Diurnal variations of energetic particle radiation
at the surface of Mars as observed
by the Mars Science Laboratory
Radiation Assessment Detector
Scot C. R. Rafkin1, Cary Zeitlin2, Bent Ehresmann1, Don Hassler1, Jingnan Guo3, Jan Köhler3,
Robert Wimmer-Schweingruber3, Javier Gomez-Elvira4, Ari-Matti Harri5, Henrik Kahanpää5,
David E. Brinza6, Gerald Weigle7, Stephan Böttcher3, Eckart Böhm3, Söenke Burmeister3,
Cesar Martin3, Güenther Reitz8, Francis A. Cucinotta9,10, Myung-Hee Kim11, David Grinspoon12,
Mark A. Bullock1, Arik Posner13, and the MSL Science Team
1Southwest Research Institute, Boulder, Colorado, USA, 2Southwest Research Institute, Durham, New Hampshire, USA,
3Department of Extraterrestrial Physics, Christian-Albrecths University, Kiel, Germany, 4Centro de Astrobiología (CSIC-INTA),
Madrid, Spain, 5Finnish Meteorological Institute, Helsinki, Finland, 6Jet Propulsion Laboratory, California Institute of
Technology, Pasadena, California, USA, 7Big Head Endian, Burden, Kansas, USA, 8GermanAerospace Center, Cologne, Germany,
9NASA Johnson Space Center, Houston, Texas, USA, 10University of Nevada Las Vegas, Las Vegas, Nevada, USA,
11Universities Space Research Association, Houston, Texas, USA, 12Library of Congress, Washington, District of Columbia, USA,
13NASA Headquarters, Washington, District of Columbia, USA
Abstract The Radiation Assessment Detector onboard the Mars Science Laboratory rover Curiosity is
detecting the energetic particle radiation at the surface of Mars. Data collected over the first 350Martian
days of the nominal surfacemission show a pronounced diurnal cycle in both the total dose rate and the neutral
particle count rate. The diurnal variations detected by the Radiation Assessment Detector were neither
anticipated nor previously considered in the literature. These cyclic variations in dose rate and count rate are
shown to be the result of changes in atmospheric column mass driven by the atmospheric thermal tide that is
characterized through pressure measurements obtained by the Rover Environmental Monitoring Station, also
onboard the rover. In addition to bulk changes in the radiation environment, changes in atmospheric shielding
forced by the thermal tide are shown to disproportionately affect heavy ions compared to H and He nuclei.
1. Introduction
The Radiation Assessment Detector (RAD) is an energetic particle detector aboard the Mars Science
Laboratory (MSL) rover Curiosity. At the time of writing, RAD has been on the surface of Mars for 1 Earth year
(landing 6 August 2012), measuring almost continuously the energetic particle radiation environment
[Hassler et al., 2013]. Prior to this, RAD operated during the interplanetary cruise from Earth to Mars. The
results from the cruise period were presented in Zeitlin et al. [2013].
Energetic particles must pass through the atmosphere of Mars to reach the surface. Some of these particles
may pass through without any interaction with the atomic nuclei in the atmosphere. In particular, the large
majority of galactic cosmic rays (GCRs) retain most of the energy they had when they entered at the top
of the atmosphere. Some of the particles entering the atmosphere do undergo nuclear interactions, resulting
in the production of secondary particles: e.g., pions that decay to muons and γ-rays and fragments from
atmospheric nuclei, especially neutrons and protons [Allkofer, 1975]. Both the primary and secondary
particles may further interact with nuclei in the atmosphere, producing a shower of particles. Eventually, both
the primary and secondary particle radiation reaches the surface where it enters the solid regolith that
contains minerals at various degrees of hydration, and possibly CO2 ice, water ice, and adsorbed or pore
space water vapor. Secondary neutrons are generated from the interaction of incident radiation within the
regolith, and some of these are backscattered, that is, upward directed to the surface. Such “leakage” or
“albedo” neutrons have previously been measured by orbital detectors [Boynton et al., 2004; Feldman et al.,
2002; Mitrofanov et al., 2002, 2004], and the intensity of reflection has been used to produce near-surface
hydrogen abundance maps. The MSL DAN (Dynamic Albedo of Neutrons) instrument in its passive mode
RAFKIN ET AL. ©2014. American Geophysical Union. All Rights Reserved. 1345
PUBLICATIONS
Journal of Geophysical Research: Planets
RESEARCH ARTICLE
10.1002/2013JE004525
Special Section:
Results from the first 360 Sols
of the Mars Science Laboratory
Mission: Bradbury Landing
through Yellowknife Bay
Key Points:
• Dose rate is inversely related to varia-
tions in atmospheric column mass
• Neutral count rate is proportional to
variations in atmospheric mass
• Heavy ions are disproportionately
affected by atmospheric shielding
Correspondence to:
S. C. R. Rafkin,
rafkin@boulder.swri.edu
Citation:
Rafkin, S. C. R., et al. (2014), Diurnal
variations of energetic particle radiation
at the surface of Mars as observed by
the Mars Science Laboratory Radiation
Assessment Detector, J. Geophys. Res.
Planets, 119, 1345–1358, doi:10.1002/
2013JE004525.
Received 8 SEP 2013
Accepted 14 MAY 2014
Accepted article online 22 MAY 2014
Published online 18 JUN 2014
[Mitrofanov et al., 2012] also measures the backscattered low-energy (thermal and epithermal) neutrons to
provide information about mineralogical and regolith hydration underneath the rover. RADmeasures higher-
energy, downward going neutrons produced in the atmosphere and higher-energy albedo neutrons in order
to determine their contribution to dose and dose equivalent on the surface.
