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Background Information Background Information
Solar particle models

Table of contents

Introduction
Solar proton effects on space systems
Predicting solar proton events
Solar proton fluence models
The King model
The JPL model
The Rosenqvist et al. (2005, 2007) model
The ESP models
The SAPPHIRE model
Solar heavy ion fluence models
The PSYCHIC model
The SAPPHIRE model
Using the solar particle fluence models
The King model
The JPL model
The Rosenqvist et al. (2005, 2007) model
Comparison of the King and JPL models
The ESP models
The PSYCHIC model
The SAPPHIRE model
Solar particle flux models
The CREME86 models
The CREME96 models
The Xapsos et al. (2000) model
The SAPPHIRE model
Geomagnetic attenuation and Earth shadowing
References

Introduction

Together with geomagnetically trapped particles and galactic cosmic rays, solar protons (and other ions) contribute to the terrestrial radiation environment and can present a hazard to both manned spaceflight and to the sensitive components used in satellite subsystems and instrumentation. Depending on the mission requirements of an Earth orbiting spacecraft, it may be possible to use the Earth's magnetic field to shield partially, or even completely, against solar particles. However, on interplanetary trajectories or on high altitude or high latitude Earth orbits, this is clearly not an option.

A number of significant events associated with past solar cycles may have been responsible for several spacecraft operational anomalies. Furthermore, radiation protection is a prime issue for space station operatons, for extended missions to the planet Mars, or for a return visit to the Moon. For these reasons and others, considerable interest has been shown in recent years concerning the prediction of solar proton fluences from data collected during past solar cycles.

Solar proton effects on space systems

The two most well known elements of satellite systems most susceptible to damage by solar protons are micro-electronics (single event upsets and total dose) and solar cells. Both are affected by ionisation and atomic displacement processes which in extreme cases can lead to the complete loss of a spacecraft. Charged Coupled Devices (CCDs) and other optoelectronic components such as opto-couplers, used in modern space-borne scientific instruments, are also prone to damage by energetic solar protons. Finally, the potentially lethal effects of high energy radiation on man also need to be considered. The physical parameter quantifying the ionisation effects of radiation on both materials and man is dose, which is defined as the energy deposition per unit mass. Equivalent fluence is used to quantify displacement damage in solar cells and CCD detectors.

The trend in recent years towards smaller and faster electronic components and more sensitive detectors has resulted in a need to understand and protect against solar proton effects on spacecraft systems. In earlier satellites, larger components were used which meant that single particles could only affect a limited volume of the device, and thus only cumulative damage resulting from multiple particle interactions could lead to malfunction. With the size of modern devices minimised to improve processing speed and power consumption, a single particle can have a significant effect and even cause irreversible damage to an electronic device. As a consequence, these devices are more susceptible to radiation effects than older components.

The main mechanism which allows an energetic proton to deposit energy as it passes through matter is ionisation. The energy given up by the incident particle results in the formation of electron-hole pairs which in turn causes the device performance to degrade.

Displacement damage occurs when the incoming energetic proton transfers momentum to atoms of the target material. If sufficient energy is transferred, the atom can be ejected from its location, leaving a vacancy or defect. The ensuing physical processes are varied and complex, but once again reduced device performance is the ultimate consequence. This is an important mechanism in solar cell, CCD, opto-coupler and material degradation.

Two further mechanisms of importance are those of the single event upset (SEU) and the single event latch-up (SEL) which occur when an incident charged particle deposits a short but intense charge trail in the sensitive volume of a component. This charge trail is capable of reversing the logic state of a memory element (SEU) or causing destructive latch-up where a parasitic current path is created, allowing large currents to destroy the device. This process is mainly limited to ions of higher atomic number than protons, since the linear energy transfer (LET or dE/dx) of heavy ions is significantly greater than that of protons. However, energetic protons can undergo nuclear interactions with component materials and the short range reaction products lead to an intense local charge generation, producing an SEU or even a latch-up.

Solar cell performance is also adversely affected by the ionisation and displacement mechanisms described above. Degradation results in the reduction of both the voltage and current output, which may have severe implications for the spacecraft lifetime.

Solar cells are usually made of silicon, although gallium arsenide cells can provide enhanced efficiency at increased production cost. They are arranged in series and in parallel to provide desired voltage and current levels, respectively, and collectively form the solar array. Thus, if a single cell fails in a string of cells, an open circuit will develop resulting in total power loss. Solar cell strings can be arranged in such a way as to minimise power loss from a complete array, but degradation is inevitable.

Solar cells are protected at the front by coverglass, providing shielding against protons. Annealing processes can also offset performance degradation caused by the ambient radiation environment. This is especially true for gallium arsenide cells and to a lesser extent for silicon cells.

Future interplanetary manned missions will need to consider solar flare activity very carefully due to the obvious detrimental effects of radiation on man. Very high doses during the transit phase of a mission can result in radiation sickness or even death. This is equally true for extended visits to surfaces of other planets and moons lacking a strong magnetic field capable of deflecting solar particles. The risk of developing cancer several years after a mission is somewhat more difficult to quantify, but must also be considered in mission planning.

Adequate radiation protection measures must be conceived for any lengthy interplanetary endeavours. Storm shelters will be necessary both on the transit spacecraft and on the planet surface. The latter can be provided to a certain extent by geological features of the visited body. The design of radiation shielding for a spacecraft is much more difficult given the inherent limitations associated with the construction of an interplanetary space vehicle.

SPENVIS Provides access to the following radiation effects models:

Predicting solar proton events

It is not possible to predict the exact occurrence, intensity or duration of solar proton events and consequently mission planning on both a short term and a long term basis can be problematic.

Short term forecasts are necessary for any tasks requiring extravehicular activity (EVA) and the operation of radiation sensitive scientific detectors. Real time observation of the Sun can provide useful warning of solar flare activity, as large proton events are usually associated with the strong emission of electromagnetic radiation, such as visible light, radio waves and soft X-rays during a flare.

