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Abstract

GEOMAGNETIC CUTOFF RIGIDITIES
HISTORICAL BACKGROUND.
Experimental studies using mobile cosmic ray detectors such as ionization chambers and later neutron monitors (see, for example, Clay, 1934; Clay et al., 1936; Compton and Turner, 1937; Rose et al., 1956; Simpson et al., 1956; Katz, et al., 1958; Pomerantz and Agarwal, 1962) demonstrated that the cosmic ray intensity was a minimum in the earth's equatorial regions and increased to a maximum value as one approached the polar latitudes. These experimental results confirmed the predictions of theoretical studies by Störmer (1930) and Lemaitre and Vallarta (1936). The reason for this increase in cosmic radiation intensity between the equatorial and polar regions is that the earth's magnetic field provides a shield against the incoming charged particle nucleon radiation.
Störmer (1930), Vallarta (1938) and Rossi (1940) recognized that the accurate determination of particle access to a specific location from a specified direction on the earth would require a series of calculations of charged particle orbits in a mathematical model of the earth's magnetic field. The general equation of particle motion in a magnetic field does not have a solution in closed form, even in a simple dipole field. To determine which particles are allowed at a specific/ geographic location, it is necessary to perform detailed and extensive numerical calculations of cosmic ray trajectories in a mathematical model of the earth's magnetic field.
The initial calculations were made using a dipole approximation to the geomagnetic field. The method used was to launch a particle of negative charge and a specific rigidity in a specified direction from a specific location on the earth and numerically calculate the particle trajectory to a location far enough from the earth that the particle trajectory could be declared "allowed" or "forbidden". Since most of the cosmic ray particles are positively charged, the trajectory of a negative particle outward from the earth would be identical to the path of a similar positive particle moving from the interplanetary medium to the detection location. An "allowed" particle meant that the trajectory extended to interplanetary space; a "forbidden" particle meant that the particle trajectory intersected the solid earth or did not have enough momentum to escape the magnetic field (i.e. became trapped). Because of this labor-intensive effort, only a relatively few particle trajectories could be calculated in this manner.
One of the most important aspects of the work to delineate charged particle access was to define the lowest rigidity a charged particle could possess and still arrive from a specified direction at a specific point within the magnetosphere. This rigidity value became known as the "cutoff rigidity". Strictly speaking the cutoff rigidity of any geographic location is a function of the zenith and azimuth angles of arrival, the altitude of the detection location, and the geomagnetic conditions at the time of the measurement. However, there is an additional important aspect that must be considered in the determination of cosmic ray cutoff rigidities — the cosmic ray penumbra.
The cosmic ray penumbra is a region, identified by the work of Störmer, where there are alternating allowed and forbidden orbits. Particle trajectories are typically traced at successively decreasing rigidity values. The initial value is selected such that all particles above this value will be allowed at a specific location from the specified direction. As the rigidity value is decreased, a value is reached where the negative particle cannot escape the geomagnetic field. This is called the main cone cutoff or the upper cutoff value. As the particle rigidity decreases, alternating allowed and forbidden particle trajectories are identified until a value is reached below which all orbits are forbidden. The lowest allowed rigidity value is called the Störmer cutoff or lower rigidity cutoff value. The region between the upper cutoff rigidity and the lower cutoff rigidity is the cosmic ray penumbra. (See Paper 20 for a complete definition of cosmic ray cutoff terminology.) To accurately estimate the effect of the cosmic ray penumbra, which can extend over rigidity ranges for more than 3 GV, was extremely difficult using the initially available methods. Because of the complexities involved, calculated cutoff rigidities were usually determined for only the vertical direction at the desired location.
Based upon the initial work of Störmer (1930) and Vallarta (1938), and with the onset of space research, new methods were developed to estimate vertical cutoff rigidity values. Quenby and Webber (1959) included nondipole terms for the geomagnetic field model. Quenby and Wenk (1962) employed field line calculations to estimate cutoff values for high latitudes, a modified Störmer method for equatorial latitudes, and a combination of the two methods for mid latitudes. Makino (1963) modified the Quenby and Webber approximations by introducing different penumbral corrections than those of Quenby and Wenk and by introducing an empirical eastward shift of the impact point of the particle. Several tables of world wide cutoff rigidity values were published (Quenby and Webber, 1959; Quenby and Wenk, 1962; Makin°, 1963). Although these values represented improvements over the values derived from the Störmer dipole equation or the eccentric dipole approximations of Vallarta (1935), inconsistencies were still noted when these values were utilized in cosmic ray data analyses (Kodama, 1960).
With the availability of high speed digital computers in the early 1960s, it became tractable to use numerical methods to calculate a large number of trajectories of charged particles as they traversed the earth's magnetic field. In an effort to resolve an inconsistency related to the study of the relativistic solar particle events in November 1960, Freon and McCracken (1962) numerically calculated a series of cosmic ray trajectories in a high order mathematical model of the geomagnetic field. These calculations resulted in the determination of the vertical cutoff rigidity for a single location: Port aux Francais, Kerguelen Islands. This was the general status of cosmic radiation cutoff rigidities when I became interested in this type of research problem.

