We report new measurements of the vertical geomagnetic cutoff for cosmic rays with rigidities from ~500 to 1700 MV, made using data from the MAST instrument on SAMPEX. A total of ~10,000 nuclei were used to measure the latitude cutoff in nineteen separate rigidity intervals. These results show that cosmic rays and solar particles can penetrate several degrees lower in latitude than would be estimated from commonly used relations for the geomagnetic cutoff, which has implications for the radiation exposure expected on the Space Station. An excellent fit to our measured cutoffs is given by the relation Rc = 15.062cos4 (Λ) - 0.363 GV, where Rc is the geomagnetic cutoff in rigidity, and λ is the invariant latitude. We suggest that this relation is useful over invariant latitudes from Λ = 0° to 64°, corresponding to rigidity cutoffs from ~0.2 to 15 GV

Leske, R. A.

Mewaldt, R. A.

Ogliore, R. C.

Stone, E. C.

von Rosenvinge, T. T.

Caltech Authors - Main

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Proceedings of ICRC 200 l: 4112 © Copernicus Gesellschaft 200 I ICRC 2001 
A Direct Measurement of the Geomagnetic Cutoff for Cosmic Rays 
at Space Station Latitudes 
R. C. Ogliore1, R. A. Mewaldt1, R. A. Leske1, E. C. Stone', and T. T. von rR,osenvinge2 
'California Instilule of Technology, Pasadena, CA 91125 USA 
2NASA/Goddard Space Flighl Cenler, Greenbell, MD 20771 USA 
Abstract: We report new measurements of the vertical 
geomagnetic cutoff for cosmic rays with rigidities from 
- 500 to 1700 MV, made using data from the MAST 
instrument on SAMPEX. A total of -10,000 nuclei were 
used to measure the latitude cutoff in nineteen separate 
rigidity intervals. These results show that cosmic rays and 
solar particles can penetrate several degrees lower in 
latitude than would be estimated from commonly used 
relations for the geomagnetic cutoff, which has implications 
for the radiation exposure expected on the Space Station. 
An excellent fit to our measured cutoffs is given by the 
relation Re= 15.062cos4(A) - 0.363 GV, where Re is the 
geomagnetic cutoff in rigidity, and /... is the invariant 
latitude. We suggest that this relation is useful over 
invariant latitudes from A = 0° to 64°, corresponding to 
rigidity cutoffs from -0.2 to 15 GV. 
1 Introduction 
Stonner (J 930) first described the behavior of cosmic rays 
in the Earth' s dipole field. He was able to derive a relation 
for the geomagnetic cutoff rigidity - the minimum-rigidity 
particle that can reach a given latitude above the magnetic 
equator as a function of its direction of arrival. Most of our 
subsequent knowledge of the geomagnetic cutoff has 
resulted from studies that trace (negatively charged) 
particles backwards through models of the Earth's field. 
Such studies have produced a grid of geomagnetic cutoff 
rigidities distributed over the Earth' s surface (e.g., Shea and 
Smart 1985). Smart and Shea (1994) summarized a number 
of useful relations to estimate the geomagnetic cutoff in a 
given direction at a given location and pointed out the 
usefulness of the Mcllwain L-parameter for organizing 
geomagnetic cutoffs. Cn this paper we consider particles 
arriving from the vertical direction, for which the 
Correspondence to: RMewaldt@srl.caltech.edu 
recommended relation is Rev (in GV) = CsvL-2, where the 
constant Csv gradually decreases with time as the Earth's 
dipole moment decreases. For the 1990 epoch, Smart and 
Shea (1994) recommend Csv = 14.5 GV. 
Although there have been relatively few satellite surveys 
of geomagnetic cutoffs, comparisons of such measurements 
with the particle-tracing studies generally show that the 
measured cutoff latitudes are several degrees lower than the 