By virtue of travelling at the speed of light, electromagnetic radiation reaches the vicinity of the Earth (or any other location in space) before any particulate radiation arrives (it takes electromagnetic radiation 8.5 minutes to reach the Earth from the Sun, whereas non-relativistic particles reach the Earth only hours or days later, depending on the particle energy). Protons first need to propagate through the solar corona to the foot of an interplanetary magnetic field line by diffusion. This process can already cause significant attenuation of particle fluxes if the flare site is a great distance from the field line. The next step is propagation through the interplanetary medium along the magnetic field lines, which during quiet conditions adopt an Archimedean spiral configuration. During this stage of propagation, the solar proton population can be significantly modified by several physical processes such as diffusion and acceleration caused, for example, by interplanetary travelling shocks or corotating interaction regions. Protons are usually scattered by the interplanetary medium, resulting in quasi-isotropic fluxes. However, certain large scale features of the magnetic field such as magnetic bottles or clouds can cause charged particles to temporarily adopt highly anisotropic distributions.

The most direct interplanetary field line connection with the Earth originates close to a heliographic longitude of 60° west. Thus it is quite possible that a large flare sited well away from this longitude will produce an insignificant increase of solar proton fluxes at the Earth. It is therefore important to be able to distinguish such false alarms which would otherwise interfere with spacecraft operations for no valid reason. Equally essential is to be able to obtain prior warning of solar protons when no electromagnetic activity has been monitored. This can happen when the flare site is hidden behind the solar limb, thus making optical, radio or X-ray observations difficult, if not impossible. An idealised sketch of the interplanetary medium and the propagation of radiation between the Sun and the Earth is shown in Fig. 1.

Interplanetary medium between the Sun and the Earth
Figure 1. An idealised representation of the interplanetary medium between the Sun and the Earth (adapted from Smart [1988]).

Long term predictions of the radiation levels resulting from events are required if costly overdesign or mission threatening underdesign are to be avoided. The dose accumulated over a mission lifetime is a function of the solar proton fluence (except for low inclination low Earth orbits, where geomagnetic shielding provides protection), so a reliable estimate of this fluence is needed by a spacecraft engineer to optimise design parameters.

As with any form of long term forecasting based on past observations, the statistical interpretation of data plays a central role in the final model definition. The size of the data set used will always be a limiting factor to the level of confidence associated with any solar proton model. In situ measurements of solar event particles by satellites have only been available since the early days of the space age. Prior to that, solar event fluences could only be inferred through ground based or low altitude measurements made by sounding rockets or balloons. Unfortunately, such techniques are prone to inaccuracy and can only be used with any real confidence for the last solar cycle before the advent of satellite technology.

Solar proton models

Essentially three solar proton event models are available to the spacecraft engineer for predicting long term solar proton fluences: the King [1974] model, the JPL model [Feynman et al., 1993], and the ESP models developed by Xapsos et al. [1999, 2000] for total fluence and worst event fluence. The King model was for a long time the standard model used to predict mission integrated solar proton fluences. It has been coded and made available to the community by NSSDC [Stassinopoulos, 1975]. The JPL model has been recommended for use for mission planning [Shea et al., 1988]. The ESP models were developed in the NASA Space Environment and Effects (SEE) framework.

The King model

The King solar proton model was constructed using data obtained exclusively during the active years of solar cycle 20 (1966-1972). The activity of the Sun during cycle 20 was different from that observed during the previous cycle in two important respects. Firstly, the largest annual mean sunspot number of cycle 19 was significantly greater than that of cycle 20 (see Fig. 2). Secondly, the event frequency and intensity of cycle 19 were much higher than those of the following cycle.

Annual mean sunspot number
Figure 2. Annual mean sunspot number. The blue and green vertical lines indicate the dates of solar maximum and minimum, respectively; the red rectangles show the solar maximum periods defined by Feynman et al. [1993] for the JPL models.

Predictions for solar cycle 21 indicated that the sunspot number would most probably be less than that measured during cycle 20, although this turned out to be false. Assuming that sunspot number and annual integrated solar proton fluence were linearly related, King chose to ignore the solar cycle 19 data set and took measurements made only in cycle 20 as representative of cycle 21.

The data set was mainly constructed from proton measurements (in the energy range 10-100 MeV) made by instruments on IMP 4, 5 and 6, which all flew in geocentric, highly elliptic orbits. The data from any individual instrument or satellite were cross-calibrated with independent measurements whenever possible, to check the mutual consistency of the complete data base.

There are 25 individual events used in the King data base, including the great proton event of August 1972, which accounted for about 70% of the total >10 MeV fluence for the complete solar cycle. Since this large event made such a dominant contribution to the total solar cycle fluence, King decided to separate it from the remaining 24 events, and to class it as an anomalously large (AL) event, in contrast to the remaining ordinary events. It is commonly accepted that if an Apollo mission had flown during the August 1972 event, the astronauts would have received severe (and potentially lethal) doses of radiation. Apollo 16 flew in April 1972 and the following (and final) mission of the programme flew in December of the same year.

The statistical approach used by King was based on methods employed by Yucker [1972] and Burrell [1972] in their analyses of earlier solar proton data. Yucker introduced the concept of compound probability to define the probability P of exceeding a specified fluence f of protons with energy greater than E during a mission lasting t years as


where f = 10F and N is the observed number of events occurring in T years. The probability p of observing exactly n events in t years is given by Burrell's [1972] extension of Poisson statistics:


which is valid for populations having a small number of samples. The probability Q that the logarithm of the combined fluence of n events will exceed F is given by:


where the recursive Q in the integrand is defined to be unity if the argument of the logarithm is less than or equal to zero, and to be zero if x<F and n=1 simultaneously. If the logarithmic fluences are normally distributed,


where <F> is the mean logarithmic fluence and sigma is the standard deviation.

