Stochastic simulation of cosmic ray modulation including a wavy heliospheric current sheet

Alanko-Huotari, K.; Usoskin, Ilya; Мурсула, К.; Kovaltsov, Gennady A.

doi:10.1029/2007ja012280

Cited by 49 publications

(34 citation statements)

References 31 publications

(45 reference statements)

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“…In previous models of CR propagation in the heliosphere, the parallel diffusion coefficient ( || K ) was assumed to have a sharp break at ∼1 GV in the transitional region between the two regimes at high and low rigidities(e.g., see Perko 1987;Alanko-Huotari et al 2007;Strauss et al 2011;Bobik et al 2012). However, as the accuracy of the collected data increases, it becomes clear that a smooth transition between the two regimes is necessary.…”

Section: Helmod Code For Heliospheric Cr Transportmentioning

confidence: 99%

HelMod in the Works: From Direct Observations to the Local Interstellar Spectrum of Cosmic-Ray Electrons

Boschini

Torre

Gervasi

et al. 2018

ApJ

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The local interstellar spectrum (LIS) of cosmic-ray (CR) electrons for the energy range 1 MeV to 1 TeV is derived using the most recent experimental results combined with the state-of-the-art models for CR propagation in the Galaxy and in the heliosphere. Two propagation packages, GALPROP and HELMOD, are combined to provide a single framework that is run to reproduce direct measurements of CR species at different modulation levels, and at both polarities of the solar magnetic field. An iterative maximum-likelihood method is developed that uses GALPROP-predicted LIS as input to HELMOD, which provides the modulated spectra for specific time periods of the selected experiments for model-data comparison. The optimized HelMod parameters are then used to adjust GALPROP parameters to predict a refined LIS with the procedure repeated subject to a convergence criterion. The parameter optimization uses an extensive data set of proton spectra from 1997 to 2015. The proposed CR electron LIS accommodates both the low-energy interstellar spectra measured by Voyager 1 as well as the high-energy observations by PAMELA and AMS-02 that are made deep in the heliosphere; it also accounts for Ulysses counting rate features measured out of the ecliptic plane. The interstellar and heliospheric propagation parameters derived in this study agree well with our earlier results for CR protons, helium nuclei, and anti-protons propagation and LIS obtained in the same framework.

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Section: Helmod Code For Heliospheric Cr Transportmentioning

confidence: 99%

HelMod in the Works: From Direct Observations to the Local Interstellar Spectrum of Cosmic-Ray Electrons

Boschini

Torre

Gervasi

et al. 2018

ApJ

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“…Some historical and contemporary models are discussed by e.g. Yamada, Yanagita and Yoshida (1998), Alanko-Huotari et al (2007), Bobik et al (2012), and Kopp et al (2012) who also discussed the mathematical and practical implementation of SDEs for a variety of general transport equations.…”

Section: Introductionmentioning

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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“…Results from such earlier drift studies have since been confirmed qualitatively and in some cases quantitatively in numerous numerical modulation studies (see, e.g., Potgieter & Moraal 1985;Zhang 1999;Yamada et al 1999;Florinski & Jokipii 1999;Alanko-Huotari et al 2007;Pei et al 2010).…”

Section: Introductionmentioning

confidence: 72%

“…For the case of a flat neutral sheet, Burger & Potgieter (1989) show that a boundary condition method, first implemented by Jokipii & Kopriva (1979), gives virtually identical results to the drift velocity field method of Burger et al (1985). In twodimensional modulation models, the effect of a wavy neutral sheet is either simulated by taking averages over a solar rotation (see, e.g., Burger & Potgieter 1989; or by taking into account the drift along the actual wavy neutral sheet but neglecting the azimuthal component (Caballero-Lopez & Moraal 2003;Alanko-Huotari et al 2007). Note that Alanko-Huotari et al (2007) carry out this procedure at all longitudes and then find an average of the radial and latitudinal components of the drift, while CaballeroLopez & Moraal (2003) assume azimuthal symmetry.…”

Section: Introductionmentioning

confidence: 99%

“…In twodimensional modulation models, the effect of a wavy neutral sheet is either simulated by taking averages over a solar rotation (see, e.g., Burger & Potgieter 1989; or by taking into account the drift along the actual wavy neutral sheet but neglecting the azimuthal component (Caballero-Lopez & Moraal 2003;Alanko-Huotari et al 2007). Note that Alanko-Huotari et al (2007) carry out this procedure at all longitudes and then find an average of the radial and latitudinal components of the drift, while CaballeroLopez & Moraal (2003) assume azimuthal symmetry. Turning now to fully three-dimensional models, Kóta & Jokipii (1983) state that they use numerical differentiation to determine drift velocities, and that this procedure gives finite drift at the neutral sheet.…”

Section: Introductionmentioning

confidence: 99%

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Modeling Drift Along the Heliospheric Wavy Neutral Sheet

Burger

2012

ApJ

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Drift along the wavy heliospheric neutral sheet is believed to play an important role in cosmic-ray modulation and can explain the peaked versus flat intensity profiles during consecutive solar magnetic epochs. Modulation models are becoming more and more realistic and in order to determine the role of the wavy neutral sheet more accurately, we revisit a previous calculation for drift along it. While mathematically correct, we argue that the previous expression for neutral sheet drift, which follows naturally from the standard expression for gradient and curvature drift, must be adapted in order for the drift speed to be less than particle speed. We compare the effect of both the previous and the current more accurate version of neutral sheet drift on cosmic-ray modulation with results obtained by other methods.

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Stochastic simulation of cosmic ray modulation including a wavy heliospheric current sheet

Cited by 49 publications

References 31 publications

HelMod in the Works: From Direct Observations to the Local Interstellar Spectrum of Cosmic-Ray Electrons

HelMod in the Works: From Direct Observations to the Local Interstellar Spectrum of Cosmic-Ray Electrons

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

Modeling Drift Along the Heliospheric Wavy Neutral Sheet

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