Solar modulation model with reentrant particles

Bobík, P.; Kudela, K.; Boschini, M.; Grandi, D.; Gervasi, M.; Rancoita, P.G.

doi:10.1016/j.asr.2007.02.085

Cited by 8 publications

(6 citation statements)

References 7 publications

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“…To the best of our knowledge, these modulation effects have not been discussed before, especially not the effect of particle confinement in the heliosphere. Note that this confinement has to be distinguished from the extended so-called residence times of energetic particles in the IHS (Florinski & Pogorelov 2009) and also from the re-entering of particles from the OHS as has been studied by Bobik et al (2008).…”

Section: Conclusion and Discussionmentioning

confidence: 99%

On Cosmic Ray Modulation Beyond the Heliopause: Where Is the Modulation Boundary?

Scherer

Fichtner

Strauss

et al. 2011

ApJ

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Two of the paradigms in modeling the transport of galactic cosmic rays are that the modulation boundary is the heliopause and that the local interstellar spectra are identical to the galactic cosmic ray spectra. Here we demonstrate that the proton spectrum is already modulated due to an altered interstellar diffusion in the outer heliosheath as a consequence of the heliospheric "obstacle" in the interstellar flow. The main modulation effect however is adiabatic energy losses during a "confinement time" of cosmic rays inside the heliosphere.

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Section: Conclusion and Discussionmentioning

confidence: 99%

On Cosmic Ray Modulation Beyond the Heliopause: Where Is the Modulation Boundary?

Scherer

Fichtner

Strauss

et al. 2011

ApJ

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“…The dashed line denotes the finite difference method results [ Burger and Hattingh , 1995]. The crosses denote results using the first formula – [ Bobik et al , 2008], and the open circles are for results using the second formula – [ Jokipii and Levy , 1977]. Here we use for κ with κ 0 = 2 × 10 23 cm 2 sec −1 GV −1 .…”

Section: Benchmarksmentioning

confidence: 99%

“…In order to benchmark our new method, a steady state three‐dimensional finite difference method [ Burger and Hattingh , 1995], following the approach of Kóta and Jokipii [1983], is used in this paper. The other major method is the stochastic or Monte Carlo method used by Jokipii and Owens [1975], Jokipii and Levy [1977], Yamada et al [1998], Zhang [1999a, 1999b], Gervasi et al [1999], Miyake and Yanagita [2005], Ball et al [2005], Alanko‐Huotari et al [2007], Bobik et al [2008], Alanko‐Huotari et al [2009], and Pei et al [2009]. For 1‐D and 2‐D problems, the finite difference method is much faster than the stochastic method.…”

Section: Introductionmentioning

confidence: 99%

A general time‐dependent stochastic method for solving Parker's transport equation in spherical coordinates

et al. 2010

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[1] We present a detailed description of our newly developed stochastic approach for solving Parker's transport equation, which we believe is the first attempt to solve it with time dependence in 3-D, evolving from our 3-D steady state stochastic approach. Our formulation of this method is general and is valid for any type of heliospheric magnetic field, although we choose the standard Parker field as an example to illustrate the steps to calculate the transport of galactic cosmic rays. Our 3-D stochastic method is different from other stochastic approaches in the literature in several ways. For example, we employ spherical coordinates to integrate directly, which makes the code much more efficient by reducing coordinate transformations. What is more, the equivalence between our stochastic differential equations and Parker's transport equation is guaranteed by Ito's theorem in contrast to some other approaches. We generalize the technique for calculating particle flux based on the pseudoparticle trajectories for steady state solutions and for time-dependent solutions in 3-D. To validate our code, first we show that good agreement exists between solutions obtained by our steady state stochastic method and a traditional finite difference method. Then we show that good agreement also exists for our time-dependent method for an idealized and simplified heliosphere which has a Parker magnetic field and a simple initial condition for two different inner boundary conditions.

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“…4, 5, and allow one a better understanding on HelMod capabilities to deal with solar modulation, within the inner part of the heliosphere. At present, the model only treats GCRs with energies 0.5 GeV/nucleon, thus modulation effects occurring in the outer heliosphere -i.e., beyond the termination shock (TS) (see, e.g., Langner et al, 2003;Langner and Potgieter, 2004;Bobik et al, 2008;Potgieter, 2008;Florinski and Pogorelov, 2009;Luo et al, 2013;Senanayake and Florinski, 2013) -are not accounted for. It has to be pointed out that the HelMod model is capable of describing the current large set of observation data, which were collected during solar cycles 23 and 24 with the occurrence of two solar minimum.…”

Section: Introductionmentioning

confidence: 99%

Propagation of cosmic rays in heliosphere: The HelMod model

Boschini

Torre²,

Gervasi

et al. 2018

Advances in Space Research

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The heliospheric modulation model HelMod is a two dimensional treatment dealing with the helio-colatitude and radial distance from Sun and is employed to solve the transport-equation for the GCR propagation through the heliosphere down to Earth. This work presents the current version 3 of the HelMod model and reviews how main processes involved in GCR propagation were implemented. The treatment includes the so-called particle drift effects -e.g., those resulting, for instance, from the extension of the neutral current sheet inside the heliosphere and from the curvature and gradient of the IMF -, which affect the transport of particles entering the solar cavity as a function of their charge sign. The HelMod model is capable to provide modulated spectra which well agree within the experimental errors with those measured by AMS-01, BESS, PAMELA and AMS-02 during the solar cycles 23 and 24. Furthermore, the counting rate measured by Ulysses at ±80 • of solar latitude and 1 to 5 AU was also found in agreement with that expected by HelMod code version 3.

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Solar modulation model with reentrant particles

Cited by 8 publications

References 7 publications

On Cosmic Ray Modulation Beyond the Heliopause: Where Is the Modulation Boundary?

On Cosmic Ray Modulation Beyond the Heliopause: Where Is the Modulation Boundary?

A general time‐dependent stochastic method for solving Parker's transport equation in spherical coordinates

Propagation of cosmic rays in heliosphere: The HelMod model

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