theoretical cutoffs (e.g., Fanselow and Stone 1972, who 
studied 1.2 to 39 MeV protons). At lower latitudes, 
measurements of - 2 and - 5 GV oxygen nuclei by HEA0-3 
also gave cutoffs 3% to 5% lower in rigidity than 
theoretical cutoffs (Petrou et al. 1981; Byrnak et al. 1981; 
Copenhagen - Saclay Collaboration 1981;). Thus, particles 
of a given rigidity generally have access to lower latitudes 
than expected (Smart and Shea 1994). 
More recently, cutoff measurements carried out using 
solar energetic particles (SEPs) with - 1 to tens of 
MeV/nucleon (Leske et al. 1995; 1997; 2001; Mason et al. 
1995; Boberg et al. 1995; Mazur et al. 1999) have provided 
detailed evidence of variations in the high-latitude cutoff 
with geomagnetic activity and also verified that the rigidity 
cutoff at a given latitude is generally less than derived from 
particle-tracing techniques. New calculations by Smart, 
Shea and Fliickjger (1999) and Smart et al. (1999a, 1999b) 
using an improved geomagnetic field model have resulted 
in generally lower rigidity cutoffs than derived from earlier 
particle-tracing studies. 
Precise knowledge of the geomagnetic cutoff has recently 
become more important because it affects the extent to 
which the Space Station is subjected to radiation hazards 
during large solar particle events (Siscoe et al. 1999). In this 
paper we present the results of direct measurements of the 
geomagnetic cutoff which show that at a given latitude the 
quiet-time geomagnetic cutoff is systematically lower than 
is given by the standard R.: = CsvL-2 relation given above 
and by the latest particle-tracing calculations. As a result, 
the flux of solar particles that can reach the Space Station is 
significantly greater than would have been expected. 
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41 .13 
2 Approach 
Galactic cosmic rays are stripped of their orbital electrons 
during passage through - 5 to 10 g/cm2 of interstellar 
material, and therefore have an ionic charge state (Q) equal 
to their nuclear charge (Z). We determine the rigidity (R) of 
individual particles by specifying Z, their mass (M) and 
their kinetic energy per nucleon in MeV/nucleon (E), and 
using the relation 
R (inMV) = (M/Ze)[E2 + 2mE] 112• (I) 
Here R is the rigidity in MV, e is the electron charge, and m 
is the equivalent of an atomic mass unit in Me V. 
The Mass Spectrometer Telescope (MAST) on SAMPEX 
measures the elemental and isotopic composition of solar, 
magnetospheric, and cosmic ray nuclei with - 20 to 200 
MeV/nucleon in low-Earth orbit. The nuclear charge, mass, 
and kinetic energy of particles that stop in the telescope is 
determined using the conventional AE-E technique (Cook et 
al. 1993). Therms mass resolution varies from -0.1 amu for 
Z = 6 to -0.3 to 0.4 amu for Z = 26, while the energy 
resolution is -0. l %. The resulting uncertainty in particle 
rigidity is - 1 %. 
SAMPEX was launched on July 3, 1992 into a polar orbit 
with 82° inclination, with an average altitude of - 600 km. It 
is known that geomagnetic cutoffs are well organized by the 
Mcllwain L parameter (e.g., Selesnick et al. 1995). From 
the SAMPEX orbital elements the L-shell where each 
particle was measured was identified using the 1990 IGRF 
magnetic field model. It is convenient to organize the 
geomagnetic cutoffs using the invariant latitude (A), 
defined by L = cos-2(A) (Roederer, 1970). During this study 
SAMPEX was oriented towards tbe zenith while at latitudes 
above ~45°, ideal fo r measuring the vertical cutoff. 
Although MAST has a 50° -opening angle, averages of the 
estimated azimuthal variations in the cutoff over the MAST 
