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13.4. CRÈME96 and Related Error Rate Prediction MethodsJames H. Adams, Jr., NASA Marshall Space Flight Center1. IntroductionPredicting the rate of occurrence of single event effects (SEEs) in space requiresknowledge of the radiation environment and the response of electronic devices to thatenvironment. Several analytical models have been developed over the past 36 years to predictSEE rates. The first error rate calculations were performed by Binder, Smith and Holman [1].Bradford [2], [3] and Pickel and Blandford, in their CRIER (Cosmic-Ray-Induced-Error-Rate)analysis code [4], [5], introduced the basic Rectangular ParallelePiped (RPP) method for errorrate calculations. For the radiation environment at the part, both [3], [2] and [5] made use of theCosmic Ray LET (Linear Energy Transfer) spectra calculated by Heinrich for various absorberdepths [6]. A more detailed model for the space radiation environment within spacecraft wasdeveloped by Adams and co-workers [7]-[14]. This model, together with a reformulation of theRPP method published by Pickel and Blandford [5], was used to create the CRÈME (CosmicRay Effects on Micro-Electronics) code [15], [16]. About the same time Shapiro wrote theCRUP (Cosmic Ray Upset Program) [17] based on the RPP method published by Bradford [2]. Itwas the first code to specifically take into account charge collection from outside the depletionregion due to deformation of the electric field caused by the incident cosmic ray. Other early rateprediction methods and codes include the Single Event Figure of Merit [18], NOVICE [19], theSpace Radiation code [20] and the effective flux method of Binder [21] which is the basis of theSEFA (Scott Effective Flux Approximation) model [22].By the early 1990s it was becoming clear that CRÈME and the other early models needed
2revision [23], [24]. This revision, CRÈME96 [25], was completed and released as a WWWbased tool, one of the first of its kind. The revisions in CRÈME96 included improvedenvironmental models and improved models for calculating single event effects. The need for arevision of CRÈME also stimulated the development of the CHIME (CRRES/SPACERADHeavy Ion Model of the Environment) [26] and MACREE (Modeling and Analysis of CosmicRay Effects in Electronics) [27]. The Single Event Figure of Merit method was also revised touse the solar minimum galactic cosmic ray spectrum [28] and extended to circular orbits down to200 km at any inclination [29]. More recently a series of commercial codes was developed byTRAD (Test & Radiations) which includes the OMERE code [30] which calculates single eventeffects.There are other error rate prediction methods which use Monte Carlo techniques. Thesewill be discussed in chapter 3.5 “MRED and Monte Carlo Based Tools”. In this chapter theanalytic methods for estimating the environment within spacecraft will be discussed.2. The Radiation EnvironmentThe principle components of the interplanetary space radiation environment are galacticcosmic rays (GCRs), solar energetic particles (SEPs), and trapped radiation. In addition to these,there are some minor components that usually do not play an important role in causing singleevent effects. These are the anomalous cosmic rays and particles accelerated in co-rotatinginteraction regions. While the anomalous component is a minor contributor in the neighborhoodof the Earth it makes an important contribution to the ionizing radiation environment in the outerheliosphere.For satellites in Earth orbit, the interplanetary environment must be modulated by the
3orbit-averaged effect of the Earth’s magnetic field. Satellites also encounter the radiation trappedin the Earth’s magnetic field. In all cases, the radiation environment as the surface of thespacecraft will be modified by passage through spacecraft material on its way to the electroniccomponents within. These aspects of error rate prediction were recently reviewed by Janet Barth[31].2.1 Galactic Cosmic RaysGCRs include all the nuclei of all the elements in nature. Their abundances are roughlythe same as the general abundance of elements in the solar system [32]. Except for the heaviestelements, all the nuclei are completely stripped of their orbital electrons during their passagethrough the interstellar medium. GCRs originate from sources far away in our Galaxy. The originof GCRs has not yet been determined; however, there is circumstantial evidence, based on thepower budget for sustaining