The integrated energy spectrum of the August 1972 event was found to be best represented analytically by an exponential in energy:

J(>E) = J0 exp[(30-E)/E0] ,

with J0 = 7.9x109 cm-2 and E0 = 26.5 MeV. The ordinary events were found to best approximated by an exponential in rigidity R, which for protons is related to energy as:

R = (E2 + 1862 E)1/2 / 1000

and is measured in units of GV. Adams et al. [1981] have fitted the mean fluence for ordinary events as

J = 8.38x107 (e-E/20.2 + 45.6 e-E/3) .

This is the typical proton spectrum expected to arrive in the interplanetary medium near Earth as the result of an ordinary event, integrated over the period of the event. Adams et al. [1981] also provide a worst case spectrum:

J = 2.865x108 (e-E/30 + 22.0 e-E/4) ,

which is the most intense spectrum (with a 90% confidence level) expected in the interplanetary medium near the Earth as the result of an ordinary event. The three spectra are shown in Fig. 3.

King proton event spectra
Figure 3. Spectra used for the King [1974] solar proton model: ___ AL event spectrum; ___ mean ordinary event; ___ 90% worst case ordinary event.

The JPL model

Several assumptions made by King [1974] in his solar proton model were questionable and have been addressed by Feynman and colleagues in the development of the JPL model [Feynman et al., 1990]. Firstly, the omission of data from solar cycle 19 on account of the relationship between the cycle integrated fluence and maximum annual sunspot number was clearly not justified given the eventual history of cycle 21. Secondly, the separation of solar events into anomalously large and ordinary classes can be considered artificial if the major events of cycles 19 and 21 are considered. Furthermore, the relatively low number of events recorded during cycle 20 could only be expected to yield a model of limited statistical validity.

The data set used by Feynman et al. [1990] for the first version of the JPL model (JPL-85) includes observations obtained between 1956 and 1963 (during solar cycle 19) using detectors flown on rockets and balloons. After 1963, satellite monitoring of the near-Earth radiation environment became routine and an essentially continuous data base has been collected from measurements made by several spacecraft. The data used for the JPL-85 model cover three solar cycles.

Using the exact dates of solar maximum (1957.9, 1968.9, 1979.9 and 1989.9) as the zero reference year for each cycle, Feynman and colleagues were able to demonstrate that the active phase of the solar cycle lasted for 7 years of the complete 11 year cycle. The years of high fluence begin 2.5 years prior to the zero reference date, and end 4.5 years after this date (see Fig. 2). An asymmetry in the event frequency and intensity therefore exists with respect to the peak in solar activity. The JPL model only considers solar proton fluences throughout the seven hazardous years of a solar cycle, and ignores fluences during the remaining four quiet years.

The JPL-85 model has been replaced by a newer version, JPL-91 [Feynman et al., 1993]. The occurrence frequeny of the major events that dominate the total fluence do not appear to be randomly distributed in time. Instead, they appear to be much more common in some solar cycles than in others. In particular, in the 25 years between 1963 and 1988 there was only one major event (1972). In contrast, 3 or 4 major events occurred in the short time period from 1957 to 1963, and 4 or 5 major events have occurred between 1989 and 1991. It is therefore essential that the data set for a solar proton model is collected over several solar cycles so that it contains a good statistical sample of the major events. At the time the JPL-85 model was constructed, only one major proton event had taken place since 1963 when data collection in space had become routine. In the JPL-85 model this problem was dealt with by using data that had been collected before 1963. Although these data were of surprisingly good quality, they were collected and analysed with different techniques from the data collected after 1963. For that reason, the data set used in the JPL-85 model did not form a uniform data set. The occurrence of major proton events in the early nineties provided the opportunity to correct this weakness of the JPL-85 model. At the same time, the model energy range was extended.

The data set used for the JPL-91 model consists of a nearly continuous record of daily average fluxes above the energy thresholds of 1, 4, 10, 30, and 60 MeV. The proton events considered in the JPL models are defined as the total fluence occurring over series of days during which the proton fluence exceeded a selected threshold. The thresholds for the JPL-91 model (in cm-2 s-1 sr-1) are 10, 5, 1, 1, and 1 for the five energy thresholds.

The statistical properties of the events occurring during active periods of the solar cycle are considered separately from those occurring during the quiet periods. For the JPL models, it was assumed that no significant proton fluence exists during quiet periods and that the only model needed is one for the active periods. Therefore, only data collected during the 7 active years of the cycles were used.

The cumulative probability distribution of the high fluence portion of the data can be fit quite well with a lognormal distribution. Figure 4 shows the distribution of the solar event fluences for protons of energy >60 MeV. The events have been ordered according to the log of the fluence and plotted versus the percent of observed events that have a magnitude less than the given event. The horizontal axis of the plot is scaled so that a data set that is distributed lognormally will appear as a straight line. The real distribution of the data is not lognormal since in the real data there are always more events the smaller the size of the event, whereas for a lognormal distribution there is a mean event size and the number of events decreases for events both smaller and larger than that mean. For this reason, the distributions cannot be expected to be fit by a straight line for fluences less than the average of the data set. However, the estimate of the total fluence accumulated during a mission is dominated by the estimate of the probability occurrence for large events and will not be changed due to the underestimate of the probability of occurrence of the small events. The important question is the estimate of occurrence of the largest events. The straight line fit to the event fluence distribution is superimposed in Fig. 4.

Distribution of solar event fluences for protons of energy >60 MeV
Figure 4. Distribution of solar event fluences for solar active years between 1963 and 1991 for protons of energy >60 MeV for which daily averaged flux exceeds 1.0 cm-2 s-1 sr-1. The straight line is the fitted lognormal distribution (from [Feynman et al., 1993]).

The formulation of the JPL models is exactly the same as that used by King with the exception of the definition of the function p(n,t;N,T). The JPL data set has a significantly larger population of events so that pure Poisson statistics are applicable:


where omega is the average number of events that occurred during the observation period: omega = N/T. The function Q(>F,E;n) which gives the probability that the logarithm of the combined fluence of n events will exceed F, can be generated by a Monte Carlo technique which simulates a large number (100,000) of random fluences from the inverse of the lognormal distribution.