The energetic particle radiation measured by RAD at the surface at any given time depends on the characteristics
of the primary radiation at the top of the atmosphere, the composition and mass of the atmosphere, and the
composition of the surface. In addition to the shielding effects of the atmosphere, which vary according to the
atmospheric mass, the surface radiation also depends on the shielding effects of any mechanical structures from
the RAD instrument and the Mars Science Laboratory rover Curiosity. Finally, because MSL is powered by a
radioisotope thermal generator (RTG), RAD is continuously flooded by neutrons and γ-rays with energies ≲5MeV.
RAD is sensitive to this energy range (and up to ~100MeV), but since the RTG source is expected to dominate
over natural sources, particularly from the regolith, thresholds are set to reject these detections.
The focus of this paper is strictly on the variations of energetic particle radiation driven by the variations in
atmospheric column mass on diurnal time scales. This paper is further restricted to the GCR-dominated
interactions with the atmosphere and not to solar events. The input spectrum of particles at the top of the
atmosphere is a mix of GCRs and those emanating from the Sun. The solar wind has little influence on the
surface radiation dose, because even the thin Martian atmosphere is sufficient to stop these relatively low
energy solar particles. Higher-energy solar particles from coronal mass ejections (CMEs) and solar energetic
particle (SEP) events may have the potential to affect the surface. During solar maximum conditions, which are
the case at present, the GCR flux is reduced compared to solar minimum conditions [e.g., Heber et al., 2006].
The current Solar Cycle 24 is very weak compared to historical averages, and the modulation of the GCR flux
has not been as strong as typical [e.g., Komitov and Kaftan, 2013]. Normally, CMEs and SEP events are more
common during solar maximum, but this has been an atypical solar cycle maximum, and no direct solar
particle events were observed by RAD over its first 200 sols (1 sol = 1 Mars day) on the surface of Mars. Indirect
impacts of solar events have been observed in the form of Forbush decreases in the GCR flux [Forbush, 1938].
Mars has a strong thermal tide excited by direct solar heating of the atmosphere on the dayside and strong
infrared cooling on the nightside. This thermal tide drives a diurnal variation in column mass of>10% over
the course of a sol, as measured at Gale Crater with the Rover Environmental Monitoring Station (REMS)
[Gómez-Elvira et al., 2012]. Because the column mass varies, the characteristics of the particle radiation
at the surface also vary. As will be shown, RAD has detected changes in the amount, type, and energy
spectrum of radiation at the surface over the course of a typical sol.
2. The Thermal Tide and Column Mass Changes
The mean molar fraction composition of the Martian atmosphere is ~95% CO2, ~2.7% Ar, and ~1.6% N [Owen
et al., 1977]. Recent measurements by MSL suggest that the abundance of Ar and N, given above and as
measured by Viking, are in error [Mahaffy et al., 2013], but this has little impact on this study, because the
dominant gas remains CO2, and by far, the largest effect of the atmosphere on the surface radiation is the total
columnmass rather than the composition. The rest of the atmosphere is a mixture of minor gases, including O2,
CO, H2O, and other noble gases. Roughly 25% of the CO2 in the atmosphere condenses seasonally onto the
winter pole, and the remaining noncondensable gasses increase in concentration as atmospheric CO2 mass
decreases [e.g., Sprague et al., 2004]. The seasonal CO2 condensation produces a direct, global response in
surface pressure, which rises and falls in concert with the atmospheric mass [e.g., Hess et al., 1980].
The connection between surface pressure and atmospheric column mass (and therefore atmospheric
shielding) follows directly from hydrostatic physics. If the local vertical acceleration of the atmosphere is small
compared to the gravitational acceleration, then the vertical pressure gradient acceleration is nearly equal to
the gravitational acceleration
∂p
∂z
¼ ρg: (1)
See Appendix A for an explanation of all symbols. Hydrostatic balance is a very good approximation for large-
scale and global-scale circulations that include the global thermal tide [Holton, 1979; Charney, 1949]. The
equation holds exactly for a nonaccelerating (motionless) atmosphere. Integration of equation (1) from the
Journal of Geophysical Research: Planets 10.1002/2013JE004525
RAFKIN ET AL. ©2014. American Geophysical Union. All Rights Reserved. 1346
surface (z = 0, p = ps) to the top of
the atmosphere (z = ∞, p = 0),
assuming a negligible variation of g
with height, yields
ps=g ¼ ∫∞0 ρ∂z: (2)
The right-hand side of equation (2) is
exactly the mass of the atmosphere per
unit area. Thus, in a hydrostatic
atmosphere (with a constant value for g),
the surface pressure is an exact measure
of the column mass. An increase
(decrease) in pressure demands an
increase (decrease) in columnmass. This
explains the CO2 condensation cycle
signal in the surface pressure.
From the ideal gas law, p = ρRT,
equation (1) may also be written as
∂lnp
∂z
¼  g
RT
: (3)
Therefore, the change in pressure
with height is strictly a function of
the temperature.
The relatively low density of the Martian atmosphere means that a given input of solar energy can produce a
much larger change in temperature compared to a planet with a denser atmosphere, such as Earth. The mean
volumetric heat capacity (ρCp) of the Martian atmosphere is ~1/200th of Earth’s; a given input of energy will
produce nearly 200 times an increase in temperature on Mars compared to Earth, all other things being equal.
Furthermore, the thin Martian atmosphere has a very short radiative time constant (~1 sol). The combination of
these two factors means that Mars has a large diurnal temperature variation that can respond very quickly to
changes in radiative forcing.
