solar modulation of dose rate onboard the mir station

IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 44, NO. 6, DECEMBER 1997 2529

Solar Modulation of Dose RateOnboard the Mir StationG. D. Badhwar, V. A. Shurshakov, and V. V. Tsetlin

Abstract—Models of the radiation belts that are currently usedto estimate exposure for astronauts describe the environment attimes of either solar minimum or solar maximum. Static models,constructed using data acquired prior to 1970 during a solar cyclewith relatively low solar radio flux, have flux uncertainties ofa factor of two to five and dose-rate uncertainties of a factorof about two. The inability of these static models to provide adynamic description of the radiation belt environment limits ourability to predict radiation exposures for long-duration missionsin low earth orbits. In an attempt to add some predictive capa-bility of these models, we studied the measured daily absorbeddose rate on the Mir orbital station over roughly the complete22nd solar cycle that saw some of the highest solar flux valuesin the last 40 y. We show that the daily trapped particle doserate is an approximate power law function of daily atmosphericdensity. Atmospheric density values are in turn obtained fromstandard correlation with observed solar radio noise flux. Thiscorrelation improves, particularly during periods of high solaractivity, if the density at roughly 400 days earlier time is used.This study suggests the possibility of a dose- and flux-predictivetrapped-belt model based on atmospheric density.

Index Terms—Atmospheric density, dose, radiation belt.

I. INTRODUCTION

T HE TRAPPED radiation belt particles present a verysignificant hazard to the astronauts and flight equipment

electronics in low earth orbit. The International Space Station(ISS) will be a permanently manned facility in a 51.65inclination orbit with altitude varying from 370 to 470 km, de-pending upon the solar activity level. In addition, the assemblyof the station will require the crew to spend considerable timeexternal to the station. The currently used trapped-belt modelsAP-8 and AE-8 [1], [2] are based on data acquired prior to1970 during solar cycle 20 with relatively low solar flux. Thesemodels describe the environment at solar minimum (solarradio noise 10.7 cm flux, ) and solar maximum( ). Cycles 21 and 22 were much larger, with

in excess of 250. No valid radiation model exists forsuch large values of . The AP-8 model and other staticmodels CRRESPRO [3] and GOST [4] describe the flux toan accuracy of a factor two to five. The CRRESPRO modeldescribes the environment at high values, but only forproton energies below 90 MeV. Above this energy, it is stillthe AP-8 MAX model only.

Manuscript received April 28, 1997; revised August 4, 1997.G. D. Badhwar is with NASA Johnson Space Center, Houston, TX 77058-

3696 USA (e-mail: [email protected]).V. A. Shurshakov and V. V. Tsetlin are with the Institute of Biomedical

Problems, Moscow, 100051 Russia.Publisher Item Identifier S 0018-9499(97)09035-7.

Comparison of AP-8 model predictions with measured doserates in the Space Shuttle and Mir show model uncertaintiesof factors of two [5]. Comparison with dose-rate measure-ments on the CRRES satellite [6] confirm these findings. Inorder to improve the dose-rate prediction capability, Hardy[7] developed empirical modifications to the AP-8 modeldose predictions to better describe the then-existing Shuttledosimetry data. Golightly [8], using these empirical curves,compared the predictions of crew doses on Space Shuttleflights with actual measurements, and found that the dosepredictions of the empirically adjusted AP-8 model were off bymore than 70% for many flights. This prediction accuracy hasbeen acceptable for short duration Shuttle flights, but the longstay times on Mir and ISS, with increased numbers of youngerastronauts, and larger numbers of female astronauts, requireimproved accuracies of model prediction. Incorporating thesolar cycle dependence of flux (dose rate) is an important stepin this direction.