The JPL models are presented as probability curves of exceeding a given fluence during a mission of a selected duration. The fluence probability curves for various misison durations are represented in Fig. 5 for protons of energy >60 MeV. The probability curves give the probability of exceeding a given fluence during the life of the mission assuming a constant heliocentric distance of 1 AU. To use the probability curves, find the line that corresponds to the desired mission length during solar active years (the fluence in a single 11 year cycle should be assumed to be equal to 7 year fluence). Locate the confidence level required, recalling that a confidence level of say 95% means that only 5% of missions identical to the one considered will have fluences larger than that determined for the 95% confidence level (i.e., probability + confidence level = 100%). Then, the abscissa gives the fluence that will not be exceeded with the selected confidence level. In the numerical implementation of the models, the probability curves are represented as a discrete set of points between which linear interpolation is performed. Interpolation or extrapolation for energies different from the model thresholds uses an exponential fit of the fluence in terms of rigidity.

Fluence probability curves for protons of energy >60 MeV
Figure 5. Fluence probability curves for protons of energy >60 MeV for various mission durations (from [Feynman et al., 1993]).

Feynman et al. [2002] have studied the observations of solar particle events that have occurred since the JPL 1991 model was developed (up to 1998) and concluded that the new observations fall well within the distribution of fluences upon which the JPL 1991 model was based. Hence, the authors conclude that no change need be made to the probability distribution used in the JPL 1991 model and that it is no longer necessary to label the JPL model by the year during which the data set terminated. The model can now be called simply the JPL model.

The Rosenqvist et al. (2005, 2007) models

It has been shown recently that the values of the parameters μ, σ and w derived from the data for JPL-91 give an underestimation of the fluence. Using a complete list of solar proton event fluences from January 1974 to May 2002 based on measurements from the IMP-8, GOES-7 and GOES-8 spacecraft, updated values have been proposed for the fluence specification in the energy ranges > 10 MeV (Rosenqvist et al., 2005) and > 30 MeV (Glover et al., 2007). They are given in the table below. The model Rosenqvist et al. (2005, 2007) implemented in SPENVIS uses these updated values in combination with the JPL-91 parameter values in the energy ranges > 1 MeV, > 4 MeV and > 60 MeV.

Updated values of the parameters of the JPL model
Parameter >10 MeV >30 MeV
log10(μ) 8.07 7.42
log10(σ) 1.10 1.2
w 6.15 5.40

The ESP models

The King and JPL models are very useful for predicting event fluences for long-term degradation but do have limitations due to the incomplete nature of the data sets upon which they were based. The first limitation is the proton energy range. Fluence levels below 10 MeV are desirable for accurate predictions of solar cell degradation, whereas the higher energy protons, with their ability to penetrate shielding, are important to consider for total dose degradation and single event effects in system electronics. The second limitation is that neither model includes the full 3 solar cycles for which high quality space data are available. This is important because the 3 cycles were dissimilar from one another. Cycle 20 had one anomalously large event that accounted for most of the accumulated fluence. Cycle 21 was a rather quiet cycle with no such large events. Cycle 22 was very active and had several very large events.

Previous approaches to modelling solar proton event fluence distributions have been largely empirical in nature. Lognormal distributions have been used to describe large event fluences, but deviate from the measured distributions for smaller event fluences [King, 1974; Feynman et al., 1993]. Power laws, which describe the smaller event fluences very well, but overestimate the probability of large events, have also been used [Gabriel and Feynman, 1996]. Both of these types of approaches have merit. However, they do not accurately describe the complete distribution, allow for the possibility of infinitely large events, and lack strong physical and mathematical justification.

The basic difficulty in describing a solar proton event fluence distribution arises from the incomplete nature of the data, especially for large fluence events. For example, in the last 3 complete cycles, which span approximately 33 years, only 3 separate events have produced a >10 MeV fluence of approximately 1010 cm-2 or greater. Characterising the probabilistic nature of these very large events is critical for radiation effects applications.

Another reason for reassessing the cumulative solar proton event fluence models is that an accurate approach has emerged for describing the underlying or initial distribution of solar proton event fluences [Xapsos et al., 1999]. It is based on maximum entropy theory [Kapur, 1989] and predicts an initial distribution that is a truncated power law in the event fluence. The maximum entropy principle provides a mathematical procedure for generating or selecting a probability distribution when the data are incomplete. It states that the distribution which should be used is the one that maximises the entropy, a measure of uncertainty, subject to constraints imposed by available information. Such a choice results in the least biased distribution in the face of missing information. An example is shown in Fig. 6, which is a plot of the number of events per solar active year that exceed a given event fluence vs. fluence. The points represent the measured >30 MeV event fluences during active years of solar cycles 20-22. These are compared to the distribution predicted by the maximum entropy technique, shown by the line. This approach is a significant improvement in describing the distribution of events compared to previous empirical methods such as those using lognormal distributions and power laws. Since a model of cumulative fluences must be based on some initial distribution of event fluences, it is worthwhile to use the improved distribution obtained from the maximum entropy approach.

Distribution of >30 MeV event fluences
Figure 6. Distribution of >30 MeV solar proton event fluences.

Solar proton event data from the last 3 complete solar cycles (20-22) were processed to obtain the event fluences. The source of the data for cycle 20 was the IMP-3, -4, -5, -7 and -8 satellites. The data from cycle 21 was from IMP-8. The GOES-5, -6 and -7 satellite data, which extends to much higher proton energies, was used for cycle 22. Only events having some minimum fluence Φmin were considered. This minimum fluence depends on the proton energy range [Xapsos et al., 1999] and is listed in Table 1. In identifying events, the practice of NOAA was followed, where the beginning and end of an event are identified by a threshold proton flux so that a large event may consist of several successive rises and falls in flux. Since a very large portion of the accumulated fluence occurs during solar active years, it is reasonable to neglect the solar inactive years, following the practice of Feynman et al., [1993].

