Drifts are one of the major cosmic ray modulation mechanisms in the heliosphere. Three types of drifts occur in the background heliospheric magnetic field, namely curvature, gradient and current ...sheet drifts. The last component occurs because of the switch in magnetic field polarity across the heliospheric current sheet and is the main topic of study. We discuss and implement a new approach to model drifts in a numerical modulation model. The model employs stochastic differential equations to solve the relevant transport equation in five (three spatial, energy and time) dimensions. What is of interest is the fact that the model can handle current sheet tilt angles up to the theoretical maximum of
α
=90° and still remain numerically stable. We use the additional insights gained from the numerical model to investigate the effectiveness of drifts along the current sheet by examining the relationship between the current sheet path length and the cosmic ray propagation time. It is found that diffusion can disrupt the drift process very effectively, leading to diffusive short circuiting of the current sheet by the cosmic rays.
The global features of the modulation of galactic cosmic ray protons and helium nuclei in a very quiet heliosphere are studied with a comprehensive, three-dimensional, drift model and compared to ...proton and helium observations measured by PAMELA from 2006 to 2009. Combined with accurate very local interstellar spectra (VLIS) for protons and helium nuclei, this provides the opportunity to study in detail how differently cosmic ray species with dissimilar mass-to-charge ratio (
A
/
Z
) are modulated down to a few GV. The effects at Earth of the difference in their VLIS’s and those caused by the main modulation mechanisms are illustrated. We find that both the PAMELA proton and helium spectra are reproduced well with the numerical model, assuming the same set of modulation parameters and diffusion coefficients. A comparative study of
3
He
2
(He-3) and
4
He
2
(He-4) modulated spectra reveals that they do not undergo identical spectral changes below 3 GV mainly due to differences in their VLIS’s. This result is important to uncover and investigate the effects on the proton to total helium ratio (
p
/He) caused by the difference in their VLIS’s and those by
A
/
Z
. The computed
p
/He displays three modulation regimes, reflecting the complex interplay of modulation processes in the heliosphere. At rigidities above ∼3 GV, the
p
/He ratio at the Earth is found to deviate modestly from a value of ∼5.5, largely independent of the assumed modulation conditions. This result indicates that the PAMELA measurement of
p
/He reveals at these rigidities the shapes of their VLIS’s. Below ∼0.6 GV,
p
/He increases with decreasing rigidity from 2006 to 2009 and significant variations are predicted depending on the assumed solar modulation conditions. This result indicates that as modulation levels decreased from 2006 to 2009, the contribution of adiabatic energy changes dissipated faster for protons than for helium nuclei at the same rigidity mainly due to different slopes of their VLIS’s. The differences between modulation effects for protons and helium are found to be the consequence of how the combined interplaying modulation mechanisms in the heliosphere affect the modulated spectra based on their
A
/
Z
and particularly on their VLIS’s.
An analysis of the data of spacecraft that scanned large areas of the heliosphere, as well as the results of magnetohydrodynamic calculations, indicates that corotating interaction regions of solar ...wind (SW), which are almost always present in the low- and mid-latitude heliosphere, sometimes strongly change the large-scale characteristics of the heliosphere that are important for long-term variations in the intensity of galactic cosmic rays (GCRs). In particular, for Carrington rotation no. 2066 (January–February 2008), these regions enhance magnetic fields in the inner (
r
< 3–5 AU) heliosphere and weaken them in the middle and far heliosphere, as well as significantly changing the polarity distribution of heliospheric magnetic fields. The assumption is made that in this situation the influence of the corotating interaction regions should lead to an increase in the GCR intensity in many regions of the heliosphere. This paper discusses the process of changing the polarity distribution of heliospheric magnetic fields due to the interaction of SW streams for Carrington rotation no. 2066 of different speeds, the simple model of the heliospheric magnetic field without an interaction between the SW streams of different speeds, as well as the results of numerical two-dimensional finite-difference calculations of longitude-averaged GCR intensity with the use of this model in comparison with a three-dimensional Monte Carlo calculation based on three-dimensional magnetohydrodynamic simulation of the heliosphere.
CME Theory and Models bes, T G; Linker, JA; Chen, J ...
Space science reviews,
03/2006, Letnik:
123, Številka:
1-3
Journal Article
Recenzirano
This chapter provides an overview of current efforts in the theory and modeling of CMEs. Five key areas are discussed: (1) CME initiation; (2) CME evolution and propagation; (3) the structure of ...interplanetary CMEs derived from flux rope modeling; (4) CME shock formation in the inner corona; and (5) particle acceleration and transport at CME driven shocks. In the section on CME initiation three contemporary models are highlighted. Two of these focus on how energy stored in the coronal magnetic field can be released violently to drive CMEs. The third model assumes that CMEs can be directly driven by currents from below the photosphere. CMEs evolve considerably as they expand from the magnetically dominated lower corona into the advectively dominated solar wind. The section on evolution and propagation presents two approaches to the problem. One is primarily analytical and focuses on the key physical processes involved. The other is primarily numerical and illustrates the complexity of possible interactions between the CME and the ambient medium. The section on flux rope fitting reviews the accuracy and reliability of various methods. The section on shock formation considers the effect of the rapid decrease in the magnetic field and plasma density with height. Finally, in the section on particle acceleration and transport, some recent developments in the theory of diffusive particle acceleration at CME shocks are discussed. These include efforts to combine self-consistently the process of particle acceleration in the vicinity of the shock with the subsequent escape and transport of particles to distant regions.
