Geomagnetic cutoffs: a review for space dosimetry applications.

The earth's magnetic field acts as a shield against charged particle radiation from interplanetary space, technically described as the geomagnetic cutoff. The cutoff rigidity problem (except for the dipole special case) has "no solution in closed form". The dipole case yields the Stormer equation which has been repeatedly applied to the earth in hopes of providing useful approximations of cutoff rigidities. Unfortunately the earth's magnetic field has significant deviations from dipole geometry, and the Stormer cutoffs are not adequate for most applications. By application of massive digital computer power it is possible to determine realistic geomagnetic cutoffs derived from high order simulation of the geomagnetic field. Using this technique, "world-grids" of directional cutoffs for the earth's surface and for a limited number of satellite altitudes have been derived. However, this approach is so expensive and time consuming it is impractical for most spacecraft orbits, and approximations must be used. The world grids of cutoff rigidities are extensively used as lookup tables, normalization points and interpolation aids to estimate the effective geomagnetic cutoff rigidity of a specific location in space. We review the various options for estimating the cutoff rigidity for earth-orbiting satellites.     

Evaluation of the dynamic cutoff rigidity model using dosimetry data from the STS-28 flight.

We have a developed a dynamic cutoff rigidity model based on computed world grids of vertical cutoff rigidities derived from employing the Tsyganenko magnetospheric model. The dynamic range of this model covers all magnetic activity levels specified by integer values of the Kp magnetic index. We present comparisons of the measured dose observed on the space shuttle during the August 1989 solar proton event with the dose computed from solar particles predicted to be allowed through the magnetosphere to the space shuttle position. We find a one-to-one correspondence between the portion of the orbit predicted to be subjected to solar protons and the portion of the orbit where solar particle dose measurements were obtained.     

The limitations of using vertical cutoff rigidities determined from the IGRF magnetic field models for computing aircraft radiation dose.

Vertical cutoff rigidities derived from the International Geomagnetic Reference Fields (IGRF) are normally used to compute the radiation dose at a specific location and to organize the radiation dose measurements acquired at aircraft altitudes. This paper presents some of the usually ignored limits on the accuracy of the vertical cutoff rigidity models and describes some of the computational artifacts present in these models. It is noted that recent aircraft surveys of the radiation dose experienced along specific flight paths is sufficiently precise that the secular variation of the geomagnetic field is observable.     

Flight safety implications of the extreme solar proton event of 23 February 1956

There is considerable speculation about the effects at aircraft altitudes resulting from extreme solar proton events. The ground level event (GLE) of 23 February 1956 (GLE 5), remains the largest solar proton event of the neutron monitor era in terms of its influence on count rates at monitors near sea level. During this GLE the count rate was increased by as much as 4760% (15-min average) at the Leeds monitor relative to the count rate from galactic cosmic radiation (GCR). Two modern models of the event cumulative solar proton spectrum for this event, a 6-parameter fit in energy and a 4-parameter Band fit in rigidity, are compared with 1-h of GCR at solar minimum. While effective doses calculated with CARI-7A for both models at low geomagnetic cutoff rigidities are indeed high when compared with GCR and can exceed recommended exposure limits, both GLE spectra exhibit a much stronger dependence on cutoff rigidity than GCR, and a larger fraction of the dose from neutrons. At locations with cutoff rigidities above 4.2 and 6.4?GV, respectively, the GLE effective doses are smaller than the GCR hourly dose. At locations with cutoff rigidities above about 4?GV, GCR was the dominant source of exposure in 10?h or less at all altitudes examined. This suggests that if a similar event occurs in the future, low- and mid-latitude flights at modern jet flight altitudes could be well-protected by Earth’s magnetic field.     