Table 1. Energy range and minimum and maximum event fluences considered
Proton
energy range
(MeV)
Minimum event
fluence
Φmin (cm-2)
Worst case event
maximum fluence
Φmax (cm-2)
>1 5.0x108 1.55x1011
>3 1.0x108 8.71x1010
>5 1.0x108 6.46x1010
>7 2.5x107 4.79x1010
>10 2.5x107 3.47x1010
>15 1.0x107 2.45x1010
>20 1.0x107 1.95x1010
>25 3.0x106 1.55x1010
>30 3.0x106 1.32x1010
>35 3.0x106 1.17x1010
>40 1.0x106 8.91x109
>45 1.0x106 7.94x109
>50 3.0x105 6.03x109
>55 3.0x105 5.01x109
>60 3.0x105 4.37x109
>70 1.0x105 3.09x109
>80 1.0x105 2.29x109
>90 1.0x105 1.74x109
>100 1.0x105 1.41x109

As discussed above, the maximum entropy principle provides a mathematical basis for selecting a probability distribution for an incomplete set of data. For a continuous random variable M having a probability density p(M), the entropy S is defined as:


where the integral is taken over all values of M. Here, M represents the solar proton event fluence: M = logΦ. A series of mathematical constraints are imposed upon the distribution, using known information, two obtain two different models: a model of worst case event fluences, and a model for cumulative fluences.

Worst case event fluence model

The constraints on the initial distribution are:
  1. the distribution can be normalized;
  2. the distribution has a well defined mean;
  3. the distribution has a known lower limit in the event fluence (given in Table 1);
  4. the distribution is bounded, i.e. infinitely large events are not possible.
The resulting system of mathematical equations is used to find the solution p(M) that maximizes S, by means of the Lagrange multiplier technique. Once p(M) is known, the following key result can be obtained:

where N is the number of events per solar active year having a fluence greater than or equal to Φ, Ntot is the total number of events per solar active year having a fluence greater than or equal to Φmin, b is the index of the power law, and Φmax isthe maximum event fluence. The truncated power law given by this equation behaves like a power law with index b for Φ<<Φmax, and goes smoothly to zero at the upper limit Φmax.

Regression fits to the above equation for N were performed for solar proton event fluence distributions with threshold energies ranging from >1 MeV to >100 MeV, with adjustable parameters Ntot, b and Φmax. A typical example of the fitted results is shown in Fig. 6 for >30 MeV protons. The figure shows N as a function of event fluence Φ: data is shown by the points, and the solid line is the best fit to the above equation for N. It is seen that the model describes the data well over its full 3.5 orders of magnitude. The fitted parameters are Ntot=4.41 events per active year, b=0.36 and Φmax=1.32x1010 cm-2. It is interesting to note that the index obtained here for the truncated power law is close to the value of 0.40 reported by Gabriel and Feynman [1996] for an ordinary power law. Whether or not this distribution should be truncated should ultimately be determined by the data. It is seen in the figure that the measured event frequencies begin to tail off noticeably above about 109 cm-2, thus supporting the truncated distribution obtained with the maximum entropy principle. The maximum event fluence parameter Φmax is about 1.5 times the largest observed >30 MeV fluence up to 1999. Generally, this parameter was within a factor of 2 of the largest event fluence in solar cycles 20-22.

Knowing the initial distribution of solar proton event fluences, the worst case event can be determined as a function of confidence level and mission duration. Assuming that the occurrence of solar proton events is a Poisson process, it can be shown from extreme value theory [Xapsos et al., 1998] that a cumulative, worst case distribution for T solar active years is given by:

FT(M) = exp{-Ntot T[1-P(M)]} .

Here, the cumulative probability FT(M) is equal to the desired confidence level, and P(M) is the cumulative distribution corresponding to the known probability density p(M). Recalling that M=logΦ, P(M)=1-N/Ntot can be rewritten directly in terms of the event fluence:

Applying these equations to the results for >30 MeV protons, the worst case event distributions shown in Fig. 7 are obtained. The ordinate represents the probability that the worst case event encountered during a mission will exceed the event fluence indicated on the abscissa. This is shown for mission lengths of 1, 3, 5 and 10 solar active years. Also shown in the figure by the vertical line (design limit) is the maximum event fluence Φmax. This limit can be used as an upper limit guideline: if essentially no risk is to be taken in a design, then the maximum event fluence of Φmax=1.32x1010 cm-2 should be used (or the corresponding values for the other proton energies in the model, as listed in Table 1). The Φmax values, corresponding to a confidence level of 1.0, are independent of mission length.

The upper limits on solar proton event fluences are fitted parameters that are derived from limited data. By its very nature, there must be some amount of uncertainty associated with this parameter. Thus, it should not be interpreted as an absolute upper limit. A reasonable interpretation for the upper limit fluence parameter is that it is the best value that can be determined for the largest possible event fluence, given limited data. It is not an absolute upper limit but is a practical and objectively determined guideline for use in limiting design costs.

Probability of exceeding worst case fluences
Figure 7. Probability that the worst case solar proton event fluence encountered during a mission exceeds the value shown on the abscissa with 1, 3, 5 and 10 solar active year periods. The probability of exceeding the design limit of 1.32x1010 cm-2, shown as a vertical line, is essentially zero.


Extrapolation of the energy range

The limited solar proton data at energies beyond 100 MeV prevents the implementation of the probabilistic models at these energies. However, the available high energy data from GOES satellite measurements during cycle 22 were examined for their spectral shape. This included the large events of 12 Aug 89, 29 Sep 89, 19 Oct 89, 23 Mar 91, 4 Jun 91 and 30 Oct 92, and the CREME96 [Tylka et al., 1997a] worst day spectrum. Based on comparisons with the model results, it was determined that the spectral shape for the GOES measurements between >100 MeV and >300 MeV is a good approximation for extending the probabilistic model spectra. Thus, the >100 MeV to >300 MeV GOES data were scaled to extrapolate the probabilistic model spectra to >300 MeV.

