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Equatorial field intensity in recent millenia, as deduced from
measurements on archeological samples and recent observatory data.
~10 nT/year
Reversals have been documented as far back as 330 million years. During that time more
than 400 reversals have taken place, one roughly every 700,000 years on average.
However, the time between reversals is not constant, varying from less than 100,000
years, to tens of millions of years. In recent geological times reversals have been
occurring on average once every 200,000 years, but the last reversal occurred 780,000
years ago. At that time the magnetic field underwent a transition from a "reversed" state
to its present "normal state".
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Alfred Wegener
"The Origin of Continents and
Oceans" [Wegener, 1929]
Map of magnetic striping of the
seafloor near the Reykjanes
ridge [Heirtzler, 1968]
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A radiation belt is a population of energetic particles fairly-trapped by the magnetic field.
2
The Radiation Belts
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A radiation belt is a population of energetic particles fairly-trapped by the magnetic field.
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Review of Charged Particle Motions
• Gyromotion motion: =p2/2mB (1st), T_g~10-3 sec
• Bounce Motion: J= p||ds
(2nd), T_b~100 sec
• Drift motion: =BdA
(3th) , T_d~103 sec
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According to Faraday's Law of Magnetic Induction,
a time rate of change of magnetic flux will induce an electric field
( and hence a force on the particle ):

B   E dl

t
   BdA
B


dl
Therefore, the requirement that no forces act in the direction of
motion of the rotating particle demands that
 B
0
t
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In other words, that the magnetic flux enclosed by the
cyclotron path of the charged particle is constant:
 B   B dA const
Assuming B does not vary spatially within the gyropath,
2
 B  B dA Br
mv 
where r = gyroradius =
. We previously defined
qB
the magnetic moment
2
mv
1


2 B
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,
implying
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First Adiabatic Invariant
Note: same as
saying that K.E.
does not
change
if there are no
forces parallel
to v
m 2 v 2  2 m
 B    2 2 B  2   const
q
q B 
Or,  = constant . This is called the first adiabatic invariant of
particle motion in a magnetic field.
We should note that the above has assumed that  is
constant within at least one orbital period of the particle. This is
only approximately true, and the term "invariant" is also an
approximation, but one that reflects the first-order constraints on
the particle motion.
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Since
1
2
mv  const
2
, (i.e, the K.E. of the particle
remains constant since the only forces act  to V), then  must
increase as B increases, and correspondingly the distribution of K.E.
between
v
and
v||
v
changes:

 v sin
v  v co s
||
If  increases to 90° before the particle collides vigorously with the
neutral atmosphere, the direction of v
will change sign (at the
"mirror point") and the particle will follow|| the direction of decreasing
B.
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For a given particle the position of the mirror point is
determined by the pitch angle as the particle crosses the equator
(i.e., where the field is weakest) since
sin2 
 const 
B

sin2  eq
Beq
B 
M sin2 
Beq
1

BM
eq
Therefore, the smaller eq the larger BM , and the lower down in
altitude is the altitude of BM.
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Loss Cone and Pitch Angle Distribution
Particles will be lost if they encounter the atmosphere
before the mirror point.
Obviously this will happen if eq is
too small, because that then
requires a relatively large BM (|B| at
the mirror point).
The equatorial pitch angles
that will be lost to the atmosphere
at the next bounce define the loss
cone, which will be seen as a
depletion within the pitch angle
distribution.
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B
loss
cone
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Magnetic Mirroring in a Dipolar magnetic Field
Trajectory of particle
inside the loss cone.
this particle will
encounter
the denser parts of the
atmosphere (I.e., below
100 km) and precipitate
from the radiation belts.
Trajectory of particle
outside the atmospheric
bounce loss cone. This
particle will bounce
between mirror points
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Second Adiabatic Invariant (Longitudinal Invariant)
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):

M2
M1
2mv|| ds  const
where ds means integration along B and B = BM at M1, M2. Since
1/2
 B 
2 1/2
v||  v cos  v (1  sin  )
 v 1
 BM 
1/2
M2
B 
and m,v are constant, then

