new techniques for predicting solar proton fluences for radiation effects applications

6
2772 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 43, NO. 6, DECEMBER 1996 NE UES FOR PRE ICTING SOLAR PROTON LUENCES FOR ~ DIATIQN EFFECTS APPLICATIONS M.A. Xapso;, G.P. Summers*', P. Shapiro' and E.A. Burke' *Naval Research Laboratory, Washington DC 20375 "University of Maryland Baltimore County, Baltimore MD 21228 %FA, Inc., Landover MD 20875 A bsfract At geosynchronous altitudes, solar proton events can be a significant source of radiation exposure for devices such as optical imagers, memories and solar cells. These events appear to occur randomly with respect to time and magnitude during the active period of each solar cycle. New probabilistic descriptions, including extreme value theory, are given in forms applicable to assessing mission risks for both single events and the cumulative fluence of multiple events. The analyses yield simpler forms than previous models, include more recent data, and can easily be incorporated into existing computer programs. I. INTRODUCTION It is essential for spacecraft designers to have reliable methods for quantitatively assessing radiation exposure of microelectronics. One of the major forces currently driving space activity is communication satellite systems. Studies have shown that geosynchronous orbits have a significant cost advantage for such systems [l]. In geosynchronous orbits, damage is mainly due to exposure in the outer trapped radiation belt (trapped electrons) and from solar proton events. This paper focuses on the latter of these. For further information about this radiation environment, the reader is referred to Feynman and Gabriel [2]. From a radiation effects viewpoint, it is useful to have information about both the fluence due to single solar proton events, and the accumulated fluence over periods of time corresponding to various mission lengths. Fluences due to single solar events allow estimates of important quantities such as SEU rates during the event, the resulting sudden change in transistor threshold voltages, and the resulting sudden drop in the output power of solar cells. On the other hand, to determine whether or not the microelectronic components will survive the mission, the corresponding total fluence must be known. for many years to determine design specifications for structures that must withstand extreme environmental phenomena such as floods, earthquakes, high wind gusts and large temperature variations. It has an extensive theoretical and practical history [3-51, and is shown here to also be applicable to solar event phenomena. An advantage of this methodology is that only the largest events are required as input data. This makes update predictions easy to make as new data becomes available. There are several existing models for predicting the cumulative fluence of solar proton events over a given time interval [6-81. An idea common to all of these is that the events are treated as a Poisson process with magnitudes that vary. This is sometimes referred to as a compound Poisson process [9]. Such analyses are most useful when either the distribution of event magnitudes is known or the cumulative distribution is known for some time period. The reason is that this allows the subsequent distributions for larger numbers of events to be calculated. Much previous effort has been spent attempting to determine the distribution of single events. The most common assumption is that of a lognormal distribution, but it is recognized that this is probably not completely adequate [&lo]. For the purpose of predicting cumulative fluences, it will be shown that it is advantageous to initially focus on the distribution of total annual Juences rather than that of individual events. The distribution of annual fluences is shown to be well described by the lognormal distribution. The compound Poisson formalism is then used to predict total fluences for time periods greater than one year, corresponding to realistic lengths of spacecraft missions. In Section 11, characteristics of solar proton events that are important for radiation damage in microelectronics are briefly reviewed, and the sources for the proton event data used are identified. Section 111 gives the essential methodology for applying extreme value statistics to single events, followed by results. Section IV is an analogous section on the application of compound Poisson process statistics to cumulative (multiple event) fluences. In addition, comparisons to a current model are presented here. Section V is a brief review of proton event energy spectra. In this paper extreme value statistics is applied, for the first time, to model single solar proton events. Exqreme value statistics is a well established field of mathematics used 0018-9499/96$05.00 0 1996 IEEE

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Page 1: New techniques for predicting solar proton fluences for radiation effects applications

2772 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 43, NO. 6, DECEMBER 1996

NE UES FOR PRE ICTING SOLAR PROTON LUENCES FOR ~

DIATIQN EFFECTS APPLICATIONS

M.A. Xapso;, G.P. Summers*', P. Shapiro' and E.A. Burke' *Naval Research Laboratory, Washington DC 20375

"University of Maryland Baltimore County, Baltimore MD 21228 %FA, Inc., Landover MD 20875

A bsfract

At geosynchronous altitudes, solar proton events can be a significant source of radiation exposure for devices such as optical imagers, memories and solar cells. These events appear to occur randomly with respect to time and magnitude during the active period of each solar cycle. New probabilistic descriptions, including extreme value theory, are given in forms applicable to assessing mission risks for both single events and the cumulative fluence of multiple events. The analyses yield simpler forms than previous models, include more recent data, and can easily be incorporated into existing computer programs.