A method for operative calculation of charged particle penetration into the LEO

We develop a simple method for calculating the effective vertical cutoff rigidity of charged particles, taking into account the Kp-index and the local time, on the basis of generalization of the results of extensive trajectory calculations for trial particles moving in the geomagnetic field. The vertical cutoff rigidities, calculated by the Tsyganenko-89 model, are presented as an International Geomagnetic Reference Field (IGRF) model calculated and thereafter corrected in accordance with the geomagnetic disturbance and local time conditions. The fits from the proposed method agree with the results of cutoff rigidity measurements carried out by satellites. The method is intended for applications using cutoff calculations, such as evaluating particle penetration of spatial boundaries, calculating magnetospheric transmissions for low-orbital spacecrafts flights and interpreting the results of orbital experiments.     

质子地磁垂直截止刚度在2004年11月7-8日两个时刻处的数值模拟

利用单粒子轨道理论, 在T04和IGRF2000磁场模式建立的磁层模型基础上, 应用四阶龙格库塔方法, 模拟计算宇宙线带电质子在地球磁层中的运动以及沿天顶方向入射到达地球磁场内的某一特定位置, 得到了距地球表面450km高度处全球质子垂直截止刚度在2004年11月7-8日中两个时刻的计算值. 根据计算得到的684个不同位置处的截止刚度值, 分析了同一时刻地磁垂直截止刚度随磁纬和磁经的变化. 与此同时, 模拟计算了相同时刻下磁纬为30°, 磁经为0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°处, 地磁有效垂直截止刚度随高度的变化情况. 结果表明, 在磁纬30°处, 其质子有效垂直截止刚度随距离地心高度的变化沿向阳处向磁尾处方向, 变化越来越缓慢.      

Effects of geomagnetic secular variations on cosmic ray access to the terrestrial environment

Taking advantage of the cutoff computations performed for more than a hundred locations from 1955 to 1995 [every 5 years; Shea, M.A., Smart, D.F. Vertical cutoff rigidities for cosmic ray stations since 1955, in: Proceedings of the ICRC 2001, Hamburg, Copernicus Gesellschaft, vol. 10, pp. 4063–4066, 2001], we carefully checked the relationship between the vertical cutoff rigidity and the McIlwain parameter introduced by Shea et al. [Shea, M.A., Smart, D.F., Gentile, L.C. Estimating cosmic ray vertical cutoff rigidities as a function of the McIlwain L-parameter for different epochs of the geomagnetic field. Phys. Earth Planet. Int., 48, 200–205, 1987]. We derived an updated algorithm that can be used outside the polar and equatorial regions, avoiding time consuming computations. Results for the European area and 1990 epoch suggest that the fast evaluation is accurate within 0.1 GV in 26 out of the 30 considered locations.     

Variations in cosmic ray cutoff rigidities during the great geomagnetic storm of November 2004

A very strong interplanetary and magnetospheric disturbance observed on 7–13 November 2004 can be regarded as one of the strongest events during the entire period of space observations. In this paper we report on the studies of cosmic ray cutoff rigidity variations during 7–13 November 2004 showing how storm conditions can affect the direct cosmic ray access to the inner magnetosphere. Effective cutoff rigidities have been calculated for selected points on the ground by tracing trajectories of cosmic ray particles through the magnetospheric magnetic field of the “storm-oriented” Tsyganenko 2003 model. Cutoff rigidity variations have also been determined by the spectrographic global survey method on the basis of experimental data of the neutron monitor network. Relations between the calculated and experimental cutoff rigidities and the geomagnetic Dst-index and interplanetary parameters have been investigated. Correlation coefficients between the cutoff rigidities obtained by the trajectory tracing method and the spectrographic global survey method have been found to be in the limits 0.76–0.89 for all stations except the low-latitude station Tokyo (0.35). The most pronounced correlation has been revealed between the cutoff rigidities that exhibited a very large variation of ∼1–1.5 GV during the magnetic storm and the Dst index.     

