Magnetohydrodynamic Solutions Research Articles

Jet formation in post-AGB binaries

Context. Jets are launched from many classes of astrophysical objects, including post-asymptotic giant branch (post-AGB) binaries with a circumbinary disc. Despite dozens of detections, the formation of these post-AGB binary jets and their connection to the inter-component interactions in their host systems remains poorly understood. Aims. Building upon the previous paper in this series, we consider cold self-similar magnetohydrodynamic (MHD) disc wind solutions to describe jets that are launched from the circumcompanion accretion discs in post-AGB binaries. Resulting predictions are matched to observations. This both tests the physical validity of the MHD disc wind paradigm and reveals the accretion disc properties. Methods. Five MHD solutions are used as input to synthesise spectral time-series of the Hα line for five different post-AGB binaries. A fitting routine over the remaining model parameters is developed to find the disc wind models that best fit the observed time-series. Results. Many of the time-series’ properties are reproduced well by the models, though systematic mismatches, such as overestimated rotation, remain. Four targets imply accretion discs that reach close to the secondary’s stellar surface, while one is fitted with an unrealistically large inner radius at ≳20 stellar radii. Some fits imply inner disc temperatures over 10 000 K, seemingly discrepant with a previous observational estimate from H band interferometry. This estimate is, however, shown to be biased. Fitted mass-accretion rates range from ∼10−6 − 10−3 M⊙/yr. Relative to the jets launched from young stellar objects (YSOs), all targets prefer winds with higher ejection efficiencies, lower magnetizations and thicker discs. Conclusions. Our models show that current cold MHD disc wind solutions can explain many of the jet-related Hα features seen in post-AGB binaries, though systematic discrepancies remain. This includes, but is not limited to, overestimated rotation and underestimated post-AGB circumbinary disc lifetimes. The consideration of thicker discs and the inclusion of irradiation from the post-AGB primary, leading to warm magnetothermal wind launching, might alleviate these.

Shocks in the warm neutral medium

Context. Atomic and molecular line emissions from shocks may provide valuable information on the injection of mechanical energy into the interstellar medium (ISM), the generation of turbulence, and the processes of phase transition between the warm neutral medium (WNM) and the cold neutral medium (CNM). Aims. In this series of papers, we investigate the properties of shocks propagating in the WNM. Our objective is to identify the tracers of these shocks, use them to interpret ancillary observations of the local diffuse matter, and provide predictions for future observations. Methods. Shocks propagating in the WNM are studied using the Paris-Durham shock code, a multi-fluid model built to follow the thermodynamical and chemical structures of shock waves at steady-state in a plane-parallel geometry. The code, designed to take into account the impact of an external radiation field, is updated to treat self-irradiated shocks at intermediate (30 < VS < 100 km s−1) and high velocity (VS ⩾ 100 km s−1), which emit ultraviolet (UV), extreme-ultraviolet (EUV), and X-ray photons. The couplings between the photons generated by the shock, the radiative precursor, and the shock structure are computed self-consistently using an exact radiative-transfer algorithm for line emission. The resulting code is explored over a wide range of parameters (0.1 ⩽ nH ⩽ 2 cm−3, 10 ⩽ VS ⩽ 500 km s−1, and 0.1 ⩽ B ⩽ 10 μG), which covers the typical conditions of the WNM in the solar neighborhood. Results. The explored physical conditions lead to the existence of a diversity of stationary magnetohydrodynamic solutions, including J-type, CJ-type, and C-type shocks. These shocks are found to naturally induce phase transition between the WNM and the CNM, provided that the postshock thermal pressure is higher than the maximum pressure of the WNM and that the maximum density allowed by magnetic compression is greater than the minimum density of the CNM. The input flux of mechanical energy is primarily reprocessed into line emissions from the X-ray to the submillimeter domain. Intermediate- and high-velocity shocks are found to generate a UV radiation field that scales as VS3 for VS < 100 km s−1 and as VS2 at higher velocities, and an X-ray radiation field that scales as VS3 for VS ⩾ 100 km s−1. Both radiation fields may extend over large distances in the preshock depending on the density of the surrounding medium and the hardness of the X-ray field, which is solely driven by the shock velocity. Conclusions. This first paper presents the thermochemical trajectories of shocks in the WNM and their associated spectra. It corresponds to a new milestone in the development of the Paris-Durham shock code and a stepping stone for the analysis of observations that will be carried out in forthcoming works.