the GCR flux in the galaxy [33] that GCRs are accelerated bysupernovae. Eighty to ninety percent of the core-collapse supernovae occur in OB associations(associations of O and B type stars) [34] and there is experimental evidence from thecomposition of GCRs that they come mostly from these OB associations [35]. During theirpropagation through the Galaxy between their sources and the solar system, GCRs traverse 6 to10 g/cm2 of interstellar matter [36]. This alters their composition, enriching GCRs in certainelements, notably Li, Be and B and the elements just below Fe.The GCR flux outside the heliosphere is isotropic except at very high energies. To reachEarth, the GCRs must penetrate the heliosphere, overcoming the influence of the outwardflowing solar wind [37]. The GCRs must diffuse upstream in the solar wind, while losing energydue to the diminishing magnetic field strength in the adiabatically expanding solar wind. This
4alters the power-law GCR spectrum outside the heliosphere to the familiar form measured atEarth and shown as the dashed and chain-dash curves in figure 1, but the flux reaching 1 AU(Astronomical Unit) remains isotropic.(Insert figure 1 here)The model for the GCR spectrum used in CRÈME86 [8] was the result of fitting the dataavailable by the early 1980’s. At that time the GCRs were known to be modulated with theperiod solar activity cycle, but the difference in modulation during the even- and odd-numberedcycles had not yet been discovered, so the variation of GCR modulation with time was modeledas a sinusoidal function the same period as the sunspot cycle. Later, in 1992, Nymmik developedan improved model for the GCR spectra at Earth [38] which was adopted as the ISO standard.This model was used in the revision of CRÈME to create CRÈME96.2.2 Solar Energetic ParticlesAs their name suggests, SEPs are accelerated at the Sun. They are accelerated in SolarParticle Events (SPEs) resulting from explosive releases of energy stored in the magnetic fieldsnear the surface of the Sun. SPEs seemingly occur at random, but careful examinations of thenon-potential energy stored in the sun can show when the “stage is being set” for a SPE [39].Also SPEs are sometimes triggered sympathetically by preceding events as occurred in the 2003Halloween event series [40] is an example. The frequency of events varies with the solar activitycycle, peaking during the active phase of the cycle.Like GCRS, SEPs are believed to consist of all the nuclei of all the elements in nature.While their composition is also similar to the general abundance of elements in the solar system,
5variability is seen from event to event. The reasons for this variability are thought to be related totheir acceleration process [41] and the seed population from which they are selected foracceleration [42]. Except for the lightest particles, SEP nuclei may not be completely stripped oftheir orbital electrons. The variability of the ionic charge state of SEPs seems to be related to thetemperature of the seed population [43], [44] and the acceleration process [45].There are two acceleration processes for SPEs [41] resulting in impulsive and gradualevents. As the name implies, the impulsive events are short-lived and are far more numerous andtypically much smaller than gradual events. Large impulsive events are rare. Impulsive eventsare described in [45] and references therein. The acceleration sites of impulsive events arethought to be localized on the Sun near the sites of solar flares, but this remains to be proved.They are highly enriched in 3He and also enriched in heavier elements, having a Fe/O ratio of 10.Gradual events are accelerated by shocks driven by coronal mass ejections (CMEs) [46].Acceleration begins more than a solar radius above the surface of the Sun where the CMEbecomes supersonic and continues along the shock front as it expands outward intointerplanetary space. This acceleration sometimes continues until the shock reaches Earth. Thematerial accelerated in gradual events comes from suprathermal tail of the solar wind in thecorona. There sometimes may be a contribution from particles accelerated to suprathermalenergies by preceding impulsive events [42], but the composition does not show the strongdeviations from the general abundance of elements that is seen in impulsive events.At the time CRÈME86 was written, all SEPs were thought to be accelerated by solarflares. For this reason, all available data were used to derive the elemental composition of SEPs.