I   1
ds  const
2


BM
M1
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second
adiabatic
invariant
14
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
Beq
B
M
 sin2  eq
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 Lshell. Recall our previous discussion of the L-shell and its
connection with invariant latitude.
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The Earth’s magnetic field is compressed on the dayside
and drawn out on the night-side, so that the field
configuration is zonally asymmetric
solar
wind
How does this affect particles as they drift around the Earth ?
Since the dominant adiabatic invariant governing particle motion is different
for low and high pitch angle particles, we consider these separately.
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Review of Adiabatic Invariants 1 & 2
First adiabatic
Invariant:
2


1
sin

2
  mv 
 = constant
2
 B 
[K.E. (& magnetic moment) of particle
remains constant]
Second adiabatic
Invariant:
1/2
M2
B 

I   1
ds  const
2


B
M
M1
(integral of parallel momentum over one
complete bounce between mirror points is
constant)
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High Pitch Angle Particles
High pitch angle particles have mirror points not far from the
equator. They are mostly affected by the magnitude of the B-field.
High pitch angle particles originating on the night-side, when drifting to
the dayside, keep moving radially outward to stay at a constant B-value,
since the dayside field is compressed with respect to the night-side field.
By the time these particles reach
the noon meridian, they reach the
boundary of the magnetopause
and are lost.
High pitch angle particles originating
on the dayside similarly descend on
the night-side, but since they have
such large pitch angles, they are
not lost.
The above introduces a drift loss cone at high pitch angles at nighttime.
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Low Pitch Angle Particles
Low pitch angle particles travel long distances along a field
line; the second adiabatic invariant is important for these particles.
They try to stay on field lines whose lengths are about the same for a
given BM .
At a given equatorial distance from
Earth, day-side field lines are longer
than night-side field lines.
A low pitch angle particle on the
(mainly outer) day-side field lines,
when drifting over to the night-side,
will seek higher and higher field lines.
These particles can find themselves
on open field lines on the night-side
or be lost by other processes.
The above introduces a drift loss cone at small pitch angles at daytime.
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Pseudo-Trapping Regions; Shell-Splitting
These particles,
REGIONS
OF
AND
These
particles, with high
with high
pitch STABLE
Thus, there are some
pitch angles beyond ~7 RE
angles, descend
regions from which
are lost on the day-side
on the night-side,
PSEUDOTRAPPING
trapped particles are but since they
such large
unable
to stable
maketrapp
a in g reghave
• The
ion is d efin ed as
angles,
complete
of th epitch
th e vcircuit
olume within
Earth’s mag netic
they are not lost,
field
where
p
articles
drift
n clo sed
the earth, being lost ando return.
p ath s arou nd th e Earth .
en route
in the
• There are also two regio ns o f
magnetotail
or in which particles can
p seu do trapp ing
beyondd rift
the
fo r so me d istance before b ein g lost
to th e mag neto sheath
magnetopause.
• The
htsid pe seu do trapp ing
regio n is
These
arenig
called
These
particles,
created by large p itch ang le particles
the pseudofo llo wing co nstan t with
B consmall
tou rs
trapping regions.
pitch angles,
•
The dayside trapp ing region is created
mirroring
b y small p itch ang leand
particles
th at are
at
low
altitudes,
This phenomenon
lo st on to op en field lin es of th e tail lob e
are lost on the
is referred
to and
as lo cation
• The size
s of these reg io ns
night-side
ch an ges as the field ch ang es in respo nse
shell-splitting.
to th e solar win d
These particles return to the night-side
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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:
 B   BdA  const
(This is analogous to the application of Faraday’s law on p. 4,
except in this case  t 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.
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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.)
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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.
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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 Explorer I 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.