Density jump for oblique collisionless shocks in pair plasmas: physical solutions

Collisionless shocks are frequently analysed using the magnetohydrodynamics (MHD) formalism, even though MHD assumes a small mean free path. Yet, isotropy of pressure, the fruit of binary collisions and assumed in MHD, may not apply in collisionless shocks. This is especially true within a magnetized plasma, where the field can stabilize an anisotropy. In a previous article (Bret & Narayan, J. Plasma Phys., vol. 88, no. 6, 2022b, p. 905880615), a model was presented capable of dealing with the anisotropies that may arise at the front crossing. It was solved for any orientation of the field with respect to the shock front. Yet, for some values of the upstream parameters, several downstream solutions were found. Here, we complete the work started in Bret & Narayan (J. Plasma Phys., vol. 88, no. 6, 2022b, p. 905880615) by showing how to pick the physical solution out of the ones offered by the algebra. This is achieved by 2 means: (i) selecting the solution that has the downstream field obliquity closest to the upstream one. This criterion is exemplified on the parallel case and backed up by particle-in-cell simulations. (ii) Filtering out solutions which do not satisfy a criteria already invoked to trim multiple solutions in MHD: the evolutionarity criterion, that we assume valid in the collisionless case. The end result is a model in which a given upstream configuration results in a unique, or no downstream configuration (as in MHD). The largest departure from MHD is found for the case of a parallel shock.

Improving Coronal Hole Detections and Open Flux Estimates

One systematic limitation of solar coronal hole (CH) detection at extreme ultraviolet (EUV) wavelengths is the obscuration of dark regions of the corona by brighter structures along the line of sight. Another problem arises when using CHs to compute the Sun’s open magnetic flux, where surface measurements of the radial magnetic field, , are situated slightly below the effective height of coronal EUV emission. In this paper, we explore these two limitations utilizing a thermodynamic magnetohydrodynamic (MHD) model of the corona for Carrington rotation (CR) 2101, where we generate CH detections from EUV 193 Å images of the corona forward-modeled from the MHD solution, and where the modeled open field is known. We demonstrate a method to combine EUV images into a full Sun map that helps alleviate CH obscuration called the minimum intensity disk merge (MIDM). We also show the variation in measured open flux and CH area that is due to the effective height differences between EUV and measurements. We then apply the MIDM method to SDO/AIA 193 Å observations from CR 2101, and conduct an analogous analysis. In this case, the MIDM method uses time-varying images, the effects of which are discussed. We show that overall, the MIDM method and an appreciation of the effective height mismatch provide a useful new way to extract a broader view of CHs, especially near the poles. In turn, they enable improved estimates of the open magnetic flux, and help facilitate comparisons between models and observations.

Partially ionized two-fluid shocks with collisional and radiative ionization and recombination – multilevel hydrogen model

ABSTRACT Explosive phenomena are known to trigger a wealth of shocks in warm plasma environments, including the solar chromosphere and molecular clouds where the medium consists of both ionized and neutral species. Partial ionization is critical in determining the behaviour of shocks, since the ions and neutrals locally decouple, allowing for substructure to exist within the shock. Accurately modelling partially ionized shocks requires careful treatment of the ionized and neutral species, and their interactions. Here we study a partially ionized switch-off slow-mode shock using a multilevel hydrogen model with both collisional and radiative ionization and recombination rates that are implemented into the two-fluid (PIP) code, and study physical parameters that are typical of the solar chromosphere. The multilevel hydrogen model differs significantly from magnetohydrodynamic (MHD) solutions due to the macroscopic thermal energy loss during collisional ionization. In particular, the plasma temperature both post-shock and within the finite-width is significantly cooler that the post-shock MHD temperature. Furthermore, in the mid to lower chromosphere, shocks feature far greater compression than their single-fluid MHD analogues. The decreased temperature and increased compression reveal the importance of non-equilibrium ionized in the thermal evolution of shocks in partially ionized media. Since partially ionized shocks are not accurately described by the Rankine-Hugoniot shock jump conditions, it may be incorrect to use these to infer properties of lower atmospheric shocks.