Solar cycle changes in the flux of trapped-belt protons at lowaltitudes were studied by Blanchard and Hess [9] and recentlyby Huston et al. [10] using the NOAA/TIROS data. Theseinvestigations showed that: 1) the proton flux varies during thesolar cycle, changing by a factor of five from solar minimumto maximum at invariant ; 2) the peak of the protonflux lags the solar minimum by about one year at lowvaluesand nearly two years at highervalues; 3) the proton flux hasa rather broad minimum and lags the maximum of theflux; and 4) as the solar maximum is approached, the fluxdecreases more rapidly than it increases as one approaches thesolar minimum. The strong flux variation and the hysteresiseffect between the rising and falling portions of the solar cyclemust be included in the trapped-belt models if they are tobe used in risk estimation. Proton lifetimes within the beltsare determined primarily by energy losses to electrons and bycollisions with atmospheric nuclei. Cornwellet al. [11] andHeckman and Brady [12] computed the average atmosphericdensity for a model atmosphere. Dragt [13] extended thesestudies to provide the variation of trapped particle fluxes asa function of solar activity. Singer [14] and Ray [15] showedthat, for particle energies that contribute most to the radiationdose at an orbiting spacecraft, the product of theequilibriumproton flux and the average atmospheric density is a constant,a condition that is satisfied during times of low solar andmagnetic activity. Pfitzer [16] using the AP8 model, showedthat for a 28.5 inclination orbit and altitudes in the 300–600-km range, this relationship was satisfied under both solar

0018–9499/97$10.00 1997 IEEE

2530 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 44, NO. 6, DECEMBER 1997

Fig. 1. Total dose rate measured by the D2 ion chamber as a function of time.

Fig. 2. Total measured D2 rate+ a random number between 0–5 mrad/day as a function of time.

BADHWAR et al.: SOLAR MODULATION OF DOSE RATE 2531

minimum and solar maximum conditions, thus opening up thepossibility of an atmospheric density driven dynamic trapped-belt model. In these calculations Pfitzer used the density atthe altitude of crossing the South Atlantic Anomaly (SAA)and a simplified version of the U.S. Air Force atmosphericdensity model. He proposed that the dosefor all spacestation conditions can be calculated using

(1)

where is the altitude of SAA crossing, is the shieldingdistribution function, and is the atmospheric density. Thesums are over different shielding directions,. Thus, for a fixedshielding distribution, the dose rate and atmospheric densityhave a power law relationship. Since the proton lifetimes aredetermined by energy losses to electrons and collisions withatmospheric nuclei, it is the average atmospheric density alonga trapped particle trajectory that should best correlate withproton fluxes. Such calculations were first done by Heckmanand Brady [12] and have been stressed recently by Lemaireetal. [17]. Kern [18] extended the work of Ray [15] and showedthat the trajectory averaged density, in a dipole field, isproportional to the mirror point density. He pointed out thatthe density is a factor of 10 smaller if the longitudinal drift ofprotons is taken into account. In circular orbiting spacecraftsthat sample a variety of values, the trajectory averageddensity should thus be nearly proportional to the density atSAA crossings.

Golightly et al. [19] examined the dose rates measured bypassive thermoluminescent detectors (TLD’s) mounted at fixedlocations in the crew compartment of the Space Shuttle andshowed that the trapped dose rate could be fitted as a powerlaw in density ( ) as suggested by Pfitzer, but showedlarge dispersion around the mean. These flights covered nearlytwo solar cycles from 1981 to 1995 and a wide altitude rangefrom 290 to 600 km. Thus there was a large variation ofboth dose rates and atmospheric density. However, becauseof the short duration of Shuttle flights (3–16 days), the dataare sampled at discrete times only. Also, because most of theflights are at low altitude, the estimated trapped dose rate issensitive to the correction applied for the galactic cosmic ray(GCR) contribution to the total TLD dose rate (GCR doserate Total dose rate). Panasyuket al. [20] qualitativelyexamined the time variation of the absorbed dose rate onMir station for the five years from January 1991 to December1995 and suggested that the trapped particle dose rate has aseasonaldependence, reaching maximum values in summerin the northern hemisphere. They suggested that this is due tothe known seasonal variation of the atmospheric density andwould be more pronounced at 800 km than at 400 km. Thesestudies point to the fact that the atmospheric density can bean effective organizing parameter for flux and dose rates andcould lead to a model with the potential for predicting doserates at intermediate times between the solar minimum andsolar maximum.