CONTRIBUTIONS TO GEOMAGNETIC CUTOFF RIGIDITIES: INTERNAL GEOMAGNETIC FIELD MODEL CALCULATIONS
Paper 1 represents the initial publication related to the numerical tracing of cosmic ray particles in a high order mathematical model of the geomagnetic field. Although published as a technical report by the Massachusetts Institute of Technology, this publication has been extensively cited in the scientific literature. Almost 40 years since it was printed, the authors still receive requests for this landmark publication. The mathematical field model utilized for these initial trajectory calculations was the 6th order Finch and Leaton (1957) representation of the internal geomagnetic field. The coefficients for this model were derived from the British Admiralty magnetic charts for 1955.0.
Paper 1 presented the concept of particle tracing and defines the asymptotic direction of approach of a cosmic ray particle which arrives at some given point on the earth's surface as the direction from which the particle was moving prior to its entry into the geomagnetic field. A listing of the initial FORTRAN computer program to trace cosmic ray trajectories in a high degree simulation of the geomagnetic field was included together with extensive tables enabling users to verify their results when using the computer code. The report also included tables of variational coefficients, permitting calculation of time variations observed by a cosmic ray detector as a consequence of any arbitrary anisotropic flux of cosmic radiation outside the geomagnetic field. Although geomagnetic cutoff rigidities are not specifically mentioned, the particle tracing technique formed the basis of the extensive calculations required for geomagnetic cutoff calculations.
The trajectory-tracing calculations were initiated at an altitude of 20 km above the surface of the earth. This altitude was selected as optimum since the geomagnetic field controls the particle path above the atmosphere. After the first nuclear interaction with atmospheric atoms, geomagnetic forces no longer control the particle path. High-energy particles generate a nuclear cascade that propagates through the atmosphere and can be detected on the surface of the earth by cosmic ray detectors such as neutron monitors.
At the request of the organizers of the International Years of the Quiet Sun (IQSY), Paper 1 was expanded into IQSY Instruction Manual No. 10 (McCracken et al., 1965). It was later revised and included in the Annals of the IQSY (Paper 6) with supplementary tables published as a technical report (Report T2 in Table I).
As the junior member of this team, I had the responsibility of the computer calculations. These calculations were very demanding for the computer capability at the time and were made on the high speed digital computers at the Massachusetts Institute of Technology and the Air Force Cambridge Research Center. I evaluated the computational results, and as each set of calculations was completed, I compiled the data for final analysis by my co-authors.
Paper 2 was the initial paper summarizing the use of cosmic ray trajectory calculations to determine vertical cutoff rigidities for a selected set of locations along the route of a cosmic ray latitude survey. This paper was presented at the 8th International Cosmic Ray Conference and published in the non-refereed proceedings. The primary purpose of this presentation and publication was to acquaint the cosmic ray community with the powerful particle trajectory-tracing technique for the determination of geomagnetic cutoff rigidity values.
Paper 3 provided the foundation for the calculation of cutoff rigidities and the utilization of these values for cosmic radiation studies. The procedure to determine cutoff rigidities, described in the Appendix of this landmark paper, became the world standard; the basic technique is still utilized 35 years later. This Appendix described the method whereby the cosmic ray penumbra region could be evaluated and the allowed orbits within this region included in the determination of an "effective" cutoff rigidity for a specific location. The Appendix also presented a table of individual trajectory results (and associated asymptotic directions for allowed rigidities) such that scientists could utilize the program given in Paper 1 to duplicate the results. Once the results were duplicated, scientists would be able to confidently compute asymptotic directions and cutoff rigidity values.
Values of the effective cutoff rigidity for 108 cosmic ray stations and experimental locations were given in Table 4 of Paper 3. Table 4 also listed the recently published Quenby and Wenk (1962) cutoff rigidity values for most of these same locations. Major differences, some greater than 1.00 bv, were noted in some regions of the world, particularly around Africa and in South America. The largest difference was at Hermanus, South Africa, where the trajectory-derived cutoff rigidity value was 6.4 by and the Quenby and Wenk derived value was 4.9 by.
These trajectory-determined cutoff rigidity values were then utilized to order cosmic ray data acquired by a neutron monitor on board the ship Soya. Figure 1 of Paper 3 showed that using the trajectory-tracing determined cutoff rigidity values to order these cosmic radiation data resulted in a latitude curve much more consistent with latitude curves from previous surveys. Finally, although only a minor portion of this paper, but to become much more important in future work (Paper 49, Chapter 3), a comparison was made between cutoff rigidities computed using the internal field models of Finch and Leaton (1957) for Epoch 1955.0 and of Jensen and Cain (1962) for Epoch 1960.0. Small differences were noted; however, the differences between the two sets of values were not sufficient to warrant the expenditure of the necessary computer time to derive another set of cutoff rigidity values for cosmic ray stations.
Concurrent with the publication of Paper 3, a technical report was published (Report Ti in Table I) detailing not only the techniques involved but also giving extensive tables of both the asymptotic directions of approach and cutoff rigidity values. This report was distributed throughout the cosmic ray community, and was the first of many technical reports with tabular values too extensive to publish in scientific journals.
After the publication of Paper 3 and Report Ti, the cosmic ray community adopted the trajectory-tracing method to determine cutoff rigidity values in spite of the extensive computation involved. I was fortunate that my employer had a large computer available for my research work, and I was able to continue my studies of cosmic ray cutoff rigidities for the next several years. Nevertheless, when the cutoff rigidity values for a large number of locations were calculated, it was advantageous to collaborate with scientists at the Los Alamos Scientific Laboratory and the Lawrence Radiation Laboratory where even faster computers were available.