I. INTRODUCTION

It is essential for spacecraft designers to have reliable methods for quantitatively assessing radiation exposure of microelectronics. One of the major forces currently driving space activity is communication satellite systems. Studies have shown that geosynchronous orbits have a significant cost advantage for such systems [l]. In geosynchronous orbits, damage is mainly due to exposure in the outer trapped radiation belt (trapped electrons) and from solar proton events. This paper focuses on the latter of these. For further information about this radiation environment, the reader is referred to Feynman and Gabriel [2].

From a radiation effects viewpoint, it is useful to have information about both the fluence due to single solar proton events, and the accumulated fluence over periods of time corresponding to various mission lengths. Fluences due to single solar events allow estimates of important quantities such as SEU rates during the event, the resulting sudden change in transistor threshold voltages, and the resulting sudden drop in the output power of solar cells. On the other hand, to determine whether or not the microelectronic components will survive the mission, the corresponding total fluence must be known.

for many years to determine design specifications for structures that must withstand extreme environmental phenomena such as floods, earthquakes, high wind gusts and large temperature variations. It has an extensive theoretical and practical history [3-51, and is shown here to also be applicable to solar event phenomena. An advantage of this methodology is that only the largest events are required as input data. This makes update predictions easy to make as new data becomes available.

There are several existing models for predicting the cumulative fluence of solar proton events over a given time interval [6-81. An idea common to all of these is that the events are treated as a Poisson process with magnitudes that vary. This is sometimes referred to as a compound Poisson process [9]. Such analyses are most useful when either the distribution of event magnitudes is known or the cumulative distribution is known for some time period. The reason is that this allows the subsequent distributions for larger numbers of events to be calculated. Much previous effort has been spent attempting to determine the distribution of single events. The most common assumption is that of a lognormal distribution, but it is recognized that this is probably not completely adequate [&lo]. For the purpose of predicting cumulative fluences, it will be shown that it is advantageous to initially focus on the distribution of total annual Juences rather than that of individual events. The distribution of annual fluences is shown to be well described by the lognormal distribution. The compound Poisson formalism is then used to predict total fluences for time periods greater than one year, corresponding to realistic lengths of spacecraft missions.

In Section 11, characteristics of solar proton events that are important for radiation damage in microelectronics are briefly reviewed, and the sources for the proton event data used are identified. Section 111 gives the essential methodology for applying extreme value statistics to single events, followed by results. Section IV is an analogous section on the application of compound Poisson process statistics to cumulative (multiple event) fluences. In addition, comparisons to a current model are presented here. Section V is a brief review of proton event energy spectra.

In this paper extreme value statistics is applied, for the first time, to model single solar proton events. Exqreme value statistics is a well established field of mathematics used

0018-9499/96$05.00 0 1996 IEEE

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Energy Spectrum: 1 - 500 MeV Integral Fluence: > io9 cm-2 Duration: hours to days Peak Flux: > io5 cm-2 s-’ Frequency: > 1 per active year Ionizine Dose: 1000 - 5000 r a d W

Information for preparing the data for such a plot and on preparing exqreme value probability paper is given in a number of sources [3,4,16]. Any of the three distributions can be plotted on type I probability paper, but this requires a change of variables for the type I1 and 111 distributions. For our application of the type I1 distribution this change is

Damage Equivalence:

The probability of large events with characteristics where q5p is the proton fluence. The cumulative distribution similar to those shown in Table I is a function of the 11 year function of maximum values observed in time interval To for solar cycle, which is composed of 7 active and 4 inactive the type I1 distribution can then be written years. The 1 1 year cycle was first noted by nineteenth century

back to the year 1749. Thus, we are currently at the end of cycle 22. The 7 active years span a starting point 2.5 years before and an ending point 4.5 years after a peak time defined by sunspot activity. These peaks for the last 4 cycles (19-22) were at 1957.9, 1968.9, 1979.9 and 1989.9 [8].

astronomers based on sunspot data, and was reconstructed FTo(x) = exp(-exp[-a(x -U)]) (2)

where a and U are fitting parameters [16]. The corresponding cumulative distribution for time interval T is then

> 1013 1 MeV electrons/cm2

Detailed data for the magnitude and frequency of solar proton events exists for cycles 19-22. However, identification of an event is not necessarily straightforward. For example, multiple events can occur which make it difficult to separate the individual contributions. In the analyses reported here, the tables of Shea and Smart were used as data for solar cycles 19-21 [ll]. The multiple events are identfied in that tabulation. Cycle 22 data was obtained from Shea and Smart [12], Stassinopoulos [13,14] and N O M [U]. In our analyses, it is assumed that the start of the solar year is June 1.

111. APPLICATION OF EXTREME VALUE THEORY TO SINGLE SOLAR PROTON EVENT

DISTRIBUTIONS

In this section, a methodology is developed to predict the probability of encountering a large solar proton event of a given magnitude during a specified period of time. This is accomplished by using the statistics of extremes.

A . Background

An important feature of extreme value theory is that if only the largest event is considered from each of a number of equal time intervals, the number of distributions that might describe the largest events is quite limited [5]. Typically,

(3)

B. Results

Figure 1 shows results for extreme value probability plots using type I paper as described above. In this Figure, the largest event that has occurred annually (i.e. To = 1 year) for each of the 28 active years of cycles 19-22 is displayed. The two cases plotted are fluences for proton energies 2 10 MeV and 2 30 MeV. It is seen that in each case except for the few lowest fluence points, the data give an excellent fit to a straight line, indicating the applicability of the theory. To interpret the plot, note that at a fluence of 10” cm-*, the cumulative probability is about 0.9 for the 2 10 MeV case. This means that in active years, 90% of the largest annual single events have a fluence I 10” cme2. This can also be interpreted to mean that there is a 10% chance that the largest event in an active year will exceed 10” cm-2. The straight lines shown in Figure 1 are the result of a regression fit of equation (2) to the data. This yielded parameters that were a = 0.9605 and U = 20.76 for the 2 IO MeV data. For the 2 30 MeV data, a = 0.8648 and U = 19.04. These parameters can be used directly in equation (2) to obtain the probabilities analytically. The results shown in Figure 1 were compared to data that includes only cycles 19-21. The two cases give similar results. This is encouraging in that it appears that enough data has been obtained that the predictions will remain relatively stable.

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i

o o i o o 5 o i 0 2 0 8 0 4 o s O B 0 7 0 8 085 o s 099 0 % 097 om

Cumulative Probability

Figure 1 . Extreme value probability plot of the largest annual solar proton event in an active year in cycles 19-22. Flumes are shown for energies 2 10 MeV and for energies 2 30 MeV. The plot is constructed on type I probability paper. See text.

Note that for the 2 10 MeV case the fitted parameters a and LI should only be used for fluences above about 5 x 10' For the zi 30 MeV case, those parameters

used for fluences a b v e about 1 x 10' cm-2. few data points at the lowest fluences form a

distinct break with the straight line in both cases is an indication that these events are being sampled from a

[5 ] . This might be due to a different SEI. However, there is insufficient data interpretation of this finding in terms of

From a int, it is the large events that are the

the basic mechanisms of solar proton events. radiation damage most important, a are well described by the model.

The results shown in Figure 1 are for a time period of one active year in the solar cycle. This can be extended to longer time intervals using equation (3). Such results are shown for the 2 10 MeV case in Figure 2 for periods of 2 , 3 , 5 and 7 active years. In Figure 2, the ordinate is the probability

ng a given fluence, i.e., 1 - FT (x). Continuing with the previous cited example, the probability that the largest observed event exceeds 10" cm'2 is about 20% for a mission that includes 2 active years and 55% for one that includes 7 active years.