6Because the instruments of the time mostly measured low energy SEPs, the data were mostlyfrom impulsive events. This resulted in a significant over-estimate of the heavy ion content inlarge SPEs which are usually gradual. The ionic charge state of SEPs was also unknown at thetime CRÈME86 was written, so SEPs were assumed to be bare atomic nuclei like galacticcosmic rays.(Insert figure 2 here)The trajectories of SPEs from their acceleration site outward into the heliosphere areguided by the interplanetary magnetic fields. Figure 2 shows the gyroradii of solar energeticprotons at 1 AU as a function of their pitch angle for three different energies. Solar heavy ionshave gyroradii that are 2 to 4 times larger depending on their charge state, but in all cases thegyroradii of SPEs are small compared to 1 AU. As a result, SPEs accelerated near the sun closelyfollow their guiding center field line out into the heliosphere. When the interplanetary field isundisturbed, the rotation of the sun causes it to form a Parker Spiral [47] as depicted in figure 3.In this case, the guiding center field line spirals out from the Sun smoothly with the field strengthdiminishing as the square of the distance. The diminishing field strength adiabatically focuses[48] the flow of SEPs. Regardless of their initial pitch angle, by the time SEPs reaches 1 AU,their pitch angle has rotated to nearly align their velocity vector with the guiding field directionso the first SPEs to reach 1 AU are streaming along the field. This also has the effect of reducingtheir gyroradius as shown in figure 2. If the acceleration site at the sun is magnetically wellconnected to the Earth, The first particles to arrive will come at 45 to the Sun-Earth line andapproximately in the ecliptic plane.(Insert figure 3 here)
7Of course, a perfect Parker Spiral field configuration is never realized. There are alwayssome magnetic field irregularities causing deviations from the Parker Spiral. These deviationswill cause pitch angle scattering if the scale of the irregularity is comparable to or smaller thanthe distance a particle moves along the field line in a single gyroration. The effect of many suchirregularities is to cause the particles to diffuse along the guiding field rather than simplystreaming. This will delay the arrival of the fastest particles at 1 AU and result in the firstparticles having a mixture of energies. Even if there are few scattering centers between the Sunand 1 AU, the particles continue along the field beyond 1 AU and eventually encounterirregularities that scatter them, including reversing their pitch angle so that they spiral backtoward Earth. For particles streaming back toward the sun, adiabatic defocusing occurs so thattheir pitch angles increase, eventually reaching 90 which cause them to mirror and stream awayfrom the Sun once again. In this way the same particle usually passes 1 AU several times. Thenet result is that the flux arriving at 1 AU soon becomes isotropic even if it began as aunidirectional flow coming from the local interplanetary magnetic field direction.Another consequence of pitch angle scattering is that the SPE flux at Earth often takesseveral days to decay, with particles continuing to arrive long after SPE acceleration hasapparently ceased. This gives particles time to diffuse (or drift if a local gradient in the field ispresent) onto new field lines so that the SPE spreads in heliographic longitude. The result is thatSPEs, not initially magnetically connected to Earth, will eventually be observed at Earth. Thislongitudinal spread of SPEs is not well understood. In the case of gradual events, it is at leastpartly due to the extended acceleration site along the expanding shock front, but propagationeffects in the interplanetary medium (as discussed above) can also be partially responsible. Toinvestigate this Wiedenbeck and co-workers [49] have examined several impulsive events using
8simultaneous 3He measurements from the two STEREO spacecraft and the ACE spacecraftlocated near Earth. They report typical longitudinal spreads of 60 with one event having a136 spread.The models for SPEs used by analytic error rate prediction methods consist of identifyingworst-case events at various estimated levels of confidence. In CRÈME86, four reference SPEcases were presented to cover the variability in both flux and composition:1) 10%1 worst-case flux with mean elemental composition2) 10% worst-case flux with worst-case composition3) Composite worst-case flux with mean elemental composition4) Composite worst-case flux with worst-case compositionAs mentioned above, the SEP composition model in CRÈME86 overestimates the heavy ioncontent of SPEs. This is especially true of models 2) and 4) that include the worst-casecomposition. The composite worst-case flux came from combining the worst features of the Feb.23, 1956 event and the August 4, 1972 event [50].The CRUP program used the LET spectra from Adams [7]. The Single Event Figure ofMerit [18] used the 10% worst case given by Adams [7] and shown as the chain-dot curve infigure 1. The 10% worst case is a composite environment including the galactic cosmic rayspectrum, SPEs and contributions from anomalous cosmic rays and co-rotating interactionregions. The space radiation environment should be more severe only 10% of the time.1Only 10% of the SPEs will be more severe