This paper examines dose-rate data acquired by ion cham-bers onboard the Mir orbital station and its relationship to

atmospheric density with the goal, eventually, of developing atime-dependent trapped-belt dose-rate model that is applicableto the ISS. The data were acquired during solar cycles 21 and22 and cover a much broader range of values than wasused in building the AP-8 trapped-belt models. This analysisis supplemented with data acquired by a tissue-equivalentproportional counter (TEPC) operating onboard the Mir stationsince March 1995 and the Radiation Environment Monitor(REM) operating outside the Mir station since November 1994.

II. I NSTRUMENTATION

The absorbed dose-rate data onboard the Mir station wereacquired using two argon-filled ionization chambers, called R-16 [21]. One of the chambers (D2) has a self-shielding of

0.5 g/cm of glass, and the other identical chamber (D1) hasan additional 3 g/cm of tissue equivalent shielding material.These detectors are mounted in the Base Block of the Mirstation and have an isotropic response. They have quoteduncertainties of 15% on dose rate. The data are transmittedonce a day inquantized5 mrad/day intervals, androundedoff of to the next lower integer number. Thus a true doserate value of 19 mrad/day, for example, is reported as Integer(19/5) 3. The residual of 4 mrad/day (19 5 3) is addedto the next day’s dose rate. Thus one knows that the truerates lies between 15 and 20 mrad/day only, and not the truevalue of 19 mrad/day. If one added a random number between0–5 mrad/day to the value of 15 mrad/day, the new value ismore likely to be closer to the true value. This procedure justsmooths out the data and does not effect the errors in thedata. The transmitted values do not always correspond to anexact 24-h interval. The actual time interval depends upon thetime of Mir’s pass over the Russian receiving stations. Thisintroduces an uncertainty in a measured dose rate of5%.Fig. 1 shows the “daily” total absorbed dose rate as a functionof time. The steps are due to quantization of the data. Thissmoothed data set is shown in Fig. 2 and has been used insubsequent analyses. The minimum energy required to reachthese two detectors are 40 and 70 MeV for protons and 4 and8.5 MeV for electrons.

A second detector, a TEPC [22] was mounted in the BaseBlock (CORE module) in March 1995 and has been operatingsince. It simulates a 2-m-diameter tissue site. It recordslinear energy transfer spectra every minute, from which thedaily absorbed dose rates are computed. Using the dose raterecorded at 1-min intervals, the galactic and trapped-belt dosecontributions are separated and converted into daily dose ratevalues. Fig. 3 shows the TEPC’s estimated absorbed dose rateas a function of time. The sinusoidal variation has a quasi-periodicity of 27 days, corresponding to the solar rotationperiod that is seen also in the radio noise data. Theshielding distribution at the location of the TEPC and R-16 inthe Mir Base Block (CORE module) is shown in Fig. 4. TheTEPC is under approximately 4 g/cmof aluminum highershielding than the bare R-16 ion chamber (D2).

The Mir orbital station was launched in a 51.65inclinationin February 1986 and has been operating continuously since


Fig. 3. Trapped dose rate measured by TEPC as a function of time.

Fig. 4. Shielding distribution function at the location of R-16 and the TEPC in the Base Block of the Mir station.


Fig. 5. Altitude variation of the Mir station as a function of time.

Fig. 6. Plot of the daily and three solar rotation weightedF10:7 flux as a function of time.


Fig. 7. Plot of the calculated deceleration potential�, as a function of time.

Fig. 8. Estimated GCR dose rate as a function of time.


Fig. 9. Plot of the trapped-belt dose rate as a function of the altitude of SAA crossings.

then. The orbit is slightly elliptical, with apogee at times reach-ing 435 km and perigee at 365 km. It has been periodicallyboosted in altitude steps of approximately 20 km. The altitudeof the Mir station for each of the SAA crossings during agiven day was calculated using the Mir trajectory data. Theaverage of all the crossing altitudes for that day was used foranalysis.