Heating of the dusty Martian atmosphere by the Sun produces a warm, low surface pressure planetary wave
—the thermal tide—that moves synchronously with the Sun from east to west, as illustrated in Figure 1. The
origin of this tidal wave can be understood through basic thermodynamical and dynamical principles. When
air is heated, it will expand. This is manifested through an upwardmotion of the atmosphere (the atmosphere
gets deeper—it inflates) and through a lateral expansion into neighboring columns. Vertical inflation does
not change the mass in the column; thus, the surface pressure remains unchanged. However, the lateral
motion driven by expansion represents a net mass divergence, which does lower the pressure. At night, when
the atmosphere cools, the atmosphere contracts, the motions reverse, and the surface pressure rises. The
change in surface pressure is required by hydrostatics (equation (3)) due to the change in the temperature of
the column, which implies the necessary horizontal divergence or convergence of mass. The phase of the
tidal wave is locked to the solar longitude. As the planet rotates underneath the Sun-synchronous wave, the
wave sweeps over the surface from east to west with a 1 day frequency.
Hess et al. [1977] demonstrated with surface pressure observations from the Viking landers that atmospheric
dust was the major absorber of solar energy. Therefore, the strong thermal tide is largely due to the
ubiquitous presence of dust in the atmosphere. Without dust, the Martian atmosphere would be mostly
transparent to solar radiation, the heating would be smaller in magnitude, and the tide would be weaker.
Leovy and Zurek [1979] produced an analytical model coupling the dust opacity and the surface pressure and
were able to further explain the amplitude of the surface pressure signal from the landers.
Dust loading has varied during the landedMSLmission, and this should have an impact on the overall amplitude
of the thermal tide. For the purposes of this analysis, the perturbation of the tidal amplitude from these dust
LH
Figure 1. Global heating of the atmosphereby the Sunand cooling through infra-
red radiation produces a strong thermal tide on Mars. The depth of the unper-
turbed atmosphere is shown as a dotted line surrounding the planet. Notional
columns of unperturbed atmosphere are shown in yellow on the dayside and
nightside. A column of air heated by the Sun on the dayside inflates and expands
laterally. The inflation represents an increase in the scale height of the atmosphere
(i.e., the mean temperature of the column increases), while the lateral motion
results in a net divergence of mass from the column. Thus, although the atmo-
sphere is deeper, the column contains less mass than the unperturbed atmo-
sphere, and a surface low pressure consistent with the heating andmass decrease
is present. The opposite occurs on the nightside, where the column cools and
contracts. The perturbed atmosphere, consistent with the expanded or contracted
air columns, is shown as shaded. As the planet rotates, the tidal wave, which is
locked to the Sun, sweeps from east to west across the surface of the planet.
Journal of Geophysical Research: Planets 10.1002/2013JE004525
RAFKIN ET AL. ©2014. American Geophysical Union. All Rights Reserved. 1347
variations is not considered. From a statistical standpoint, it will be shown that average day-to-day variations
in the diurnal pressure cycle are an order of magnitude or larger than the variation of pressure that may
be driven by changes in dust. Statistically, as will be shown, the changes in pressure due to the changes in
dust may be neglected.
3. RAD Instrument Overview
RAD consists of a charged particle telescope of Si detectors, scintillating plastic (Bicron BC432), and a CsI
crystal for the detection of neutral particles (Figure 2). A detailed description of the instrument can be found
in Hassler et al. [2012].
Both the CsI—hereinafter referred to as the “D” detector—and the “E” plastic scintillator are surrounded by
an anticoincidence shield (also made of scintillating plastic and referred to as the “F” detector) that can be
used to discriminate and reject charged particles that do not enter through the telescope, allowing the
selection of clean samples of neutral particle events. Determining the spectra of incident neutrons and γ rays
requires a complex method to invert the spectra recorded in D and E. This inversion is done on the ground
[e.g., Köhler et al., 2011, 2014], but useful information about neutral particle fluxes can also be obtained
simply from examining count rates inD and E, as will be explained below. BothD and E are sensitive to charged
particles as well as neutral particles.
4. Observations
Figure 3 shows the total dose rate measured in E over the first 100 landed sols and the neutral count rate from
sols 282 to 350 of the MSL mission. The dose rate in E is calculated without consideration of whether events
Figure 2. Schematic of the RAD instrument (adapted from Hassler et al. [2012]). A, B, and C are solid-state silicon detectors.
D and E are the blocks of CsI and Bicron, respectively. F is an anticoincidence detector. Examples of valid particle events are
shown in green events. Paths in red are rejected. Not all possible valid events are shown.
Journal of Geophysical Research: Planets 10.1002/2013JE004525
RAFKIN ET AL. ©2014. American Geophysical Union. All Rights Reserved. 1348
were also identified in any of the
other detectors. Thus, the dose in E
can be considered the total dose of all
measurable energetic particles, both
charged and neutral. This includes
recoil protons and Compton electrons
produced by neutrons and γ-rays,
respectively. In contrast, the neutral E
count rate considers triggers in the
other detectors; none of the B, C, or F
detectors may trigger, as these
indicate that a charged particle has
entered the instrument. Since the
readjustment of the F threshold
parameter occurred at sol 282, the
statistics of the neutral count rate are
analyzed only from this point,
because discrimination of neutrals
from charged particles depends
crucially on the F trigger threshold.
Shown in Figure 4 is the atmospheric
surface pressure as recorded by the
Rover Environmental Monitoring
Station (REMS), as explained by Harri
et al. [2014]. Curiosity landed at a time
of near-minimum global pressure
when the southern CO2 ice cap was
near maximal extent. The average daily
pressure began increasing from that
time. Superimposed on the long-term
seasonal trend is a diurnal pressure
signal driven by the thermal tide.