Accretion disc backflow in resistive MHD simulations

ABSTRACT We investigate accretion onto a central star, with the size, rotation rate, and magnetic dipole of a young stellar object, to study the flow pattern (velocity and density) of the fluid within and outside of the disc. We perform resistive magnetohydrodynamic (MHD) simulations of thin discs, varying the parameters such as the stellar rotation rate and (anomalous) coefficients of viscosity and resistivity in the disc. To provide a benchmark for the results and to compare them with known analytic results, we also perform purely hydrodynamic (HD) simulations for the same problem. Although obtained for different situations with differing inner boundary condition, the disc structure in the HD simulations closely follows the analytic solution of Kluzniak and Kita – in particular, a region of ‘mid-plane’ backflow exists in the right range of radii, depending on the viscosity parameter. In the MHD solutions, whenever the magnetic Prandtl number does not exceed a certain critical value, the mid-plane backflow exists throughout the accretion disc, extending all the way down to the foot point of the accretion funnel flow where the disc transitions to a magnetic funnel flow. For values of the magnetic Prandtl number close to the critical value the backflow and the inner disc undergo a quasi-periodic radial oscillation, otherwise the backflow is steady, as is the disc solution. From our results, supplemented by our reading of the literature, we suggest that mid-plane backflow is a real, physical, and not only numerical feature of at least some accretion discs.

Numerical modeling of solar wind and coronal mass ejection in the inner heliosphere: A review

The predictions of plasma parameters in the interplanetary medium are the core of space weather forecasts, and the magnetohydrodynamics (MHD) numerical simulation is an important tool in the prediction of plasma parameters. Operational space weather forecasts are commonly produced by a heliosphere model whose inner boundary is set at 18 Rs or beyond. Such predictions typically use empirical/physics-based inner boundary conditions to solve the MHD equations for numerical simulation. In recent years, significant progress has been made in the numerical modeling of the inner heliosphere. In this paper, the numerical modeling of solar wind and coronal mass ejection in the inner heliosphere is reviewed. In particular, different inner boundary conditions used in the simulation are investigated since the MHD solutions are predetermined by the treatment of the inner boundary conditions to a large extent. Discussion is made on further development of the heliosphere model.

Coherent magnetic modon solutions in quasi-geostrophic shallow water magnetohydrodynamics

A class of exact solutions of the magnetohydrodynamic quasi-geostrophic equations (MQG), which result from rotating shallow water magnetohydrodynamics in the limit of small Rossby and magnetic Rossby numbers is constructed analytically. These solutions are magnetic modons, steady-moving dipolar vortices, which are generalizations of the well-known quasi-geostrophic modons. It is shown that various configurations of magnetic modons are possible: with or without external magnetic field, and with or without internal magnetic field trapped inside the dipole. By using the modon solutions as initial conditions for direct numerical simulations of the MQG equations, it is shown that they remain coherent for a long time, running over about a hundred deformation radii without change of form, provided the external and internal magnetic fields are not too strong, and even if a small-amplitude noise is added to initial conditions.

Radial coordinate maps, radial vectors, and binormal vectors for 5/6, 5/5 and 5/4 edge island domains in W7-X

The edge island domain in Wendelstein 7-X consists of divertor islands whose position coincide with the location of rational values of the rotational transform and surround the main confinement volume (the ‘main plasma’), providing the magnetic topology for an island divertor. The 5/5 edge consists of five individual islands that are unconnected. In contrast, a single island connects onto itself after 6 or 4 toroidal transits in the 5/6 or 5/4 edge, respectively. Many interesting phenomena are related to these islands and diagnostic analyses require a mapping from ‘laboratory’ or real space coordinates to the island coordinate system (ICS). A procedure is described here to calculate several scalar and vector quantities for closed island structures which can be utilized in fast interpolation schemes for inverse maps. For the 5/5 edge, a fixed-boundary vacuum (zero beta) magneto-hydrodynamic solution of the 5/5 island is found with the Variational Moments Equilibrium Code, VMEC. The solution is compatible with already existing routines which determine the radial and binormal vectors of VMEC solutions at arbitrary laboratory coordinates. VMEC does not support solutions for the 5/4 and 5/6 islands, but the radial and binormal vectors are available in a local 2D Fourier ICS.