The TEPC one-minute dose rates were merged with the as-flown Mir orbital trajectory. The altitude at the minute of SAAcrossing was determined from this merged data and used forfurther analyzes. Because of the higher time resolution it wasunnecessary to average the altitudes of SAA crossing as wasdone in case of the R-16 data set. This altitude, , isplotted in Fig. 5 as a function of time and shows significantvariation. In analyzing these sets, we havealwayscalculatedthe atmospheric density at the altitude of Mir station during theSAA crossing. In the case of TEPC measurements, this pointin time is also the time at which the dose rate was measured. Inthe case of R-16 and REM data, the altitudes of various SAAcrossings for one day were averaged to get the averaged SAAcrossing altitude of the day for which we have the averagedaily dose rate. Thus the dose-rate measurements and altitudeof SAA crossings correspond to essentially the same time.

III. D ATA ANALYSIS

The premise of this data analysis is that the trapped particledose rate is correlated to atmospheric density. As such, we

need to extract the trapped dose rate from the total dose rate(trapped galactic), measured by the R-16 ion chambers.The daily atmospheric densities were computed from theknowledge of average altitude of the Mir station duringSAA crossings, the daily flux, and the weighted 3-solar-rotation (81 days prior to the day of interest)flux (Fig. 6). A number of atmospheric density models ofcomparable accuracy exist [16], [23], [24]. For the purposeof these calculations, any of these models will do. Thesemodels differ significantly in their predictions only for veryhigh values of . A legitimate question that arises is whynot study the correlation of the dose rate with itselfand that of the atmospheric density, since the value isthe driver of atmospheric density? The reason is simple, thedose rate used in the study comes from a variety of altitudesand atmospheric density takes both the altitude and intoaccount, whereas does not depend on the Mir altitude.The parameter is useful for studies, such as Hustonetal. [10] when NOAA/TIROS data is coming from one altitude.In order to calculate the daily trapped dose rate from the R-16data, the daily GCR dose rate has to be estimated.

A. Estimation of GCR Dose Rate

Solar modulation of the GCR flux leads to the modulationof absorbed dose. These fluxes can be fairly accurately de-scribed by the diffusion-convection theory of Parker [25]. In aspherical symmetric heliosphere, the modulation of flux can be


Fig. 10. Plot of trapped-belt dose rate as a function of atmospheric density. The solid line is a power law fit to the data.

Fig. 11. Plot of trapped-belt dose rate (binned) as a function of atmospheric density (binned). Error bars are one standard deviation, and the solid lineis a power law fit that takes errors in both directions into account.


Fig. 12. Plot of the trapped dose rate and (1/density 400 days earlier) as a function of time.

well described in terms of a single parameter, the decelerationpotential . The deceleration parameter was calculated usingthe regression relationship of and the Climax neutronmonitor rate developed by Badhwar and O’Neill [26], as isshown in Fig. 7. The GCR dose rates can be calculated usingthe GCR environment model [27], the shielding distributionat the location of the detector, and the Langley-developedradiation transport code, HZETRN [28]. Comparing the resultsof these calculations to dose rates observed by a TEPC flownonboard 15 Space Shuttle flights, it has been shown that themodel provides GCR dose rates with a root mean square errorof 15%. Using the 57 inclination Shuttle measurements, anempirical relationship between the observed GCR dose rateand deceleration potential was developed and normalizedto the Mir-18 (March–July, 1995) measurements. GCR dose-rate values were calculated from using this empiricalrelationship with periodic checks with model calculations. Theaccuracy of these dose rates is estimated to be15%. Theresulting plot of the GCR daily dose rate versus time is shownin Fig. 8. These dose rates were subtracted from the R-16 totaldaily dose rate to estimate the trapped-belt contribution to thedose rates.

B. Trapped-Belt Dose Rate–Atmospheric Density Relationship

Fig. 9 shows an R-16 (D2)-derived trapped-belt dose rateas a function of . The average altitude of SAA crossingsvaried by nearly 60 km. There is no apparent correlationbetween the altitude and dose rate because data from different

solar activity levels have been mixed. In the 400–410-kmaltitude range, in a region containing most of the data, thereis a factor of 5–6 variation in dose rates, clearly the effect ofsolar modulation. Thus, unless the data are separated by solaractivity level, the altitude dependence cannot be used for dosepredictions. We next examine the dose–atmospheric densityrelationships.

