Secular changes in the geomagnetic field between 1955 and 1980 have been large enough to produce significant differences in both the verical cutoff rigidities and in the L-value for a specified position. A useful relationship employing the McIlwain L-parameter to estimate vertical cutoff rigidities has been derived for the twenty-five year period

Gentile, L. C.

Shea, M. A.

Smart, D. F.

English

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SH 6.1-12
332
THE USE OF THE MclLWAIN L-PARAMETERTO ESTIMATECOSMICRAY VERTICAL
CUTOFFRIGIDITIES FORDIFFERENTEPOCHSOF THE GEOMAGNETICFIELD
M.A. Shea and D.F. Smart
Air Force Geophysics Laboratory
Hanscom AFB, Bedford, Massachusetts 01731, U.S.A.
L.C. Gentile
Physics Research Division, Emmanuel College
400 The Fenwa_, Boston, Massachusetts 02115, U.S.A.
ABSTRACT
A useful relationship employing the Mcllwain L-parameter to
estimate vertical cutoff rigidities has been derived for the
twenty-five year period 1955-1980.
1. Introduction. It is intuitively pleasing to utilize the dipolar
geometry inherent in the Mcllwain L-parameter to order cosmic ray cutoff
rigidities. However, in some areas of the world, secular changes in the
geomagnetic field between 1955 and 1980 have been large enough to produce
significant differences in both the vertical cutoff rigidities and in
the L-value for a specified position. In this paper we show that these
changes are complimentary, and it is possible to derive a relationship
between the L-value and vertical cutoff rigidity that can be used for the
twenty-five year period, 1955-1980.
2. Background. The trajectory-tracing process is generally recognized
as the most accurate method for calculating cosmic ray cutoff rigidities.
Since cutoff rigidities are a function of latitude, longitude, altitude,
zenith angle, azimuthal angle, and field model, using the trajectory-
tracing method for a large number of positions and directions is imprac-
tical. For this reason, cosmic radiation data from many experiments are
often ordered by the cutoff rigidity values in the vertical direction.
One method of estimating vertical cutoff rigitities was suggested by
Smart and Shea (1967) who derived three equations for the relationship be-
tween the Mcllwain L-parameter (Mcllwain, 1961) and (I) the upper calcu-
lated cutoff, (2) the lower calculated cutoff and (3) the effective cutoff
rigidities.* These three equations were derived using cutoff rigidities
calculated for the Finch and Leaton (1957) field for Epoch 1955.0 and the
Jensen and Cain (1962) field for Epoch 1960. The equations thus derived
for the upper calculated cutoff, the lower calculated cutoff and the ef-
fective cutoff rigidities were essentially the same for both field models.
At the time of this original work, cosmic ray physicists did not rec-
ognize that the secular changes in the geomagnetic field were sufficiently
large over a relatively small time period (on the order of 25 years) to
significantly affect the detection, at the surface of the earth, of galac-
tic cosmic radiation above 1GV. It was not until Shea (1971) suggested
* In the paper of Smart and Shea (1967), these rigidity values were called
main cone cutoff, Stormer cone cutoff and effective cutoff, respectively.
Since new terminology for cosmic ray cutoffs has been agreed upon by
scientists working in this area (Cooke et al., 1985) we will use these
newer terms throughout this paper.
https://ntrs.nasa.gov/search.jsp?R=19850026772 2020-03-20T16:51:00+00:00Z
SH 6.1-12
333
that the decrease in vertical cutoff rigidity at Huancayo over a 20-year
period might possibly be observed as an increase in the background radi-
ation measured by a stable neutron monitor at this location (since veri-
fied by Cooper and Simpson, 1979), that it became apparent that the secu-
lar changes in the geomagnetic field might be sufficiently large in some
areas of the world that changes in cutoff rigidities, and consequently
measured changes in cosmic radiation, would occur.
In view of the changes in the main geomagnetic field and the rela-
ted changes in the calculated cutoff rigidities, we feel it is necessary
to re-examine the use of the Mcllwain L-parameter to estimate cosmic
ray vertical cutoff rigidities for the 25-year period 1955-1980.
3. Method. The world grid of vertical cutoff rigidities calculated
each 5 ° in latitude and 15° in longitude for Epochs 1955, 1965 and 1980
(Shea et al., 1968; Shea and Sunart, 1975, 1983) and the Mcllwain
L-values (Mcllwain, 1961) calculated for these same locations comprised
the basic data sets used for this analysis. All calculations were made
for an altitude of 20 km above the surface of the earth as defined by the
international reference ellipsoid. Both the vertical cutoff rigidities
and the Mcllwain L-values were calculated using the geomagnetic field
coefficients for the appropriate Epoch (i.e., 1955, 1965 and 1980).
Expressing the cosmic ray cutoffs by an equation of the form R=KLY
where R is the cutoff rigidity, L is the Mcllwain L-value, K is a con-
