Ratios of solar to trapped proton fluences were computed for circular-orbit, geocentric space missions to be flown during the active phase of the next solar cycle (1977-1983). The ratios are presented as functions of orbit altitude and inclination, mission duration, proton energy threshold, and the chance the mission planner is willing to take that the actually encountered solar proton fluence will exceed the design fluence provided by the statistical solar proton model. It is shown that the ratio is most sensitively dependent on orbit altitude and inclination, with trapped protons dominant for low inclination, low and mid altitude orbits and for high inclination, mid altitude orbits. Conversely, solar protons are dominant for high inclination, low altitude orbits, and for low and high inclination, high altitude orbits

King, J. H.

Stassinopoulos, E. G.

English

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ENERGETIC SOLAR PROTON vs.
TERRESTRIALLY TRAPPED PROTON FWXES
- FOR THE ACTIVE YEARS 1977-1983
"-- J. H. KING
.E. G. STASSINOPOULOS
JULY'1974
(NASA-TM-X-7C716) ENERGETIC SOLAR PROTON N74-30259
VERSUS TERRESTRIALLY TRAPPED PROTON FLUXES
FOR THE ACTIVE YEARS 1977 - 1983 (NASA)
--9" p HC $4.00 CSCL 03B Unclas
G3/29 54807
' GODDARD SPACE FLIGHT CENTER4 GREENBELT, MARYLAND-
https://ntrs.nasa.gov/search.jsp?R=19740022146 2020-03-23T04:21:39+00:00Z
X-601-74-221
Energetic Solar Proton vs. Terrestrially Trapped Proton Fluxes
for the Active Years 1977-1983
J. H. King
E. G. Stassinopoulos
July 1974
National Space Science Data Center
National Aeronautics and Space Administration
Goddard Space Flight Center
Greenbelt, Maryland 20771
ABSTRACT
Ratios of solar to trapped proton fluences have been computed for
circular-orbit, geocentric space missions to be flown during the active
phase of the next solar cycle (1977-1983). The ratios are presented as
functions of orbit altitude and inclination, mission duration, proton
energy threshold, and the chance the mission planner is willing to take
that the actually encountered solar proton fluence will exceed the
design fluence provided by the statistical solar proton model used. It
is shown that the ratio is most sensitively dependent on orbit altitude
and inclination, with trapped protons dominant for low inclination,
low- and mid-altitude orbits and for high-inclination, mid-altitude
orbits. Conversely, solar protons are dominant for high-inclination,
low-altitude orbits, and for low- and high-inclination, high-altitude
orbits.
ENERGETIC SOLAR PROTON VS. TERRESTRIALLY TRAPPED PROTON FLUXES
FOR THE ACTIVE YEARS 1977-1983
INTRODUCTION
This note is intended to demonstrate the relative importance of
solar and trapped proton fluxes in the consideration of shielding
requirements for 1977-1983 geocentric space missions. Using the
latest solar proton and trapped proton models, fluences of these
particles encountered by spacecraft in circular orbits have been
computed as functions of orbital altitude and inclination, mission
duration, threshold energy (between 10 and 100 MeV), and, for solar
proton fluxes, risk factor.* Ratios of solar-to-trapped proton
fluences were then taken. These ratios give the relative importance
of the two proton populations and indicate to the mission planner
whether he must consider both or only one of these populations. To
determine the absolute fluence level of either population, the mission
planner must refer to one of the sources cited below.
SOLAR PROTONS
The solar proton fluences used in this study are based on the
analysis of King.' Interplanetary 1 AU measurements of solar event
fluences, taken over the period 1966-1972, were handled statistically
to predict solar proton fluences for the active phase of the next
solar cycle, 1977-1983, at varying probability levels and for several
durations of exposure.
*Risk factor: a parameter expressing the chance a mission planner is
willing to take that the actually encountered fluxes will exceed the
predicted levels.
1
The salient features of the analysis are:
a) the grouping of events into ordinary and anomalously
large (AL) events,
b) the assumption that the spectrum of all anomalously
large events occurring in the 1977-1983 period will
replicate the spectrum of the August 1972 event,
c) the assumption that the probability of event occurrence
during the next active period is independent of time,
d) the process of estimating the frequency of future events
by an extension of Poisson statistics, which compensates,
to some extent, for the limited data base on which the
statistical predictions are made.
An important result of the analysis is that, except for very
short missions and relatively large risk factors, spacecraft design
fluences can now be obtained by considering anomalously large events