Effective non-vertical and apparent cutoff rigidities for a cosmic ray latitude survey from Antarctica to Italy in minimum of solar activity

In this paper we will report the results of the computation of cutoff rigidities of vertical and non-vertical incident cosmic ray particles. Non-vertical effective cutoff rigidities have been computed by tracing particle trajectories through the “real” geomagnetic magnetic field comprising the International Geomagnetic Reference Field model (IGRF95, IAGA Division 5 Working Group 8, 1996: Sabaka, T.J., Langel, R.A., Baldwin, R.T., Conrad, J.A. The geomagnetic field, 1900–1995, including the large scale fields from magnetospheric sources and NASA candidate models for the 1995 IGRF revision. J. Geomag. Geoelect. 49, 157–206, 1997.) and the Tsyganenko [Tsyganenko, N.A. A magnetospheric magnetic field model with a warped tail current sheet. Planet. Space Sci. 37, 5–20, 1989.] magnetosphere model. The computation have been done for the backward route (from Antarctica to Italy) of the Italian Antarctic ship survey 1996–1997, for geographic points corresponding to the daily average coordinates of the ship; for zenith angles 15°, 30°, 45° and 60°, and azimuth angles from 0° to 360° in steps of 45°. By means of the obtained non-vertical cutoffs the apparent cutoff rigidities have been calculated. The information on integral multiplicities of secondary neutrons detected by the neutron monitor in dependence of the zenith angle of incoming primary cosmic ray particles have also been used. This information is based on the theoretical calculations of meson-nuclear cascades of primary protons with different rigidities arriving to the Earth’s atmosphere at the zenith angles of 0°, 15°, 30°, 45°, 60° and 75°. The difference between the computed apparent and vertical cutoff rigidities reaches ∼1 GV at rigidities >7–8 GV. At rigidities of 10–16 GV, the difference between the apparent and vertical cutoff rigidities is larger than that obtained earlier by Clem et al. [Clem, J.M., Bieber, J.W., Duldig, M., Evenson, P., Hall, D., Humble, J.E. Contribution of obliquely incident particles to neutron monitor counting rate. J. Geophys. Res. 102, 26919–26926, 1997.] and Dorman et al. [Dorman, L.I., Villoresi, G., Iucci, N., Parisi, M., Tyasto, M.I., Danilova, O.A., Ptitsyna, N.G. Cosmic ray survey to Antarctica and coupling functions for neutron component near solar minimum (1996–1997), 3. Geomagnetic effects and coupling functions. J. Geophys. Res. 105, 21047–21056, 2000.].     

On the possibility to check the magnetosphere’s model by CR: The strong geomagnetic storm in November 2003

We report on a study of cosmic ray cutoff rigidity variations during the strong geomagnetic storm of 18–24 November 2003. We employed the most recent Tsyganenko magnetospheric model to represent the very strong disturbed Magnetosphere. We used this magnetic field for the cosmic ray trajectory calculations to determine the geomagnetic cutoff rigidity throughout this period of severe geomagnetic disturbance. We determine the cutoff rigidity changes during this period by two methods, by trajectory calculations and by the spectrographic global survey method. The values of the change of cutoff rigidities obtained by two different methods are correlated with the D_st and interplanetary magnetic field and plasma parameters and result in correlation coefficients in the range 0.63–0.84 for the various cosmic ray stations. The result of this study indicates that the most significant contributions to the cutoff rigidity changes are due to D_st variation although the influence of solar wind density and B_z and B_y components of IMF variations is significant.     

A new dynamical atmospheric ionizing radiation (AIR) model for epidemiological studies.

A new Atmospheric Ionizing Radiation (AIR) model is currently being developed for use in radiation dose evaluation in epidemiological studies targeted to atmospheric flight personnel such as civilian airlines crewmembers. The model will allow computing values for biologically relevant parameters, e.g. dose equivalent and effective dose, for individual flights from 1945. Each flight is described by its actual three dimensional flight profile, i.e. geographic coordinates and altitudes varying with time. Solar modulated primary particles are filtered with a new analytical fully angular dependent geomagnetic cut off rigidity model, as a function of latitude, longitude, arrival direction, altitude and time. The particle transport results have been obtained with a technique based on the three-dimensional Monte Carlo transport code FLUKA, with a special procedure to deal with HZE particles. Particle fluxes are transformed into dose-related quantities and then integrated all along the flight path to obtain the overall flight dose. Preliminary validations of the particle transport technique using data from the AIR Project ER-2 flight campaign of measurements are encouraging. Future efforts will deal with modeling of the effects of the aircraft structure as well as inclusion of solar particle events.     