stant and _ is an exponent, K and y were evaluated by a least-squares
fit of the (I) upper calculated cutoff rigidity, (2) effective cutoff
rigidity and (3) lower calculated cutoff rigidity. Each of the equations
derived for each Epoch, together with the RMSerror for each set of cal-
culations, is given in Table I. It is important to note that vertical
cutoff rigidities < 0.20 GV were omitted from these calculations. Since
the cosmic ray equator and the equator defined by the minimum L-value do
not coincide, all grid points within a band ±5 degrees of either equa-
tor (or between the two equators) were also omitted. Figure 1 illus-
trates the locations of each of these equators for Epoch 1980.
Table I. Equations to estimate cutoff rigidities for various Epochs
m
Epoch RU = RC = RE =
1955 16.727 L-2-°°54 16.192 L-2-°z77 14.992 L-z-99B6
RMS= 6.28 % RMS= 5.48 % RMS= 6.61%
1965 16.727 L-2,°212 16.222 L-2.041B 14.942 L-2.°296
RMS= 6.70 % RMS= 5.52 % RMS= 6.98 %
1980 16.717 L-2,°2o6 16.222 L-2,0441 14.823 L-2.o3zz
RMS= 7.06 % RMS= 5.74 % RMS= 7.27 %
Composite 16.762 L-e-°z74 16.237 L-2.°3s3 14.912 L-2,°18s
1955-1980 RMS= 6.67 % RMS= 5.64 % RMS= 7.19 %
SH 6.1-12
334
4. Discussion• From an inspection
of the equations in Table 1 it is _
evident that the constants K and y
for each of the three vertical cut- _ 1980
off rigidities are essentia]ly inde- _'_"._._ ,_
pendent of Epoch The root mean _'_• :"
• mm aM •
square values are also similar, with _ _ _ ..
the slightly larger RMS values for _ ""
1980 attributed to the evolution of _ o. , ___,__
the magnetic field and an increasing E
divergence between cosmic ray J 9
x mequator and the minimum L equator. _
The area between these two equators _ • CC%SMICI_ClYEQUATOR "_"
has increased approximately 10 per- _ " L-VALUEEQIJflIOR
cent between 1955 and 1980.
Since these equations were al- o 4b B_ 120 ISOZ00 24O 2BO 320 36O
most identical we combined the data
for all three Epochs in an effort LONGITUDE
to determine a suitable equation for Figure 1. Geographic location
the upper calculated cutoff, the ef- of the cosmic ray equator and
fective cutoff and the lower calcu- the minimum L equator for 1980.
lated cutoff for the entire 25-year
period from 1955 to 1980. Again all locations with cutoffs less than
0.20 GV were omitted from the analysis. Since the location of the
cosmic ray equator changed between 1955 and 1980 (Shea et al., 1983),
and different equatorial grid locations had been removed for each
Epoch, we removed all locations within ±5° of any of the three equa-
tors (i.e., if a particular location had been removed for the analysis
for one Epoch, it was removed from all three data sets for the composite
analysis)• Again the constants K and y were determined by the method
of least squares. The results for this composite set of over 1875 data
>-_b
Ru Rc RL
tL
tl_
0
I--
-.1
U
h-
>- .......i'e.............i'e....................i'o,
L VALUE
Figure 2. The upper calculated vertical cutoff rigidity (Rv), effective
vertical cutoff rigidity (Rc), and lower calculated vertical cutoff
rigidity (RL), plotted as a function of the McIlwain L-value. The data
set is a composite of the world grid locations for 1955, 1965 and 1980•
335 SH 6.1-12
points are graphically illus- _,_.,_
trated in Figure 2; the equations
are given in the bottom line of
Table 1 From these results we
feel that it is possible to use _
these three equations to estimate _,
the upper, effective and lower _ I _ _ _
cutoff rigidities for the entire _ _ __ !
period 1955 to 1980 provided the
L-values are calculated using the
field model for the same time pe-
riod that the cutoffs are needed.
I 2 3 4 5 6 7 8 9 _ II _ _ 14 _ _6 _ _ 9
Figure 3 illustrates the ac- R,GmJTY(GV_
curacy that can be expected for
an estimate of the effective ver- Figure 3: Accuracy of
tical cutoff rigidity as a function estimated vertical
of rigidity. These data were ob- cutoff rigidity.
tained by calculating for each lo-
cation the percentage difference (in rigidity) between the cutoff
rigidity value determined by the trajectory-tracing procedure and the
value estimated by using the L-value approximation equation. These
individual percentages were then averaged as a function of intervals of
estimated cutoff rigidity.
5. Conclusion. From this analysis we conclude that the Mcllwain
L-parameter can be used to estimate upper calculated, effective, and
lower calculated vertical cutoff rigidities for the period 1955 to 1980.
Acknowledgments. We gratefully acknowledge the computational assistance
of A.A. Bathurst• LCG acknowledges support from the U.S. Air Force
Geophysics Laboratory under contract No. FI9628-82-K-O039.
References
Cooke, D.J., J.E. Humble, M.A. Shea, D.F. Smart, N. Lund, I.L. Rasmussen,
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. Jensen, D.C., and J.C. Cain, J. Geophys. Res., 6_]_7,3568, 1962.
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The use of the McIlwain L-parameter to estimate cosmic ray vertical cutoff rigidities for different epochs of the geomagnetic field

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