4.1. Data Analysis
We wish to isolate the diurnal
variations in the RAD Emeasurements
from the numerous other signals that
include potential secular changes
from longer-term changes in
atmospheric shielding (i.e., pressure)
and variability of the heliosphere,
including solar energetic particle
events. One possible method is to use spectral techniques such as Fourier analysis. However, given the
sometimes nearly discontinuous changes in dose (e.g., at sols ~50, ~95, and especially after ~200 due to
Forbush decreases), such spectral analyses can produce spurious spectral signals at high frequencies that
could contaminate physical signals. Instead, we employ basic binning and averaging techniques to produce
an average diurnal dose perturbation.
The average diurnal dose perturbation is computed as follows: Let Et,S be the dose rate at time t on sol S. The
time series is then binned into hourly averages for each sol. For all t in S falling between hours h and h+1, the
hourly average dose rate on sol S is Eh;S ¼ 1N ∑Et;S, where N is the number of observations in the 1h interval, h.
The average dose rate on sol S is then Es ¼ 124 ∑ h¼24h¼1 Eh;S. We require N≥1 for all h in a given S to limit biasing of
the average. The hourly dose rate perturbation on sol S is defined as E’h;S ¼ Eh;S  Es : The hourly dose rate
Figure 3. (top) Total E dose rate for the first 350 sols, (middle) a subset of the
time series from sol 22 to 25 showing a diurnal signal, and (bottom) neutral E
count rate starting at sol 282 when the F threshold was adjusted. In Figure 3
(middle), a boxcar-smoothed average is shown with the raw data.
Journal of Geophysical Research: Planets 10.1002/2013JE004525
RAFKIN ET AL. ©2014. American Geophysical Union. All Rights Reserved. 1349
perturbation for hour h averaged over
all 350 sols is E ′h ¼ 1NS ∑S ¼ 100S ¼ 1 E′h;S, where
NS is the total number of sols with 24
valid hourly values (Figure 4). The same
method is applied to the Eneutral count
rate (N′h ) and to the surface pressure
(p′h ) obtained from REMS (Figure 4).
However, in the case of the E neutral
count rate, analysis is started at sol 282,
for reasons discussed in Appendix B.
Throughout the binning and
averaging processes, the standard
error is computed and propagated
through the calculations. Uncertainties
during each averaging operation are
added in quadrature to compute the
overall standard error [Taylor, 1997].
Standard error represents the
uncertainty on the estimate of the
average value rather than the spread of
measurements (i.e., standard deviation)
that contribute to the average. In the
case of pressure, the signal is very
repeatable with very little scatter. It is
clear from the standard error that any
variation in the thermal tide due to the
changes in dust loading is statistically
small compared to the overall signal.
Pressure is generally recorded at 1Hz
over 5min periods or longer, providing tens of thousands of measurements over a 350 sol period. This
repeatability and the large number of measurements drive the standard error to very small values. The total
dose and E neutral count rate also have small errors compared to the mean values. The great number of data
points efficiently reduces the individual variability within a given hour. The binning, perturbation analysis,
and coadding of dose rate and neutral count rate dramatically boost the diurnal signal above the noise.
Systematic instrument errors of the RAD instrument, such as the temperature-dependent gain, are not
factored into the error bars. In the case of pressure, the inherent 1.5 Pa relative accuracy of the pressure
sensor [Harri et al., 2014] is not included in the error bars of the pressure averages, although this is clearly
inconsequential given the magnitude of the diurnal pressure cycle.
4.2. Discussion
Figure 6 shows E ’h versus p
’
h and N
’
h versus p
’
h . The correlation coefficient for linear regression (Pearson R
2) is 97%
and 96%, respectively. The total dose rate (detector E) decreases as pressure increases. This is due to the increased
shielding from the atmosphere as pressure increases. On the other hand, the neutral count rate increases as
pressure increases, which is due to the production of secondary neutrals at altitudes above the Pfotzer maximum
[e.g., Richter and Rasch, 2008; Bazilevskaya and Svirzhevskaya, 1998]. This is in contrast to the behavior of neutron
monitors at the surface of the Earth, which are at altitudes below the Pfotzer maximum and record a lower
neutron count rate when atmospheric pressure increases [e.g., Nakamura et al., 1987; Florek et al., 1996; Roesler
et al., 1998]. At altitudes above the Pfotzer maximum (i.e., the situation at the surface of Mars), the number
of particles increases with increasing pressure, because many primaries remain after nuclear interaction, thus
preserving the initial flux plus the additional secondaries. At altitudes below the Pfotzer maximum, enough
primaries and secondaries are absorbed so as to produce a net decrease in flux with increasing pressure. At
pressures of 7–10hPa at Gale Crater, the shielding ofMars’ atmosphere is equivalent to being at an altitude above
the Pfotzer maximum [Richter and Rasch, 2008]; that is, the Pfotzer maximum occurs below the surface, in the
Figure 4. Surface pressure recorded by REMS over (top) the first 350 sols and
for (bottom) the same three sols as shown in the middle of Figure 2. Note
that the pressure data have been subsampled; only one out of every 200
readings has been plotted.
Journal of Geophysical Research: Planets 10.1002/2013JE004525
RAFKIN ET AL. ©2014. American Geophysical Union. All Rights Reserved. 1350
Martian regolith. Note that the pressure
of the Pfotzer maximum is effectively
independent of the atmosphere under
consideration. It is instead a function of
the column mass through which the
particles are transported. The Pfotzer
maximumoccurs at ~100g/cm2. On Earth,
this corresponds to ~20km above ground
level. For comparison, the surface pressure
on Mars is equivalent to the pressure on
Earth at ~30km. Thus, onMars, the Pfotzer
maximum is belowground.
Despite the strong linear correlation in
Figure 5, there is a slight departure from
linearity, giving the data for both doses
and count rate something similar to an
“S” shape. Further investigation reveals
that this is not due to nonlinearity in the
detector but rather is likely the result of
an interaction between the (very slight)
residual temperature dependence in
the readout electronics combined with
the time lag of pressure changes with
respect to surface temperature changes.
