Jens Kleimann

A GENERALIZED DIFFUSION TENSOR FOR FULLY ANISOTROPIC DIFFUSION OF ENERGETIC PARTICLES IN THE HELIOSPHERIC MAGNETIC FIELD

The spatial diffusion of cosmic rays in turbulent magnetic fields can, in the most general case, be fully anisotropic, i.e., one has to distinguish three diffusion axes in a local, field-aligned frame. We reexamine the transformation for the diffusion tensor from this local to a global frame, in which the Parker transport equation for energetic particles is usually formulated and solved. Particularly, we generalize the transformation formulae to allow for an explicit choice of two principal local perpendicular diffusion axes. This generalization includes the “traditional” diffusion tensor in the special case of isotropic perpendicular diffusion. For the local frame, we describe the motivation for the choice of the Frenet–Serret trihedron, which is related to the intrinsic magnetic field geometry. We directly compare the old and the new tensor elements for two heliospheric magnetic field configurations, namely the hybrid Fisk and Parker fields. Subsequently, we examine the significance of the different formulations for the diffusion tensor in a standard three-dimensional model for the modulation of galactic protons. For this, we utilize a numerical code to evaluate a system of stochastic differential equations equivalent to the Parker transport equation and present the resulting modulated spectra. The computed differential fluxes based on the new tensor formulation deviate from those obtained with the “traditional” one (only valid for isotropic perpendicular diffusion) by up to 60% for energies below a few hundred MeV depending on heliocentric distance.

A novel code for numerical 3-D MHD studies of CME expansion

Abstract. A recent third-order, essentially non-oscillatory central scheme to advance the equations of single-fluid magnetohydrodynamics (MHD) in time has been implemented into a new numerical code. This code operates on a 3-D Cartesian, non-staggered grid, and is able to handle shock-like gradients without producing spurious oscillations. To demonstrate the suitability of our code for the simulation of coronal mass ejections (CMEs) and similar heliospheric transients, we present selected results from test cases and perform studies of the solar wind expansion during phases of minimum solar activity. We can demonstrate convergence of the system into a stable Parker-like steady state for both hydrodynamic and MHD winds. The model is subsequently applied to expansion studies of CME-like plasma bubbles, and their evolution is monitored until a stationary state similar to the initial one is achieved. In spite of the models (current) simplicity, we can confirm the CMEs nearly self-similar evolution close to the Sun, thus highlighting the importance of detailed modelling especially at small heliospheric radii. Additionally, alternative methods to implement boundary conditions at the coronal base, as well as strategies to ensure a solenoidal magnetic field, are discussed and evaluated.

AN EXACT ANALYTICAL SOLUTION FOR THE INTERSTELLAR MAGNETIC FIELD IN THE VICINITY OF THE HELIOSPHERE

An analytical representation of the interstellar magnetic field in the vicinity of the heliosphere is derived. The three-dimensional field structure close to the heliopause is calculated as a solution of the induction equation under the assumption that it is frozen into a prescribed plasma flow resembling the characteristic interaction of the solar wind with the local interstellar medium. The usefulness of this analytical solution as an approximation to self-consistent magnetic field configurations obtained numerically from the full MHD equations is illustrated by quantitative comparisons.

4π Models of CMEs and ICMEs (Invited Review)

Coronal mass ejections (CMEs), which dynamically connect the solar surface to the far reaches of interplanetary space, represent a major manifestation of solar activity. They are not only of principal interest but also play a pivotal role in the context of space weather predictions. The steady improvement of both numerical methods and computational resources during recent years has allowed for the creation of increasingly realistic models of interplanetary CMEs (ICMEs), which can now be compared to high-quality observational data from various space-bound missions. This review discusses existing models of CMEs, characterizing them by scientific aim and scope, CME initiation method, and physical effects included, thereby stressing the importance of fully 3-D (’4π’) spatial coverage.

A GENERALIZED TWO-COMPONENT MODEL OF SOLAR WIND TURBULENCE AND AB INITIO DIFFUSION MEAN-FREE PATHS AND DRIFT LENGTHSCALES OF COSMIC RAYS

We extend a two-component model for the evolution of fluctuations in the solar wind plasma so that it is fully three-dimensional (3D) and also coupled self-consistently to the large-scale magnetohydrodynamic (MHD) equations describing the background solar wind. The two classes of fluctuations considered are a high-frequency parallel-propagating wave-like piece and a low-frequency quasi-two-dimensional component. For both components, the nonlinear dynamics is dominanted by quasi-perpendicular spectral cascades of energy. Driving of the fluctuations, by, for example, velocity shear and pickup ions, is included. Numerical solutions to the new model are obtained using the Cronos framework, and validated against previous simpler models. Comparing results from the new model with spacecraft measurements, we find improved agreement relative to earlier models that employ prescribed background solar wind fields. Finally, the new results for the wave-like and quasi-two-dimensional fluctuations are used to calculate ab initio diffusion mean free paths and drift lengthscales for the transport of cosmic rays in the turbulent solar wind.

TOWARD MORE REALISTIC ANALYTIC MODELS OF THE HELIOTAIL: INCORPORATING MAGNETIC FLATTENING VIA DISTORTION FLOWS

Both physical arguments and simulations of the global heliosphere indicate that the tailward heliopause is flattened considerably in the direction perpendicular to both the incoming flow and the large-scale interstellar magnetic field. Despite this fact, all of the existing global analytical models of the outer heliosheaths magnetic field assume a circular cross section of the heliotail. To eliminate this inconsistency, we introduce a mathematical procedure by which any analytically or numerically given magnetic field can be deformed in such a way that the cross sections along the heliotail axis attain freely prescribed, spatially dependent values for their total area and aspect ratio. The distorting transformation of this method honors both the solenoidality condition and the stationary induction equation with respect to an accompanying flow field, provided that both constraints were already satisfied for the original magnetic and flow fields prior to the transformation. In order to obtain realistic values for the above parameters, we present the first quantitative analysis of the heliotails overall distortion as seen in state-of-the-art three-dimensional hybrid MHD-kinetic simulations.