Note that since the model includes only active years of the solar cycle, the results obtained are dependent on both the mission duration and the start date relative to the solar

cycle. For example, a 5 year mission with a start date at the beginning of the active period is subject to proton events during the entire mission. The 5 year curve in Figure 2 should be used for assessment. If the mission starts when the 4 year inactive phase of the cycle begins, the one year curve should be used.

S I O 1 1

10 10 10

Fluence (an-2)

Figure 2. Probability that the largest solar proton event observed in the time period show exceeds a given fluencx of >- 10 MeV protons. The time periods shown refer to active years of the solar cycle.

IV. APPLICATION OF COMPOUND POISSON THEORY TO CUMULATIVE FLUENCE

DISTRIBUTIONS

In this section a method is developed to predict the probability of encountering a given total proton event fluence over the course of a mission.

A. Background

A compound Poisson process depends on the number of events, and the distribution of event magnitudes. The mathematics of constructing probability distributions for multiple events has been discussed previously [9]. There are physical phenomena described in the literature that are compound Poisson processes having an event distribution that is lognormal [17,18]. An important consequence of this is that there is a strong tendency for the distribution to remain lognormal with the occurrence and addition of subsequent events to the distribution. This will prove to be a very useful property because 3 if the multiple event distribution is

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protons, and 2.01 x lo9 cm-' for 2 30 MeV protons. The relative variance of the fluence for T active years is

lognormal for some given time period, it should remain so for longer periods.

The cumulative lognormal distribution of proton fluence #p is obtained by numerically integrating the differential distribution (probability density) over fluence P91.

The differential distribution is given by

where the parameters p and II can be expressed in terms of the mean proton fluence, , and its relative variance, V,e, :

R = In(&) - OS/?' (7)

B. Results

Figure 3 shows the total annual fluences for each of the 28 active years of the last four solar cycles plotted on lognormal probability paper. This is shown for two proton energy thresholds - 2 10 MeV and 2 30 MeV. Each point shown represents the total fluence contributed by all the solar proton events in a given active year. On this type of probability paper, a lognormal distribution is a straight line. Thus, it is demonstrated by the regression fits to the straight lines shown that the total annual fluence for active years closely resembles a lognormal distribution. Further analysis was performed by comparing these fits to those obtained for cycles 19-21 as well as to cycles 20-22. There was little difference among the comparisons, indicating that the model is stable with respect to data updates.

Thus, in order to predict the cumulative distribution for time periods 2 1 active year, equations (4) - (7) are used along with the average fluence, p, and its relative variance, Vrer , for the number of active years of interest. From known relations for compound Poisson processes [SI, the average fluence for T active years is

where is the average fluence for 1 active year. This quantity is obtained by averaging the annual fluences for the 28 active years. The results are 8.09 x lo9 cm-2 for 2 10 MeV

(9)

where V,I,, is the relative variance for 1 active year. This 1 year quantity was again calculated from the 28 active year data. The results are 1.68 for 2 10 MeV protons, and 2.12 for 2 30 MeV protons.

001 006 0 1 0 2 O S 0 4 0 5 0 6 0 7 0 8 0 9 O S 5 0963

Cumulative Probability

Figure 3. Probability plot, constructed on lognormal probability paper, of the total annual solar proton event fluence for active years in cycles 19-22. Fluences are shown for energies 2 10 MeV and for energies 2 30 MeV. The straight lines shown are regression fits to the data and indicate it is a lognormal distribution. See text.

Equations (4) - (9) can now be used to calculate the probability of exceeding a given fluence, 1 - FCm , for given mission lengths. Results for 2 10 MeV protons are shown in Figure 4 for 1, 2, 3, 5 and 7 active years. Thus, the probability of exceeding a fluence of 10" cm" in one active year is about 24%, while in 7 active years it is essentially 1.