As indicated earlier, there are a number of atmosphericdensity models. Given daily and 27, 54, and 81 dayaverages of daily fluxes, these models predict thedensity at a given altitudes. Some of these models take theindex into account also. A comparison of calculated densitiesfrom various models, however, shows that they all providenearly similar results, except for very high values ofvalues. It is not very important which model is actually used,but the chosen model is used systematically. In calculatingthe atmospheric density, we have always used the altitudeof SAA crossing, that is, the same altitude at which thedose rate is measured; Fig. 10 shows the trapped-belt doserate as a function of atmospheric density calculated using theJachia–Lineberry (J/L) model [23]. The solid line is the leastsquare power law fit to the nearly 2500 data points and isgiven by (mrad/day) , where thedensity is in units of g/cm with root mean square errorof 8.44 mrad/day. (Using the U.S. Air Force density model,the best fit line is given by .) Thereis a significant spread of the data along the best fit line. Asalready indicated, the rounding off of the telemetered dose


Fig. 13. Plot of the trapped dose rate as a function of density 400 days earlier. The solid line is a power law fit.

rate and the time interval not being exactly 24 h, results ina standard deviation of 15% in dose-rate error. Adding theerrors due to the subtraction of the GCR background rate, thetotal error would be nearly 20%. In Fig. 11, the same dataas in Fig. 10 has been replotted in binned density intervals.The error bars are each in standard deviation. The solid lineis again a power law fit to the data that takes into accounterrors in both the dose rate and density and is given by

. The standard deviation of dose ratesis slightly higher than the expected error of 20%. This arisesfrom two sources: 1) uncertainty in calculating the altitudeof Mir during SAA crossings resulting in errors in densityestimates and 2) changes in the Mir orientation required byoperational considerations that brings the known east–westasymmetry of dose rates into play.

Fig. 12 is a plot of the trapped dose rate and (1/density) asa function of time. The density curve has been shifted by 400days. If this is not performed, the alignment between thesetwo time profiles is very poor, particularly during periodsof high solar activity. However, the fit becomes worse asone approaches (1993) solar minimum, indicating that thetime lag is a function of solar activity. The dose-weightedproton energy for the R-16 location based on the Mir shieldingdistribution is 73 MeV. A 73-MeV proton at a 400 kmaltitude has a characteristic trapped lifetime of 400 days atsolar maximum. Fig. 13 is a plot of the trapped dose ratewith density calculated 400 days earlier. This fit is given by

with an rms error of 6.73 mrad/day.

The Mir orbit is frequently a 5-day repeated orbit, and if thedata are averaged over the 5-day period, the rms error dropsfrom 8.44 to 7 mrad/day with no time lag to 5 mrad/day with400 day time lag. This is shown in Fig. 14 where the powerlaw fit is given by . The R-16 dataclearly shows that the atmospheric density can be effectivelyused as a surrogate to describe the combined effects of altitudeand solar cycle variation.

The fitted lines in all cases of R-16 data have slopesof 0.3, nearly one-third of the slope (0.9) derived byGolightly et al. [19] from 56 Shuttle measurements. Most ofthese Shuttle flights were at lower altitudes (290–325 km)than the Mir station (385–425 km). As such, the derivedtrapped dose rates are prone to errors introduced by thesubtraction of the GCR dose rates. An overcorrection due tothe GCR background subtraction will lead to a steepening ofthe power law dose–density relationship. In this study, thedensity calculations were done using either the daily orstraight average over one, two, and three solar rotations. TheJachia–Lineberry atmospheric model, however, requires boththe daily and weighted values. As can be seenfrom Fig. 6, their method of density calculation would lead toerroneous density estimates during times of high solar activity,when weighted is nearly a constant, but the daily valuesfluctuate greatly. Since the Mir data spans a density rangeof 40, and the Shuttle measurements span a density range

1000, it is also possible that the slope becomes steeperwith larger density values than seen in the Mir data. Another


Fig. 14. Plot of 5-day average trapped dose rate and 5-day average atmospheric density. The solid line is a power law fit.

possible explanation lies in the relative accuracy with whichSAA crossing altitudes are estimated. Shuttle SAA crossingaltitudes have higher accuracy.