Paper 4 utilized cutoff rigidity values determined by six different methods to order cosmic radiation data acquired on a series of aircraft flights. The values calculated by the trajectory-tracing technique and those calculated by the Makino (1963) method provided the best fits to the experimental data. With computer time extremely expensive and of limited availability, the Makino approximation model was considered an adequate substitute for many cosmic ray studies.
Paper 5 was another attempt to find an acceptable method to approximate the vertical cutoff rigidities determined by the computer intensive trajectory-tracing method. In this case the L-parameter (McIlwain, 1961) was found to be an acceptable tool to estimate cutoff rigidity values except in the equatorial regions. The use of the L-parameter was deemed acceptable when the experimental errors were similar to the rms errors between the trajectory-derived cutoff values and the L-parameter derived values.
The first trajectory-derived world grid of vertical cutoff rigidities was published in Paper 7. These values, co-authored by a colleague at the Lawrence Radiation Laboratory where many of the calculations were made, became the international standard for the next several years.
In 1969 the question of different internal geomagnetic field models was again examined. This was done at the suggestion of a colleague who wanted to know if cosmic ray measurements would be affected by the secular variation in the geomagnetic field. Using a set of time derivatives developed by Nagada and Syono (1961) and applying these derivatives to the Finch and Leaton Epoch 1955.0 field model, vertical cutoff rigidities for several Epochs were determined for selected cosmic ray stations. These calculations were made at 10-year intervals between 1935 and 1965. The cutoff values for Epoch 1965.0 were then compared with cutoff values using three other geomagnetic field models developed for Epoch 1965.0. The results, shown in Paper 8, were surprising, with significant changes in the cutoff rigidities in some regions of the world, particularly in Latin America, over the thirty year interval. However, the differences in the calculated cutoff rigidities using different field models for the same epoch were relatively small. It was concluded that the calculation and utilization of cosmic ray cutoff rigidities with updated geomagnetic field models was necessary if the change in the cutoff rigidity was statistically significant with respect to the analysis being conducted.
I expanded the question of the secular variations of cutoff rigidities in a paper published in the proceedings of the 12th International Cosmic Ray Conference. Paper 10 predicted that the stable operation of a neutron monitor in Latin America should record an increase in the cosmic ray intensity between successive solar minima. This would be the result of a decrease in the magnitude of the geomagnetic field in the region of the world through which the particles pass enroute to the atmosphere above the monitor. A decrease in the magnitude of the geomagnetic field implied increased access to lower rigidity particles and hence an increase in cosmic ray intensity at the detection point. This prediction was confirmed eight years later using the cosmic radiation measurements at Huancayo, Peru (Cooper and Simpson, 1979).
With the implication that the secular changes in the geomagnetic field could have an appreciable effect on the cosmic ray intensity observations in some regions of the world, many requests were received for specific cutoff rigidity determinations using various available magnetic field models. Satellite measurements of the geomagnetic field were now being made, and in 1969 the first international geomagnetic field model derived using both ground-based and satellite field measurements became available. Called the International Geomagnetic Reference Field (IGRF), having been developed by the International Association of Geomagnetism and Aeronomy (IAGA), this Epoch 1965.0 model became the international standard for several years (IAGA Commission 2, Working Group 4, 1969).
At the request of researchers conducting cosmic radiation measurements made on balloons launched from Palestine, Texas, cutoff rigidities for Palestine were determined using the IGRF field model for 1965.0. These calculated values, initially published in the Conference Papers for the 12th International Cosmic Ray Conference (Paper 9) included both the vertical cutoff rigidity and the cutoff rigidity values for selected zenith and azimuthal directions. The angular directions were included since a detector near the top of the atmosphere would be observing over a much wider solid angle than a neutron monitor at ground level where the cosmic rays incident from off-zenith angles have additional atmospheric attenuation.
For this particular study the trajectory-tracing of cosmic ray orbits was continued well below the Störmer cutoff to allow an evaluation of the re-entrant albedo. These additional calculations showed that the invariant latitude of the origin of the re-entrant albedo particles is the same as the invariant latitude of the detection point (in this case a balloon above Palestine, Texas). These results, particularly the discussion and evaluation of the re-entrant albedo, were used by experimenters to explain the detection of cosmic ray heavy nuclei well below the geomagnetic cutoff values (Blanford et al., 1972; Larsson et al., 1973; Pennypacker et al., 1973).
Paper 12 presents an expansion of this initial work and includes two other locations in Texas in an attempt to cover the geographical range over which the balloons would travel during their observational flight times. In a final report on this work, extensive cutoff values were determined for two other balloon launching locations: Sioux Falls, South Dakota and Cape Giradeau, Missouri and summarized in Paper 14. The tables associated with the entire set of calculations for the balloon experimenters were included in two technical reports (Reports T3 and T11 in Table I). These composite results were used to evaluate cosmic ray data acquired by balloon experiments (e.g. Mathiesen et al., 1975; Lund and Sorgen, 1977) and; eventually, to isotopic composition analysis on the HEAO-C spacecraft (Soutoul et al., 1981).
An enormous number of computer hours had been expended calculating cosmic ray trajectories and evaluating these results for the determination of cutoff rigidity values. I felt that these results were sufficiently valuable that they should be made available in a more permanent form. Professional journals do not, as a general rule, accept long data tables, and since magnetic tapes were known to have a limited lifetime, a decision was made to continue to publish asymptotic directions and detailed cosmic ray cutoff tables in a series of technical reports as listed in Table I. I was the leading scientist in the writing and compilation of tables for these reports. The text and a sample set of tables from Report T7 in Table I are included as Paper 13 in Chapter 1.
