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A study of cosmic-ray positron and electron spectra in interplanetary and interstellar space and the solar modulation of cosmic rays


Cummings, Alan Coffman (1973) A study of cosmic-ray positron and electron spectra in interplanetary and interstellar space and the solar modulation of cosmic rays. Dissertation (Ph.D.), California Institute of Technology.


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We have measured the differential energy spectra of cosmic-ray positrons and negatrons with energies between ~11 and 1500 MeV during the period 1968-1971 using a balloon-borne magnetic spectrometer. These measurements fill a gap in the previously existing data and permit us to determine, within quantitative limits, the interstellar spectra of cosmic-ray positrons and electrons [...]. Knowledge of these spectra provides a crucial tool for studies of the distribution and density of matter and magnetic fields in the interstellar medium and the origin and dynamics of energetic particles contained in the fields.

From a study of the near-Earth electron spectra and their relationship to the interstellar spectrum derived from the galactic non-thermal-radio-background emission, and from a study of the near-Earth positron spectra and their relationship to the interstellar positron spectrum calculated from collisions of cosmic-ray nuclei with the interstellar matter, we have found that the differential energy spectrum of interstellar electrons may be represented as a power-law, [...] for 100 MeV [...] GeV, but must flatten considerably at lower energies. From the measured electron charge composition, which we find to be little affected by solar modulation, we have concluded that the majority of cosmic-ray electrons with energies above ~10 MeV are not the result of nuclear collisions in the galaxy but presumably originate in "primary" sources.

In the energy range of our measurements the near-Earth intensities of cosmic-ray positrons and electrons, as well as the intensity of cosmic-ray nuclei, are significantly lower than their interstellar intensities because the particles are scattered by magnetic irregularities imbedded in the outward-flowing plasma of the solar wind. Long-term changes in the scattering properties of the interplanetary medium, i.e. in the cosmic-ray diffusion coefficient, [...], are responsible for the observed long-term variations in the near-Earth cosmic-ray intensities which are as large as a factor of 10 from "solar minimum" to "solar maximum". We have used the cosmic-ray positron and electron spectra as tools to study the solar modulation mechanism. By using numerical solutions of the cosmic-ray transport equation to relate the near-Earth electron spectra to the interstellar electron spectrum, we have found that the magnetic rigidity dependence of the interplanetary cosmic-ray diffusion coefficient at rigidities from ~100 MV to ~10 GV may be represented as [...] with b increasing from 0 to ~1-2 with increasing rigidity. However, from a comparison of the near-Earth and interstellar positron spectra we find that below ~60 MV the diffusion coefficient must increase with decreasing rigidity.

The magnitude of the diffusion coefficient at 1 AU derived from the electron and positron modulation studies depends on the assumed radial dependence of [...]. In order to place limits on this radial dependence and to make estimates of the size of the solar modulation region, we have also evaluated diffusion coefficients from measurements of the power spectrum of the interplanetary magnetic field near 1 AU. Assuming [...], we have found that [...] in order that the calculated modulation beyond 1 AU agrees with the observed modulation. For K independent of radius, we obtained consistency between the diffusion coefficients derived by the two methods for boundary distances of the solar modulation region in the range of 6-25 AU.

These diffusion coefficients derived from the electron modulation study must also apply to the cosmic-ray nuclei. As a consistency check, we have used the electron diffusion coefficients to calculate solutions of the transport equation for cosmic-ray protons and He nuclei for four different time periods from 1965 to 1970. Assuming a particular, time-independent form for the interstellar spectra of these particles, we have derived spectra at l AU which are consistent with the observations over the full range of intensity variations observed during this solar half cycle.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Vogt, Rochus E. (advisor)
  • Stone, Edward C. (co-advisor)
Thesis Committee:
  • Unknown, Unknown
Defense Date:26 March 1973
Record Number:CaltechETD:etd-05062005-131722
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1652
Deposited By: Imported from ETD-db
Deposited On:09 May 2005
Last Modified:26 Dec 2012 02:40

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