9The NOVICE model offers the CRÈME86 SPE models and a version of the JPL Model[51] where the Monte Carlo approach has been replaced with a numerical integration method.The CHIME model [26] offers models for SPEs based on the events measured during theCRRES satellite mission [52]. These include models for the events of March and June, 1991. Inaddition CHIME implements the JPL Model, a probabilistic model for SPE occurrence that givesthe worst-case proton fluence as a function of confidence level.The MACREE model [27] is a re-write of CRÈME86, to make some improvements. Theprinciple improvement is in the SPE models. MACREE uses the October 1989 event as a modelworst-case event, pointing out that it is at the 99% confidence level for proton fluencies above10, 30 and 60 MeV according to the JPL Model. MACREE also uses improved elementalabundance for SPE heavy ions, including trans-iron ions. In addition, it takes into account anestimate of the mean ionic charge state of SPE heavy ions.Space Radiation [20] offers several SPE models to choose from. The SOLPRO model[53] is offered. Also included are a collection of flux and fluence models for both individualextremely large events and composite events. Among these are the CRÈME86 SPE models [8],additional heavy ion models based on CRÈME86 that are said to be somewhat improved, theKing model [54], a model for the total fluence of the October 1989 event [55] and several modelsdeveloped at Aerospace Corp. [56] in response to the shortcomings of the CRÈME86 models.These include models for the proton peak flux and event-integrated fluence for the events ofAugust, 1972 and October, 1989. The authors also provide a worst-case composite of these twoevents. Space Radiation also includes the improved models for SPEs found in MACREE [27]and CHIME [26].In CRÈME96 [25] the SPE models were replaced with three worst-case models based on
10measurements of the October, 1989 SPEs. The worst-week model is based on 180 hours of dataduring the period 19-27 October. The worst-day model comes from an 18 hour interval of datataken on 20-21 October. The peak flux model is based on the highest 5-minute average protonflux on 20 October and a scaling of the “worst-day” heavy ion fluxes using proton data. All ofthese models have been shown to be worst-case at the 99% confidence level [57]. It isimportant to note [57] that the CRÈME96 SPE models are based on data in the relevant energyrange, unlike MACREE and the model of Croley and co-workers [58]. The CRÈME96 SPEmodels are much more severe than those in CHIME so that SEU rates calculated with theCRÈME96 SPE models are significantly higher. Finally, the CRÈME96 model takes intoaccount the effect of the ionic charge states of SPE heavy ions on geomagnetic transmission tolow Earth orbits. For devices in a 28.5 orbit that have a high SEU threshold, the effect of takinginto account the ionic charge states (as opposed to assuming the SEPs are bare atomic nuclei) canincrease the predicted SEU rate by more than an order of magnitude.Like Space Radiation, SPENVIS [59] offers a selection of SPE models for use in errorrate predictions including the following long-term models: the King Model [54], the JPL Model[51], the Xapsos Models [60]-[62] and a revision of the JPL Model by Rosenqvist and coworkers [63]. The following short-term SPE flux models are also provided, the CRÈME86 [15]and CRÈME96 [25], [57] models and the Xapsos Model [64]The OMERE model [30] offers a large variety of SPE models both for peak flux andmission integrated fluence. These include SOLPRO [53], ESP [61], CRÈME86 [8] CRÈME96[25], and JPL91 [51]. OMERE has extended the JPL91 model from 0.5 to 100 MeV using anexponential function. OMERE also offers several models they have developed. These are SPOF(Solar Proton ONERA Fluence) [65], IOFLAR [66] (which fits the spectra of all the elements
11with a power law in energy), a worst case flux model based on IMP8 [67] and GOES [68]measurements form 1974 to 2002 and a series of models of individual large SPEs that occurredbetween 1972 and 2003.2.3 Geomagnetic Cutoff TransmissionTo reach satellites orbiting the Earth within the Earth’s magnetosphere, the energeticcharged particles in the local interplanetary medium must penetrate the Earth’s magnetic field.The ability of a charged particle to penetrate a magnetic field is determined by its magneticrigidity (or momentum per unit charge). Those particles with magnetic rigidities below thegeomagnetic cutoff rigidity will be turned away by the Earth’s field before they can reach thesatellite.Access to any point within the magnetosphere can be estimated using the Störmerequation [69] which gives the value of the approximate geomagnetic cutoff,(in GeV/ec), forany location and arrival direction. It is derived under the assumption that the Earth’s magneticfield is an ideal dipole. This equation is:where is the geomagnetic latitude in offset dipole coordinates, is the arrival direction of theparticle measured from local East and r is the distance from the offset dipole center in Earthradii. Examination of the Störmer equation reveals that positively charged particles can arrivewith lower rigidities from the west. In fact they can arrive (with the right rigidities) up to 50 below the horizon. For the purposes of error rate prediction, it is customary to use the cutoff forparticles arriving from the zenith because it is roughly the average cutoff.The Earth’s magnetic field is not a perfect dipole. It has two main components, one
