in the ring current, JGR, 1976 (in press)
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R Lyons, Ion cyclotron wave growth calculated from observations of the proton ring current during storm recovery, JGR, 81, 2275, 1976.
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J Williams, Storm associated variations of equator ially mirroring ring current protons, 1-800 keV, at constant first adiabatic invariant, JGR, 81, 216, 1976.
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and L J, Lanzerotti, Particle Diffusion in the Radiation Belts, Springer, Heidelberg, 1974.
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A Fritz, Energetic ionized helium in the quiet time radiation belts, (in preparation)
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