Pressure responds to the changes inmean
column temperature, not just surface
temperature. Although the surface
temperature is a good proxy for column-
wide temperature changes, it is not
perfect. The thermal tide does have
vertical structure, and any phase tilt
with height will produce a very small lag
between the surface temperature and
the mean column temperature [e.g.,
Banfield et al., 2003].
An interesting aspect of the diurnal radiation signal is that there is a preferential impact of atmospheric shielding
as Z of the primary GCRs increases. To illustrate this, consider that RAD uses coincidence logic to define multiple
event triggers. These triggers are continuously counted and are stored per observation. Two of the triggers
are particularly useful for present purposes: (1) a “heavy-ion” trigger (so-called L2[9]) that requires a very large
energy deposition (energy> 1GeV) that are mostly due to heavy ions in theD detector and (2) a “light-particle”
trigger that requires coincident hits in the A and B detectors (represented as A*B) with a veto from the “C2”
detector (so-called L2[0] + L2[1]). The C2 detector is outside the nominal viewing cone of the charged particle
telescope but nonetheless is likely to trigger (due to electronic crosstalk) when a heavy ion enters the RAD,
using it as a veto in the context of the A*B trigger, therefore effectively restricts that trigger to fire only on the
lowest Z particles (charge 1 or 2). The ratio of the count rates of these two triggers averaged over all sols for
each hour is shown in Figure 6 (top). In Figure 6 (bottom), the count rate of the heavy ions is plotted against the
light-ion count rate. The ratio of the channels in Figure 6 (top) removes through normalization similar trends
present in both data, such as might be due to heliospheric variation. That a diurnal signal is still present in
Figure 6 (top) reveals that heavy ions are being disproportionately affected by atmospheric shielding. Specifically,
there is a minimum in the ratio at the same time as the pressure perturbation minimum. At the same time,
Figure 6 (bottom) shows that the light-particle count rate averages about 6.5× 104± 3×103 day1 (i.e., <20%
peak-to-peak variation), while the heavy ions average 2000±500day1 (i.e., >50% peak-to-peak variation).
Proportionately, the heavy ions undergo much larger variation than the light ions. At pressure minimum,
-6
-4
-2
0
2
4
6
0 4 8 12 16 20
G
y/
da
y
Hour
Total E Dose Perturbation
-8.E+03
-6.E+03
-4.E+03
-2.E+03
0.E+00
2.E+03
4.E+03
6.E+03
0 4 8 12 16 20
Co
un
t R
at
e 
(d
ay
-
1 )
Hour
E Neutral (L2[6]) Hourly Perturbations
-60
-40
-20
0
20
40
60
0 4 8 12 16 20
Pa
Hour
Pressure Perturbation
(a)
(b)
(c)
Figure 5. Hourly perturbations from daily average, binned, and averaged
for total (a) E dose, (b) E neutral count rate, and (c) pressure.
Journal of Geophysical Research: Planets 10.1002/2013JE004525
RAFKIN ET AL. ©2014. American Geophysical Union. All Rights Reserved. 1351
the ratio (Figure 6 (bottom)) decreases,
which indicates that the heavy-ion
counts are going up faster than the
light ions. Conversely, as the ratio
rises, the heavy-ion count rate is
falling more quickly (i.e., they are more
affected by shielding) than the light-
ion rate. As described below, this
preferential shielding is consistent with
model results.
Numerous studies have modeled the
energetic particle radiation at the surface
of Mars. Comparing the results from
these studies to the RAD observations
is difficult, because they often make
different assumptions about the cosmic
and solar input, the depth of atmosphere,
and the energy range and types of
particles producing the dose. Further,
none of the studies exclusively
encompasses or limits the energy
ranges or species to those observable
by RAD. For all these reasons, direct
comparisons between observations and
published predictions are challenging.
No previous theoretical work has predicted the small diurnal variations of the Martian surface radiation
environment that are observed. However, calculations as a function of surface elevation have been
made, and these can be used to estimate the diurnal excursions, since changes in elevation correspond
to changes in pressure, as given by equation (1) or (2). Cucinotta et al. [2002] calculated the annual
dose equivalent and particle hits/cell/year for GCRs as a function of surface altitude and particle type at
solar maximum conditions. The quantitative data provided in tables from Cucinotta et al. [2002] do not
cover altitudes below 0m (Gale Crater is ~4.5 km), but there is still useful information to be gleaned.
At solar maximum conditions, the number of proton hits increases by ~5% going from 0 km to 8 km in
elevation. Using a reasonable scale height of 8 km for Mars, this change in altitude very nearly represents
an e-folding of pressure or about a ~63% reduction in pressure. This pressure change is almost 5 times
what is observed (~12%) in the surface diurnal pressure cycle. Thus, linearly scaling the model predictions
by a factor of 5, proton hits would only be expected to change by ~1%. He nuclei hits increase by
almost a factor of 2 (i.e., 100% increase) going from 0 km to 8 km in the model. Applying scaling
according to the observed pressure variation, an increase of ~20% would be expected for He hits over the
course of sol.
H and He account for nearly all the GCR particle hits in the model (~87% H and ~11% He), and even
though the He rates are much smaller than H, there is a much larger impact of pressure changes on these
nuclei. The total expected variation of GCR hits with ~12% pressure variation is the sum of the fractional
changes due to H and He: 0.87 × (1.0%) + 0.11 × (20%) ≈ 3%. Even though He makes up a small fraction
of the particle population, the total variation as a function of pressure is largely due to the changes in
the flux of He nuclei.