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A Schematic View of the
Locations of Radiation Belts
• Blue: inner belt, >100MeV
protons, rather stable
• Purple: outer belt, 100s keV
and MeV electrons and ions
not stable at all
• Slot region in between
• Yellow: ACRs, stable
• White line: Earth’s magnetic
field, approx. by a dipole
field
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Asymmetrical magnetic field
and SAAdrift loss cone
 The Earth’s magnetic field azimuthally
asymmetrical with internal and external factors.
 The internal magnetic field is sometimes
approximated as an off-centered and titled dipole.
 The magnetic field strength is much weaker at
the south Atlantic area, called the South Atlantic
Anomaly (SSA). It is a large sink of radiation belt
particles. It results in the drift loss cone in the
particle pitch angle distribution.
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SAMPEX measured Anomalous Cosmic Ray Particles (Oxygen Nuclei, >200 keV/nucl)
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Aerospace Environment
ASEN-5335
• Instructor: Prof. Xinlin Li (pronounce: Shinlyn Lee)
• Contact info: e-mail: [email protected]
(preferred)
phone: 2-3514, or 5-0523, fax: 2-6444,
website: http://lasp.colorado.edu/~lix
• Instructor’s office hours: 9:00-11:00 am Wed at
ECOT 534; before and after class Tue and Thu.
• TA’s office hours: 3:15-5:15 pm Wed at ECAE 166
• Read Chapter 4&5 and class notes
• HW4 due 3/13
• Quiz-4 today, close book.
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Sources and Sinks of Radiation Belt Particles
The following processes are involved:
 Injection of charged particles into the trapping region
 Radial diffusion or radial transport within the region
 Local acceleration of particles to high energy
 Loss processes removing particles from the trapping region (loss through
magnetopause and loss by precipitating into atmosphere).
Inner Zone < 2.5 RE
Production: Galactic cosmic-ray proton impinge on neutral atoms neutron
decay (half life time ~ 10 min)  proton and electron.
Loss Mechanisms: Coulomb collisions  loss cone scattering
Charge exchange  Energetic neutron escapes
(H+ energetic + H  Henergetic + H+)
These processes explains well the inner proton belt.
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There are 3 types of cosmic rays of interest here:
Galactic Cosmic Rays
Anomalous Cosmic Rays
Solar Energetic Particles
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Cosmic Rays
 Cosmic rays are high energy charged particles, originating in outer space, that travel at nearly the
speed of light and strike the Earth from all directions. Most cosmic rays are the nuclei of atoms,
ranging from the lightest to the heaviest elements in the periodic tables, but dominated by protons
(89% hydrogen, 10% helium, and about 1% heavier elements). Cosmic rays also include high
energy electrons, positrons, and other subatomic particles.
 The term “cosmic rays” usually refers to galactic cosmic rays, which originate in source outside
the solar system, distributed throughout and possibly beyond our Milky Way galaxy.
Studying the energetic particle population is very important for two reasons:
 These particles represent considerable hazard for both humans and radiation-sensitive
systems in space, because they can penetrate through large amount of shielding materials.
 They carry information about the large-scale properties of the heliosphere and the galaxy.
Discovery and Early Research: Cosmic rays were discovered in 1912 by Victor Hess, when he
found that an electroscope discharged more rapidly as he ascended in a balloon. He attributed
this to a source of radiation entering the atmosphere from above, and in 1936 was awarded the
Nobel prize for his discovery. For some time it was believed that the radiation was
electromagnetic in nature (hence the name cosmic “ray”). However, during the 1930’s it was
found that cosmic rays must be electrically charged because they are affected by the Earth’s
magnetic field (How was this known?).
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Cosmic Ray Energies and
Acceleration
 The energy of cosmic rays is usually measured
in units of MeV and GeV. Most galactic cosmic
rays have energies between 100 MeV
(corresponding to a velocity of protons of 43% of
the speed of light) and 10 GeV ( 99.6% of the
speed of light). The highest energy cosmic rays
measured to date have had more than 1020 eV,
equivalent to the kinetic energy of a baseball
traveling at about 100 mph!
 It is believed that most galactic cosmic rays