Over the next few years the basic computer program was revised to increase the computational speed (Paper 17) as we continued the trajectory-tracing calculations to determine cutoff rigidities for world grids and specialized data sets for different Epochs of the geomagnetic field. Vertical cutoff rigidity values for world grids and selected cosmic ray stations were calculated for Epochs 1965.0, 1975.0, 1980.0 and 1990.0. These values were routinely published in Cosmic Ray Conference Papers (Shea and Smart, 1975a, 1983; Shea et al., 1983, 1990; Smart and Shea, 1997). Methods to estimate the cutoff rigidities for different Epochs also continued to be developed (Papers 18 and 19), and the effect of secular changes of the geomagnetic field on the utilization of cosmic ray variational coefficients was evaluated (Paper 15).
The increased number of satellite experiments added another complication to the cutoff rigidity problem. Paper 11 was the initial paper on a method to estimate cutoff rigidities at satellite altitudes. We became heavily involved in the calculation of cosmic ray trajectories for the Danish-French isotopic composition experiment on the HEAO-C spacecraft. One of the most interesting results of these calculations was particle access to the spacecraft from directions below the optical horizon (Paper 16). I was a co-author of several papers on the characteristics of cosmic ray orbits and cutoff rigidities that were published in Cosmic Ray Conference papers (Humble et al., 1979, 1983, 1985; Smart et al., 1979).
A problem in the use of cosmic ray terminology was identified by the members of the HEAO-C group. The terminology originally developed to describe particle access and cutoff rigidities did not evolve with the scientific advances in the field, and a new nomenclature had been developed. Paper 20 presents a historical summary of the original terms and provides a cross reference between the historical terms and the more recent terms that were adopted to accommodate the innovative cosmic ray studies which had been undertaken over the past 30 years.
Paper 21 summarizes many of the characteristics of cosmic ray access and cutoff rigidity calculations for spacecraft. The problem of the extensive computer time required to determine the cutoff values is addressed and options are given for estimating these values.

CONTRIBUTIONS TO GEOMAGNETIC CUTOFF RIGIDITIES: MAGNETOSPHERIC MODEL CALCULATIONS
All my geomagnetic cutoff rigidity calculations between 1962 and 1968 were made using an internal geomagnetic field model. However, during this same time period the fledgling space program was producing a plethora of fascinating scientific discoveries within and slightly beyond the magnetosphere. The magnetic measurements from spacecraft permitted the topology to be mapped, and the initial mathematical models of the magnetosphere were developed (Mead, 1964; Mead and Beard, 1964; Williams and Mead, 1965; Mead and Fairfield, 1975).
My initial work was the computation of cosmic ray trajectories in a model of the magnetosphere represented by a sixth-degree expansion of the internal magnetic field combined with external sources due to currents in the tail and the magnetopause. The nature of the magnetosphere is such that calculations must be made for a series of local times to obtain a comprehensive description of particle access to a particular location over a 24-hour period. In addition, there is a seasonal effect resulting from the tilt of the earth with respect to the ecliptic plane. The magnitude of the computations greatly increased not only because of the local time and seasonal considerations, but also because the evaluation of the magnetic field at each position along the cosmic ray trajectory in a magnetospheric model is much more complex than the evaluation using just an internal field model.
For the above reasons the initial work in this area was extremely limited by computer time availability. At that time Professor Ruth Gall from the Universidad Nacional Autonoma de Mexico, Mexico City, Mexico was a scientific visitor at the National Center for Atmospheric Research (NCAR) in Boulder, Colorado, an institution where a state of the art computer had just been installed. Most of the initial cosmic ray trajectory tracing and cutoff rigidity calculations using a magnetospheric magnetic field model were performed on the NCAR computer.
The results of this work, detailed in Papers 22 and 23, showed that the cutoff rigidities calculated using a magnetospheric model had a pronounced daily variation at high (i.e. polar) latitudes with maximum values near noon and minimum values near midnight. The vertical cutoff rigidities were lower than the values calculated using only the internal magnetic field models. We also noted that the daily variation of the proton cutoffs was asymmetric with respect to local noon, an effect attributed to the longitudinal asymmetry of the magnetosphere. This asymmetry in proton cutoffs was also evident from values we calculated for the ATS 1 geosynchronous satellite (Paper 24).
This initial work was extended to the calculation of the daily variation expected at four cosmic ray neutron monitor locations (Paper 25). Similar calculations for Fort Churchill, Canada, discussed in Paper 26, showed qualitative agreement between calculated cutoff rigidities and balloon measurements at Fort Churchill. However, it was becoming evident that these early models of the magnetospheric field were deficient because they were unable to adequately explain the low-altitude earth-orbiting spacecraft observations of energetic particle access into the earth's high polar regions during very anisotropic solar particle events (Gall and Bravo, 1973; Morfill and Quenby, 1971; Morfill and Scholer, 1972a,b). For this reason and because of the considerable computational time involved, this work was discontinued for more than a decade.