Cosmic ray exposure factors for Shuttle altitudes derived from calculated cut-off rigidities.

The allowed cosmic radiation flux accessible to an earth-orbiting spacecraft is a complex function of the satellite position and the geomagnetic cutoff characteristics at each zenith and azimuth angle at each position. We have determined cosmic ray exposure factors for the galactic cosmic ray spectrum for typical shuttle altitudes and inclinations up to 50 degrees. We have utilized d world grid of trajectory-derived cutoff rigidity calculations at 400 km altitude to determine geomagnetic transmission functions that permit a simple and direct calculation of the allowed cosmic ray spectrum to a 400 km satellite orbit. If the interplanetary cosmic ray spectrum is multiplied by the orbit-averaged geomagnetic transmission function the result is the allowed cosmic ray spectrum at the spacecraft.     

The local neutron flux at low earth-orbiting altitudes

The COMPTEL instrument onboard the Compton Gamma Ray Observatory (CGRO) has been used to measure the variation of the atmospheric neutron flux below 5 MeV as a function of vertical cutoff rigidity and spacecraft orientation at an altitude of 450 km. The instrumental 2.2 MeV background line, resulting from thermal neutron capture on hydrogen, was used for the measurement. The dependence of the 2.2 MeV rate on rigidity and geocentre zenith can be described by an analytic function: the line rate decreases linearly with geocentre zenith, and decreases exponentially with the vertical cutoff rigidity. The flux varies on average by about a factor of 3.7 between the extremes in rigidity, and by a factor of 1.7 between the extremes of spacecraft orientation with respect to the Earth. We believe that mass shielding is more important in attenuating the atmospheric albedo than as a source of secondary neutrons. The COMF'TEL instrument is well suited for a long-duration study of the dependence of the neutron flux on the vertical cutoff rigidity and the solar cycle.     

Calculations and observations of solar particle enhancements to the radiation environment at aircraft altitudes.

Solar particle events can give greatly enhanced radiation at aircraft altitudes, but are both difficult to predict and to calculate retrospectively. This enhanced radiation can give significant dose to aircrew and greatly increase the rate of single event effects in avionics. Validation of calculations is required but only very few events have been measured in flight. The CREAM detector on Concorde detected the event of 29 September 1989 and also four periods of enhancement during the events of 19-24 October 1989. Instantaneous rates were enhanced by up to a factor ten compared with quiet-time cosmic rays, while flight-averages were enhanced by up to a factor six. Calculations are described for increases in radiation at aircraft altitudes using solar particle spectra in conjunction with Monte Carlo radiation transport codes. In order to obtain solar particle spectra with sufficient accuracy over the required energy range it is necessary to combine space data with measurements from a wide range of geomagnetically dispersed, ground-level neutron monitors. Such spectra have been obtained for 29 September 1989 and 24 October 1989 and these are used to calculate enhancements that are compared with the data from CREAM on Concorde. The effect of cut-off rigidity suppression by geomagnetic activity is shown to be significant. For the largest event on record on 23 February 1956, there are no space data but there are data from a number of ground-level cosmic-ray detectors. Predictions for all events show very steep dependencies on both latitude and altitude. At high latitude and altitude (17 km) calculated increases with respect to cosmic rays are a factor 70 and 500 respectively for 29 September 1989 and 23 February 1956. The levels of radiation for high latitude, subsonic routes are calculated, using London to Los Angeles as an example, and can exceed 1 mSv, which is significantly higher than for Concorde routes from Europe to New York. The sensitivity of the calculations to spectral fitting, geomagnetic activity and other assumptions demonstrates the requirement for widespread carriage of radiation monitors on aircraft.     

Radiation measurements aboard NASA ER-2 high altitude aircraft with the Liulin-4J portable spectrometer.