Results obtained for the cumulative fluences for a 3 active year period are compared to the JPL model [SI in Figure 5. The JPL result, shown by the dashed line, is based on data for cycles 19, 20 and 21 whereas the present model, shown by the solid line, also includes cycle 22. It is seen that the JPL model shows a steeper slope so that it tends to predict lesser fluences at low confidence levels and greater fluences at high confidence levels. As a further comparison, the distribution shown by the points in Figure 5 was obtained by repeatedly and randomly selecting 3 of the 28 active years in cycles 19-22, and summing the 3 annual fluences. It is well

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established that this is a valid technique for generating such a distribution from a discrete set of data [20]. The data distribution is in better overall agreement with the present model.

10 1 1

10 10 10

Fluence (cm * )

Figure 4. Probability of exceeding a total solar proton event fluence of 2 10 MeV protons during the number of active years indicated.

Cumulative Probabilfty

Figure 5. Cumulative fluence comparison of the present model (solid line) with the JPL model [8] (dashed line) and with data (points) for a time period of3 active years. See text.

of comparisons are shown in Figure 6 for a 7 active year period, and again similar conclusions can be drawn. It is ~ m ~ ~ n t to keep in mind that the present model is not afi t to the distribution of data points shown in Figures 5 and 6. The data distribution was constructed as an

independent method to verify the present model. One further point that should be noted about the JPL model is that it has recently been updated [lo]. Compared to results shown in Figures 5 and 6, the updated JPL model predicts a slope that is in better agreement with our model and the data distributions shown. However, the magnitude of the predicted fluences show worse agreement.

Cumulative Probability

Figure 6 . Cumulative fluence comparison ofthe present model (solid line) with the P L model [SI (dashed line) and with data (points) for a time period of 7 active years. See text.

V. REVIEW OF SOLAR. PROTON EVENT ENERGY SPECTRA

In terms of assessing radiation risk, variations in the solar proton event energy spectrum are often secondary in importance compared to variations in event fluences. However, the proton energy spectrum must be characterized. A number of approaches to describe this have been reported, and some results that may be helpful are briefly summarized here.

If the effect of interest is insensitive to the energy spectrum, the average energy above a given threshold can be useful [13j. The average energy for several recent events with a 10 MeV threshold ranged from 25 to 50 MeV. For a 30 MeV threshold, the average ranged from 45 to 95 MeV. More elaborate descriptions of the spectra are also available, In some cases, it has been found to fit an exponential in energy [21] but more generally an exponential in rigidity has been used 1221. The rigidity for a number of events from November 1972 to February 1986 has been tabulated [22]. More recently, the energy spectrum has been fitted with an acceleration model [23]. Finally, worst case models have

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been proposed and published in a NASA Environment Guidelines report [24]. The information contained therein is probably the most conservative approach to use for risk assessment.

VI. SUMMARY AND CONCLUSIONS

Two new methods for describing solar proton event fluences have been presented. One is based on extreme value theory, and describes the probability of encountering a single large event over the course of a space mission. The other is based on compound Poisson process theory, and describes the probability of encountering various total fluence levels over the course of the mission. Both models describe all of the available data for cycles 19-22 quite well and are stable with respect to the addition of new data. Results for space missions of typical lengths have been given in the form of probability graphs, which can be used for risk assessment. In addition, the new models are described by more convenient expressions than earlier models, which should lend itself to incorporation in available computer programs for space radiation effects.

ACKNOWLEDGMENT

The authors thank Dr. E.G. Stassinopoulos of NASA- Goddard Space Flight Center for kindly providing tabulated solar proton event data for cycle 22.

REFERENCES

[l] G.P. Summers, R.J. Walters, S.R. Messenger and E.A. Burke, “Role of Radiation-hard Solar Cells in Minimizing the Costs of Global Satellite Communications Systems”, Prog. Photovoltaics: Res and Applic., 4, 147-154 (1996).

[2] J. Feynman and S.B. Gabriel, “High-Energy Charged Particles in Space at One Astronomical Unit”, IEEE Trans. Nucl. Sci.,

[3] E.J. Gumbel, Statistics of Extremes, Columbia University Press, NY, 1958.

[4] E. Castillo, Extreme Value Theory, Academic Press, Inc., Boston, 1988.