The SAPPHIRE model

The Solar Accumulated and Peak Proton and Heavy Ion Radiation Environment (SAPPHIRE) model [Jiggens et al., 2018a] covers all SEP environment timescales across all relevant species in a consistent probabilistic manner.

The basic SAPPHIRE provides the following set of model outputs:

  1. mission cumulative fluence;
  2. largest Solar Particle Event (SPE) fluence;
  3. SEP peak flux.
For both protons and solar helium during solar minimum and solar maximum conditions. The distinction between solar maximum and minimum periods follows the same prescription as the earlier King, JPL and ESP model with 7 years of solar maximum in each ˜11-year cycle distributed 2.5 years before and 4.5 years after the peak in sunspot number.

SAPPHIRE is developed through ESA's (Solar Energetic Particle Environment Modelling (SEPEM) application server [Crosby et al., 2015] which is available at: sepem.eu. The SAPPHIRE model is based on data from the SEPEM Reference Data Set (RDS) v2.1 which is available here on the SEPEM server: http://sepem.eu/help/SEPEM_RDS_v2-01.zip The RDS uses as its basis data from the energetic particle sensor (EPS) on-board the National Oceanographic and Atmospheric Administration (NOAA) Geostationary Operational Environmental Satellite (GOES) series and similar instruments on-board the earlier NASA Synchronous Meteorological Satellite (SMS) series. These data have been cross-calibrated with science-class data from the Goddard medium energy (GME) instrument on-board NASA's Interplanetary Monitoring Platform (IMP-8) following the algorithms detailed by [Sandberg et al., 2014]. The result is a contiguous data set spanning over $gt;40 years (from 1974-2016) built using a fully consistent processing chain.

The Reference Event List (REL) defines SPEs by requiring that the differential flux value in the 7.38-10.4 MeV channel is above 0.01 dpfu (dpfu = differential particle flux units = particles. cm-2.sr-1.s-1.MeV/nuc-1), the minimum peak flux over the period is at least 0.5 dpfu, a dwell time of no more than 24 hours is permitted between consecutive enhancements (else they are treated as a continuation of the same SPE) and events must have a duration of at least 24 hours. The version of the REL applied in SAPPHIRE v1.0 includes 266 SPEs from between 1974 and 2016 with of the 237 SPEs occurring during solar maximum periods and the remaining 29 SPEs occurred during solar minimum.

SAPPHIRE deploys the virtual timelines methodology which generates interspersed waiting times (between SPEs) and SPE fluxes with durations based on numerical regression. This is analogous to the monte-carlo procedure of the JPL model with the additional consideration of the non-negligible duration of SPEs. The waiting time distribution for solar maximum is based on a Lèvy distribution previously applied to solar flares [Lepreti et al., 2001] and later to SPEs [Jiggens and Gabriel, 2009]. Due to the limited number of SPEs at solar minimum the time-dependent Poisson distribution [Wheatland, 2000, 2003] was applied to waiting times for these conditions.


The flux distribution applied in SAPPHIRE is the exponential cut-off power law [Nymmik, 2007]:

F(φ) = φγ / exp(φ/φlim) (exp(φmin/φlim) / φmin ≈ (φγ φγmin) / exp(φ/φlim)     [φlimφmin]

where F(φ) is the probability of a random event exceeding a fluence (peak flux), φ, γ is the power law exponent, φmin is the minimum fluence (peak flux) and φlim is the exponential cut-off parameter which determines the deviation from a power law at high fluences (peak fluxes). The figure below shows an example comparison of the exponential cut-off power law and the lognormal distribution (used in the JPL model) and the truncated power law (used in the ESP models) for SPE proton fluences in the energy channel from 31.62–45.73 MeV.


The number of SPEs considered in each channel have been selected as part of the procedure which optimises the fitted distribution parameters [Jiggens et al., 2018b].

A total of 100,000 virtual timelines are used for each model result at each energy with an output of probability of exceeding (1- confidence level) as a function of flux. The figure below shows the proton mission cumulative fluence output for the energy channel from 31.62–45.73 MeV for solar maximum conditions for a range of prediction periods (mission durations).


Extrapolation of the energy range

Finally, the model outputs from each channel, confidence level and prediction period are combined into a single spectrum which is then extrapolated down to 0.1 MeV/nuc and up to 1 GeV/nuc through application of a Band Fit to particle rigidity:

dJ/dR = C R-a exp(-R/R0)     {for R ≤ (b-a) R0}
dJ/dR = C R-b ([(b-a) R0](b-a) exp(b-a))     {for R ≥ (b-a) R0}

where R is the particle rigidity (momentum divided by charge), J is the fluence or peak flux, and a, b, C and R0 are fitted parameters. The fit is made only to 4 reference cases and the remaining model output extrapolations are interpolated/extrapolated from these in order to retain self-consistent results. The spectral fits for the solar helium cumulative fluence results are shown in the figure below along with the remaining > 1,000 results (grey traces).

Large event fluence model

In addition to recording the total fluence in each iteration the SAPPHIRE code also records the largest event which is sampled. The (sorted) results across all energies are used and extrapolated to provide the model output. The input parameters are the same as the cumulative fluence model: prediction period (mission length) and confidence. The figure below shows comparisons of SAPPHIRE and ESP-PSYCHIC (and SAPPHIRE run on the ESP-PSYCHIC proton dataset) for model outputs the event fluence which will not be exceeded during a mission of 1 year at a confidence level of 90% (solid lines) and during a mission of 7 years at a confidence of 95% (dashed lines) during solar maximum conditions.