Effects of mesh topology on MHD solution features in coronal simulations

Magnetohydrodynamic (MHD) simulations of the solar corona have become more popular with the increased availability of computational power. Modern computational plasma codes, relying upon computational fluid dynamics (CFD) methods, allow the coronal features to be resolved using solar surface magnetograms as inputs. These computations are carried out in a full three-dimensional domain and, thus, selection of the correct mesh configuration is essential to save computational resources and enable/speed up convergence. In addition, it has been observed that for MHD simulations close to the hydrostatic equilibrium, spurious numerical artefacts might appear in the solution following the mesh structure, which makes the selection of the grid also a concern for accuracy. The purpose of this paper is to discuss and trade off two main mesh topologies when applied to global solar corona simulations using the unstructured ideal MHD solver from the COOLFluiD platform. The first topology is based on the geodesic polyhedron and the second on$UV$mapping. Focus is placed on aspects such as mesh adaptability, resolution distribution, resulting spurious numerical fluxes and convergence performance. For this purpose, first a rotating dipole case is investigated, followed by two simulations using real magnetograms from the solar minima (1995) and solar maxima (1999). It is concluded that the most appropriate mesh topology for the simulation depends on several factors, such as the accuracy requirements, the presence of features near the polar regions and/or strong features in the flow field in general. If convergence is of concern and the simulation contains strong dynamics, then grids which are based on the geodesic polyhedron are recommended compared with more conventionally used$UV$-mapped meshes.

3D Exact Analytical Solutions of Two-fluid Plasma, Magnetohydrodynamics, and Neutral Fluid Equations for the Creation of Ordered Structures as well as Jet-like Flows

Abstract The 3D exact analytical solutions of ideal two-fluid plasma, single-fluid plasma, and neutral fluid equations have been found using physically justifiable assumptions. Surprisingly these solutions satisfy all nonlinearities in the systems. It is pointed out that these solutions explain the fundamental mechanism behind the creation of a vast variety of ordered structures in plasmas and fluids. In the limiting case of 2D dependence of fields, the theoretical model for plasma is applied to explain the formation of spicules in the solar chromosphere. It is pointed out that the main contribution of electron (ion) baroclinic vectors is to produce vorticity in the plasma, and that magnetic field generation is coupled with the flow of both electrons and ions.

Numerical study of δ-function current sheets arising from resonant magnetic perturbations

General three-dimensional toroidal ideal magnetohydrodynamic equilibria with a continuum of nested flux surfaces are susceptible to forming singular current sheets when resonant perturbations are applied. The presence of singular current sheets indicates that, in the presence of non-zero resistivity, magnetic reconnection will ensue, leading to the formation of magnetic islands and potentially regions of stochastic field lines when islands overlap. Numerically resolving singular current sheets in the ideal magnetohydrodynamics (MHD) limit has been a significant challenge. This work presents numerical solutions of the Hahm–Kulsrud–Taylor (HKT) problem, which is a prototype for resonant singular current sheet formation. The HKT problem is solved by two codes: a Grad–Shafranov (GS) solver and the Stepped Pressure Equilibrium Code (SPEC) code. The GS solver has built-in nested flux surfaces with prescribed magnetic fluxes. The SPEC code implements multi-region relaxed magnetohydrodynamics (MRxMHD), whereby the solution relaxes to a Taylor state in each region while maintaining force balance across the interfaces between regions. As the number of regions increases, the MRxMHD solution appears to approach the ideal MHD solution assuming a continuum of nested flux surfaces. We demonstrate agreement between the numerical solutions obtained from the two codes through a convergence study.

Stable and unstable supersonic stagnation of an axisymmetric rotating magnetized plasma

The Naval Research Laboratory ‘Mag Noh problem’, described in this paper, is a self-similar magnetized implosion flow, which contains a fast magnetohydrodynamic (MHD) outward propagating shock of constant velocity. We generalize the classic Noh (OSTI Tech. Rep. 577058, 1983) problem to include azimuthal and axial magnetic fields as well as rotation. Our family of ideal MHD solutions is five parametric, each solution having its own self-similarity index, gas gamma, magnetization, the ratio of axial to the azimuthal field and rotation. While the classic Noh problem must have a supersonic implosion velocity to create a shock, our solutions have an interesting three-parametric special case with zero initial velocity in which magnetic tension, instead of implosion flow, creates the shock at $t=0+$ . Our self-similar solutions are indeed realized when we solve the initial value MHD problem with the finite volume MHD code Athena. We numerically investigated the stability of these solutions and found both stable and unstable regions in parameter space. Stable solutions can be used to test the accuracy of numerical codes. Unstable solutions have also been widely used to test how codes reproduce linear growth, transition to turbulence and the practically important effects of mixing. Now we offer a family of unstable solutions featuring all three elements relevant to magnetically driven implosions: convergent flow, magnetic field and a shock wave.