The risks to aircrew health posed by prolonged exposure to low levels of ionizing radiation at aircraft altitudes have recently received renewed attention. Civil and military aircraft currently on the drawing board are expected to operate at higher altitudes (>12 km) and fly longer ranges than do existing aircraft, thereby exposing their crews to higher levels of ionizing radiation, for longer periods of time. We are currently carrying out dosimetric measurements of the ionizing radiation environment at approximately 20 km altitude using portable Si detectors aboard NASA's two ER-2 high altitude research aircraft. The instruments, Liulin-4J, have been extensively calibrated at several particle accelerators. With these instruments, we can measure not only absorbed dose, but also variation of the absorbed dose as a function of time. We report radiation dose measurements as function of time, altitude, and latitude for several ER-2 missions.     

The atmospheric cosmic- and solar energetic particle radiation environment at aircraft altitudes

Galactic cosmic rays interact with the solar wind, the earth's magnetic field and its atmosphere to produce hadron, lepton and photon fields at aircraft altitudes. In addition to cosmic rays, energetic particles generated by solar activity bombard the earth from time to time. These particles, while less energetic than cosmic rays, also produce radiation fields at aircraft altitudes which have qualitatively the same properties as atmospheric cosmic rays. We have used a code based on transport theory to calculate atmospheric cosmic-ray quantities and compared them with experimental data. Agreement with these data is seen to be good. We have then used this code to calculate equivalent doses to aircraft crews. We have also used the code to calculate radiation doses from several large solar energetic particle events which took place in 1989, including the very large event that occurred on September 29^th and 30^th of that year. The spectra incident on the atmosphere were determined assuming diffusive shock theory.     

World grid of cosmic ray vertical cut-off rigidity for the last decade

Cosmic ray cut-off rigidity tables and maps over the world concerning the epochs 2010, 2015 and the current one 2020 have been constructed. These maps display the effective cut-off rigidity in every five degrees in latitude and in longitude at the altitude of 20 km above the surface of the international reference ellipsoid. The values of the geomagnetic cut-off rigidity were calculated in every 5° in latitude and in every 15° in longitude applying the well-known method of particle trajectory calculations resulted from the theory of the particle motion in the Earth's magnetic field. The applied software employed the 12th Generation of the International Geomagnetic Reference Field (IGRF 12) and trajectories were calculated at 0.01 GV intervals in order to determine the vertical cut-off rigidity for each location. Beyond the use of the calculated cut-off rigidity values as a basic reference of charged particle access to different geographical locations during quiet and/or more intense geomagnetic periods, these results can be used for a long- term forecasting of the geomagnetic conditions variations.     

Modeling solar proton access to geostationary spacecraft with geomagnetic cutoffs

Solar energetic particle (SEP) cutoffs at geosynchronous orbit are sensitive to moderate geomagnetic activity and undergo daily variations due to the day–night asymmetry of the magnetosphere. At geosynchronous orbit, cutoff rigidity also has a large directional dependence, with the highest cutoff rigidity corresponding to ions arriving from magnetic east and lowest cutoff rigidity corresponding to ions incident from the west. Consequently, during geomagnetically quiet periods, the SEP flux observed by an eastward facing particle detector is significantly lower than observed by a westward facing particle detector. During geomagnetically disturbed periods the cutoff is suppressed allowing SEPs access well inside of geosynchronous, so that the east–west SEP flux ratio approaches unity. Variations in the east–west SEP flux ratio observed by GOES Energetic Particle Sensors (EPS) have recently been reported by Rodriguez et al. (2010). In NOAA’s operational processing of EPS count rates into differential fluxes, the differential flux is treated as isotropic and flat over the energy width of the channel. To compare modeled SEP flux with GOES EPS observations, the anisotropy of the flux over the EPS energy range and field of view must be taken into account. A technique for making direct comparisons between GOES EPS observations and SEP flux modeled using numerically computed geomagnetic cutoffs is presented. Initial results from a comparison between modeled and observed flux during the 6–11 December 2006 SEP event are also presented. The modeled cutoffs reproduce the observed flux variations well but are in general too high.