Low Rigidities Research Articles

Modulation of cosmic ray protons and helium nuclei near solar maximum

Balloon observations of proton and helium spectra in 1970, 1971 and 1972, reveal a factor of approximately 1.85 deviation from a single valued regression at low rigidities. This deviation decreases with increasing rigidity for both species. The period 1969-1970 is unique because time variations at low and high energies were anti-correlated. When satellite observations are used to extend the balloon observations to energies below 100 MeV/Nucleon, the proton spectrum showed a steeper slope in 1970 and 1972 than the characteristic J = AT spectrum observed during 1965-1969. The slope of the helium spectrum became continuously flatter during the same period (1970-1972). Computer generated spectra based on simple two parameter modulation models describe the basic features of the observations if one of the variable parameters is used to characterize the rigidity dependence of the diffusion coefficient. Models which do not allow such a variation are not consistent with the observations.

A Rigorous Cosmic-Ray Transport Equation with no Restrictions on Particle Energy

view Abstract Citations (46) References (19) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A Rigorous Cosmic-Ray Transport Equation with no Restrictions on Particle Energy Klimas, A. J. ; Sandri, G. Abstract A new transport equation for the cosmic-ray omnidirectional intensity is obtained. This equation follows exactly from the coupled pair of differential moment equations we presented earlier. It can be characterized as a nonlocal convection-diffusion equation in which the usual transport coefficients are replaced by time integral operators. The nonlocal equation is shown to reduce to the standard convection-diffusion form if the adiabatic approximation can be applied. In general, the adiabatic approximation does not apply; however, by going to the limits of infinite and zero gyroradius and, in addition, applying the adiabatic approximation, the large- and small-gyroradius transport theories due originally to Jokipii are regained. The validity of these theories as asymptotic limits and as approximate theories in the interplanetary magnetic field is discussed. It is concluded that the small-gyroradius limit cannot be considered an approximate theory for low-energy particles even when the random field strength is weak. In addition, by scaling the length and time appropriately, a low-energy scaling law is derived. This law can be used to obtain low rigidity solutions to the nonlocal convection-diffusion equation. Thus, the nonlocal convection-diffusion equation can be used to study solar-modulation or solar-particle event phenomena down to arbitrarily low rigidities, provided the particle distribution function is nearly isotropic. Subject headings: cosmic rays - hydromagnetics - interplanetary medium Publication: The Astrophysical Journal Pub Date: March 1973 DOI: 10.1086/152018 Bibcode: 1973ApJ...180..937K full text sources ADS |

A comparative study of the rigidity dependence of forbush decreases and 11-year variation in cosmic ray intensity

Results of a comparative study of Forbush decreases and the 11-year variation observed at Calgary, Sulphur Mountain and other neutron monitor stations during the current cycle of solar activity are presented. The 11 -year variation since 1965 is well accounted for by a modulation function of the form e −k(t) P , the same as that found suitable for the previous solar cycle. No definite difference between modulation functions applicable to Forbush decreases and 11-year variation from a comparative analysis of data on daily average counting rates from different latitude stations was found. However, hourly data from Calgary and Sulphur Mountain do suggest a difference in modulation at low rigidities, the modulation tending to become rigidity-independent.

Analysis of changes in the modulated cosmic-ray spectrum near Solar Minimum

Direct inspection of the usual expressions for describing solar modulation as a function of particle parameters shows that changes in the form of the modulating function will result in a rigidity-dependent phase lag or ‘hysteresis’ near solar minimum. As a means of investigating any such changes in modulation, regression analysis is performed among three groups of cosmic-ray particles: (a) 50–100 Mev/nucleon protons and helium nuclei, (b) the integral intensity of protons with kinetic energies >450 Mev, and (c) particles contributing to the neutron intensity at Climax. The analysis is for the period from mid-1963 to mid-1966. These analyses reveal no evidence for any hysteresis before and after solar minimum and set an upper limit of ±0.09 for the fractional deviation of the flux of 50–100 Mev protons from a single valued relation with respect to the Climax neutron intensity and ±0.02 for that of protons >450 Mev. Since the absolute fluxes of these protons vary over a range of more than 36% and 16%, respectively, in this time interval this implies that any changes in the modulating function at low rigidities (<3 Gv) with respect to high rigidities (∼8 Gv) are less than 20% near solar minimum. This conclusion is discussed with respect to other recent observations of hysteresis effects.

The rigidity dependence of the solar modulation at solar minimum, 1965

The spectral data on primary cosmic ray protons and helium nuclei, presented in the previous paper, are analyzed with the assumption that the solar cycle modulation is due to a diffusion-convection process in which the scattering mean free path is both a function of rigidity and radial distance from the Sun. In addition to these measurements made in 1965, balloon measurements made in 1963 and 1964 at low rigidities, ion chamber measurements at intermediate rigidities, and neutron monitor intensities at high rigidities are used to investigate the rigidity dependence of the scattering mean free path near solar minimum. A function of the form (1 + P/ P 0), where P is the particle rigidity and P 0 is a time-varying parameter related to the scale size and magnetic field intensity of the scattering irregularities, is found to describe the modulation above 0·4 BV rigidity. The assumed radial power law form for the scattering mean free path is found to have an exponent in the range 1·00–1·08 from the observed time variations.