derive their energy from supernova explosions,
which occur approximately once every 50 years
in our Galaxy. To maintain the observed intensity
of cosmic rays over millions of years requires that
a few percent (even >10%) of the more than 1051
ergs released in a typical supernova explosion be
converted to cosmic rays.
The energy contributed to the Galaxy by cosmic
rays (~1eV/cm3 ) is about that contained in
galactic magnetic fields, and in the thermal
energy of the gas that pervades the space
between the stars,
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Cosmic Rays in the
Galaxy
 Because cosmic rays are electrically charged
they are deflected by magnetic fields, and their
directions have been randomized, making it
impossible to tell where they originated. However,
cosmic rays in other regions of the Galaxy can be
traced by the electromagnetic radiation they
produce. Supernova remnants such as the Crab
Nebula are known to be a source of cosmic rays
from the radio synchrotron radiation emitted by
cosmic ray electrons spiraling in the magnetic
fields of the remnant.
 Observations of high energy (10 MeV – 1000
MeV ) gamma rays resulting from cosmic ray
collisions with interstellar gas show that most
cosmic rays are confined to the disk of the
Galaxy, presumably by its magnetic field.
Observations show that, on average, cosmic rays
spend about 10 million years in the Galaxy before
escaping into inter-galactic space.
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Show above is an image of the Crab Nebula
in the X-ray band. In the center lies the
powerful Crab pulsar, a spinning neutron
star with mass comparable to our Sun but
with the diameter of only a small town. The
pulsar expels particles and radiation in a
beam that sweeps pass the Earth 30
times/sec. The supernova that created the
Crab Nebula was seen by ancient Chinese
astronomers and possibly even the Anasazi
Indians in 1054, perhaps glowing for a week
as bright as the full moon.
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Differential Flux
Particles
m 2 s  sr  (MeV / nucleon)
101
100
10-1
The figure to the right
Illustrates differential energy
spectra for GCR outside the
magnetosphere at maximum
and minimum solar activity.
10-2
10-3
10-4
GCR typically consists of
108-109 eV particles, but
some GCR particles can
have energies as high as
1020 eV.
SSMIN
10-5
SSMAX
10-6
10-7
101
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102
103
104
105
kinetic energy (MeV/nucleon)
106
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Cosmic Rays in the Solar System
 Just as cosmic rays are deflected by the magnetic field in interstellar space, they are
also affected by the IMF embedded in the solar wind, and therefore have difficulty
reaching the inner solar system. Spacecraft venturing out towards the boundary of the
solar system have found that the intensity of galactic cosmic rays increases with distance
from the Sun. As solar activity varies over the 11 year solar cycle the intensity of cosmic
rays at Earth also varies, so does the inner radiation belt particles, in anti-correlation with
the sunspot number. Ionosphere expansion also plays a key role …..
SAMPEX measured protons (19-27.4 MeV) and the sunspot numbers
 The Sun is also a sporadic source of cosmic ray nuclei and electrons that are accelerated
by shock waves traveling through the corona, and by magnetic energy released in solar
flares. The solar particle events are more frequent during the active phase of the solar cycle.
The maximum energy reached in solar particle events is typically 10 to 100 MeV,
occasionally reaching 1 GeV (roughly once a year) to 10 GeV (roughly once a decade). Solar
energetic particles can be used to measure the elemental and isotopic composition of the
Sun, thereby complementing spectroscopic studies of solar materials.
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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.
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 Since the beginning of the space age, it
was known that two main sources of
energetic particles that pervade the
interplanetary space:
Anomalous Cosmic Rays
(ACRs)
(a) Galactic Cosmic Rays (GCR),
originated from supernova explosions,
which occur approximately once every 50
years in our galaxy.
(b) Solar Energetic Particles (SEP) , from
solar flares or CME.
So the Anomalous Cosmic Rays (ACRs)
belong to neither of them by definition.
 In 1973, the anomalous excesses of
several elements in low-energy cosmic
rays led to the discovery of this so called
ACRs.
For Examples: O/C > 30, He/H>1
 Fisk et al. [1974] proposed the origin of