opening angle differ from the vertical cutoff by only a few 
tenths of a per cent. In order to eliminate SEPs, which are 
not generally fully stripped (e.g., Leske et al. 1995), we 
accepted for analysis only time periods when the daily-
average flux of- 8 to 15 MeV/nucleon He was <4 x 104 per 
cm2sr-sec. 
To avoid contamination by singly-charged anomalous 
cosmic rays (ACRs), we excluded Band C nuclei with <50 
MeV/nucleon, N with <60 MeV/nucleon, 0 with <90 
MeV/nucleon, and F and Ne with <65 MeV/nucleon. 
Recently discovered low-energy enhancements in Mg, Si, 
and S, which may consist of singly-charged ions (e.g., 
Reames 1999, Cummings et al. 1999) contribute less than 
0.1 % of the nuclei in the energy interval covered by MAST. 
During geomagnetic storms the cutoff at high latitudes is 
often variable and temporarily lowered by a significant 
amount (e.g., Leske et al. 2001). We therefore eliminated 
periods within ±12 hours of times when the geomagnetic 
index Dst was less than - 100 nT. The mean value of Dst for 
the remaining periods was - 17 nT. The final cutoff 
measurements were not sensitive to this Dst cut. 
0 30 100 
Proton Energy (MeV~ 
300 000 2000 
90 
80 
70 
60 
50 
40 
0 500 1000 1500 2000 
Rigidity (MV) 
Figure I : A plot of the measured invariant latitude versus rigidity 
for all accepted nuclei. The relation R0 = 14.5cos
4Ac GV is shown 
for comparison. Note that the actual cutoff is uniformly lower than 
is given by this relation. Also shown is a curve derived from 
calculations by Smart et al. (1999) that are discussed below. 
A plot of the measured latitude versus rigidity for 
particles satisfying the above cuts is shown in Fig. 1, where 
the cosmic-ray cutoff is clearly defined down to rigidities as 
low as - 500 MV. These data were used to measure the 
minimum latitude to wh ich cosmic rays with a given 
rigidity could penetrate. Latitude distributions were plotted 
for 19 rigidity intervals, taking into account the exposure 
time in each latitude bin (example in Fig. 2). The cutoff 
latitude (Ac) at a given rigidity was defined to be the 
latitude at which the number of events per degree dropped 
to 50% of the average level at latitudes >60°. 
140 
120 
(/I 
'O 100 c 
0 
0 
.. (/I 
<O 
0 
80 
-
... 
.. 60 a. 
(/I 
c Holf Aver :> 40 0 
<.> 
20 
Cvloff=56.7 
0 
30 40 50 60 70 80 90 
Invariant Lotitude 
Figure 2: An example of the method for determining the cutoff 
latitude for a given rigidity interval. In each case the mean 
number of events per 106 seconds was determined (averaged over 
latitudes ~60°). The cutoff latitude was defined to be that latitude 
where the event rate dropped to 50% of the mean value above 60°. 
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41.14 
~ 
~ 0. 14 
.~ 
.§ 
::: 0.12 
0 
a 
.!:! 0.10 
Qi 
c: 
"' 0 ~ 0.08 
~ 
-T~ 
~ 0.06 
0 
0 
-
-
-
-
0.04~~~~~~~~~~~~~~~~~~ 
400 600 800 1000 1200 1400 1600 1800 
Rigidity (MV) 
Figure 3: Measured values of cos4Ac plotted versus rigidity are 
weU fit by the relation Re = 15.062cos4Ac - 0.363 GV. 
In Fig. 3 we plot the quantity cos4Ac as a function of 
rigidity, as suggested by earlier work. From a least squares 
fit wc find cos4Ac = (6.639 x 10"5)Rc + 0.0241 (where Re: is 
in GV), which can be inverted to give 
Re= 15.062cos4Ac - 0.363 GY, (2) 
or equivalently, Re= 15.062L"2 - 0.363 GY. 
Tbe uncertainties on the Ac values have been estimated in 
several ways. Based on the uncertainty in the plateau value 
and the slope of the distribution in the region of the cutoff 
we find a typical uncertainty of 0. 1° to 0.2°. By considering 
the nineteen points in Fig. 4 as 17 sequences of three 
adjacent values, and assuming that cos4Ac varies linearly 