Paper 27 was a renewed attempt to ascertain magnetospheric effects on cosmic ray cutoff rigidities with the emphasis on the decreased magnitude of the geomagnetic field during geomagnetic storms. Paper 28 presented a procedure to estimate the changes in the cosmic ray cutoff rigidity and asymptotic directions during geomagnetically active times using geomagnetic field measurements.
It was only in the 1990s that more accurate magnetospheric models such as the Tsyganenko (1989) model started to be used for the calculation of geomagnetic cutoff values. The nature of these newer models, with a realistic representation of the magnetospheric tail, added additional complexity to the calculation of cosmic ray trajectories. However, the availability of "super computers" could be brought to bear on this problem, and a team effort culminated in the first comprehensive set of cutoff rigidity values for both quiet and disturbed magnetic fields for satellite altitudes (Papers 29 and 30). These cutoff rigidity values were used in a favorable comparison of the Tsyganenko (1989) model predicted and measured geomagnetic cutoff latitudes (Paper 32). Paper 31 is a review of the trajectory calculations in magnetospheric models.

CONTRIBUTIONS ON THE APPLICATION OF GEOMAGNETIC CUTOFF RIGIDITIES AND ASYMPTOTIC DIRECTIONS TO COSMIC RAY MEASUREMENTS AND ANALYSES
My interest in the application of geomagnetic cutoff rigidities and asymptotic directions to analyses of cosmic radiation measurements began with my studies of the relativistic solar proton events of May and November 1960 (Papers 33 and 34). Large solar cosmic ray events, called ground-level events when detected as an increase upon the cosmic radiation background by a surface cosmic ray detector such as a neutron monitor, are relatively rare with only 59 of these events identified from 1942 through 2000. The largest event recorded by a neutron monitor was the event on 23 February 1956 (Meyer et al., 1956). This event was highly anisotropic, as were the events on 4 May and 15 November 1960.
Expanding upon the impact zone theory proposed by Firor (1954) it seemed feasible to apply the trajectory-tracing method to determine asymptotic directions and cutoff rigidities for the analysis of these events.
The concept was relatively simple: knowing the viewing direction of the asymptotic cones and cutoff rigidities for several cosmic ray neutron monitors, it should be possible to determine the direction of solar particle flux in the interplanetary medium, the degree of anisotropy and the solar particle spectrum as a function of time throughout the event. This basic concept was applied in the analysis of the November 1960 ground-level events (Paper 34). My initial results showed that while the concept was correct, several refinements were necessary. We found that the mean asymptotic direction of viewing to approximate the asymptotic cone, while applicable to polar cosmic ray stations, was not appropriate for mid latitude and equatorial stations since these stations have wide asymptotic cones extending over many degrees in longitude. It was necessary to compute the differential response at each rigidity interval to find the direction of maximum response. The aggregate of the direction of maximum response for each station gave the direction of particle anisotropy in interplanetary space. This was a major factor for the analysis of an anisotropic solar cosmic ray enhancement. When these individual particle directions were used in the analysis, better agreement was found between the calculated and measured increases for stations having wide asymptotic cones of acceptance. This improved concept was first presented at a meeting of the American Geophysical Union (Shea and Smart, 1965), and later expanded to introduce the differences between asymptotic directions calculated with an internal magnetic field model and a magnetospheric field model (Papers 42 and 44).
Since detailed analyses of ground-level events requires the asymptotic directions for many cosmic ray neutron monitors, we calculated and provided these values as a service to the community. The initial asymptotic directions for cosmic ray stations were published in Reports T1, T7 and T9 in Table I. The calculations using magnetospheric models or updated geomagnetic field models were event specific and published in scientific data reports prepared by World Data Center A. These reports are listed in Table II.
My interest in the use of asymptotic directions and cutoff rigidities to study solar cosmic ray events continued at a lower level until the major events in 1989. The event on 29 September 1989 has been identified as the third largest ground-level event in the history of neutron monitor measurements (Smart and Shea, 1991). Using measurements from an underground muon telescope, Paper 48 identifies particles > 20 GeV in the solar proton flux for this event.
With the first positive identification of solar neutrons at the earth (Debrunner et al., 1983, Chupp et al., 1987), I initiated a search for other solar neutron events. While satellite and related space measurements identified solar neutrons in near earth space on 25 April 1984 (Evenson et al., 1985; Chupp, 1990), the neutron monitor measurements were inconclusive (Paper 47). The unusual anisotropy during the initial 20 minutes of the 19 October 1989 ground-level event led to the possibility that this anisotropy may have been the result of solar neutron decay protons (Paper 50). On 24 May 1991, the worldwide network of neutron monitors at polar and mid latitudes recorded a major increase in the cosmic ray intensity in time association with major solar activity. However, there was a large and unusual precursor for stations closest to the sub-solar position at the time of the related solar flare. Furthermore, this initial increase was not a function of geomagnetic cutoff rigidity. The entire event appeared more consistent with a significant solar neutron component recorded by those stations nearest to the sub-solar point, followed by the relativistic solar proton component recorded at many other stations few minutes later. Using asymptotic direction calculations, geomagnetic cutoff rigidity values, and the cosmic ray measurements from seven neutron monitors, Paper 51 presented the first positive identification of a major solar neutron event together with a ground-level solar proton event detected by ground-based sensors. I continued to study the solar emissions associated with this event (Paper 52) and the propagation of secondary particles from a directional flux impinging on the top of the atmosphere (Paper 53).