the ACRs.
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Origins of ACRs
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A Schematic View of the
Locations of Radiation Belts
• Blue: inner belt, >10MeV
protons, rather stable
• Purple: outer belt, 100s keV
and MeV electrons and ions,
not stable at all
• Slot region in between
• Yellow: ACRs, stable
• White line: Earth’s magnetic
field, approx. by a dipole
field
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Origin of Anomalous Cosmic Rays
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Trapping ACRs
 ACRs singly charged, picked up
by solar wind, heading to the
termination shock, where some of
them can be further energized
and some of them come back.
 Gyroradius inversely
proportional to the number of the
charge. A singly charged ion can
be further stripped of its electrons
when it happens to skim the
Earth’s atmosphere, the
gyroradius is reduced many times
and the ion can become trapped.
 This scenario was predicted far
in advance [Blake et al., 1978].
 First evidence from Russian
COSMOS satellites.
SAMPEX pin pointed the location
of the narrow belt of ARCs.
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Solar Cycle
Variations of ACRs
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Sinks of ACRs
Loss Mechanisms: Coulomb collisions  loss cone scattering
Charge exchange  Energetic neutron escapes
SAA is the largest sink.
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The SAMPEX
(Solar Anomalous and Magnetospheric
Particle Explorer) Satellite Mission
Launched July 3, 1992; Polar elliptical non-Sun-synchronous Orbit;
inclination 82°, 520 km x 670 km (now at about 450x550)
SAMPEX was designed to study energetic particles in the geospace
environment, including GCR and ACR.
SAMPEX discovered a new "radiation belt" consisting of trapped
Anomalous Cosmic Ray particles.
The ACR of order > 15 MeV are capable of penetrating farther into the
magnetosphere than the multiply-charged GCR of similar energy.
They then become trapped. (The GCR stop at higher L-shells and
enter the atmosphere)
The ACR belt is located around L = 2, or within the inner van Allen
proton radiation belt.
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THE FOLLOWING FIGURE ILLUSTRATES THE GEOGRAPHICAL
DISTRIBUTION OF OXYGEN IONS DETECTED BY SAMPEX,
WHICH CONSIST OF THREE DISTINCT POPULATIONS:
1. For latitudes > 60° there is a mixture of GCR and ACR which have
directly penetrated the magnetic field.
2. Between 50° and 60° there is a mid-latitude component composed
of multiply-ionized ACR, and also possiblely highly-charged GCR. The
cutoff latitude is strongly dependent on the charge states.
3. A 8000 km-long band southeast of the South Atlantic Anomaly (L is
about 2 here).
Note: The following figure is given in terms of cutoff energy. For cosmic rays to reach a
spacecraft in Earth orbit, they must penetrate the Earth’s magnetic field, which tends to
deflect the (charged) particles. However, this tendency is opposed by the energy of the
particles as they move at high velocity towards the Earth. A particle’s penetrating ability
is determined by its momentum divided by its charge, and this quotient is referred to as
its ‘magnetic rigidity’. A cosmic ray will require a minimum magnetic rigidity to reach
each point within the Earth’s magnetic field. Particles below the minimum will be
deflected and this minimum is called the geomagnetic cutoff value.
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SAMPEX Observations of Untrapped Oxygen Ions
This figure
illustrates
one of the
important
causes of
spatial
variability of
cosmic
radiation -the geometry
of the
terrestrial
magnetic
field.
There is
also a
height-dependent shielding provided by the atmosphere.
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Outer Zone L ≥ 3 RE
Source : Most 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.
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Outer Radiation Belt Observations by SAMPEX (Solar
Anomalous and Magnetospheric Particle Explorer)
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(Courtesy of M. Looper)
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ENERGETIC PARTICLE/RADIATION NOMENCLATURE
There exist several ways to express particle flux (J):
J(E)
=
unidirectional differential intensity
(particles/cm2/s/str/MeV)
J(>E)
=
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.
=
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 4r2 divided by the radius squared, or 4 sr.
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Very often, the omnidirectional fluxes are expressed as
J(E)  J E
o
J( E)  J