Theoretical Refinements to the Heliospheric Upwind eXtrapolation Technique and Application to in-situ Measurements

The large-scale structure and evolution of the solar wind are typically reproduced with reasonable fidelity using three-dimensional magnetohydrodynamic (MHD) models. However, such models are difficult to implement by the scientific community in general, because they require technical expertise and significant computational resources. Previously, we demonstrated how a simplified two-dimensional surrogate solar wind model, the Heliospheric Upwind eXtrapolation (HUX) technique, could reconstruct MHD solutions in the ecliptic plane, given either an inner (or outer) radial boundary condition. Here, we further develop the HUX technique and apply it to a range of solar wind in-situ datasets. Specifically, we: (1) provide a thorough mathematical analysis of the underlying reduced momentum equation describing the solar wind. (2) Propose flux-limiter numerical schemes that more accurately capture stream interaction regions and rarefaction regions; and (3) Apply the HUX technique to a variety of in-situ spacecraft measurements, focusing on Helios (1 and 2) and near-Earth spacecraft (Wind/ACE), for which near-latitudinal alignments occurred. We suggest that this refined HUX tool can be used for both retrospective studies as well as real-time predictions to better understand and forecast the large-scale structure and origin of the solar wind.

Analytical solution of magneto-hydrodynamics with acceleration effects of Bjorken expansion in heavy-ion collisions

In this article, we aim to study, in an analytical manner, the 1 + 1 longitudinal acceleration expansion of hot and dense quark matter as a conducting relativistic fluid with the electric conductivity \(\sigma \). To this end, the plasma is inserted in the presence of electric and magnetic fields, which are perpendicular together in the transverse plane. To be more realistic, we generalize the Bjorken solution, which includes the acceleration effects on the fluid expansion. We then apply a perturbation fashion in the initial condition to solve the relativistic magneto-hydrodynamics equations. This procedure leads us to achieve the exact algebraic expressions for both electric and magnetic fields. In the process, we also find the effects of the electromagnetic fields on the fluid’s acceleration and the energy density correction obtained from the magneto-hydrodynamics solutions.

Quasisymmetric magnetic fields in asymmetric toroidal domains

We explore the existence of quasisymmetric magnetic fields in asymmetric toroidal domains. These vector fields can be identified with a class of magnetohydrodynamic equilibria in the presence of pressure anisotropy. First, using Clebsch potentials, we derive a system of two coupled nonlinear first order partial differential equations expressing a family of quasisymmetric magnetic fields in bounded domains. In regions where flux surfaces and surfaces of constant field strength are not tangential, this system can be further reduced to a single degenerate nonlinear second order partial differential equation with externally assigned initial data. Subclasses of solutions are then constructed by specifying as input the form the flux function, which enforces boundary shape and nested flux surfaces. In particular, we exhibit smooth quasisymmetric vector fields, which correspond to local solutions of anisotropic magnetohydrodynamics in asymmetric toroidal domains such that tangential boundary conditions are fulfilled on a portion of the bounding surface. These solutions are local because they lack periodicity in the toroidal angle. The problems of boundary shape and locality are also discussed. We find that magnetic fields with Euclidean isometries can be fitted into asymmetric domains and that the mathematical difficulty encountered in the derivation of global quasisymmetric magnetic fields lies in the topological obstruction toward global extension affecting local solutions of the governing nonlinear first order partial differential equations.

A numerical method for self-similar solutions of ideal magnetohydrodynamics

We present a numerical method to obtain self-similar solutions of the ideal magnetohydrodynamics (MHD) equations. Under a self-similar transformation, the initial value problem (IVP) is converted into a boundary value problem (BVP) by eliminating time and transforming the system to self-similar coordinates (ξ≡x/t,η≡y/t). The ideal MHD system of equations is augmented by a generalized Lagrange multiplier (GLM) to maintain the solenoidal condition on the magnetic field. The self-similar solution to the BVP is solved using an iterative method, and implemented using the p4est adaptive mesh refinement (AMR) framework. Existing Riemann solvers (e.g., Roe, HLLD etc.) can be modified in a relatively straightforward manner and used in the present method. Numerical tests illustrate that the present self-similar solution to the BVP exhibits sharper discontinuities than the corresponding one solved by the IVP. We compare and contrast the IVP and BVP solutions in several one dimensional shock-tube test problems and two dimensional test cases include shock wave refraction at a contact discontinuity, reflection at a solid wall, and shock wave diffraction over a right angle corner.

