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Apogee is the maximum altitude above the Earth's surface attained during the spacecraft's orbit. Its value is input to the CREME software in either km or nautical miles.
Perigee is the minimum altitude above the Earth's surface attained during the spacecraft's orbit. Its value is input to the CREME software in either km or nautical miles.
Nautical Mile

1 international nautical mile = 1.852 km = 1.1508 miles = 6076.1155 feet

The international nautical mile is also known as the international air mile.

The geographical nautical mile is 6080 feet (0.064% larger).

Orbital Inclination Angle
The orbital inclination is the angle between the orbital plane and Earth's geographic equatorial plane, measured in degrees. Retrograde orbits have inclinations greater than 90 and less than or equal to 180 degrees.
Initial Longitude of the Ascending Node

The ascending node is the point on a spacecraft's orbit at which it crosses the equator from south to north. The initial longitude of the ascending node is the east longitude for the position in space at which the orbit will first pass over the equator from south to north. The initial longitude is defined in an inertial coordinate system, not the geographical coordinate system which rotates with the Earth. That is, the initial longitude is defined using the initial time t0, and is not the longitude at time t=t0+dt, corresponding to the actual first crossing of the equator from south to north.

This parameter specifies an initial condition. In general, its value is not important for design studies, which typically average over many orbits. However, this parameter may be important if you are trying to evaluate a very specific orbital segment.

East longitude is measured eastward from the prime meridian, e.g. the U.S. is at east longitudes between 180 and 270 degrees.

The initial longitude of the ascending node is equivalent to the right ascension of the ascending node for the initial epoch used in CREME. The right ascension of the ascending node is "the angle in the equatorial plane measured eastward from vernal equinox to the ascending node of the orbit" (Wertz, 1978, p. 44). Thus, the initial longitude of the ascending node is equivalent to the right ascension of the ascending node when the prime meridian is aligned with the vernal equinox.

Reference: Spacecraft Altitude Determination and Control, James R. Wertz, D. Reidel Publishing Company, Dordrecht, Holland, 1978.

Initial Displacement of the Ascending Node

This is a non-standard orbital parameter that is effectively used in place of one of the classical orbital elements, e.g. the mean anomaly at initial epoch of the orbit (Wertz, 1978, p. 46). The displacement is measured in degrees relative to the the ascending node along the spacecraft's orbital plane (not the equatorial plane). The physical interpretation of this parameter is fairly complicated.

For circular orbits, this displacement angle is positive for initial displacements along the direction motion. When combined with the initial location of the ascending node, it uniquely specifies the spacecraft's position (e.g. latitude and longitude).

For elliptical orbits, this displacement angle is positive for initial displacements opposite the direction of the spacecraft's motion. When combined with both the initial location of the ascending node and the displacement of the perigee from the ascending node, it uniquely specifies the spacecraft's position (e.g. latitude and longitude). This second condition arises essentially because CREME solves for the mean anomaly at the initial epoch of the orbit. Since the initial epoch is fixed and the mean anomaly at the initial epoch depends on the displacement of the perigee from the ascending node, the spacecraft's initial location must be determined to be consistent with these constraints.

In the special case in which the displacement of the perigee from the ascending node is 0 degrees, the initial displacement from the ascending node becomes the spacecraft's initial displacement from the ascending node in the direction opposite to the spacecraft's motion.

This parameter specifies an initial condition. In general, its value is not important for design calculations, which typically average over many orbits. However, this parameter may be important if you are trying to evaluate a very specific orbital segment.

For more information on this parameter, please contact

Reference: Spacecraft Attitude Determination and Control, p. 46, James R. Wertz, D. Reidel Publishing Company, Dordrecht, Holland, 1978.

Displacement of Perigee from the Ascending Node (Argument of Perigee)

This parameter, which is also known as the argument of perigee, is the displacement from the perigee to the ascending node, as measured in degrees in the orbital plane, along the satellite's direction of motion. This parameter is only defined for elliptical orbits (obviously).

The value chosen for this parameter can significantly affect orbit-averaged trapped proton fluxes calculated with the TRP module, since this parameter controls the latitudes at which apogee and perigee are encountered and hence the sampling of the radiation belt. (The value of this parameter generally has less effect on geomagnetic transmission (GTRN) calculations.)

For design calculations, if you do not know the actual argument of perigee for your orbit, you should explore a range of values (between 0o and 360o), to see how this might affect your results.