The TEPC data set does not suffer from many of theproblems associated with the R-16 data, and one would expectthe data spread to be smaller in this case. However, the TEPChas been operating only for the last two years during thetime of solar minimum and thus the density range coveredby the data set is limited. Fig. 15 shows both the data fromR-16 and TEPC. The TEPC instrument was in one of theattached modules (SPEKTR) and under higher shielding thanthe R-16 detectors. Thus the dose rates are smaller. Thesolid line is a least square fit to TEPC data and is givenby . It has a slightly steeper slope,much smaller data scatter than the spread from the R-16 data.The rms error is 3 mrad/day. The slopes of these lines arenot expected to be identical because the shielding geometrymodifies the transmitted radiation spectrum, and thus the twolocations do not see the same spectrum of particles. Buhleret al. [29] have reported a 25% increase of SAA dose ratesmade by their REM instrument outside the Mir station fromNovember 1, 1994 to February 1, 1996. This increase coincideswith the lowering of fluxes and a resulting decrease of

20% in atmospheric density. This is shown in Fig. 15. Theleast square fitted line is given bywith rmse of 3 mrad/day. The power law index of the REMand R-16 data are nearly the same. These data set also boundthe trapped-belt daily dose rates very well.

In examining the R-16 data it appears that the appropriateatmospheric density is that for times earlier than the dose-rateobservation times. This time lag, however, depends on the timein the solar cycle because of proton lifetime considerations.Further improvements in the correlation of dose rate withdensity can be made if this can be taken into account and offerpotentially the benefit of developing a predictive trapped-beltmodel.

The data analyzed in this paper pertains to absorbed doserates, whereas the AP-8 model is a flux-based model. Pfitzer[16] showed that the integral flux above a given proton energypredicted by the AP-8 could be represented by a quadraticequation

where ’s are the coefficient obtained from the fit. In the heartof the inner belt ( ) the count rate in the SAMPEX(Polar, 600-km orbit) PET 19-27 MeV channel increased fromabout 1 s to nearly 6 s as the flux dropped from

130 to 72 in the period from July 1992 to October 1995.These rates are correlated with the flux observations[30]. Such data sets can be used to estimate the a coefficients.

Differential energy spectra from instruments onboard CR-RES (18.1 inclination, perigee 350 km, and apogee 33 500km), SAMPEX (Polar orbit, 600 km altitude), and otherradiation monitors on various platforms should be analyzedusing atmospheric density as the organizing parameter to builda new dynamic trapped-belt model.


Fig. 15. Plot of trapped dose rate measured by TEPC in the SPEKTR module and the R-16 data (Fig. 10) as a function of atmospheric density. Solidlines are power law fits.

Fig. 16. Plot of trapped dose rate measured by TEPC, R-16, and REM as a function of atmospheric density. Solid lines are power law fits.


IV. CONCLUSIONS

Analyses of dose rates measured by R-16 ionization cham-bers onboard the Mir orbital station from September 1989to January 30, 1995, by a TEPC from March 2, 1995 toJanuary 10, 1997, and by REM instruments from November1994 to February 1996, show that: 1) trapped-belt dose ratescorrelate well with atmospheric density and this follows apower law relationship; 2) the correlation improves if theatmospheric density at an earlier time is used; 3) the root meansquare error of the fitted relation varies from 7–8.5 mrad/day(approximately 20% of the dose rate) and is consistent withknown error of ion chamber dose-rate measurements; 4) therms error for fitted TEPC data is 3 mrad/day, which, asexpected, is smaller than the rms errors from the R-16 data; 5)these power law relationships allow one to predict dose ratesat Mir locations dynamically; and 6) the studies suggest thepossibility of creating a density-dependent dynamic trapped-belt model.

ACKNOWLEDGMENT

The authors are grateful to O. Baltaji and J. Flanders,Lockheed-Martin Inc., Houston, TX, for help in the analysisof these data sets. They also want to thank Dr. T. Cleghorn,NASA, and Dr. J. Kern, Boeing, for carefully reading themanuscript.

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solar modulation of dose rate onboard the mir station

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