Concurrent with my investigation of solar cosmic ray events, I continued research on the use of vertical cutoff rigidities to analyze cosmic radiation data. Since cutoff rigidity calculations are relatively quick and straightforward for equatorial locations (where there is no cosmic ray penumbra), we calculated the latitude of the cosmic ray equator at longitudes where experimental data had defined the location of the equator (Papers 35 and 38). Paper 38 shows that care must be taken in the routing of an experimental latitude survey, as it is possible to observe a minimum in cosmic ray intensity that will define a "virtual" cosmic ray equator instead of the actual equator at a specific longitude.
The calculation of the vertical cutoff rigidity for locations along the Soya voyage (Paper 3) showed that the latitude curve generated from the computer derived cutoff rigidity values was consistent with other latitude surveys. At the time of this research, it was not feasible to calculate the vertical cutoff rigidity for a large number of latitude surveys. Consequently, to determine cutoff rigidity values for a large number of locations on a cosmic ray latitude survey, an interpolation procedure was derived. For the results shown in Paper 36, a widely spaced world grid of vertical cutoff rigidity values was calculated using the trajectory-tracing procedure with an internal model of the geomagnetic field. The initial grid size, 150 in latitude and 15° in longitude, was extended to 5° in latitude in the equatorial regions. An interpolation technique based on the McIlwain (1961) L parameter was used to determine cutoff rigidities for each point on the latitude surveys. Figure 8 of Paper 36 illustrates that when the cosmic ray cutoff rigidities interpolated from the world grid were used to order the cosmic ray intensity data, excellent coherence of the data was obtained.
Papers 37, 39 and 40 present analyses of cosmic radiation data acquired during three cosmic ray latitude surveys in the United States, Canada and Mexico. The primary purpose of these surveys was to obtain a cosmic ray latitude curve appropriate for solar minimum conditions (solar sunspot minimum was in 1964). The initial surveys were restricted to surface measurements. As I became involved in the data analysis of these initial surveys, I realized that we could expand the cutoff rigidity range with measurements in Hawaii. I also recognized that we could extend the altitude range of the attenuation coefficients by collaborating with scientists at the Los Alamos scientific laboratory. The Los Alamos group had been operating a small neutron monitor onboard a KC-135 aircraft. I planned and created a sequence of experiments along the west coast of the United States and Hawaii coordinating simultaneous cosmic ray measurements utilizing the small airborne neutron monitor on the Los Alamos KC-135 aircraft and the 3-NM64 mobile neutron monitor developed by the Atomic Energy of Canada (Carmichael, 1968). These simultaneous measurements were made at Mt. Palomar, California, Mt. Hood, Oregon and Mt. Haleakala, Hawaii. I was a major participant on this field trip in the Western United States and Hawaii. In addition to operating the equipment and acquiring the experimental cosmic radiation data, I arranged logistical support to transport the monitor from California to Hawaii, arranged for measurement sites at airports and government facilities and coordinated the simultaneous measurements between the Los Alamos KC-135 aircraft and the ground-based experiment. I then determined the cutoff rigidity values for each experimental location and participated in the overall analyses of the data.
Paper 39 is a lengthy description of the survey; Paper 37 summarizes the technique used for the attenuation coefficients. Paper 40 illustrates that vertical cutoff rigidity values alone are often not adequate for the analysis of precise cosmid radiation measurements. This is because the cosmic ray penumbra may be vastly different between two near-by locations or even between two directions (e.g. vertical and some arbitrary zenith and azimuthal directions) at the same geographic location. Since it still was not feasible to calculate a large number of trajectories to determine the cutoff values for different zenith and azimuthal directions, the concept of smoothing the vertically determined cutoff values evolved. Further investigations (Paper 41) determined that angular compensated cutoff rigidity values produced an adequate set of cutoff rigidities for an improved cosmic ray latitude curve. These angular compensated cutoff rigidity values allowed for the access of cosmic rays over a solid angle above the measurement site instead of assuming that one direction (i.e. vertical) would be sufficient for all cosmic ray analyses.
The inclusion of non-vertical directions was initially assumed to be inconsequential for the analyses of relativistic solar cosmic ray events (Shea et al., 1979); however, with faster computers to perform the calculations necessary for the investigation of increasingly more precise cosmic ray measurements, the inclusion of non-vertical directions was found to be important for some analyses. Whereas the original angular compensated cutoff rigidity values utilized nine directions based on an analysis by McCracken (1958), Clem et al., (1997) advocated the use of 41 directions for proper analysis of a sea level cosmic ray experiment. Cramp et al. (1997) also found it essential to include the particle flux from non-vertical directions in the analysis of the 22 October 1989 ground-level event.
Non-vertical directions were also included in the determination of the "transmittance functions" necessary for cosmic ray measurements from high altitude balloons (Paper 43). This work was extended to determine the cosmic ray exposure factor for near-earth spacecraft altitudes (Papers 16 and 45) and was incorporated into the CREME code to determine cosmic ray effects on micro-electronics (Paper 68 in Chapter 5).
The question of whether or not secular changes in the geomagnetic field would be an appreciable factor for cosmic ray measurements continued to be raised. We had already identified changes in the location of the cosmic ray equator, particularly in the western hemisphere, over a 20-year period (Shea and Smart, 1975b). With the calculation of a world grid of vertical cutoff rigidity values using an internal geomagnetic field model appropriate for 1980.0, and comparing these cutoff values with those calculated using a magnetic field model for 1955.0, we found significant changes in the iso-rigidity contours in some regions of the world. Figure 2 of Paper 46 shows that the change in vertical cutoff rigidity over this 25- year period was greater than 1% per year in the North Atlantic Ocean area. Changes of 1% per year are extremely significant to a community striving for measurement stability better than 1% over several decades.
