1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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 (~ minutes), the assumptions underlying this invariant law are usually not obeyed.
ASEN 5335 Aerospace Environments -- Radiation Belts

8. 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

9. 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

10. 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

11. 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 = x erg )
ASEN 5335 Aerospace Environments -- Radiation Belts

12. 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

13. 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 > This is how
particles enter during magnetic storms when the
day-side field is compressed.
ASEN 5335 Aerospace Environments -- Radiation Belts

14. 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

15. 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

16. ASEN 5335 Aerospace Environments -- Radiation Belts

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

18. 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

19. 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

20. 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

21. 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 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

22. 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

23. ASEN 5335 Aerospace Environments -- Radiation Belts

24. 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.

25. 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

26. 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

27. ASEN 5335 Aerospace Environments -- Radiation Belts

28. 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

29. 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

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

31. 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