[SI R.V. Canfield, D.R. Olsen and T.L. Chen, “Extreme Value Theory with Application to Hydrology” pp.336-350, in Statistical Distributions in Scientific Work Vol 6, edited by C. Taillie, G.P. Patil and B.A. Baldessari, D. Reidel Publishing Co., Boston, 1980.

[6] J.H. King, “Solar Proton Fluences for 1977-1983 Space Missions”, J. Spacecrafl, 11,401 408 ( 1974).

[7] E.G. Stassinopoulos and J.H. King, “Empirical Solar Proton Models for Orbiting Spacecrafl Applications”, IEEE Trans. Aerospace and Elect. Sys., 10,442450 (1974).

[SI J. Feynman, T.P. Armstrong, L. Dao-Gibner and S.M. Silverman, “New Interplanetary Proton Fluence Model”, J. Spacecraft, 27,403410 (1990).

43,344-352 (1996).

[9] A.M. Kellerer, “Fundamentals of Microdosimetry”, in The Dosimetv of Ionizing Radiation, Vol. I , edited by K.R. Kase, B.E. Bjamgard and F.H. Attix, Academic Press Inc., NY, 1985.

[lo] J. Feynman, G. Spitale, J. Wang and S. Gabriel, “Interplanetary Fluence Model: JFL 1991”, J. Geophys. Res., 98, 13281-13294 (1 993).

[l I ] M.A. Shea and D.F. Smart, “A Summary of Major Solar Proton Events”, Solar Phys., 127,297-320 (1 990).

[12] M.A. Shea and D.F. Smart, “A Comparison of Energetic Solar Proton Events During the Declining Phase of Four Solar Cycles (Cycles 19-22)”, Adv. Space Res., 16, (9)37-(9)46 (1995).

[13] E.G. Stassinopoulos, G.J. Brucker, D.W. Nakamura, C.A. Stauffer, G.B. Lee and J.L. Barth, “Solar Flare Proton Evaluation at Geostationary Orbits for Engineering Applications”, IEEE Trans. Nucl. Sci., 43, No. 2, 369-382 (Apr. 1996).

[ 14) E.G. Stassinopoulos - private communication. [15] Solar Geophysical Data, No. 603 - Part II, pp.28-31, published

by National Oceanic and Atmospheric Administration, Boulder, CO, Nov. 1994.

[16] A.H-S. Ang and W.H. Tang, Probabiliv Concepts in Engineering Planning and Design. Vol. I - Basic Pnnciples, John Wiley & Sons, NY, 1975.

1171 M.A. Xapsos, E.A. Burke, P. Shapiro and G.P. Summers, “Probability Distributions of Energy Deposition and Ionization in Sub-micrometer Sites of Condensed Media”, Radiat. Meas.,

I181 W.E. Wilson, N.F. Metting and H.G. Paretzke, “Microdosimetric Aspects of 0.3- to 20-MeV Proton Tracks”, Radiat. Res., 115, 389-402 (1988).

[19] J. Aitchison and J.A.C. Brown, The Log Nonnul Distribution, Cambridge University Press, Cambridge, U.K., 1957.

[20] B. Efron and R.J. Tibshirani, An Introduction to the Bootstrap, Chapman & Hall, NY, 1993.

[21] C. Tranquille and E.J. Daly, “An Evaluation of Solar-Proton Event Models for ESA Missions’’, ESA Journal, 16, 275-297 ( 1992).

[22] J.N. Goswami, R.E. McGuire, R.C. Reedy, D. La1 and R. Jha, “Solar Flare Protons and Alpha Particles During the Last Three Solar Cycles”, J. Geophys. Res., 93,7195-7205 (1988).

[23] P.P. Majewski, E. Normand and DL. Oberg, “A New Solar Flare Heavy Ion Model and Its Implementation Through MACREE, An Improved Modeling Tool to Calculate Single Event Effect Rates in Space”, IEEE Trans. Nucl. Sci., 12,2043- 2050 (1 995).

[24] B.J. Anderson and R.E. Smith, “Natural Orbital Environment Guidelines for Use in Aerospace Vehicle Development”, NASA Technical Memorandum 4527, Marshall Space Flight Center, Alabama, June 1994.

26, NO. 1, 1-9 (1 996).