The intercalibration of the cosmic-ray neutron monitors at 9 European sea-level stations and the deduction of a daily latitude effect in 1963

The intercalibration of 9 European monitors of the cosmic-ray micleonic component from Rome to Bergen (geomagnetic rigidity thresholds from 6.4 to 1 GV) was carried out in 1963 by means of a standard IGY neutron monitor mounted on a lorry. At each station the ratio of the fixed to the mobile monitor counting rate was measured along with the differences in the simultaneous readings of the « official » fixed barometer and of the mercury barometer of the expedition. Using these parameters the daily intensity data from each station were normalized and reduced to a single pressure level to draw daily sea-level latitude curves for the period June to October 1963. The curves obtained show the interest the experiment offers for the study of short-term perturbations of the primary spectrum at low rigidities. In fact a displacement of the latitude « knee » towards high threshold rigidities during Forbush decreases is observed, similar to the one already known to take place in the long-term perturbation.

Primary Cosmic-Ray Intensity near Solar Maximum

Measurements of the primary cosmic-ray proton and alpha-particle fluxes and energy spectra were extended to the recent period of solar maximum. While the rigidity dependence of both components changed greatly during the solar cycle, it is observed that alpha particles and protons maintain the same relative rigidity spectra during the solar cycle. Measured geomagnetic cutoff values are in agreement with those obtained at solar minimum. An electric field model gives excellent agreement for the general form of the long-term change. However, at low rigidities this model predicts a splitting of the proton and alpha-particle differential rigidity spectra which is not observed. (auth)

Variations in the Cosmic-Ray Rigidity Spectrum

Variations in the counting rates of two different high-latitude neutron monitors, a high-latitude meson telescope, and a low-latitude neutron monitor are studied for the period August, 1956, to January, 1958. A long-term decrease in counting rate was observed at all stations, superposed on which there were numerous short-term variations of from 3 to 30 days duration. The long-term variation in neutron counting rate at high latitudes was four times greater than that at low latitudes, indicating that the change in the cosmic-ray spectrum was most pronounced at low rigidities. The high-latitude short-term variations in neutron counting rate were about 2.5 times greater than those at low latitudes, the ratio varying from event to event. This is interpreted as evidence that the spectrum changes during short-term variations are less strongly dependent upon rigidity than in the case of the long-term variation, and that they are of a variable character. Comparison of the neutron data with simultaneous meson data supports this view. It is concluded that the long- and short-term variations in intensity are produced by different mechanisms.

Changes in the Low-Energy Particle Cutoff and Primary Spectrum of Cosmic Radiation

The low-rigidity cutoff for particles in the primary cosmic-ray spectrum has decreased within the period 1948 through 1951. This decrease corresponds to a 3\ifmmode^\circ\else\textdegree\fi{} change (northward) in the "knee" position of the geomagnetic latitude curve for the nucleonic component. The phenomenon is accompanied by both a change in the primary spectrum for particle rigidities less than approximately 4 Bv and by an increase in total primary intensity. The spectral change is such that if the differential primary intensity, $j$, at low rigidities in 1948 was $j=C{(\frac{p}{z})}^{\ensuremath{-}2}$; then the new spectrum for 1951 through 1954 is approximately $j\ensuremath{\approx}{C}^{\ensuremath{'}}{(\frac{p}{z})}^{\ensuremath{-}2.7}$. The total change of intensity arising from the changes in spectrum and low-rigidity cutoff is more than 13%.The measurements were obtained in 1948 and 1951, and have been confirmed and extended in November, 1954 using nucleonic component detectors. The vertical charged particle intensity was also measured and displays changes equivalent to those reported for the nucleonic component.Three regions of space are considered for the location of the mechanism producing the low energy cutoff; namely, the vicinity of the earth, the region of the solar system, and regions of the galaxy outside our solar system. Although the general solar dipole moment is at least an order of magnitude too small to account for the observations, it is concluded that the mechanism is operative within the solar system and is not a terrestrial phenomenon.

59—An Investigation into Bending and Torsional Rigidities of Some Fibres

Bending rigidities by static and dynamic methods, and torsional rigidities by a simple dynamic method, have been measured for a series of fibres. Bending rigidities are discussed in relation to tensile measurements, and, for fibres with approximately round cross-sections, the tensile modulus usually falls between the dynamic and static bending moduli. The acrylic fibres have high bending and torsional rigidities and the regenerated proteins are characterised by low bending rigidities. Bending rigidity of viscose varies as the 1·96th power of the denier and torsional rigidity as the 1·9th power.