Neural Network Reconstruction of Plasma Space-Time

We explore the use of Physics-Informed Neural Networks (PINNs) for reconstructing full magnetohydrodynamic solutions from partial samples, mimicking the recreation of space-time environments around spacecraft observations. We use one-dimensional magneto- and hydrodynamic benchmarks, namely the Sod, Ryu-Jones, and Brio-Wu shock tubes, to obtain the plasma state variables along linear trajectories in space-time. These simulated spacecraft measurements are used as constraining boundary data for a PINN which incorporates the full set of one-dimensional (magneto) hydrodynamics equations in its loss function. We find that the PINN is able to reconstruct the full 1D solution of these shock tubes even in the presence of Gaussian noise. However, our chosen PINN transformer architecture does not appear to scale well to higher dimensions. Nonetheless, PINNs in general could turn out to be a promising mechanism for reconstructing simple magnetic structures and dynamics from satellite observations in geospace.

A mathematical model for calculation of the influence of ferromagnetic components in Vertical Displacement Events and stability simulations of tokamak plasmas

Iron core transformer tokamaks have a distinct element, namely the iron core which can affect the plasma stability of the plasma. As a consequence of the high non-linear dependence of the magneto-hydrodynamic solutions on the iron permeability μ Fe in JET tokamak for example, Vertical Displacement Events (VDEs), equilibrium and stability calculations are more complicated and more time consuming than in air core transformer tokamaks. By considering the ferromagnetic components as a linear, isotropic and homogeneous media on subdomains, it is known that these media can be replaced by a homogeneous one (vacuum) and a surface-current density distribution i Fe(l) on the separation surfaces between subdomains, with l the curve taken along the curve separating two different magnetic media. For the case of geometry with rotational symmetry, this surface-current density distribution along a curve, in a meridian plane, is given by a Fredholm integral equation of second kind. Practically, the advantage of this method is more obvious for the inverse formulation of the VDEs and stability problems by moving the non-linear term (due to the iron permeability μ Fe ) from the differential operator to the r.h.s. of the equations. In this paper, we are presenting how the influence of ferromagnetic components in the equations of the surface currents developed in the vessel structures during Wall Touching Kink Modes (WTKMs) can be taken into account and are reviewing the equations to be solved in order to simulate the influence of the ferromagnetic components in VDEs and equilibrium stability calculations. The numerical results of these simulations for a real JET tokamak structure and plasma parameters will be reported in a future paper.

The Coronal Global Evolutionary Model: Using HMI Vector Magnetogram and Doppler Data to Determine Coronal Magnetic Field Evolution

Abstract The Coronal Global Evolutionary Model (CGEM) provides data-driven simulations of the magnetic field in the solar corona to better understand the build-up of magnetic energy that leads to eruptive events. The CGEM project has developed six capabilities. CGEM modules (1) prepare time series of full-disk vector magnetic field observations to (2) derive the changing electric field in the solar photosphere over active-region scales. This local electric field is (3) incorporated into a surface flux transport model that reconstructs a global electric field that evolves magnetic flux in a consistent way. These electric fields drive a (4) 3D spherical magnetofrictional (SMF) model, either at high resolution over a restricted range of solid angles or at lower resolution over a global domain to determine the magnetic field and current density in the low corona. An SMF-generated initial field above an active region and the evolving electric field at the photosphere are used to drive (5) detailed magnetohydrodynamic (MHD) simulations of active regions in the low corona. SMF or MHD solutions are then used to compute emissivity proxies that can be compared with coronal observations. Finally, a lower-resolution SMF magnetic field is used to initialize (6) a global MHD model that is driven by an SMF electric field time series to simulate the outer corona and heliosphere, ultimately connecting Sun to Earth. As a demonstration, this report features results of CGEM applied to observations of the evolution of NOAA Active Region 11158 in 2011 February.