with rigidity over an interval of - I 00 MY, we fmd that the 
rms uncertainty on the points is 0.39°. We therefore 
assume that all points have equal statistical uncertainties of 
0.4°. A least-squares fit to the data in Fig. 3 then gives a 
reduced chi-square of 1.4. 
3 Comparison with Previous Studies 
Fanselow and Stone (1972) measured 1.2 to 39 MeV 
protons in several rigidity intervals and found that the cutoff 
varied with local time. Fig. 4 shows our new measurements 
and their values for local midnight. The extrapolation of our 
cutoff relation agrees quite well with their results. Fig. 4 
also includes SAMPEX measurements of the cutoff using 
SEP H and He nuclei. Note that the cutoffs from SEPs 
differ somewhat from each other, presumably because the 
measurements were generally made during disturbed 
geomagnetic conditions (see, e.g., Leske et al. 1995, 2001). 
However, the extrapolat ion of our relation to lower 
rigidities is consistent with the ensemble of the SEP results. 
Smart and Shea (1994) summarized a number of useful 
representations of the geomagnetic cutoff. Figure 4 includes 
the relation Re= 14.5 GY/L2, which they recommended for 
the vertical cosmic ray cutoff. We find that cosmic rays of a 
given rigidity can penetrate several degrees lower in 
latitude than is predicted by this well-known relation. 
Equivalently, our results show that at a given geomagnetic 
lati tude it is possible to observe cosmic rays with rigidities 
-200 to 300 MY lower than expected from this relation. 
,..., 
-8 65 
~ 
0 
_, 
' 
', Morur el ol (1999) 
\ 
\ fonselow & Stone 
• \ 0000 >!l.l 
• > • 
... \ ', 
\\ ',, ' 
•. " ... ' c: ·,. ·.... .. ', 
. : This work 
·~ 60 Mason ~;·:~··,... ''' 
.f (1995) ..... :.... ',, R :14.5cos4(>.) 
. , c 
(/) 
"' ~ 
"'55 e, 
0 
.< 
Leske et al, SEP~ .. ;·;·995) ' ' '', 
' 
' 
' 
' 
50~~~~~~~~~~~~~~~~~~~ 
0 500 1000 
Rigidity (MV) 
1500 2000 
Figure 4: Comparison of the quiet-time geomagnetic cutoff 
determined here with average cutoffs determined using SAMPEX 
data during solar energetic particle events in 1992 and 1997 by 
Leske et al. (1995), Mason et al. (1995) and Mazur et al. (1999). 
Also shown are OG0-4 measurements at local midnight 
(Fanselow and Stone 1972). In SEP events the geomagnetic cutoff 
often varies due to associated geomagnetic activity. Note that the 
quiet-time cutoff reported here is significantly less than that given 
by the well-known relation, R., = 14.5L"2 GV 
60 
58 
56 
54 
52 
50 ~-L..c.-a.-a....1....1.~.~_.._......_._._,_~_._..........__._.i.~..._, 
400 600 800 1000 1200 1400 1600 1800 2000 
Rigidity <MV> 
Figure 5: Comparison of the geomagnetic cutoff determined by 
SAMPEX with the results of new cutoff estimates by Smart et al. 
(1999) using particle trajectory tracing techniques in an improved 
magnetic field model. The points shown are for protons with 100, 
150, 200, 300, 500, 700, and 1000 MeV and were interpolated 
from their Fig. 2 for Kp :::: 2.3. 
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41.15 
Smart, Shea and Fliickiger ( 1999) and Smart et al. 
(1999a, 1999b) recently presented new estimates of the 
geomagnetic cutoff based on particle-trajectory tracing in 
magnetic field model that combined a Tsyganenko (1989) 
magnetospheric field model with the International 
Geomagnetic Reference Field for epoch 1995.0. They 
detennined the cutoff over a grid of geographic points for 
several values of the geomagnetic index Kp. The average 
value of Kp during our study was 2.3. Smart et al. (1999b) 
provide a summary of cutoff latitudes as a function of 
rigidity for Kp values from 1 to 10 (see their Figure 2). In 
