Engineering Models for Galactic
Cosmic Rays and Solar Protons:
Current Status
Stephen Gabriel
Professor of Aeronautics and Astronautics
School of Engineering Sciences
University of Southampton
England
Email : sbg2@soton.ac.uk
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Outline
• Phenomenology : GCRs and Solar
Energetic Particle
Events(SEPEs)
• Requirements on engineering models
• Existing Models : GCRs
SEPEs
• Issues and the future
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Cosmic Rays: Origins and Acceleration

Galactic Cosmic Rays
Present consensus: Fermi acceleration by supernova
shock- wave remnants

Anomalous Cosmic Rays
Thought to originate as neutral interstellar gas that
drifts into the heliosphere, becomes singly-ionized
near the sun and then convected to outer
heliosphere where accelerated to higher energies
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Cosmic Rays: Time Variations
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Cosmic Rays: Propagation
where
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Cosmic Rays –
Energy Spectra
Quiet-time energy spectra for
the elements H, He, C, N and
O measured at 1 AU over the
solar minimum period from
1974 to 1978 (from Mewaldt
et al., 1984).
Note the “anomalous”
enhancements in the lowenergy spectra of He, N and O.
The data are from the Caltech
and Chicago experiments on
IMP-7 and IMP-8.
(from Mewaldt, 1988)
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Cosmic Rays –
Energy Spectra
(contd)
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Cosmic Rays
- Composition
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Solar Protons: Origins and Acceleration (1)
Energetic Particle Events at the Sun
Current view:
Particle acceleration is caused by
coronal mass ejection (CME) driven
shocks in the corona and
interplanetary medium
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Solar Protons:Origins and Acceleration (2)
X -ray events detected by GOES 7 spacecraft in
geosynchronous orbit. The vertical lines are hour markers. The
left-hand panel shows an impulsive event at about 9:00 UT
(Universal Time) on May 3,1992. The right-hand panel shows a
gradual event at about 15:45 UT on May 8, 1992. (From SolarGeophysical Data, Prompt Reports, Number 574-Part 1, June
1992, National Geophysical Data Center, Boulder CO.)
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Solar Protons:
Origins and
Acceleration (3)
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Solar Protons:
Propagation (1)
Propagation of solar
energetic particles.
Those propagating
along the “favorable
path” will be
anisotropic at Earth.
(From Shea, 1988)
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Solar Protons: Propagation (2)
Longitude distribution of propagation times of solar particles from the flare to
the Earth. The various symbols indicate data from different studies. The line is
added to guide the eye. (From Smart and Shea, 198,5, and Barouch et al., 1971)
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Solar Protons:
Time Variations
Solar Cycle
Solar cycle
variation of yearly
integrated fluences
observed at 1 AU
(From Feynman et
al., 1990)
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Solar Protons: Energy Spectra
Exhibit large range both in fluence and peak flux spectra
From R.A. Mewaldt et al, “Solar Particle Energy Spectra during the Large
Events of October-Novemeber 2003 qnd January 2005”, 29th International
Cosmic Ray Conference Pune (2005) 00, 101-104
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Solar Protons: Time Variations
Event Duration
Proton fluxes from
two major solar
proton events
(E > 60 MeV).
Data from IMP 8
(T.P Armstrong,
personal
communication)
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Solar Protons: Time Variations (cont)
From R.A. Mewaldt et al, “Solar Particle Energy Spectra during the Large
Events of October-Novemeber 2003 qnd January 2005”, 29th International
Cosmic Ray Conference Pune (2005) 00, 101-104
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Solar Protons:
Composition
Solar Energetic
Particle
Abundances
From Reames,
1997
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Annual Proton Fluence vs
Sunspot Number
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Engineering Models :
Requirements
• For all high energy particle
species(electrons, protons and heavy ions):
–
–
–
–
–
–
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Flux spectrum ( instantaneous)
Fluence spectrum
Directionality
Spatial dependence
At any time ( including solar cycle variations)
High Velocity Coronal Mass Ejections(CMEs)
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Important Parameters for
Engineering Design
•
•
•
•
•
•
•
Total Event Fluence
Peak Flux
Duration
Hardness (Spectral Form)
Heavy ion abundance
Propagation
Confidence Level/uncertainty (Design Margins)
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GCR Models
• CREME 96 regarded as the most up-to-date and
comprehensive model
• CREME96 is an update of the Cosmic Ray Effects
on Micro-Electronics code, a widely-used suite of
programs for creating numerical models of the
ionizing-radiation environment in near-Earth
orbits and for evaluating radiation effects in