12generated in the core of the Earth and a second from currents in the magnetosphere. The internalfield is described by the International Geomagnetic Reference Field (IGRF) [70] which changeson time scales of 10 years, and the external field is described by Tsyganenko magnetosphericfield model [71] which changes rapidly with solar activity. Finding the geomagnetic cutoff forany location and arrival direction requires a computer simulation in which a positively chargedparticle arriving from beyond the magnetosphere is simulated by a negatively charged particletraveling out of the magnetosphere. This negative particle must be launched with a specificrigidity and direction from the location being investigated then followed to determine if itescapes to deep space. Such calculations have been carried out by Shea and Smart [72], [73].CRÈME86 [11] calculates the orbit-averaged vertical cutoff for a satellite using a preciseworld-wide grid of vertical cutoffs at an altitude of 20 km that were calculated by ray-tracing[72] as described above. The cutoffs from this grid were interpolated to intermediate pointswithin the grid and to the altitude of the satellite using the Störmer equation, normalized to thefour nearest grid points. The cutoff calculations were then averaged along the two-day orbitalpath to obtain the orbit-averaged geomagnetic cutoff transmission function.These calculations were then corrected for the shadow that the Earth casts on the satellite(since the Earth blocks the cosmic rays) and for the suppression of the cutoff during largegeomagnetic storms. These storms increase the ring current which has the effect of partiallycancelling the Earth’s field, thus reducing the cutoff.The NOVICE code [19] uses the CRÈME86 procedure for geomagnetic shielding.MACREE [27] also uses the geomagnetic transmission function from CRÈME86. CHIME [26]simply calculates the geomagnetic cutoff transmission function using the Störmer equation [69]for an offset and tilted dipole fit to the Earth’s field. OMERE [30] also uses the Störmer
13equation. Space Radiation [20] does an exact calculation of geomagnetic shielding by detailedray-tracing.For CRÈME96, a new geomagnetic cutoff ray-tracing calculation was performed [25]using both the updated IGRF [70] and the external field is described by the Tsyganenkomagnetospheric field model [71]. Unfortunately, the support for CRÈME96 ended before aworld-wide grid using these new calculations could be completed. Calculations for only twoorbits; a typical International Space Station orbit (51.6 by 450 km, circular) and a typical SpaceShuttle orbit (28.5 at 450 km, circular) were finished. The geomagnetic cutoff transmission toother orbits are calculated using the method of CRÈME86 with interpolating/extrapolating froma more recent ray-tracing calculation of the world-wide cutoff grid based on the geomagneticfield as it was in 1980. Since CRÈME96 was completed work on a vertical cutoff rigidityinterpolation tool has been finished [73]. It is based on a 5 by 5 world-wide grid at 450 kmcalculated by ray-tracing in the combined IGRF and Tsyganenko fields.SPENVIS [59] uses the Magnetocosmics [74] application, based on GEANT4, forsimulating the propagation of cosmic rays through the Earth's magnetic field. It uses a magneticfield model that includes the IGRF along with the user’s choice of three Tsyganenko models[71], [75]-[78].2.4 Trapped RadiationIn addition to the radiation coming from outside, energetic charged particles trapped inthe Earth’s radiation belt are capable of producing single event effects. The dominant componentfor single event effects is protons which are principally due to cosmic ray neutron albedo decay[79]. The radiation belt also contains electrons and a small population of low-energy heavy ions,
14He, O, Ne, Ar, etc. that come from anomalous cosmic rays that are stripped of their orbitalelectrons in the upper reaches of the Earth’s atmosphere [80], [81]. Electrons are not effective inproducing single event effects. The heavier ions make a contribution to the radiationenvironment only under light shielding as shown in figure 5 of reference [7].Charged particles trapped in the radiation belt gyrate around a guiding center magneticfield line in the Earth’s dipole magnetic field. As a particle approaches one of the magneticpoles, the magnetic field lines converge causing the pitch angle of the particle to rotate to 90 and then beyond causing the particle to spiral back toward the other magnetic pole. This is calledmirroring. Particles are thus trapped between their mirror points. The altitude of a particle’smirror points is determined by its pitch angle at the geomagnetic equator. Particles with thesmallest equatorial pitch angle will have the lowest mirror point altitudes (particles with lowermirror points are removed by the atmosphere). A result of this is that satellites orbiting at lowaltitudes experience a higher flux of protons coming