Abstract
Using measurements from the PAMELA and ARINA spectrometers on board the Resurs-DK1 satellite, we have examined the 27 day intensity variations in galactic cosmic ray (GCR) proton fluxes in ...2007–2008. The PAMELA and ARINA data allow for the first time a study of time profiles and the rigidity dependence of the 27 day variations observed directly in space in a wide rigidity range from ∼300 MV to several gigavolts. We find that the rigidity dependence of the amplitude of the 27 day GCR variations cannot be described by the same power law at both low and high energies. A flat interval occurs at rigidity
GV with a power-law index
γ
= −0.13 ± 0.44 for PAMELA, whereas for
R
≥ 1 GV, the power-law dependence is evident with index
γ
= −0.51 ± 0.11. We describe the rigidity dependence of the 27 day GCR variations for PAMELA and ARINA data in the framework of the modulation potential concept using the force-field approximation for GCR transport. For a physical interpretation, we have considered the relationship between the 27 day GCR variations and solar wind plasma and other heliospheric parameters. Moreover, we have discussed possible implications of MHD modeling of the solar wind plasma together with a stochastic GCR transport model concerning the effects of corotating interaction regions.
While the high-energy part of the Galactic cosmic ray spectrum is well observed, its nature at energies below about 1 GeV nucleon super(-1) is still not known well. Recent in situ measurements made ...with the Voyager 1 spacecraft in the heliosheath between the solar wind termination shock and the heliopause have added further constraints on the local interstellar spectrum of Galactic cosmic rays at low energies. We show here that they also suggest how the low-energy proton part is formed locally in the heliosphere and globally in the Galaxy. The measured flux of anomalous cosmic rays in the heliosheath is unexpectedly high compared to expectations before Voyager 1 reached the shock, which might be a temporal effect or due to an additional acceleration beyond the termination shock. Combining this finding with recent model results for astrospheres immersed in different interstellar environments shows that the astrospheric anomalous cosmic ray fluxes of solar-type stars can be a hundred times higher than thought earlier and, consequently, their total contribution to the lower end of the interstellar spectrum can be significant.
Very local interstellar spectra (vLIS’s) for protons and total Helium (He) were observed in situ by Voyager 1 below about 340 MeV/
since it had moved across the heliopause (HP). Together with high ...precision PAMELA and AMS observations at the Earth, we previously reported on new vLIS calculated from 1 MeV to 100 GeV for protons, electrons, total He, Oxygen, Carbon, and Boron. We now follow this up to report on the vLIS’s for positrons and for the isotopes He-3, He-4, and Deuteron (H-2) by combining computations with the galactic propagation code, GALPROP, and our 3D modulation model for GCRs in the heliosphere as done previously. Similarly, we also have computed updates of the vLIS’s for antiprotons and antideuteron. We assume that the modulation processes between the HP and the Earth for protons and other GCR nuclei are essentially similar, which is also the case for electrons and positrons, except for particle drifts of oppositely charged particles. The procedures followed to obtain these updates are summarized and a compilation of the mentioned vLIS’s is presented.
The numerical solution of transport equations for energetic charged particles in space is generally very costly in terms of time. Besides the use of multi-core CPUs and computer clusters in order to ...decrease the computation times, high performance calculations on graphics processing units (GPUs) have become available during the last years. In this work we introduce and describe a GPU-accelerated implementation of Parker’s equation using Stochastic Differential Equations (SDEs) for the simulation of the transport of energetic charged particles with the CUDA toolkit, which is the focus of this work. We briefly discuss the set of SDEs arising from Parker’s transport equation and their application to boundary value problems such as that of the Jovian magnetosphere. We compare the runtimes of the GPU code with a CPU version of the same algorithm. Compared to the CPU implementation (using OpenMP and eight threads) we find a performance increase of about a factor of 10–60, depending on the assumed set of parameters. Furthermore, we benchmark our simulation using the results of an existing SDE implementation of Parker’s transport equation.
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, increases in the heliospheric magnetic field as they propagate from the Sun throughout the heliosphere, time-dependent gradient, curvature, and current- sheet drifts, and other basic modulation mechanisms. The model results are compared with those of the observed 11 year and 22 year cycles for 1.2 GV electrons and 1.2 GV helium at Earth for the period of 1975-1998. The model solutions are also compared with the observed charge-sign-dependent modulation along the Ulysses trajectory for the period of 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 account for the latitude dependence of cosmic-ray protons and electrons by assuming a 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. It is found that less than 10% of the available drifts are needed at solar maximum, when the solar magnetic field reverses, to explain, e.g. the observed electron-to-proton ratio along the Ulysses trajectory.
The study addresses the question of the origin of low-energy electrons measured by Voyager 1 in the multi-keV range in the inner heliosheath. It intends to demonstrate that the observed keV-fluxes of ...electrons are consistent with their transmission through the termination shock under the influence of the associated electrostatic field. A power-law representation of the electron velocity distribution just downstream of the solar wind termination shock is motivated and formulated in terms of a so-called κ-distribution function. From this initial function spectral electron fluxes in the range 40-70 keV are derived and compared to the data. It is shown that with κ-values between 7 and 8 the data can be satisfactorily explained. Given these comparatively high κ-values, it is concluded that the electron distribution just downstream of the termination shock relaxes toward but does not reach a Maxwellian shape in the inner heliosheath.
PDF