1-in-x-year SPEs

The above description of an event size which will not be exceeded in a given time period at a given confidence is often confusing. In addition, in many cases it is desirable to have a stable environment input for worst-case analyses of the elevated SEP environment. Unfortunately, statistical model outputs are given as a function of prediction period (D) and confidence (1 - p [probability]). However, it is possible to transform these outputs into SPEs which will occur, on average, once in every x years by assuming that large SPEs occur randomly in time. This is expressed applying the following Poisson relationship [Jiggens et al., 2018b]:

PrD(N = 0) = 0.3679(D/x)(11/7) = 1 - p

where 11 is the assumed average number of years of a solar cycle and 7 is the assumed number of maximum years in each cycle as the 1-in-x-year SPE fluence is based on the solar maximum output. SAPPHIRE provides 7 static outputs for worst-case analyses. Table 2 gives these examples along with the prediction period and confidence level which was found to best represent these average return times:

Table 2. Model output parameters used to derive SAPPHIRE 1-in-x-year SPEs
SPE frequency (years) Prediction period (years) Confidence level (%)
10 2 73
20 3 79
50 3 91
100 6 91
300 18 91
1000 26 96
10000 32 99.5

The extrapolated outputs for the SAPPHIRE 1-in-x-year SPE fluences as a function of energy are shown below:

Solar heavy ion fluence models

The PSYCHIC model

Because of a lack of heavy ion data, solar heavy ion models are less advanced than solar proton models. However, it has been shown that long-term solar heavy ion fluxes exceed galactic cosmic ray fluxes during solar maximum for shielding levels of interest [Xapsos et al., 2007]. Therefore they may be of concern for single event effects, and alpha particles may contribute significantly to the degradation of photovoltaics [Tylka et al., 1997b]. The PSYCHIC model (Prediction of Solar particle Yields for CHaracterizing Integrated Circuits), developed by Xapsos et al. [2007], includes cumulative solar heavy ion fluences for nearly all naturally occurring elements across the Periodic Table, during the solar maximum period.

The SAPPHIRE model

The SAPPHIRE model includes outputs for all naturally occurring species by use of abundances for heavier particles (Z>2) relative to helium (Z=2) which vary as a function of particle energy. The abundances are based on data from NASA's Advanced Composition Explorer (ACE) spacecraft. Following an initial inspection of the data set 13 SPEs from the SEPEM REL were identified, which could be utilized to derive abundance ratios. Only measurements made for the seven most abundant elements could be trusted for a significant fraction of the 13 SPEs: C, N, O, Ne, Mg, Si and Fe. Data for Na, Al, S, Ar, Ca, and Ni could not be trusted because for much of the time their uncertainty was comparable to the measurement itself (i.e., 100% uncertainty). The figure below shows the analysis performed for Fe (Z = 26).


The next figure shows the derived abundances as a function of energy for the 7 species for which sufficient data was available. All other species' abundances were based on a scaling of the curves for the nearest element in the periodic table based on single energy abundances found in literature [Reames, 1998] [Asplund et al., 2009].

Using the solar particle fluence models

This section describes the implementation of the King, JPL, ESP and PSYCHIC model in SPENVIS.

The King model

One way to use the King model is to specify the number of events (either ordinary or anomalously large) that will occur within a given number of years and to allow the model to provide probabilities that this number will not be exceeded. The King data set contains only one anomalously large event in a 7 year period, and so predicting the occurrence of such an event over a shorter interval may be considered pessimistic, as might the inclusion of more than one of these events during a typical mission life time.

Alternatively, the King model can be used by specifying a confidence level. With Burrell's extension of Poisson statistics, the number of events that will occur over the mission duration can be calculated, and hence the minimum number of events that need to be included. The total event fluence is then obtained by multiplying the AL or OR spectra by the number of predicted events (if only one OR event is predicted for a confidence level of 90% or higher, the 90% worst case spectrum is used). Table 3 contains the probabilities for occurrence of anomalously large events for selected mission durations.

Table 3. Probability that <=n AL events will occur in t years at solar maximum
  Mission duration t (years)
Number of events n 1 3 5 7
0 76.56 49.00 34.03 25.00
1 95.70 78.40 62.38 50.00
2 99.29 91.63 80.11 68.75
3 99.89 96.92 89.95 81.25
4 99.98 98.91 95.08 89.06
5 99.99 99.62 97.65 93.75

Thus, if a confidence level of 90% is required for a space mission lasting 3 years during solar maximum, it would be necessary to include two anomalously large events in the radiation analysis. Although this seems unnecessarily conservative, it might be preferable to setting the number of events arbitrarily.

The JPL model

The ambiguity of setting confidence levels for the King model is a consequence of the separation of the anomalously large event from the remaining events in the data base used to build the model. The statistical significance of observing a single event in a seven year period is of limited value for predictive purposes. The JPL model overcomes this problem by virtue of its continuous distribution of event-integrated fluences.

On the basis of an analysis of worst case periods, Tranquille and Daly [1992] recommend the confidence levels listed in Table 4 for the JPL models.

Table 4. Recommended confidence levels for the JPL models
Mission duration (years) Confidence level (%)
1 97
2 95
3 95
4 90
5 90
6 90
7 90

The Rosenqvist et al. (2005, 2007) model

The use of the Rosenqvist et al. (2005, 2007) model is equivalent to the use of the JPL model.

Comparison of the King and JPL models

Figure 8 compares the King (dashed line) and JPL-91 (solid line) models for a mission duration of seven years and a confidence level of 90%. From the confidence levels tabulated in Table 3 for the Burrell statistics, it follows that 5 AL events are needed for the King model.

In general, the JPL model predicts higher fluences at low energies than the King model. Low energy protons are most important for solar cell degradation, and thus the JPL model is more severe for predicting this effect. It should be noted that the lower energy threshold in the King model is 10 MeV, while the JPL-91 model includes data for a threshold of 1 MeV. For intermediate energies the King model is higher than the JPL-91 model, while for energies above about 80 MeV the situation is reversed.

The spectral form used to extrapolate solar proton fluences at energies other than the model energies is an important consideration. The anomalously large event of the King model is represented by an exponential in energy, but for ordinary events and for the JPL models an exponential in rigidity should be used. The difference between the two spectral form is illustrated in Fig. 8 by the dotted line which represents the JPL-91 fluence extrapolated as an exponential in energy. The difference with the extrapolation in rigidity reaches an order of magnitude at 200 MeV.