Cosmic ray transport in heliospheric magnetic structures. I. Modeling background solar wind using the CRONOS magnetohydrodynamic code

The transport of energetic particles such as Cosmic Rays is governed by the properties of the plasma being traversed. While these properties are rather poorly known for galactic and interstellar plasmas due to the lack of in situ measurements, the heliospheric plasma environment has been probed by spacecraft for decades and provides a unique opportunity for testing transport theories. Of particular interest for the 3D heliospheric transport of energetic particles are structures such as corotating interaction regions (CIRs), which, due to strongly enhanced magnetic field strengths, turbulence, and associated shocks, can act as diffusion barriers on the one hand, but also as accelerators of low energy CRs on the other hand as well. In a two-fold series of papers we investigate these effects by modeling inner-heliospheric solar wind conditions with a numerical magnetohydrodynamic (MHD) setup (this paper), which will serve as an input to a transport code employing a stochastic differential equation (SDE) approach (second paper). In this first paper we present results from 3D MHD simulations with our code CRONOS: for validation purposes we use analytic boundary conditions and compare with similar work by Pizzo. For a more realistic modeling of solar wind conditions, boundary conditions derived from synoptic magnetograms via the Wang-Sheeley-Arge (WSA) model are utilized, where the potential field modeling is performed with a finite-difference approach (FDIPS) in contrast to the traditional spherical harmonics expansion often utilized in the WSA model. Our results are validated by comparing with multi-spacecraft data for ecliptical (STEREO-A/B) and out-of-ecliptic (Ulysses) regions.

Shock structures of astrospheres

The interaction between a supersonic stellar wind and a (super-)sonic interstellar wind has recently been viewed with new interest. We here first give an overview of the modeling, which includes the heliosphere as an example of a special astrosphere. Then we concentrate on the shock structures of fluid models, especially of hydrodynamic (HD) models. More involved models taking into account radiation transfer and magnetic fields are briefly sketched. Even the relatively simple HD models show a rich shock structure, which might be observable in some objects. We employ a single fluid model to study these complex shock structures, and compare the results obtained including heating and cooling with results obtained without these effects. Furthermore, we show that in the hypersonic case valuable information of the shock structure can be obtained from the Rankine-Hugoniot equations. We solved the Euler equations for the single fluid case and also for a case including cooling and heating. We also discuss the analytical Rankine-Hugoniot relations and their relevance to observations. We show that the only obtainable length scale is the termination shock distance. Moreover, the so-called thin shell approximation is usually not valid. We present the shock structure in the model that includes heating and cooling, which differs remarkably from that of a single fluid scenario in the region of the shocked interstellar medium. We find that the heating and cooling is mainly important in this region and is negligible in the regions dominated by the stellar wind beyond an inner boundary.

Magnetic clouds in the solar wind: a numerical assessment of analytical models

Context. Magnetic clouds (MCs) are “magnetized plasma clouds” moving in the solar wind. MCs transport magnetic flux and helicity away from the Sun. These structures are not stationary but feature temporal evolution as they propagate in the solar wind. Simplified analytical models are frequently used to describe MCs, and they fit certain observational data well. Aims. The goal of the present study is to numerically investigate the validity of an analytical model that is widely used to describe MCs, and to determine under which conditions this model’s implied assumptions cease to be valid. Methods. A numerical approach is applied. Analytical solutions derived in previous studies are implemented in a 3D magnetohydrodynamic simulation code as initial conditions. Besides the standard case in which MCs only expand and propagate in the solar wind, the case of an MC rotating around its axis of symmetry is also considered, and the resulting influence on the MC’s dynamics is studied. Results. Initially, the analytical model represents the main observational features of the MCs. However, these characteristics prevail only if the structure moves with a velocity close to the velocity of the background flow. In this case an MC’s evolution can quite accurately be described using an analytic, self-similar approach. The dynamics of the magnetic structures that move with a velocity significantly above or below that of the velocity of the solar wind is investigated in detail. Conclusions. Comparison of the numerical results with observational data indicates reasonable agreement especially for the intermediate case, in which the MC’s bulk velocity and the velocity of the background flow are equal. In this particular case, analytical solutions obtained on the basis of a self-similar approach indeed describe the MC’s evolution quite accurately. In general, however, numerical simulations are necessary to investigate the evolution as a function of a wide range of the parameters, which define the initial conditions.

The interaction of multiple stellar winds in stellar clusters: potential flow

While several studies have investigated large-scale cluster winds resulting from an intra-cluster interaction of multiple stellar winds, as yet they have not provided details of the bordering flows inside a given cluster. The present work explores the principal structure of the combined flow resulting from the interaction of multiple stellar winds inside stellar clusters. The theory of complex potentials is applied to analytically investigate stagnation points, boundaries between individual outflows, and the hydrodynamic structure of the asymptotic large-scale cluster wind. In a second part, these planar considerations are extended to fully three-dimensional, asymmetric configurations of wind-driving stars. We find (i) that one can distinguish regions in the large-scale cluster wind that are determined by the individual stellar winds, (ii) that there are comparatively narrow outflow channels, and (iii) that the large-scale cluster wind asymptotically approaches spherical symmetry at large distances. The combined flow inside a stellar cluster resulting from the interaction of multiple stellar winds is highly structured.