Modulation effects of anisotropic perpendicular diffusion on cosmic ray electron intensities in the heliosphere

Ferreira, S. E. S.; Potgieter, M. S.; Burger, R. A.; Heber, B.

doi:10.1029/2000ja000043

Cited by 38 publications

(27 citation statements)

References 30 publications

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“…Kóta and Jokipii, 1998). Drifts effects can effectively be reduced by increasing K ⊥θ (Potgieter, 2000;Ferreira et al, 2000). The exact enhancement of this coefficient in the polar direction is still somewhat controversial and may change if a non-Parkerian HMF is used.…”

Section: Resultsmentioning

confidence: 99%

Charge-sign dependent modulation in the heliosphere over a 22-year cycle

et al. 2003

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Abstract.A time-dependent model based on a numerical solution of Parker's transport equation is used to model the modulation of cosmic ray protons, electrons and helium for full 11-year and 22-year modulation cycles using a compound approach. This approach incorporates the concept of propagating diffusion barriers based on global increases in the heliospheric magnetic field as they propagate from the Sun throughout the heliosphere, combined with gradient, curvature and current sheet drifts and the other basic modulation mechanisms. The model results are compared to the observed 11-year and 22-year cycles for 1.2 GV electrons and 1.2 GV Helium at Earth for the period 1975-1998. The model solutions are also compared to the observed chargesign dependent modulation along Ulysses' trajectory for the period 1990-1998. This compound approach to long-term modulation, especially charge-sign dependent modulation, is found to be remarkably successful. It is shown that the model can easily account for the latitude dependence for cosmic ray protons and the lack thereof for cosmic ray electrons by assuming large perpendicular diffusion in the polar direction. This approach contributes to an improved understanding of how diffusion and drifts vary from solar minimum to maximum modulation, and what the time-dependence of the heliospheric diffusion coefficients may be.

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Section: Resultsmentioning

confidence: 99%

Charge-sign dependent modulation in the heliosphere over a 22-year cycle

et al. 2003

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“…In addition, observations from the Ulysses spacecraft have revealed that the latitude dependence of CR protons is significantly less than predicted by classical drift models (Potgieter and Haasbroek, 1993), which led Kóta and Jokipii (1995) to propose the concept of an anisotropic perpendicular diffusion, where κ ⊥θ > κ ⊥r in the off-equatorial regions (e.g. Burger, Potgieter and Heber, 2000;Ferreira et al, 2000;Potgieter, 2000). This anisotropy of κ ⊥ is accounted for in this work, as was done by e.g.…”

Section: The Transport Model For Galactic Protonsmentioning

confidence: 99%

The effects of magnetic field modifications on the solar modulation of cosmic rays with a SDE-based model

Raath

Potgieter

Strauss

et al. 2016

Advances in Space Research

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A numerical model for the solar modulation of cosmic rays, based on the solution of a set of stochastic differential equations, is used to illustrate the effects of modifying the heliospheric magnetic field, particularly in the polar regions of the heliosphere. To this end, the differences in the modulation brought about by each of three choices for the heliospheric magnetic field, i.e. the unmodified Parker field, the Smith-Bieber modified field, and the Jokipii-Kóta modified field, are studied. It is illustrated that both the Jokipii-Kóta and Smith-Bieber modifications are effective in modifying the Parker field in the polar regions. In addition, it is argued that the modification of Smith and Bieber is based on observational evidence and has a firm physical basis, while these motivations are lacking in the case of the Jokipii-Kóta modification. From a cosmic ray modulation point of view, we found the Smith-Bieber modification to be the most suitable choice for modifying the heliospheric magnetic field. The features and effects of these three modifications are illustrated both qualitatively and quantitatively. It is also shown how the Smith-Bieber modified field can be applied in cosmic ray modulation models to reproduce observational cosmic ray proton spectra from the PAMELA mission during the solar minimum of 2006 -2009. These results are compared with those obtained in previous studies of this unusual solar minimum activity period and found to be in good qualitative agreement.

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“…The difference between minimum and moderate maximum conditions in this model is contained in the change of the current-sheet ''tilt angle'' from 10 to 75 , as well as a change in the solar wind and changes in the values of perpendicular diffusion (see also Ferreira et al 2000) as indicated in the model section, where the latter implies decreasing drift with increasing solar activity. Preliminary reports were made by Potgieter et al (2001a) and Potgieter, Langner, & Ferreira (2001b).…”

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Heliospheric Modulation of Cosmic‐Ray Positrons and Electrons: Effects of the Heliosheath and the Solar Wind Termination Shock

Potgieter

Langner

2004

ApJ

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The importance of the solar wind termination shock (TS) and the modulation that may occur in the heliosheath have become most relevant, as emphasized by cosmic-ray observations of the Voyager spacecraft in the distant heliosphere close to the TS. The role of the TS and that of the heliosheath on cosmic-ray electrons and positrons are studied with a numerical model, including global drifts and a Jovian electron source. The consequent chargesign dependence is computed using improved local interstellar spectra and new fundamentally derived diffusion coefficients. The importance of modulation in the heliosheath is studied for the two species, as well as the differences between a model with and one without a TS. We found that the modulation in the heliosheath depends on the particle species, is strongly dependent on the energy of the cosmic rays and the magnetic polarity cycle, and is enhanced by the inclusion of the TS. From the computations it is possible to estimate the ratio of modulation occurring in the heliosheath to the total modulation between the heliopause and Earth. For electrons the factor modulation in the heliosheath becomes comparable to the factor between the TS and Earth at low energies for both polarity epochs. During A > 0 cycles the heliosheath cannot really be considered a modulation ''barrier'' above $150 MeV for electrons, while for positrons this occurs at somewhat higher energies during the A < 0 cycle. The presence of the TS is thus more pronounced for electron modulation during A > 0 polarity cycles but for positron modulation during A < 0 cycles. For positrons, with a completely differently shaped local interstellar spectrum, the modulated spectra have a very mild energy dependence below $300 MeV, even at Earth, in contrast to electrons, protons, and antiprotons. These characteristic spectral features may be helpful for distinguishing between electron and positron spectra when measured near and at Earth. These simulations can be of use for future missions to the outer heliosphere and beyond.

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Modulation effects of anisotropic perpendicular diffusion on cosmic ray electron intensities in the heliosphere

Cited by 38 publications

References 30 publications

Charge-sign dependent modulation in the heliosphere over a 22-year cycle

Charge-sign dependent modulation in the heliosphere over a 22-year cycle

The effects of magnetic field modifications on the solar modulation of cosmic rays with a SDE-based model

Heliospheric Modulation of Cosmic‐Ray Positrons and Electrons: Effects of the Heliosheath and the Solar Wind Termination Shock

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