In addition, the value of this parameter can undergo significant precession during the course of an extended mission. This precession is generally unimportant below ~1000 km. For orbits between 1000 km and geosynchronous orbit (~36,000 km), this precession is primarily caused by the oblateness of the Earth and can be significant. In this case, an approximate formula (Wertz & Larson 1991) for the precession rate caused by the Earth's oblateness is:

R (deg/day) = 1.03237 x 1014 a-3.5 (4-5sin2 i) (1-e2 )-2


  • a = semi-major axis (in km) = 0.5*(apogee+perigee) + RE
  • i = inclination angle
  • e = eccentricity = (apogee-perigee)/(apogee+perigee+2RE)
  • RE = mean radius of the geoid = 6378.14 km

(Recall that apogee and perigee are defined as distance above the surface of the Earth.)

For example, for the CRRES orbit (apogee=33,582 km, perigee = 348 km, inclination = 18.2o), the oblateness of the Earth causes the argument to perigee to precess at a rate of 0.767 deg/day. (The real value is slightly larger, due to additional contributions caused by the Moon and Sun.)

For orbits beyond geosynchronous, perturbations due to the Moon and Sun dominate the precession rate. For further information, see Wertz & Larson 1991.

At present, the CREME orbit generator does not automatically include orbital precession terms. Consequently, for studies of an extended mission, you should repeat your trapped proton calculations with various values of argument of perigee which reflect the precession you expect to see in the course of your mission. See TRP limitations for further information.

Also, for post-flight comparison with on-orbit measurements, you should determine the actual parameter values for your orbit, and not simply use "default values."

For an example of such calculations, see the CRRES/MEP results.


Space Mission Analysis and Design, by James R. Wertz and Wiley J. Larson (editors), Kluwer Academic Publishers, Dordrecht, Holland 1991, pp. 125-126.

Spacecraft Attitude Determination and Control, James R. Wertz, D. Reidel Publishing Company, Dordrecht, Holland, 1978, p. 45.

Number of Orbits

The TRP module allows you to specify (via a pull-down menu) the number of orbits to be tracked while accumulating the orbit-averaged and peak trapped proton fluxes. Because the TRP module is very CPU-intensive, please use 50-100 orbits for exploratory calculations. For final calculations, however, the recommended number of orbits is 200.

Trapped proton fluxes are evaluated along each orbit at 200 locations, which are equally spaced in time.

Please see limitations for more details on the orbit generator presently used for these calculations.

McIlwain L
McIlwain L is a geomagnetic coordinate used to label magnetic field lines and (more properly) particle drift shells in the magnetosphere. L roughly corresponds to the distance from the center of Earth's magnetic dipole to the magnetic field line's location at the magnetic equator, measured in units of Earth radii. For example, a geosynchronous orbit is roughly at L = 6.6. The geomagnetic equator is at about L=1. (Because of the offset of Earth's magnetic dipole with respect to the geoid, McIlwain L values slightly less than one are occasionally encountered.) The heart of the South Atlantic Anomaly (SAA), where the van Allen radiation belts have their closest approach to the surface of the Earth, is roughly at L=1.2-2.
Geomagnetic Transmission Function

The geomagnetic transmission function ("GTF") expresses, as a function of magnetic rigidity, the fraction of the specified orbit (or segment thereof) for which a cosmic-ray of the given rigidity could reach the orbit from interplanetary space. Geomagnetic transmission functions are calculated by the CREME GTRN routine.

In using the CREME transmission functions to calculate cosmic-ray fluxes inside Earth's magnetosphere, several important simplifying assumptions have been made:

  • The GTF calculation is averaged over all directions, without any preferred spacecraft orientation or lookout direction (due to thin shielding, for example) from the spacecraft. (The calculation does take into account, however, that some lookout directions are blocked by the solid Earth.)
    • The pre-calculated transmission functions are explicitly averaged over arrival directions, through use of trajectory-tracing calculations for various lookout angles.
    • For other orbits, the vertical geomagnetic cutoff is used as an effective average over arrival directions. However, this approximation can underestimate the flux of lower-energy particles in low-inclination, low-altitude orbits.
    • For further details about the techniques used in calculating geomagnetic transmission functions in this release of CREME, see Tylka et al. 1997, IEEE Trans. Nucl. Sci 44 (December,1997), pp. 2155-57.
  • To calculate the orbit-averaged transmission function, GTRN employs an orbital mechanics routine which tracks the specified orbit for seven days. The calculations therefore may not accurately reflect observations made over a significantly shorter period of time. Also, this seven-day averaging may not be sufficient for orbits with periods of several hours or longer. In this case, calculations with different values of the satellite's initial position may be helpful in assessing this possibility. See orbital parameters for further details.
  • Flux calculations using these GTFs assume that the interplanetary source flux is isotropic.

Anisotropies in the interplanetary energetic particle fluxes are generally small, except in the very early stages of solar particle events.