The observed variation in the E dose rate over a diurnal cycle averages about 10 μGy/sol peak to peak
(Figure 4) out of ~206 μGy/sol (Figure 3), or ~5% from peak to peak. The dose measured by E includes
charged particles plus neutrals, whereas Cucinotta et al. [2002] exclude neutral contributions. Also, a comparison
between dose and particle hit rates is not physically meaningful without taking into account the energy
deposition associated with each event. Nonetheless, since the total dose in RAD is dominated by charged
y =-8.5987x -6E-06 
R² = 0.9728
-60
-40
-20
0
20
40
60
-5 -4 -3 -2 -1 0 1 2 3 4 5
Pr
es
su
re
 
Pe
rt
ur
ba
tio
n 
(P
a)
E Dose Perturbation ( Gy/day)
Total E Dose and Pressure Correlation
y = 0.0084x + 1E-06
R² = 0.9558
-60
-40
-20
0
20
40
60
-8.E+03 -6.E+03 -4.E+03 -2.E+03 0.E+00 2.E+03 4.E+03P
re
ss
ur
e 
Pe
rt
ur
ba
tio
n 
(P
a)
Neutral Count (/day)
Neutral (L2[6]) and Pressure 
Correlation
Figure 6. Correlation of perturbation (top) E dose and (bottom) E neutral
count rates with pressure perturbations.
Journal of Geophysical Research: Planets 10.1002/2013JE004525
RAFKIN ET AL. ©2014. American Geophysical Union. All Rights Reserved. 1352
particles, and assuming that the change in total dose results primarily from attenuation of particle number
rather than energy, the observed trend of increasing dose with decreasing pressure (or increasing
altitude) is qualitatively consistent with the model results and not far off from the ~3% we estimated for
variations in the hydrogen and helium fluxes based on the results in Cucinotta et al. [2002]. Since the
model estimates were based on simple linear interpolation and extrapolation to the altitudes below the
0m datum, such differences are not unexpected.
The strong diurnal signal seen in the ion ratios can largely be explained by nuclear fragmentation in the
atmosphere. A simulation using the Bethe-Bloch confusion and apprehension in the scientific community
fragmentationmodel [Zeitlin et al., 1996; Guetersloh et al., 2006] was performed to give insight into the behavior
of the heavy-ion flux under varying atmospheric conditions. The model combines the Badhwar-O’Neill (BO)
GCR fluxmodel [O’Neill, 2010] with the nuclear fragmentationmodel version 2 (NUCFRG2) nuclear cross-section
model [Wilson et al., 1994] and a detailed energy loss calculation based on the Bethe equation [Beringer et al.,
2012]. Ions with charges Z≥ 4 were generated according to the abundances and energy distributions in the BO
model and were transported through varying depths of CO2 to a simplified model of the RAD. A simulated
count in L2[9] was defined to be an energy deposition greater than 1GeV in the D detector, as it is in the data.
This is our operational definition of a heavy ion for present purposes.
Simulations were run for several depths of CO2. The number of particles that meet the heavy-ion criterion is
found to fall exponentially with increasing column depth, at a rate of about 6.4%/g cm2 of CO2 over the
range of depths seen in themission to date. The diurnal variations in pressure are on the order of 100 Pa, peak
to peak, corresponding to a column density change of about 2.7 g cm2. This implies that the heavy-ion
count rate should vary by about 17% peak to peak, in reasonable agreement with the 20% peak-to-peak
variation visible in Figure 7 (top).
Keating et al. [2005] made note of the dependence of Mars surface neutron radiation on atmospheric
temperature but only in the context of seasonal changes. Neutron fluence was found to decrease
with increasing temperature. From scale height arguments, this is consistent with the pressure and
atmospheric mass column decreasing and the commensurate decrease in atmospheric neutron production
(assuming that the surface temperature is a proxy for mean column temperature). However, the
atmospheric data used to produce these results were taken from the European Mars Climate Database
[Forget et al., 2006], which inherently also has the seasonal CO2 cycle. It is not possible to discern whether
the variation in fluence is being driven by changes in scale height or from the net change in atmospheric
mass due to the CO2 condensation cycle. Finally, DeAngelis et al. [2006, 2004] show neutron flux for
energies greater than 100MeV decreasing with topographic elevation. Again, this is consistent with what is
observed by RAD.
Observations of thermal and epithermal neutrons have been previously made from orbit using the High Energy
Neutron Detector (HEND) as part of the Gamma Ray Spectrometer experiment on Mars Odyssey [e.g., Feldman
et al., 2002;Mitrofanov et al., 2002; Boynton et al., 2002]. Despite the use of “high energy” in HEND, the detected
neutrons are of much lower energy (below ~0.5MeV) than those detected by RAD. Further, the bulk of the
neutrons originating from the Mars system and detected from orbit are produced and thermalized in the
regolith, whereas the bulk of the neutrons detected by RAD are produced in the atmosphere. As noted by
Mitrofanov et al. [2002], the depth of the atmosphere between Odyssey and the surface changes as the
topography changes. In the case of HEND, calculations suggested an ~15% variation in neutron flux from
themean column associated with column changes of 5 g/cm2 to 15g/cm2. These variations are far smaller than
the variations driven by the heterogeneity of H in the regolith. Further, because of the far different energies,
the different physics involved in generation, and the different regolith and atmospheric transport processes
compared to neutrons measured by RAD, it is difficult to draw any quantitative connection between the
Odyssey and the RAD observations. Two points are relevant, however. First, both Odyssey and RAD neutron
measurements are impacted by the atmosphere. Second, HEND is most sensitive to neutrons from the regolith,
while RAD is most sensitive to neutrons from the atmosphere.