Comparison of the King and JPL models
Figure 8. Comparison of the JPL-91 and King models for a seven year mission in solar maximum conditions and confidence level 90%: ___ JPL-91 exponential in rigidity; ___ JPL-91 model exponential in energy; ___ King model (5 AL events).

The ESP models

Sample spectra of the ESP models
Figure 9. Sample spectra of the ESP models for a seven year mission in solar maximum conditions and confidence level 90%: ___ total fluence model; ___ worst case event fluence model; ___ JPL model for the same conditions.

The PSYCHIC model

In SPENVIS the PSYCHIC model is tacked to the ESP model i.e. the heavy ion differential fluences are obtained by multiplying the ESP computed differential fluence of 5.92 MeV protons, with scale factors (provided by M. Xapsos upon request) that range from 0.173 to 547.7 MeV/nucleon. Figure 10 shows the differential energy spectra for 5 of the major elements and a summed spectrum for all elements with Z > 28. The results are for a 2-year period mission during solar maximum at a 90% confidence level and without spacecraft shielding.

Sample spectra of the PSYCHIC model
Figure 10. Differential fluence energy spectra for protons, alpha particles, oxygen, magnesium , iron and summed spectra for Z>28 elements for a 2-year mission during solar maximum at the 90% confidence level.

The SAPPHIRE model

All instructions on how the SAPPHIRE model is implemented are available here. Owing to the complete description of the SEP environment the user can insert any range of ions from Z=1 (protons) to Z=92 (uranium), prediction periods from 0.5 to 55 years (5 solar cycles) and either select from either cumulative mission fluence, largest SPE fluence and peak flux for a desired confidence level. The combination of solar maximum and minimum periods results in a result different from a simple summation due to the probabilistic nature of the model. This is shown in the figure below for the solar proton and solar helium cumulative fluences for a 16-year mission with 12 years at solar maximum conditions and 4 years at solar minimum conditions.

The solar particle flux models

Solar particle flux models are only appropriate for evaluating single-event upset rates and are therefore based on particle measurements near Earth at energies relevant to SEE effects. In SPENVIS the following models (for protons and heavy ions) are implemented:

The CREME86 models

From the CREME86 environment models the cosmic ray component (M=1) has been subtracted to obtain only the solar fluxes:

The CREME96 models

The CREME96 solar fluxes are based on averaged fluxes observed (on GOES for protons and on IMP for heavy ions) during the 19-27 October 1989 episode. Three cases have been implemented:

The Xapsos et al. (2000) model

The events 19, 22 and 24 October 1989 have been fitted to Weibull spectra forms as suggested by Xapsos et al. (2000). Their differential flux spectrum can be described by the form: J(E) = A κ α E(α-1) exp(-κEα)
with the energy E in MeV and the flux J in protons/cm2/s/sr/MeV. The fitting parameter values are given in Table 5.

The energy range used for solar particle flux calculations is from 0.1 MeV/nucleon up to 500 MeV/nucleon. For geomagnetic shielding calculations all ions are treated as fully ionised.

Table 5. Parameters for the fit to the peak fluxes from the October 1989 events
Event A (cm-2s-1sr-1MeV-2) κ α
19 Oct. 1989 214 0.526 0.366
22 Oct. 1989 429 0.458 0.3908
24 Oct. 1989 54900 2.38 0.23

The SAPPHIRE model

The SAPPHIRE model provides statistical outputs for peak fluxes based on the same input parameters as the fluence models: prediction period (mission length) and confidence. The figure below shows comparisons of SAPPHIRE and ESP-PSYCHIC (and SAPPHIRE run on the ESP-PSYCHIC proton dataset) for model outputs the peak flux which will not be exceeded during a mission of 1 year at a confidence level of 90% (solid lines) and during a mission of 7 years at a confidence of 95% (dashed lines) during solar maximum conditions.

Similarly to the largest SPE fluence, results from SAPPHIRE can be transformed to provide outputs of 1-in-x-year SPE peak fluxes as a function of energy are given below:

Geomagnetic attenuation and Earth shadowing

The ability of charged particles to penetrate into the magnetosphere from outside is limited by the Earth's magnetic field. A particle's penetrating ability is determined uniquely by its momentum divided by its charge. For each point in the magnetosphere and for each direction of approach to that point, there exists a threshold value of magnetic rigidity, called the geomagnetic cutoff. Below this value, no charged particle can reach the specified point from the specified direction.

As the geomagnetic cutoff varies with the particle's arrival direction, the geomagnetic cutoff transmission is averaged over all arrival directions. For a given location and rigidity, the integrated solid angle from where particles with this rigidity can reach the location, divided by 4pi, is called the attenuation or exposure factor. The attenuation factor for each proton energy is averaged over the spacecraft orbit and then multiplied with the interplanetary proton fluence provided by the proton models. For a given energy, the exposure time is defined as the total time that the orbit is in regions where the attenuation factor is non-zero. SPENVIS provides the attenuation for each orbital point and each proton energy, the orbit averaged attenuation factor, and the exposure time.

The presence of the solid Earth occults part of the solid angle from which particles can arrive at a given location. This effect is included in the calculation of the attenuation factor.

During magnetic storms, the geomagnetic cutoff is altered, usually allowing penetration to any given point in the magnetosphere by lower energy particles than is normally possible. A simple expression is used to account for this effect on the attenuation factor. Solar events are often, but not always, accompanied by magnetic storms at the Earth. Therefore, the user has the option of selecting a quiet or disturbed magnetosphere.

The calculation of the attenuation factor is based on a number of approximations that limit the validity of the result. It is well established that solar protons can penetrate much deeper in the magnetosphere than predicted by the simple attenuation model. Therefore, the user has the option of switching off the geomagnetic attenuation (this does not affect the Earth shadowing effect) to have an idea of the worst case effect of solar events.

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Last update: Fri, 27 Apr 2018