The cosmic radiation in the heliosphere at successive solar minima: 3. Steady state drift solutions of the transport equation

Reinecke, J. P. L.; Moraal, H.; McDonald, F. B.

doi:10.1029/96ja02221

Cited by 27 publications

(8 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This gives different diffusion coefficients for alternate solar cycles in qualitative agreement with Reinecke et al (1996) and Potgieter (2000), who found that these coefficients were different for consecutive solar minimum periods. This might also indicate that an additional charge-sign dependent mechanism could be contributing to modulation such as magnetic helicity (e.g.…”

Section: Model and Parameterssupporting

confidence: 71%

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

et al. 2003

View full text Add to dashboard Cite

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.

show abstract

Section: Model and Parameterssupporting

confidence: 71%

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

et al. 2003

View full text Add to dashboard Cite

show abstract

“…This new spectrum may call for the repetition of some previous work. Reinecke et al [1993Reinecke et al [ , 1996, for instance, performed modulation calculations on ACRs, but they guessed what the input spectra might be, without having a physical model.…”

Section: Discussionmentioning

confidence: 99%

Form of the anomalous cosmic ray spectrum at the solar wind termination shock

Steenberg¹,

Moraal²

1999

J. Geophys. Res.

View full text Add to dashboard Cite

Abstract. New insights regarding the form of the accelerated anomalous cosmic ray spectrum at the solar wind termination shock, obtained from solutions of the cosmic ray transport equation, are presented. A simple analytical expression for the spectrum on the shock is derived, and its dependence on the acceleration parameters is shown. Particular attention is paid to the high-energy cutoff of this spectrum. This expression and its parameterization should be applicable for the acceleration of charged particles in any spherical shock.

show abstract

“…This suggests that different diffusion coefficients can be assumed for different polarity cycles (e.g. Reinecke, Moraal, and McDonald, 1996;Burger, Potgieter, and Heber, 2000;Potgieter, 2000; to improve compatibility with the observations. However, C 1 = 3.0 and C 2 = 0.8 are considered as the overall best compatible scenario.…”

Section: Effect Of Different C 1 and C 2 Valuesmentioning

confidence: 99%

Time-Dependent Modulation of Cosmic Rays in the Heliosphere

2013

View full text Add to dashboard Cite

The time-dependent modulation of galactic cosmic rays in the heliosphere is studied by computing intensities using a time-dependent modulation model. By introducing recent theoretical advances in the transport coefficients in the model, computed intensities are compared with Voyager 1, International Monitoring Platform (IMP) 8, and Ulysses proton observations in search of compatibility. The effect of different modulation parameters on computed intensities is also illustrated. It is shown that this approach produces, on a global scale, realistic cosmic-ray proton intensities along the Voyager 1 spacecraft trajectory and at Earth upto ∼2004, whereafter the computed intensities recovers much slower towards solar minimum than observed in the inner heliosphere. A modified time dependence in the diffusion coefficients is proposed to improve compatibility with the observations at Earth after ∼2004. This modified time dependence led to an improved compatibility between computed intensities and the observations along the Voyager 1 trajectory and at Earth even after ∼2004. An interesting result is that the cosmic-ray modulation during the present polarity cycle is not determined only by changes in the drift coefficient and tilt angle of the wavy current sheet, but is also largely dependent on changes in the diffusion coefficients.

show abstract

The cosmic radiation in the heliosphere at successive solar minima: 3. Steady state drift solutions of the transport equation

Cited by 27 publications

References 13 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

Form of the anomalous cosmic ray spectrum at the solar wind termination shock

Time-Dependent Modulation of Cosmic Rays in the Heliosphere

Contact Info

Product

Resources

About