  • The orbit-averaged flux calculation further assumes that the interplanetary flux varies slowly compared with the orbital period.

This last assumption may be invalid in some very large solar particle events. In this case, accurate flux calculations inside the magnetosphere require careful correlation between the interplanetary flux's timeline and the spacecraft's location.

Magnetic Rigidity

Magnetic rigidity is a particle's momentum per unit charge. It is the relevant quantity for characterizing a cosmic ray's ability to penetrate Earth's magnetic field. In terms of the ion's atomic mass number A (i.e, number of neutrons and protons in the nucleus), its charge Q (in units of the proton's charge) and kinetic energy E (in units of GeV/nucleon), the rigidity of an ion is given by:

R (in GV) = (A/Q) (E2 + 2M0E)1/2

where M0 = 0.9315016 GeV/c2 is the atomic mass unit.

Note: 1 GeV = 103 MeV = 109 eV

Galactic Cosmic Rays

Galactic cosmic rays (GCRs) are the highest energy particle radiation to reach Earth. These particles are predominantly accelerated in our own galaxy, the Milky Way, at sites and by mechanisms which remain to be discovered. At the very highest energies, the particles are actually believed to be extragalactic; that is, originating from powerful astrophysical accelerators located outside of the Milky Way.

The composition and spectra of GCRs evolve during the course of their travel through the Galaxy, due to collisions between the GCRs and interstellar gas. For example, nuclei which are relatively rare in terrestrial and solar material (such as Li, Be, B and the sub-Fe nuclei with atomic numbers Z=21-25) are produced in these interstellar collisions and therefore have relatively high abundances in Galactic cosmic rays. These effects are included in the CREME GCR model.

When GCRs enter our Solar System, they must overcome the outward-flowing solar wind. This wind impedes and slows the incoming GCRs, reducing their energy and preventing the lowest energy ones from reaching Earth. This effect is known as solar modulation. Because of solar modulation, GCRs at Earth typically have much higher energies than the other components of the space radiation environment.

The Sun has an 11-year activity cycle which is reflected in the characteristics of the solar wind and the ability of the solar wind to modulate GCRs. As a result, the GCR intensity at Earth is anti-correlated with the level of solar activity, i.e., when solar activity is high and there are lots of sunspots, the GCR intensity at Earth is low, and visa versa.

The number of sunspots provide a general measure of the level of solar activity and correlates with the properties of the solar wind leaving the Sun. The solar wind, however, takes several months to propagate through the heliosphere (i.e., the region of space, extending to ~100 AU, which is dominated by the Sun's solar wind). As a result, it should be possible to use the sunspot number as a predictor of future levels of solar modulation, with lead times on the order of 1-3 months. (At present, longer-term predictions must rely upon the assumption of cyclic repetition in the pattern of solar modulation.) A model which utilizes this empirical correlation between sunspot numbers and GCR flux levels and the historical record is incorporated in CREME.

In addition to the general level of solar activity, galactic cosmic ray penetration into the heliosphere is also affected by the structure of the solar magnetic field. Superimposed on the 11-year solar-activity cycle is a 22-year cycle of solar magnetic field reversals. As a result, two successive cosmic-ray maxima differ significantly in their durations. This pattern is also incorporated into the CREME GCR model.

The current CREME GCR model, as described above, is based on "A Model of Galactic Cosmic Ray Fluxes", by R.A. Nymmik, M.I. Panasyuk, T.I Pervaja, and A.A. Suslov, Nuclear Tracks and Radiation Measurements, 20, 427-429 (1992). This model has solar minimum flux levels generally comparable to those found in the old CREME (1986) model but provides a substantially better description of solar cycle variation.

For more information on the improved solar-cycle variation in this model, see A.J. Tylka et al., "CREME96: A Revision of the Cosmic Ray Effects on Micro-Electronics Code", IEEE Transactions on Nuclear Science 44, 2150-2160 (1997).

Anomalous Cosmic Rays

Anomalous Cosmic Rays (ACRs) are the third primary component (along with Galactic Cosmic Rays and Solar Energetic Particles) of the interplanetary ionizing radiation environment.

ACRs were first discovered in 1973 as a "bump" in the spectra of certain elements (He, N, O, Ne) at energies of ~10 MeV/nucleon. To date, ACRs have also been observed in H, Ar, and (at highly-suppressed levels) C.