J  Jo exp  E E
o
or
J  Jo Eo exp  E E
o


1
E
o
 1
 
or
 
where Eo = spectral e-folding energy and 
spectral index.
These representations will be used later when we discuss shielding.
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J(>E)
=
unidirectional integral intensity
=
intensity of particles with energy greater
than a threshold energy E
=

 J (E)dE
E
=
particles/cm2/s/str
Omnidirectional intensities are J(E) or (J>E) integrated
steradians solid angle.
over
4
Omnidirectional Units
J(E)
particles
/cm2/s/MeV
Differential
energy
spectrum
(J > E)
particles
/cm2/s
E
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Integral
energy
spectrum
E
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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.
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Invariant
latitude
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The AP8 and AE8 Models also contain some local time
dependencies; although these were derived by "binning" data from
several satellite missions, there are many regions of spotty data
coverage.
The "uncertainty" generally attributed to these models is
about a factor of two for 2 to 5 year averages.
It is important to note that these models represent average
statistical distributions, and there exists much variability about such
mean values.
The following figure illustrates about a year's worth of
hourly 1.9-MeV omnidirectional electron fluxes at L=6.6 at the
equator during 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
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The following figure illustrates 10-day average electron
fluxes for energies > .28 MeV, for several L-values.
Inside L=1.8 (generally referred to as the inner electron zone) the
time variations are quite small, demonstrating the usefulness of an
average model in this region.
In contrast, outside L = 1.8, the fluxes at L = 2.2 vary greatly with
time due to geomagnetic activity.
The steady decay of flux levels in this figure is due to the decay
of residue from the artificial Starfish injection event (nuclear explosion)
of July, 1962.
-- 1.4 megaton nucelar explosion 248 miles over Johnston
Island on July 9, 1962
-- 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
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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.
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The CRRESRAD Model
Based upon the CRRES (Combined Release and Radiation
Effects Satellite) Mission.
-- complete complement of radiation environment
sensors (dosimeter, e- and H+ monitors, etc.)
-- July 25, 1990 - 12 October 1991;
18.1°, 350 km x 33,000 km orbit (a.k.a Geotransfer orbit)
PC- based software program that provides estimates of the
dose behind 4 shielding thicknesses of hemispherical aluminum
shielding (0.57, 1.59, 3.14, and 6.08 gm/cm2) --- corresponding to
electron energies > 1, 2.5, 5, and 10 MeV and proton energies > 20, 35,
52, and 75 MeV. Different levels of magnetic activity are included.
Comparisons indicate that in some cases the differences
between CRRESRAD and equivalent results for AP8 and AE8 can be
substantial (see following figures).
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Comparison of dose rate along magnetic equator as a
function of L for quiet and active CRRES dose models and
for AP8MAX.
Due to variable
Proton belt L = 2- 4
In CRRES, not in AP
L-Shell (in RE)
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Comparison of dose rate along magnetic equator as a function
of L for quiet and active CRRES dose models and for
AP8MAX/AE8MAX.
ACTIVE CRRES MAP
Absence of
> 5 MeV
Electrons in
AE model
L-Shell (in RE)
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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.
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In addition to the SAA,
in LEO, radiation belt
particles are also
encountered at
high latitudes.
particles from the lowaltitude extension of the
radiation belts (or "horns")
are apparent at high
latitudes.
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SOLAR ENERGETIC PARTICLES
As discussed
previously in
connection
with solar
flares, a few
times each
solar cycle,
SCR's
consisting of
electrons,
protons and
heavy nuclei
can achieve
energies of
107 - 109 eV
(10-100 MeV)
during large
flares.
Flare-associated energetic particle events are associated with a
number of descriptive phrases:
solar cosmic rays (SCRs) solar proton events
solar electron events
polar cap absorption (PCA) events
ground-level events (GLEs)
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Exposure to GCRs/SCRs
------------------------------------------------------------------------------high-altitude/polar |
geostationary orbits
|
unattenuated exposure
----------------------- |---------------------------------------------low-altitude
|
polar orbits
|
intermittent exposure
----------------------- |---------------------------------------------low-altitude/low- |
well shielded
inclination orbits |
up to 10 MeV
----------------------- |---------------------------------------------low-altitude/
|
well shielded
equatorial orbits |