Figure 3 of this same paper shows that the maximum shift in the location of the cosmic ray equator over this same 25-year period was slightly more than 4° in latitude between longitudes 310°E and 325°E. Furthermore the location of the cosmic ray equator had a "westward" shift over a longitudinal width ~ 90°.
The answer to the question of whether the secular changes in the geomagnetic field were sufficiently large to be a significant factor in the analyses of latitude survey measurements is clearly illustrated in Figure 4 of Paper 49. In October 1976, a neutron monitor on board an aircraft recorded the cosmic ray intensity between Johannesburg, South Africa and New York City, USA (Konig and Stoker, 1981). Using the then available world grid of cosmic ray cutoff rigidities calculated for a 1965.0 Epoch of the magnetic field, and after making all known corrections to the experimental data, the cosmic ray intensity in the northern hemisphere appeared to be lower than the cosmic ray intensity in the southern hemisphere for locations having the same vertical cutoff rigidity. By determining the vertical cutoff rigidity for this flight path using a geomagnetic field model appropriate for the month of the actual measurements, agreement was found in the cosmic ray data for both hemispheres. This paper alerted the cosmic ray community to the fact that for precise cosmic ray measurements where the cutoff rigidity was necessary for analyses, the effect of the secular variations in the calculation of the cutoff rigidity values must be considered.
Many of the analyses I have undertaken required cosmic radiation data from a number of stations and a number of sources. Data sources include various publications, original data exchanged by individual scientists, and the World Data Center archives. Over the time period of cosmic radiation data and the conversion of printed records to punched cards to magnetic tape to CDROM, some inconsistencies have been noted. Some stations have had more than one name; some equipment has been replaced by more modem equipment, and, in some cases, the actual physical location has been changed while the name of the station remains the same. Paper 54 represents an extensive survey of cosmic ray neutron monitors in operation over a 50-year period.

CONTRIBUTIONS TO COSMIC RADIATION AND ASSOCIATED SOLAR-TERRESTRIAL PHENOMENA
As frequently occurs over the course of a career, the investigation of a particular problem leads to a, side excursion into a study of related phenomena. The exploration of the solar system by the Pioneer and Voyager space probes in the late 1970s led to the question "How far away is the heliospheric boundary?" In my case, my increased interest in solar-terrestrial phenomena made me wonder if it might be possible to predict the location of the boundary by correlating the cosmic ray modulation with the geomagnetic aa index (Mayaud, 1973). While investigating this problem I discovered a statistically significant correlation between the aa index and the cosmic radiation intensity during the years of negative polarity of the northern polar solar magnetic field. However, this correlation did not exist during the years of positive polarity of the northern polar solar magnetic field. This result, presented in Paper 55, contributed significantly to the research being conducted by proponents of the drift theory of cosmic radiation (Jokipii, 1981, 1986; McKibben, 1987).
This work led to the question of the role of the solar magnetic field in the propagation of high-energy cosmic radiation. To resolve this question, it was necessary to utilize long term measurements of the high energy cosmic radiation intensity measured by underground muon detectors in both the northern and southern hemispheres. These results were reported in Papers 56-59.
In an additional paper on this subject (Paper 60) Swinson and I offered historical evidence of a link between the asymmetry in solar activity and a displacement of the average position of the interplanetary neutral sheet above or below the ecliptic plane. Using solar data from four solar activity cycles between 1930 and 1967 we found that if there was excess solar activity in the northern hemisphere, the neutral sheet was displaced south of the ecliptic plane while if there was excess solar activity in the southern hemisphere, the neutral sheet was displaced north of the ecliptic plane. This results in an excess of either "toward" or "away" interplanetary magnetic field days near the earth, the nature of the excess depending on the direction of the solar activity asymmetry and the prevailing magnetic configuration of the heliosphere.

CONTRIBUTIONS ON THE EFFECTS OF SOLAR- INDUCED DISTURBANCES TO THE NEAR-EARTH ENVIRONMENT: SPACE WEATHER
The International Geophysical Year (IGY) and its extension (July 1957 — December 1959) occurred during the 19th solar cycle. This was the largest solar sunspot cycle since 1700 (McKinnon, 1987) . The major solar flares, solar proton events and related geomagnetic disturbances, extensively measured during the IGY, afforded scientists a unique and previously unparalleled scientific database on solar-terrestrial phenomena. The launch of the first earth-orbiting satellites during the IGY provided exciting new data for broader analysis than envisioned by the IGY organizers.
The era of routine interplanetary energetic particle measurements by spacecraft began in December 1965, approximately one year after the start of the 20th solar cycle. This solar cycle was relatively benign until the extremely large solar-terrestrial disturbances in August 1972 — the first major event with extensive spacecraft and ground-based data coverage. A plethora of scientific papers resulted from this one event (Dryer, 1976) and increased my interest in the inter-relationships between the various solar-induced phenomena in the solar-terrestrial system. Paper 61 summarizes the transport of solar emissions through the interplanetary medium to the related geomagnetic disturbances during an unusual period of solar activity that occurred during solar sunspot minimum in 1976.
