ASEN 5335 Aerospace Environments -- Radiation Belts Mercator Projection of Guiding Center Motion in the Radiation Belts Plasma particles will gyrate, bounce and longitudinally drift ions will longitudinally drift west electrons will longitudinally drift east ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts Second Adiabatic Invariant (Longitudinal Invariant) where ds means integration along B and B = BM at M1, M2. The second adiabatic invariant says that the integral of parallel momentum over one complete bounce between mirror points is constant (this once again results from no external forces): Since Second adiabatic invariant and m,v are constant, then ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts The second adiabatic invariant (I2 = const) assumes that B does not change appreciably during 1 bounce period (about 1 second). I2 is a property of the field configuration and also of the mirror point (or equivalently, the equatorial pitch angle) since I2 = const defines the surface, or shell, on which the particle remains as it drifts around the earth. This is called the longitudinal invariant surface or L-shell. Recall our previous discussion of the L-shell and its connection with invariant latitude. ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts Second Adiabatic Invariant and McIlwain (B-L) Coordinates I2 is function of position and proportional to the field-line length between the mirror points (once pitch angle is defined we know the mirror points). While there are other lines of force with similar I2 values, there is only one line where the particle can satisfy the conditions B=BM and I2 = I0 McIlwain (1961) modified this description to make it more physical by creating the L-parameter that is a function of B and I2 ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Geomagnetism The B-L Coordinate System: Curves of Constant B and L The B-L coordinates implicitly incorporate the first and second invariant motions of radiation belt plasmas and are, therefore, the natural coordinates to best organize radiation belt plasma populations ASEN 5335 Aerospace Environments -- Geomagnetism

ASEN 5335 Aerospace Environments -- Radiation Belts Invariant Latitudes associated with L-shell values By analogy with our previous formula for calculating the dipole latitude of intersection of a field line with the earth's surface, we can determine an invariant latitude, L , in terms of L-value: ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts Third Adiabatic Invariant The third adiabatic invariant, or flux invariant, states that the magnetic flux enclosed by the charged particle longitudinal drift must be a constant: (This is analogous to the previous application of Faraday’s law, except in this case is due to longitudinal drift of particle) In other words, as B varies (with longitude), the particle will stay on a surface such that the total number of field lines enclosed remains constant. However, since most temporal fluctuations in B occur over time scales short compared to the longitudinal drift period (~ 30-60 minutes), the assumptions underlying this invariant law are usually not obeyed. ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts Violations of the Invariant Constraints The adiabatic invariants are said to be violated when electric or magnetic field variations take place near or above the adiabatic motion frequency in question, i.e., 1/Tgyro, 1/Tbounce, 1/Tdrift For instance, violation of the third invariant permits transport of the particles across field lines. If these violations occur frequently enough, in a statistical sense the net result can be thought of as radial diffusion. Similarly, the paths of radiation belt particles are affected by collisions with neutral atoms and by E-M interactions of plasma waves. On time scales short compared to Tgyro and Tbounce, these interactions manifest themselves statistically in what is called pitch angle diffusion. (leading to diffusion into the loss cone.) ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts Radial diffusion transports radiation belt particles across the di-polar-like magnetic field lines in the radial direction. Pitch angle diffusion alters the particle pitch angle (or equivalently, the mirror point location). In both cases the earth's atmosphere is a sink; for radial diffusion by transport to very low L-shells, and for pitch angle diffusion by lowering the mirror points into the atmosphere. A conceptual representation of pitch angle and radial diffusion in Earth’s radiation belts. Diffusion occurs in either direction, but in most cases there is a net diffusion flux towards the atmosphere, because that is where the net sink is. ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts Obviously trapping is not perfect, and there exist mechanisms for introducing particles into the radiation belts, as well as loss mechanisms. Before discussing these mechanisms, let us get a rough idea of the distributions of particles and their energies. The Pioneer-3 spacecraft carried a geiger counter to measure cosmic rays. However, there were times when the counter became saturated, and Van Allen and his group correctly concluded that this was the result of energetic particles. On the basis of these measurements, the 'radiation belts' were defined, at that time consisting of an inner zone and an outer zone. ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts However, things are not so simple; actually the "zones" depend on the energy and type of particle. (Note: 1 eV = K.E. a charged particle gains by being accelerated through a potential difference of 1 Volt = 1.602 x 10-12 erg ) ASEN 5335 Aerospace Environments -- Radiation Belts