spacecraft.
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CREME 96
• Has many significant features, including
• (1) improved models of the galactic cosmic ray, anomalous
cosmic ray, and solar energetic particle components of the
near-Earth environment;
• (2) improved geomagnetic transmission calculations;
• (3) improved nuclear transport routines;
• (4) improved single-event upset (SEU) calculation
techniques, for both proton-induced and direct-ionizationinduced SEUs; and
• (5) an easy-to-use graphical interface, with extensive online tutorial information.
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Cosmic Rays:
Solar Cycle
Modulation
CREME 96
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SEPE models
• All current models are statistical/probabilistic in
nature
• 3 most recent proton models :
– JPL – 91
– Xapsos et al
– Nymmik(MSU)
• Heavy Ion Model : Tylka : PROBABILITY
DISTRIBUTIONS OF HIGH-ENERGY SOLAR- HEAVY-ION
FLUXES FROM IMP-8: 1973-1996
IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 44,
NO. 6, DECEMBER 1997
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Comparison of 3 Models
• Nymmik assumes that the mean event frequency is
proportional to the average sunspot number while
others assume that there are 7 active years of a
solar cycle
• JPL models assume a log normal distribution,
Nymmik model assumes a power law, Xapsos
determines the distribution using maximum
entropy ( truncated power law)
• JPL model only goes up to >60MeV, MSU model
up to 100s of MeV
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Comparison of 3 Models
• JPL model is for fluences only while MSU
and Xapsos have peak flux models too
• Event definition appears to be different
between JPL and MSU models
• Different data sets for all three models
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ESP and JPL-91 comparison
Sample spectra of the ESP models for a seven year mission in solar
maximum conditions and confidence level 90%: ___ total fluence
model; ___ worst case event fluence model; ___ JPL model for the
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same conditions.
Fluence Probability Curve (1)
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Distribution of Solar Event Fluences (1)
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Sensitivity of fluence model to the
size of the event data set
• Rosenqvist and Hilgers1 have shown that
the current size of the event data set ( ~ 200
events) can lead to significant errors in the
prediction of the fluence probability
distribution function
•
1 Rosenqvist, L. and Hilgers, A. “Sensitivity of a statistical solar proton
fluence model to the size of the event data set”, Geophysical Research Letters,
30, 1865, 2003
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Geomagnetic Shielding: Simple Theory
• During quiet periods, Stormer Theory can be used :
• Assumes Earth's magnetic field is dipolar
• Gives cut-off rigidity, RC (minimum momentum per
unit charge) for a particle arriving from a given direction
to reach a given location at the Earth
• Useful approximation for lowest value, RCW, which is
from magnetic west, is
RCW = [CScos4] / {r2[1+ (1+ cos3)1/2]2}
where CS a constant, r is distance from dipole centre in earth
radii and  is magnetic latitude
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Geomagnetic Shielding: Störmer Theory (2)
Cut-off rigidity in the dipole approximation of the Earth's magnetic
field for west, east, and vertical direction as a function of magnetic
latitude (from Klecker, 1996)
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Geomagnetic Shielding: Simple Theory
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Conclusions
 Concentrated on existing engineering models and their
inadequacies,ideally what is needed and some of the basic
physics
 Models :
Cosmic Rays: CREME 96:
 Uses Nymmik's semi-empirical model for solar cycle
modulation based on Wolf sunspot number (includes
large-scale structure of heliospheric magnetic field)

Incorporates multiply-charged ACR component (above
~ 20 MeV/nucleon), from Sampex results

~ 25% error on average for solar modulation and
spectra, compared to data
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Conclusions (contd.)
 Geomagnetic Shielding

More data analysis/modelling during active periods to
understand cut-off depression/predict transmission
(CRÈME 96 combined IGRF and extended
Tsyganenko model)

Importance of partially-ionised heavy ions
(mean-ionic charge ~14 rather than 26)
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Conclusions (contd.)
 Solar Protons
• Importance of CMEs and CME-driven shocks
• Currently,most generally accepted statistical models are
JPL-91
(“The JPL proton fluence model : an update”,
Feynman et al, Journal of Atmospheric and Solar-Terrestrial
Physics) and ESP(Xapsos) models.
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Conclusions (contd.)
Solar Protons
• New ESA model under development:
– Data driven models
– Must address user needs
– Better Radial Scaling needed for missions like
Bepi Colombo, Solar Orbiter, Solar Dynamic
Observer, Heliospheric Sentinels, STEREO,
Mars missions, etc
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