During the next decade, scientists studying individual regions in the solar-terrestrial system became increasingly aware of the inter-relationships between solar, interplanetary and geophysical phenomena. Solar emissions could affect earth-based communications and electronics in space as well as contributing to the radiation dose to astronauts. The impact of a major interplanetary disturbance on the earth's magnetosphere could affect mid latitude communications as well as electrical power grids and oil pipeline corrosion. Changes in the earth's ionosphere affected satellite drag. In the early 1990s the study and prediction of these various solar-terrestrial phenomena were grouped under the name "Space Weather".
Throughout this time period, there was a need to decrease the power requirement and weight of satellite payloads. To meet these needs, spacecraft instrumentation was being assembled with improved and smaller components. To ascertain that these components would function adequately in the magnetosphere or interplanetary medium the engineering community required knowledge about the space radiation environment. Of particular importance was the variability in the conditions that spacecraft would encounter during specific missions. Starting with the mid 1980s and continuing to the present, I was invited to be a key speaker at several symposia bringing together engineers and scientists for the purpose of bridging the gap between these two diverse communities (Presentations T18-T23, T26, T28-T33 in Table III).
The major solar-terrestrial events in March 1991 resulted in many spacecraft anomalies (Papers 63, 64 and 66). In a study of many solar proton events we found that single event effects in vulnerable spacecraft electronic semi-conductors are likely to occur when the > 50 MeV proton flux exceeds 10 particles (cm\(^2\)-sec-sr)\(^{-1}\) (Paper 72). Paper 68 is a summary of a model to assess the particulate radiation environment on spacecraft electronics as a function of position in the magnetosphere.
With the possibility of a permanent presence of man in space, I was asked to summarize the particulate radiation environment to workshops and groups involved in assessing biological risks to astronauts (Presentations T17, T25 and T27 in Table III). With the utilization of my cutoff values by the United States Federal Aviation Agency, I became involved in studies on the potential hazard of long exposure to low levels of galactic cosmic radiation that is experienced by commercial aircrews (Presentation T24 in Table III). Paper 62 combines my work on anisotropic high-energy solar proton propagation in the interplanetary medium and the knowledge of asymptotic cones of acceptance to estimate that air flights in the polar regions at a local time around 6 am would receive the highest rate of radiation exposure during the initial part of a major anisotropic solar proton event.
An accurate knowledge of the geomagnetic cutoff rigidity is essential in the development of models of particle access and radiation dose to man. The cutoff rigidity models are key components necessary for the computation of radiation dose to astronauts and aircrew members. Papers 29 and 30 present a set of cutoff rigidity values appropriate for the International Space Station. These values were calculated using different magnetic activity conditions and provide the baseline material needed to estimate the radiation exposure to astronauts on the Space Station. Paper 73 addresses the issue of possible effects of naturally occurring cosmic radiation on airplane crews and space flight personnel. This paper also presents a summary of the variables controlling the cosmic ray flux in the atmosphere.
In the past decade I have concentrated on the galactic and solar particle environment in near-earth space, and the effects of this environment on man and his technology (Paper 67). These studies combine the results and knowledge gained from my three decades of research on geomagnetic cutoff rigidity values and the utilization of these values for a better understanding of cosmic ray access to near-earth space. In addition this research includes investigations on solar phenomena, perturbations in the interplanetary medium, and particle entry into the magnetosphere during quiet and disturbed conditions. Paper 69 summarizes the effects of solar-induced phenomena on operations in space. Paper 65 considers radiation exposure from solar protons in low earth-orbiting spacecraft during geomagnetic storm conditions and Paper 70 presents a statistical study of geomagnetic activity levels and solar proton fluxes at the earth.
Analysis of induced radioisotopes in moon rocks (Reedy, 1996) indicates the possible occurrence of events much larger than those observed in the satellite era. Consequently, in planning for various space missions, a question often asked by both engineers and space biologists is "What is the largest particle event that will be experienced during the lifetime of a particular mission?" Paper 71 shows that large fluence solar proton events generate impulsive NO\(_x\) distributions in the polar atmosphere that precipitates into the polar ice. The analysis of these impulsive NO\(_x\) precipitation events in polar ice is a promising technique to develop a history of large fluence solar proton events prior to the contemporary era. The results of McCracken et al. (2001a,b) analyzing impulsive nitrate deposition events in a Greenland ice core extending back to 1561 shows that the maximum > 30 MeV solar proton fluence can exceed the fluence measured during the October 1989 events by a factor greater than 20. Furthermore the distribution is totally consistent with the particle event size distribution derived from the induced radioisotopes in moon rocks. The effect of the geomagnetic field offers some protection against solar proton events for a permanently manned Space Station (Space Studies Board, 2000). However, while events of the magnitude identified by Reedy (1996) and McCracken et al. (2001,a,b) are rare, the possibility of their occurrence must be addressed for space missions, particularly those beyond the influence of the geomagnetic field such as a permanent station on the moon or a manned trip to Mars.

Item Type:	Thesis - DSc
Authors/Creators:	Shea, MA
Keywords:	Solar-terrestrial physics, Solar activity, Cosmic rays, Geomagnetism
Copyright Information:	Copyright 2001 the author
Additional Information:	This thesis consists of 73 papers which cannot be made available due to copyright. The front matter, which includes citations for these papers can be downloaded to allow for sourcing the papers elsewhere.
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