Fig. 5 we compare their calculated cutoffs (for Kp = 2.3) 
with our measured values, and with our best-fit cutoff 
relation. Although their estimates agree much better with 
our measurements than does the standard relation, there 
remains an average difference of -0.7° between their 
calculated cutoffs and our best-fit relation. 
Our results indicate that the cutoff grid in Smart, Shea 
and Fluckiger ( l 999) systematically overestimates the 
quiet-time cutoff for invariant latitudes from 52° to 60° by 
8% to 14%. In spite of these differences, these new 
calculations are significantly improved over earlier studies 
that employed less-sophisticated magnetic field models. 
4 Implications for the Space Station 
The International Space Station (ISS), in low-Earth orbit 
with an inclination of -55°, has access to invariant latitudes 
up to -66°. Although much of the radiation dose equivalent 
experienced by ISS astronauts is due to galactic cosmic rays 
and trapped radiation , the largest SEP events can contribute 
a significant radiation dose from high-energy protons and 
He (Siscoe et al. 2000). As an illustration, we use the proton 
spectrum measured by the GOES spacecraft during the 
large ("Bastille Day") SEP event of 14 July, 2000. For> 100 
MeY protons we find that the fluence reaching the ISS 
during this event would be -4 times as great with the new 
cutoff relation as with the standard relation. Previous 
studies have concluded that the ISS is not subjected to 
significant fluxes of solar protons with <30 MeV during 
quiet geomagnetic conditions (e.g., Figure 1.5 in Siscoe et 
al. 2000). However, using our relation 30 MeV protons can 
be observed down to A ::::: 63° during geomagnetically-quiet 
periods. We find that the orbit-averaged intensity of >30 
MeY solar protons is -20 times greater with our relation 
[Eq. (2)] than with the older relation Re = 14.5L"2 GY. 
5 Summary 
The measured quiet-time geomagnetic cutoff from 0.5 to 
1.7 GV is well represented by the relation R: = (15.062L.2 -
0.363) GV. At a given invariant latitude the geomagnetic 
cutoff given by this relation is anywhere from 200 to 300 
MY lower than is given by the commonly-used relation Re 
= 14.5 GV/L2• It is also somewhat lower than given by 
recent calculations using improved geomagnetic field 
models. The new relation also appears to provide good 
estimates of the cutoff well outside the range over which it 
is measured. 
Use of our improved geomagnetic cutoff relation leads to 
significantly larger estimates of the radiation exposure of 
the ISS due to SEPs than are obtained with commonly-used 
relations for the cutoff. Recent particle-tracing techniques 
based on improved models of the geomagnetic field (Smart, 
Shea, and Fliickiger 1999) appear to be in better agreement 
with the results presented here than arc previously used 
relations, but the theoretical cutoffs still overestimate the 
rigidity cutoff at a given latitude. 
Acknowledgements: This research was supported by NASA under 
grant NAS5-30704. During the summer of L999, when most of 
this work was conducted, Ryan Ogliore was a student at 
Clarcmont-McKcnna College, working at Caltech as the recipient 
of a Caltech Summer Undergraduate Research Fellowship 
(SURF). We thank Georgia de Nolfo for helpful discussions and 
Jay Cummings for contributions to the data analysis routines. 
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A Direct Measurement of the Geomagnetic Cutoff for Cosmic Rays at Space Station Latitudes

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A Direct Measurement of the Geomagnetic Cutoff for Cosmic Rays at Space Station Latitudes

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