only, without concern for ordinary events.
Of particular interest to the present analysis is the manner by
which magnetospheric solar proton fluxes are determined from the
interplanetary values of King.' As discussed in Stassinopoulos and
King, 2 the assumption was made that 10-100 MeV solar protons have a
common geomagnetic cutoff (Lc) in the McIlwain shell parameter L.
This is probably an adequate treatment, given the fact that diurnal
and geomagnetic-disturbance-level variations in the cutoff value are
greater than those variations due to energy dependence alone over the
indicated range. Results based on this assumption (with Lc=5) were
published in Stassinopoulos and King 2 and in King,' and are used in the
present analysis. It should be noted that the common cutoff approxi-
mation becomes less accurate as particle energies increase above 100
MeV, causing the orbit-integrated flux of solar protons with energies
2
E>100 to be underestimated. However, flux levels of such energetic
particles decrease markedly relative to the lower energy particles.
TRAPPED PROTONS
The models of magnetospherically trapped protons used in this
analysis are AP6 in Lavine and Vette,3 and AP7 in Lavine and Vette.4
These models are based on data obtained by several satellite experi-
ments between 1962-1964 and 1961-1966, respectively. In each model,
the integral omnidirectional flux is given as:
J(>E;B,L) = J(>E1 ;B,L) N (E;B,L).
The spectral function N was chosen as a power law for AP6
N = (E/EI )P(BL)
and as an exponential for AP7
N = exp (-(E-E 1 )/Eo(B,L)).
The model then consists of the specification of
J(>E1 ;B,L) and P(B,L) or Eo(B,L).
Typically the models agree to within a factor of 2 with all the
data from which they were generated.
Time dependences were handled by ignoring possible solar cycle
variations (about which too little was known to do otherwise) and by
presenting the model for periods unaffected by magnetic storms. It is
3
now realized that, although solar cycle variations may be insignificant
above 600 km, below that level they become increasingly important due
to the variation in atmospheric density as discussed in Dragt. s Inte-
gral fluxes above 10 MeV may have a solar cycle variation amplitude of
a factor of 2 to 4 at low altitudes (with largest flux at solar minimum).
This question will be discussed in detail in the next trapped proton
model to be published in the near future by Sawyer.6
Thus, the models AP6 and AP7, when applied to the solar active
period 1977-1983, should be valid to a factor of 2 above 600 km and
may overestimate fluxes by a factor of 2 to 4 below 600 km. These
uncertainties are insignificant relative to the intrinsic statistical
uncertainties in the solar proton model.
THE CALCULATIONS
It is desired to specify the ratio R:
S(h,i;E;T,Q)
Rh,i;E;T,Q) = T(h,i;E;T) (1)
Here S and T are fluences associated with solar and trapped
protons, respectively. The independent variables are: h and i, the
altitude and inclination of the circular orbit; E, the proton energy
threshold; T, the mission duration; and Q, the risk factor. Note that,
owing to the statistical and deterministic natures of solar and trapped
fluences respectively, S is a design fluence which may or may not
occur, while T is the trapped proton fluence which the spacecraft is
actually expected to encounter.
From King,1 we have
S(h,i;E;T,Q) = S 1 (h,i) [S 2 (E) S3(T,Q) + S4(E;T,Q)] . (2)
4
Here S1 (h,i) represents orbit-integrated effect of geomagnetic
shielding (assumed energy independent), S2 (E) gives the integral flux
and spectrum of each anomalously large event, while S3(T,Q) gives the
number of such events expected, and S4 (E;T,Q) gives the fluence
contributed by ordinary events. For values of T and Q such that
S 3>0, we may take S4 = 0.
For time scales long compared to one orbital period, the trapped
proton fluences are obtained from
T(h,i;E;T) = T2 (h,i;E) x T (3)
where T2 is an annual trapped proton fluence and T is the mission
duration in units of years.
With equations 2 and 3, the ratio R may be rewritten as
R(h,i;E;T,Q) = RI(h,i;E) R2 (E;T,Q) (4)
where R, = S1 S2 /T 1 and R2 = T- 1 x (S3 + S4/S2). The R1 functions have
the significance of being the solar-to-trapped proton fluence ratios
for 1-year missions for which exactly one anomalously large event
must be anticipated. R1 functions are plotted in Figures la-ld in
terms of iso-ratio contours in h-i space for a series of energy
thresholds. The R2 functions are R1 modifiers, adjusting the ratios
to reflect the Q, T dependent variation in the number of AL events to
be expected. Values of R2 are inserted in matrix form into Figures
la-ld for mission duration between 2 months and 5 years and for risk
factors between .01 and 0.1 (1 and 10 percent). Note that R2 values