The Dynamic Albedo of Neutron (DAN) experiment on the MSL rover is also currently making
measurements of the Mars neutron environment [Mitrofanov et al., 2012]. When observing in passive
mode, DAN is most sensitive to the thermal and epithermal neutrons generated by the interaction of
cosmic rays with the regolith and any H within. Thus, it is similar to HEND, except that it is a more
Journal of Geophysical Research: Planets 10.1002/2013JE004525
RAFKIN ET AL. ©2014. American Geophysical Union. All Rights Reserved. 1353
localized experiment and atmospheric
shielding effects are not important. In
activemode, DAN fires ~14MeVneutrons
into the regolith in order to generate
lower energy (thermal and epithermal)
albedo neutrons in the regolith that
are diagnostic of H. These actively
generated neutrons are at the low end
of the range measured by RAD. As with
HEND, the energy sensitivity of DAN
and RAD are quite different, and the two
instruments primarily measure neutrons
of different origin.
5. Summary and Conclusion
The measurements of the total dose
rate and the neutral count rate made by
the MSL RAD instrument on the surface
of Mars at Gale Crater show that the
energetic particle flux is influenced by
diurnal pressure changes associated
with the atmospheric thermal tide. This
detection of the diurnal variation is a
novel finding that has not previously
been considered in the literature.
At the relatively low atmospheric pressures of Mars, the total dose rate increases (decreases) as pressure
decreases (increases). The neutral count rate shows an opposite effect. The absolute magnitude of the
correlation between the radiation rates and the pressure is greater than 90%, and these variations with
pressure are fully consistent with an atmospheric column mass equivalent to being well above the altitude of
the Pfozter maximum. Furthermore, the atmospheric shielding was found to be disproportionately effective
on heavy ions. Again, this effect is qualitatively consistent with linearly scaled model results, but the overall
magnitude of the effect appears somewhat smaller in the observational data.
The scaling arguments invoked to compare the RAD data with the model results in the literature illustrate the
challenges in making direct, quantitative comparisons. Few if any published model results provide
quantitative information for elevations substantially below the 0m topography datum. Yet it is these low
altitudes where robotic spacecraft tend to land and where future human missions will go to take advantage
of the additional atmospheric mass during entry, descent, and landing. None of the modeling results
provides exclusive information on the energetic particles that are measured by RAD. Future comparisons
would greatly benefit from modeling studies that provide results based on energy cuts and detection
efficiencies as described by Hassler et al. [2012].
Besides the thermal tide, there are other processes that can change the column mass and modulate the
flux of energetic particle radiation at the surface. The seasonal condensation cycle will produce as much
as a 25% change in column mass [e.g., Hess et al., 1980]. By definition, the seasonal effect would require
a longer time scale to observe than the diurnal effect noted in this paper, and RAD is collecting long-term
statistics to make an assessment of any seasonal impact. Mars, like Earth, has low-pressure storm systems,
but these are generally confined to higher latitudes. At the near-equatorial location of Gale Crater, it is
unlikely that such middle-latitude storm systems will have much of an impact. Dust devils can also
produce a substantial drop in pressure, but these occur on such a short time scale (e.g., much less than the
typical 32min integration period of a RAD observation) that any corresponding changes in radiation
will not be detectable. If a local dust storm were to occur at or near the landing site, it is possible that
the pressure could drop for hours to days [Rafkin, 2009], and this should be detectable in the radiation
environment at the surface.
Figure 7. Ratio of the binned to (top) L2[0] + L2[1] light-ion count rates
to L2[9] heavy-ion count rates and (bottom) light- versus heavy-ion
count rates.
Journal of Geophysical Research: Planets 10.1002/2013JE004525
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Finally, there is additional work to be done to better understand the impact of column mass changes on the
radiation environment, whether due to the seasons, the tide, or dust storms. Future work in this area will
benefit from the inversion of the neutral dose into neutron and gamma ray dose, and further analysis of RAD
histogram and pulse height analysis (PHA) data will provide additional information on how different Z
particles interact with the atmosphere as a function of energy. At the same time, additional work is needed to
validate existing models against the wealth of the RAD data that has been and continues to be collected.
Appendix A: Definition of Symbols
ADC Analog-to-digital converter
Cp Heat capacity of air (770 J Kg
1 K1)
Et,S E dose rate at time t on sol S (μGy/d)
Eh,S E dose rate in hourly bin h on sol S (μGy/d)
E ’h;S Hourly E dose rate perturbation from Es (μGy/d)
E ’h The hourly perturbation E dose rate averaged over all sols (μGy/d)
Es Average E dose rate on sol S (μGy/d)
g Gravitational acceleration (3.72m/s2)
G Gain of ADC response (MeV/ADC count)
H= RT/g Scale height
N’h The hourly perturbation neutral count rate averaged over all sols (s
1)
M Baseline ADC (i.e., noise floor)
P Atmospheric pressure
ps Surface pressure
po Arbitrary reference pressure
p’h The hourly pressure perturbation averaged over all sols (Pa)
ρ Atmospheric density
R Ideal Gas Law Constant (192 Jkg1 s1)
T Kinetic temperature
z Vertical distance
Z Nucleon charge
Appendix B: E Channel Bias Corrections
The total energy deposited in E is recorded in real time by the onboard software; this total energy provides
a measure of dose of both charged particles and neutral particles in a tissue-like material. The overall count
rate of valid hits in E is recorded, and a count rate of neutral particles in E is also kept. The latter is
determined from the E channel by counting only the subset of events with valid hits in E and no significant
energy in B, C, or F. A valid hit is one above threshold, where threshold levels are set to be just above
electronic noise levels. For E specifically, a valid hit is a hit in the scintillator, which generates light that is in
turn collected in two or more of the three light collection diodes.