up to 10 GeV
-------------------------------------------------------------------------------Low-altitude low-inclination orbits experience almost no dose variations due to the
strong shielding imposed by the combined effects of the atmosphere and geomagnetic
field.
NOTE: For very thin shields (< .3g/cm2) trapped electrons are more important than
trapped protons (critical during EVAs).
NOTE: the very high energy GCR can pass through human tissue with almost no effect.
The particles that do pose danger are those that are stopped by tissue. As these
particles decelerate, their energy is converted to EM radiation. This radiation can
ionize atoms, in a crew member's body for instance.
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Mars and Venus have only some spotty magnetic fields; Mercury has weak
magnetic fields, and no radiation belts. All the giant outer gas planets possesses
radiation belts.
The Pioneer and Voyager 1 and 2 spacecraft encounters with Jupiter
have led to the first model Jovian radiation belt models, below.
Contours for electron fluxes above
1 MeV at Jupiter
>> Earth (~104) for 1 MeV
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Contours for proton fluxes above
1 MeV at Jupiter
Comparable to Earth for 1
MeV at lower L-shells (RE)
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Differential Flux
Particles
m 2 s  sr  (MeV / nucleon)
101
100
10-1
The figure to the right
Illustrates differential energy
spectra for GCR outside the
magnetosphere at maximum
and minimum solar activity.
10-2
10-3
10-4
GCR typically consists of
108-109 eV particles, but
some GCR particles can
have energies as high as
1020 eV.
SSMIN
10-5
SSMAX
10-6
10-7
101
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103
104
105
kinetic energy (MeV/nucleon)
106
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Cosmic Rays in the Solar System
 Just as cosmic rays are deflected by the magnetic field in interstellar space, they are
also affected by the IMF embedded in the solar wind, and therefore have difficulty
reaching the inner solar system. Spacecraft venturing out towards the boundary of the
solar system have found that the intensity of galactic cosmic rays increases with distance
from the Sun. As solar activity varies over the 11 year solar cycle the intensity of cosmic
rays at Earth also varies, so does the inner radiation belt particles, in anti-correlation with
the sunspot number. Ionosphere expansion also plays a key role …..
SAMPEX measured protons (19-27.4 MeV) and the sunspot numbers
 The Sun is also a sporadic source of cosmic ray nuclei and electrons that are accelerated
by shock waves traveling through the corona, and by magnetic energy released in solar
flares. The solar particle events are more frequent during the active phase of the solar cycle.
The maximum energy reached in solar particle events is typically 10 to 100 MeV,
occasionally reaching 1 GeV (roughly once a year) to 10 GeV (roughly once a decade). Solar
energetic particles can be used to measure the elemental and isotopic composition of the
Sun, thereby complementing spectroscopic studies of solar materials.
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Trapping ACRs
 ACRs singly charged, picked up
by solar wind, heading to the
termination shock, where some of
them can be further energized
and some of them come back.
 Gyroradius inversely
proportional to the number of the
charge. A singly charged ion can
be further stripped of its electrons
when it happens to skim the
Earth’s atmosphere, the
gyroradius is reduced many times
and the ion can become trapped.
 This scenario was predicted far
in advance [Blake et al., 1978].
 First evidence from Russian
COSMOS satellites.
SAMPEX pin pointed the location
of the narrow belt of ARCs.
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A Schematic View of the
Locations of Radiation Belts
• Blue: inner belt, >10MeV
protons, rather stable
• Purple: outer belt, 100s keV
and MeV electrons and ions,
not stable at all
• Slot region in between
• Yellow: ACRs, stable
• White line: Earth’s magnetic
field, approx. by a dipole
field
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Charged Particle Motions in Earth’s Magnetic Field
• Gyromotion motion: =p2/2mB (1st), T_g~10-3 sec
• Bounce Motion: J= p||ds
(2nd), T_b~100 sec
• Drift motion: =BdA
(3rd) , T_d~103 sec
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Equatorial field intensity in recent millenia, as deduced from
measurements on archeological samples and recent observatory data.
~10 nT/year
Reversals have been documented as far back as 330 million years. During that time more
than 400 reversals have taken place, one roughly every 700,000 years on average.
However, the time between reversals is not constant, varying from less than 100,000
years, to tens of millions of years. In recent geological times reversals have been
occurring on average once every 200,000 years, but the last reversal occurred 780,000
years ago. At that time the magnetic field underwent a transition from a "reversed" state
to its present "normal state".
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