are independent of energy for all Q, T matrix elements except for the
5 and 10 percent risk factors of the 2-month missions, for which no
5
AL event is predicted. For all other elements, S 3>0 and S /S2 becomes
insignificant.
DISCUSSION
Many features are immediately visible in Figures la-ld. First of
all, the solar-to-trapped ratio is zero for orbits in the shaded areas
where, by virtue of geomagnetic shielding, no solar particle reaches a
spacecraft anywhere along its orbit. In the cross hatched region (high
altitude, low inclination) the ratio is meaningless because neither
solar nor trapped protons reach the spacecraft.
At a fixed altitude (below a few hundred kilometers or so) the
dominant fluence source shifts rapidly from trapped to solar protons as
orbit inclination is increased through the 50-to 60-degree range. Thus,
for low-altitude, polar-orbiting spacecraft, solar protons are very
important relative to trapped protons. As the altitude of a polar
orbit mission is increased, the solar-to-trapped ratio declines and
then increases again. This is mainly due to the low latitude portion
of the orbit moving out to, and then beyond, the regions of maximum
trapped particle fluxes. The energy dependence of R1 , apparent from a
sequential examination of Figures la-ld, results from the variability
of the trapped proton spectrum at differing spatial points and the
dissimilarity of the trapped and solar spectra.
By examination of the inset matrices in Figures la-ld, it is appar-
ent that for a fixed risk factor, solar particles tend to become rela-
tively less important than trapped particles as mission duration in-
creases. At fixed mission duration, however, solar protons become
relatively more important than trapped particles as the permissible risk
factor is decreased. Note, however, that as long as at least one AL
6
event is anticipated, the variation in the solar-to-trapped ratio due
to the mission duration and risk factor dependences is very small
relative to the variation associated with the altitude and inclination
dependences.
CONCLUSIONS
The purpose of the analysis has been to permit the space mission
planner to readily determine whether he must consider solar and trapped
proton fluences, or only one or the other, in his shielding 
require-
ments. The analysis is not intended to provide actual fluence values,
which are available in the references cited.
The mission planner must specify orbit altitude and inclination
(circular orbits only), mission duration, and the percent risk he is
willing to take that the actually encountered solar proton fluence will
exceed his design fluence. Then from the appropriate figure for the
energy threshold of interest, he multiplies the appropriate factor
from the inset matrix by the appropriate plotted R, value in order to
determine the ratio of solar-to-trapped proton fluences he must allow
for in his mission planning. Typically, interpolation will be required.
It is clear that for low-altitude polar and very high-altitude
missions (any inclination), solar protons dominate trapped protons.
Conversely, for low-inclination, low- and medium-altitude missions and
for high-inclination, medium-altitude missions, trapped protons dominate
the solar protons.
Due to the uncertainties in the models, we would recommend that if
the value of the S/T ratio fell between 0.1 and 10, the mission planner
ought to consider both trapped and solar proton fluences. Likewise, if
the desired h, i point is in a region of rapidly changing S/T ratio,
both trapped and solar fluxes should be considered.
7
REFERENCES
1. King, J. H., "Solar Proton Fluences for 1977-1983 Space Missions",
J. Spacecraft and Rockets, 11, 401-408, 1974.
2. Stassinopoulos, E. G., and J. H. King, "Empirical Solar Proton Model
for Orbiting Spacecraft Application", IEEE Transactions on Aerospace
and Electronic Systems, Vol. 10, No. 4, July 1974.
3. Lavine, J. P. and J. I. Vette, "Models of the Trapped Radiation
Environment, Volume V: Inner Belt Protons", NASA SP-3024, 1969.
4. Lavine, J. P. and J. I. Vette, "Models of the Trapped Radiation
Environment, Volume VI: High Energy Protons", NASA SP-3024, 1970.
5. Dragt, A. J., "Solar Cycle Modulation of the Radiation Belt Proton
Flux", J. Geophys. Res., 76, 2313-2344, 1971.
6. Sawyer, D. M., to be published, 1975.
8
Figure 1
Constant Value Contours for Ratios of Solar-to-Trapped Proton Fluences
as a Function of Orbit Altitude and Inclination for One Year Missions
and for 10 Percent Risk Factor. Inset Matrix gives Multiplication
Factors for Other Mission Durations (T, in years) and Risk Factors (Q).
9
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Energetic solar proton versus terrestrially trapped proton fluxes for the active years 1977 - 1983

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