This logic excludes charged particles that enter RAD through the telescope or from the side or bottom; actual
neutral particles produce signals in D and/or Ewithout triggering any of the other detectors. The inversion to
determine neutron dose is not required for this study; only neutral count rates are considered.
The minimum detectable energy of particles in E depends on the amount of shielding presented by the
combined RAD and MSL mechanical structures. Protons with energies greater than ~95MeV incident at the
top of RAD have a high probability of making it through the telescope, through D, and into E. The energies at
which particles stop in D depend on their charge, Z; for example, Fe nuclei (Z=26) with energies up to
~500MeV/nuc stop in D. Of course, many charged particles need not pass through the telescope or D to be
counted in the total E dose. For instance, a proton of ~20–30MeV coming from the side has sufficient range to
pass through F and into E. Such particles count toward the total dose in E, but are not counted as neutrals,
because they trigger F.
Initial surface data from RAD showed that one of the F threshold triggers was set too high. The result of this
was the contamination of the E neutral count rate by charged particles that failed to trigger the
Journal of Geophysical Research: Planets 10.1002/2013JE004525
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anticoincidence shield. This threshold setting was adjusted at sol 282 of the surface mission. Consequently,
the neutral count rate presented here is obtained from after sol 282. The total dose rate in E is unaffected by
the F threshold, and the data from this channel through sol 100 are used.
In addition to the instrument and rover shielding, the temperature sensitivity of the detectors and the
electronics needs to be considered. The work function of silicon is nearly temperature independent, as is the
light output of plastic scintillator (E), but the preamplifiers and back-end electronics are known to have a
slight temperature dependence that varies from channel to channel. Prior to launch, RAD underwent
calibration studies to characterize the temperature dependence of its response.
The energy deposited in a detector is obtained from digitized pulses by the following relationship:
Energy MeVð Þ ¼ ADCMð Þ * G; (4)
where ADC is the amplitude as determined by the analog-to-digital converter, M is the baseline value (i.e., the
ADC reading with no energy deposit), and G is the gain in units of MeV per ADC count. Both M and G can be
temperature dependent with sensitivity determined during preflight calibration [Hassler et al., 2012]. G was
studied for eight channels, all of which showed a relatively flat gain curve over the operating temperature range
during the first 100 sols on Mars. All the channels are consistent with an ~2% decrease in G in going from10°C
to 40°C. This temperature dependence
is not taken into account in the
onboard processing but has been
applied in ground processing of dose
rate data, as presented in this paper.
The temperature dependence of M is
taken into account in onboard
processing, based on data obtained
during thermal vacuum testing. The
onboard correction is given in
uploaded tables as a delta offset to the
baseline value, M, for each channel
(many offsets are found to be 0). The
baseline shifts for the E readout
channels are shown in Table B1. The
record of instrument temperatures is
shown in Figure B1. Corrections of as
much as 5ADC counts are subtracted
from baseline M values that are in the
range from 1600 to 2000, with G
values ranging from 0.04 to 0.83. An
ADC value of 400 counts above
baseline in a high-gain channel would,
without correction, result in an energy
of ~18MeV, depending on the
channel. Applying a correction of (for
example) 5ADC counts to the baseline
would change the energy by 0.2MeV
or about 1.3%. For larger-energy
depositions, the relative baseline
Table B1. Temperature Corrections for Baseline Shifts
Low-Gain Channel Medium-Gain Channel High-Gain Channel #1 High-Gain Channel #2
15°C offset Δ 3 0 3 1
25°C offset Δ 0 0 0 0
30°C offset Δ 2 0 2 1
≥35°C offset Δ 5 0 5 2
Figure B1. The time series of RAD temperatures shows that the instrument is
warmest during the day and coldest just prior to sunrise. These temperatures
are used to determine baseline shifts as shown in Table B1 and as deter-
mined from preflight and in-flight cruise calibration.
Journal of Geophysical Research: Planets 10.1002/2013JE004525
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correction becomes even smaller. These minor corrections should be interpreted in the context of the average
energy deposit that contributes to the E dose rate calculation. The flux-weighted average is ~23MeV, and the
dose-weighted average is ~97MeV. Therefore, even if the compensation offsets were 100% in error, we expect
that they would have a negligible effect on the E dose rate variations. We tested and affirmed this hypothesis
by taking the data for seven sols with the baseline compensation disabled; no changewas seen in themagnitude
or direction of the diurnal effect.
An additional potential effect is found in the threshold settings that determine the validity of an event.
Thresholds are generally set to signal levels that are just above the noise peak. Since the width of the noise
peak for a given channel can be temperature dependent, errors in setting the threshold could conceivably
result in some noise being confused with a valid event or some valid events being classified as noise and
ignored. Careful study of the surface data shows no significant temperature dependence of the E or F trigger
thresholds. However, as previously noted, one of the F trigger thresholds was not optimally set (regardless of
temperature) in the early surface mission.
Besides the calibration studies, some information about temperature dependence can be obtained by
looking at the data during cruise and the aforementioned period on the surface when all internal
temperature corrections were disabled. During the cruise, RAD temperatures were extremely stable and
decreased slowly as the spacecraft increased its distance from the Sun. In contrast, on the surface, RAD
temperatures change diurnally. Also, it is possible to investigate during nominal operational configuration
when temperature corrections are applied, whether any substantial contribution from the noise peak leaks
into the signal due to inaccurate threshold or ADC correction offsets. In all cases, the E detector results were
robust. The offset in M had an undetectable effect compared to the situation on the surface where it was
disabled. This result is consistent with the small delta values. At lower energies, where the delta has the
greatest (but still minor) effect, the number of particles may be relatively large, but the contribution to the
dose from these energy depositions is small. Since no onboard correction is done with the gain settings, any
influence from this effect still needs to be considered.
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at the Jet Propulsion Laboratory,
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