  • ACRs arise primarily from neutral interstellar atoms which are swept into the solar cavity by the motion of the Sun through the interstellar medium. (The unusual composition of ACRs reflects the fact that only atoms with high first-ionization potentials (above ~13.6 eV) are abundant as interstellar neutrals.)
  • At ~1-3 AU, these neutral atoms become singly-ionized either by photoionization by solar UV photons or by charge-exchange collisions with solar wind protons.
  • These singly-ionized particles are then entrained in the outward-flowing solar wind, which carries them to the solar-wind termination shock (located somewhere in the region of ~70 -100 AU).
  • At this shock, these ions are accelerated from ~1 keV/nucleon to energies of tens of MeV/nuc. Recent observations from the SAMPEX satellite indicate that singly-ionized ions are accelerated to a maximum energy of ~250-350 MeV total energy.
  • However, collisions in the termination shock region cause some ions to become further stripped of electrons, thereby reaching higher ionic charge states (+2, +3, +4, etc.) With these higher charges, the electric fields in the termination shock accelerate ions to even higher energies. In fact, SAMPEX has observed anomalous cosmic ray oxygen ions at Earth with energies up to at least ~100 MeV/nuc, albeit with a very steep spectrum.

Because anomalous cosmic rays are less-than-fully-ionized, they are not as effectively deflected by Earth's magnetic field as galactic cosmic rays of the same energies, which are bare nuclei.

The original CREME code (1986), which was based on the best-available data at the time, significantly overestimated the ACR radiation hazard. In particular, the original CREME (1986) code:

  • used a spectral shape which was too hard, thereby overestimating the ACR flux at energies required to penetrate typical minimum satellite shielding.
  • included highly-ionizing elements (such as Mg, Si, and Fe) at levels far above present experimental upper limits on the presence of these nuclei among ACRs at 1 AU.
  • treated ACRs as singly-ionized at all energies. This charge state is correct (for example, for oxygen) up to ~20 MeV/nuc. But SAMPEX has shown that at higher energies, ACRs are multiply-ionized, with charges states of +2, +3, and probably higher. It is especially important to correctly account for these charge states in evaluating ACR fluxes in low-inclination, low-altitude orbits.
  • ignored solar-cycle variation in the ACR flux.

The ACR model in CREME corrects all of these shortcomings. It is based on the latest spectral, composition, and charge state measurements from SAMPEX and other satellites, as well as the 22-year historical record of anomalous cosmic-ray measurements.

For more information about the ACR modeling CREME, see:

  • A.J. Tylka et al., "CREME96: A Revision of the Cosmic Ray Effects on Micro-Electronics Code", IEEE Transactions on Nuclear Science, 44, 2150-2160 (1997).

For more information on ACR observations used in the CREME ACR model, see:

  • R.A. Mewaldt et al., "The Return of Anomalous Cosmic Rays to 1 AU in 1992", Geophysical Research Letters, 20, 2263-2266 (1993).
  • R.A. Mewaldt et al., "Evidence for Multiply Charged Anomalous Cosmic Rays", Astrophysical Journal Letters 466, L43-L46 (1996).

Another interesting consequence of the ACR charge state is that ACRs penetrate to Earth's upper atmosphere, where they become a distinct population of trapped heavy ions in Earth's inner magnetosphere. However, measurements to date indicate that trapped ACRs have steep spectra and are therefore unlikely to be a significant radiation hazard except possibly for lightly-shielded systems (less that ~50 mils Al equivalent) and in parts of certain orbits. For more information on trapped ACRs, see:

  • N.L. Grigorov et al., "Evidence for Trapped Anomalous Cosmic Ray Oxygen Ions in the Inner Magnetosphere", Geophysical Research Letters 18, 1959-1962 (1991).
  • R.S. Selesnick et al., "Geomagnetically Trapped Anomalous Cosmic Rays", Journal of Geophysical Research, 100, 9503-9518 (1995).

For an assessment of the potential radiation hazard due to trapped anomalous cosmic rays, see:

  • A.J. Tylka et al., "LET Spectra of Trapped Anomalous Cosmic Rays in Low-Earth Orbit", Advances in Space Research 17, (2)47-(2)41 (1996).

In some devices, the deposited charge which contributes to the SEU is apparently augmented by ionization from regions outside of the nominal sensitive volume. This phenomenon is known as "funneling", and its calculation is a simple modification to the standard RPP formalism. In general, funnels lead to a decrease in the calculated SEU rate, since they imply that the amount of deposited charge required to cause an SEU is actually larger.

For more information on funnels, see:

E.L. Petersen, J.C. Pickel, E.C. Smith, P.J. Rudeck, and J. R. Letaw,, "Geometrical Factors in SEE Rate Calculations", IEEE Transactions on Nuclear Science, NS-40, no.6, 1888-1909 (1993).

J.C. Pickel, "Single-Event Effects Rate Prediction", IEEE Transactions on Nuclear Science, NS-43, no. 2, 483-495 (1996).

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