Cosmic ray cutoff rigidities and associated solar-terrestrial phenomena

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