Sources and Sinks of Radiation Belt Particles The following processes are involved: injection of charged particles into the trapping region acceleration of particles to high energy diffusion within the region loss processes removing particles from the trapping region ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts Inner-Zone ( ≤ 2.5 RE ) Production Mechanisms About 10% leave the atmosphere -- “albedo neutrons” Cosmic rays protons with ---> energies > 1 GeV Impinge on neutral atoms ---> free neutrons Galactic Cosmic Ray Proton Collision Electron Decay Proton neutron atmosphere Decay half-life ~ 12 min H+ + e- proton + electron + neutrino (production of ≥50 MeV energetic particles (L ~ 1.5) that can now be trapped.) Somewhat lower energy protons enter radiation belts via radial diffusion, dominant for L > 1.8. This is how particles enter during magnetic storms when the day-side field is compressed. ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts Inner-Zone ( ≤ 2.5 RE ) Loss Mechanisms Coulomb collisions Charge Exchange : ≥100 KeV escapes Basis for ENA measurements nuclear collisions (most typical for 75 MeV protons) loss cone scattering protons with large gyro-radii enter atmosphere at mirror points ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts Outer Zone L ≥ 3 RE Source : Most are probably solar wind/magnetospheric particles (in the case of H+) which have undergone acceleration, for instance in the tail region. Indirect evidence for this lies in the strong correlation with solar activity (see following figure). -- In the case of O+, source is probably the ionosphere Loss Mechanism : Pitch angle diffusion, i.e., plasma waves cause violation of the first adiabatic invariant, implying diffusion into the loss cone and entry into the atmosphere. Note: High-energy protons are not found in the outer belts because their gyroradii mv/qB are very large (100’s to 1000’s of km), and at the mirror points the gyroradii are large enough to bring them into the atmosphere. Only low-energy protons can remain at high altitudes. The high-energy protons only remain trapped where B is large. ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts

Radiation Belt Observations by SAMPEX ASEN 5335 Aerospace Environments -- Radiation Belts

ENERGETIC PARTICLE/RADIATION NOMENCLATURE There exist several ways to express particle flux (J): J(E) = unidirectional differential intensity (particles/cm2/s/sr/MeV) = flux of particles (# / time) of a given energy per unit energy level in a unit solid angle about the direction of observation, incident on a unit area perpendicular to the direction of observation. J(>E) = unidirectional integral intensity steradian (sr) = angle subtended at the center of a sphere of unit radius by unit area of the surface of a sphere = unit of solid angle. The solid angle encompassing all directions at a point is given by the total area of a circumscribed sphere 4pr2 divided by the radius squared, or 4p sr. ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts J(>E) = unidirectional integral intensity = intensity of particles with energy greater than a threshold energy E = = particles/cm2/s/sr Omnidirectional intensities are J(E) or (J>E) integrated over 4 steradians solid angle. Omnidirectional Units J(E) particles /cm2/s/MeV (J > E) particles/cm2/s E Differential energy spectrum Integral ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts Very often, the omnidirectional fluxes are expressed as or where Eo = spectral e-folding energy and spectral index. These representations will be used later when we discuss shielding. ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts The trapped flux environment specification models currently in use at NASA are -- AP8MAX, AP8MIN: proton models, solar max/min -- AE8MAX, AE8MIN: electron models, solar max/min These models are based largely on satellite data taken between 1960 and 1970; consequently, given the secular variation in earth's magnetic field, one must use the proper epoch magnetic field, i.e., -- IGRF 1960 80-term model for SSMIN -- Hurwitz USCGS 1970 field for SSMAX Due to the tendency to obey the adiabatic invariants, the two parameters B and L (or equivalently, the invariant latitude) form a convenient 2-dimensional space upon which to map 3-dimensional particle flux distributions. Some examples from the AP8 and AE8 models follow. ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts The "uncertainty" generally attributed to these models is about a factor of two for 2 to 5 year averages. Invariant latitude ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts

The steady decay of flux levels in this figure is due to the decay of residue from the artificial Starfish injection event (1.4-megaton nuclear explosion) of July 9, 1962, 248 mi. over Johnston Island.

ASEN 5335 Aerospace Environments -- Radiation Belts Starfish Injection Event Widespread aurora occurred in the central Pacific. Within a few days, the trapped energetic particles damaged solar panels on several weather and communications satellites. Within 7 months, Starfish destroyed 7 satellites due to solar cell damage. Effects of Starfish lasted until the early 1970’s. Telstar was Launched 1 day after Starfish, and was the first satellite failure due to radiation exposure. Telstar received a total radiation dose 100 times that expected. ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts South Atlantic Magnetic Anomaly Near the coast of Brazil, a decrease in the intensity of earth's magnetic field exists called the South Atlantic Magnetic Anomaly. This causes an increase in the energetic particle fluxes encountered, for instance, at LEO. Proton fluxes near 300 km associated with the anomaly are shown in the following figure, with the ground track of a 30° inclination satellite superimposed. Since the magnetic field is weaker, and particles mirror at a constant magnetic field strength, these particles find themselves mirroring at much lower altitudes in this geographical region. ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts In addition to the SAA, in LEO, radiation belt particles are also encountered at high latitudes. satellite orbit particles from the low-altitude extension of the radiation belts (or "horns") are apparent at high latitudes. ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts NASA Radiation Belt Mappers Mission Mission Planning: Launch 2012 multiple spacecraft configuration Mission Objectives Obtain scientific understanding of the sources, transport and losses of radiation belt particles with special emphasis on penetrating radiation during geomagnetic storms Acquire the data required for the development of empirical and science-driven radiation belt models Acquire the data for real time telemetry needed by the operations community ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts Additional Slides ASEN 5335 Aerospace Environments -- Radiation Belts

ASEN 5335 Aerospace Environments -- Radiation Belts This figure illustrates about a year's worth of hourly 1.9-MeV omnidirectional electron fluxes at L=6.6 at the equator at midnight. -- Note the variation about the AE Model value (represented by the horizontal line) -- Note the bias towards the large magnetic storms as a result of averaging fluxes for the model ASEN 5335 Aerospace Environments -- Radiation Belts