from the west because such protons aregyrating about a guiding center field line above the satellite’s altitude and experience lessatmospheric loss than protons striking the satellite from the east (because they are gyratingaround a field line that is below the satellite).In addition to gyrating around their guiding center field line and bouncing between theirmirror points, trapped particles drift around the Earth. This is because as they circle their guidingcenter field line, the field is a little weaker at the furthest point from the Earth and a littlestronger at the nearest point. This causes the particles to execute cycloidal rather than circularmotion as they gyrate causing protons to drift westward around the Earth.The Earth’s magnetic field dipole axis is tilted at 11 relative to the Earth’s spin axisand the center of the dipole is offset by 550 km toward the north Pacific with the result that the
15Earth “sticks up” farther into the dipole magnetic field pattern in the south Atlantic thanelsewhere. As trapped particles drift over the south Atlantic those with the lowest mirror pointsencounter the atmosphere and are lost. This is where the lower edge of the radiation belt isdefined. While satellites in low-Earth orbit can pass below the radiation belt at other locationsaround the Earth, they must enter it over the south Atlantic, a region called the South AtlanticAnomaly.During the active phase of the solar cycle (called solar maximum), the Sun emits more xrays, heating the upper atmosphere and causing its scale height to increase. This pushes theatmosphere farther up into the radiation belt at solar maximum increasing loss rates of trappedparticles with low mirror points. This results in fewer trapped protons being encountered bysatellites in low-Earth orbit during the maximum of the solar cycle.The most widely used model for trapped protons is the AP8 Model [82] (also see [31] formore details of the AP-8 Model). This model is being updated to create AP-9. The expectedrelease date for AP-9 is November, 2011. In addition to these models there are the followingmodels: CRRESPRO [83], the SAMPEX/PET model [84] and NOAAPRO model [85].Trapped protons are introduced into CRÈME86 [8] using the STASS subroutine. Theuser is expected to obtain orbit-averaged trapped proton data in the form of a differentialspectrum in units of protons/(cm2-s-KeV) versus proton energy in MeV. Under control of theSTASS program, this spectrum table is to be entered as pairs of energy and flux with the energymonotonically increasing. This input table can be generated, for example, using SPENVIS [59].SPENVIS offers the AP-8 MIN and MAX, CRRESPRO, and the SAMPEX/PET models. SpaceRadiation [20] also uses an imported trapped proton spectrum. CRÈME96 [25], NOVICE [19]and OMERE [30] use AP-8 for trapped protons. The CHIME model [26] and the MACREE
16model [27] do not include trapped radiation.2.5 Radiation Transport through ShieldingTo reach the device of interest within the spacecraft, the radiation must penetrate thesurrounding spacecraft structure. When charged particles pass through the structure, they loseenergy through interactions with atomic electrons and through nuclear interactions. Sinceinteractions with electrons are so frequent, they can be treated as a continuous process. Nuclearinteractions are infrequent and must be treated as individual events. These interactions can beelastic collisions in which some energy is lost through the momentum transfer to a nucleus in thestructure, but the projectile nucleus remains intact. Other interactions are inelastic. Theseinteractions increase the internal energy in the projectile nucleus and/or the target nucleus.Nuclei can lose internal energy in a variety of ways. Many of these ways involve the emission ofneutrons but charged particles can also be emitted. This changes elemental or isotopic identitiesof the incident nuclei. As a result of such interactions, the projectile nuclei can even break upinto much lighter nuclei and nucleons.The net effect on radiation penetrating spacecraft is for it to lose energy with the slowestenergy particles stopping before reaching the device of interest. The elemental composition ofthe flux is also altered by the breakup of nuclei reducing the fluxes of the most abundant heavynuclei while the fluxes lighter and less abundant nuclei are increased by the breakup of heavierprogenitors. A rough rule of thumb is that the error rates decrease by a factor of 10 behind 6.5inches of aluminum shielding [86].The thickness of the spacecraft surrounding the device of interest is rarely uniform withthe result that the intensity and elemental composition of the radiation striking the device from
17different directions will be different. This detail is usually ignored in error rate prediction, andthe average intensity and composition is assumed to arrive uniformly from all directions. Thiscan lead to significant errors [87], [88], especially when the radiation environment is d
RPP method published by Pickel and Blandford [5], was used to create the CRÈME (Cosmic . The model for the GCR spectrum used in CRÈME86 [8] was the result of fitting the data available by the early 1980’s. At that time the GCRs were known to be modulated with the . In this case, the guiding
