MAGE: Coupled Atmosphere-Geospace Model

• MAGE is a fully coupled global MHD–ionosphere–thermosphere framework that integrates GAMERA, RCM, REMIX, and a nested conductance module to simulate geospace interactions.
• It employs advanced finite-volume schemes and electrodynamic closures to accurately capture field-aligned current generation and auroral precipitation.
• Validation against AMPERE data confirms MAGE’s ability to resolve feedbacks between current systems and auroral energetics, enabling robust space weather analysis.

Searching arXiv for the specified paper and related MAGE literature. The Multiscale Atmosphere-Geospace Environment Model (MAGE) is a fully coupled global MHD–ionosphere–thermosphere framework used to simulate coupled magnetospheric, ionospheric, and auroral dynamics across multiple spatial scales. In Burkholder et al., MAGE is applied to the April 2023 storm under sustained sub-Alfvénic driving and, when validated against Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) data, is used to identify the field-aligned-current generation mechanism and to predict auroral precipitation during Earth’s terrestrial Alfvén wing state (Burkholder et al., 22 Feb 2025). Within the scope documented there, MAGE is defined operationally by its coupling of GAMERA, RCM, REMIX, and a nested ionosphere–thermosphere conductance module.

1. Framework composition and model scope

MAGE couples three main components. GAMERA is a global 3-D ideal MHD solver on a non-orthogonal curvilinear grid. RCM is the Rice Convection Model for ring-current and inner-magnetosphere drift physics. REMIX is a magnetosphere–ionosphere coupler/solver that carries field-aligned currents (FACs) into an ionospheric electrodynamics solver. A nested ionosphere–thermosphere module computes height-integrated conductances from precipitating electrons, then solves for ionospheric potentials (Burkholder et al., 22 Feb 2025).

Component	Role	Description in the documented configuration
GAMERA	Global plasma dynamics	Global 3-D ideal MHD solver
RCM	Inner-magnetosphere physics	Ring-current and drift physics
REMIX	M–I coupling	FAC transport and ionospheric electrodynamics
Nested ionosphere–thermosphere module	Conductance closure	Height-integrated conductances from precipitation

This architecture places MAGE in the class of coupled geospace system models in which the magnetosphere, ionosphere, and thermosphere are not treated as separable subsystems. In the documented application, the practical significance of that coupling is that FACs, precipitating electron energy flux, conductance, and ionospheric potential are all embedded in a closed loop rather than imposed independently. A plausible implication is that MAGE is designed to resolve feedbacks that are especially important during strongly driven or topologically unusual states such as terrestrial Alfvén wings.

2. Governing equations and electrodynamic closure

In the GAMERA component, the global dynamics are represented by the ideal, adiabatic MHD system. The mass continuity equation is

$$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho v) = 0 .$$

The momentum equation is

$$\frac{\partial (\rho v)}{\partial t} + \nabla \cdot \left[\rho v v + \left(p + \frac{B^2}{2\mu_0}\right)I - \frac{B B}{\mu_0}\right] = 0 .$$

The induction equation is

$$\frac{\partial B}{\partial t} = \nabla \times (v \times B) .$$

The energy equation is

$$\frac{\partial E}{\partial t} + \nabla \cdot \left[\left(E + p + \frac{B^2}{2\mu_0}\right)v - \frac{(B \cdot v)B}{\mu_0}\right] = 0 .$$

In the ionosphere, MAGE uses height-integrated electrodynamics. The Pedersen and Hall conductances satisfy

$$\Sigma_P = f(\Phi_e), \qquad \Sigma_H = \alpha \Sigma_P ,$$

and the potential equation on a spherical shell is

$$\nabla \cdot [\Sigma \cdot \nabla \Phi(\theta,\phi)] = - j_{||}(\theta,\phi) .$$

For FAC generation, the formulation emphasized in the documented study follows Liu et al. (2022), in which FAC from flow vorticity dominates:

$$j_{||} \simeq \int \left(\frac{\rho}{B}\right)\left(\frac{d\Omega}{dt}\right)d\ell , \qquad \Omega = (\nabla \times v)\cdot \hat{b} .$$

A field-line-integrated proxy is also defined as

$$\mathcal{J} \equiv \frac{1}{L}\int \Omega\, d\ell .$$

These equations organize the central physical interpretation advanced in the study: FAC morphology is not treated merely as an output of large-scale convection, but as the electrodynamic manifestation of localized flow-shear and vorticity structure. The explicit use of $\Omega$ and $d\Omega/dt$ is therefore fundamental to how MAGE diagnoses current generation in the Alfvén-wing regime (Burkholder et al., 22 Feb 2025).

3. Numerical realization for the April 2023 event

For the April 2023 storm simulation, GAMERA uses a finite-volume, solution-adaptive upwind scheme. Near-Earth resolution is approximately 1,200 km, corresponding to about $$\frac{\partial (\rho v)}{\partial t} + \nabla \cdot \left[\rho v v + \left(p + \frac{B^2}{2\mu_0}\right)I - \frac{B B}{\mu_0}\right] = 0 .$$0, and degrades smoothly to a few $$\frac{\partial (\rho v)}{\partial t} + \nabla \cdot \left[\rho v v + \left(p + \frac{B^2}{2\mu_0}\right)I - \frac{B B}{\mu_0}\right] = 0 .$$1 at distances beyond $$\frac{\partial (\rho v)}{\partial t} + \nabla \cdot \left[\rho v v + \left(p + \frac{B^2}{2\mu_0}\right)I - \frac{B B}{\mu_0}\right] = 0 .$$2. The upstream boundary is placed at $$\frac{\partial (\rho v)}{\partial t} + \nabla \cdot \left[\rho v v + \left(p + \frac{B^2}{2\mu_0}\right)I - \frac{B B}{\mu_0}\right] = 0 .$$3 sunward rather than $$\frac{\partial (\rho v)}{\partial t} + \nabla \cdot \left[\rho v v + \left(p + \frac{B^2}{2\mu_0}\right)I - \frac{B B}{\mu_0}\right] = 0 .$$4 in order to avoid reflected waves during sub-Alfvénic driving (Burkholder et al., 22 Feb 2025).

The solar-wind driver is OMNIWeb 1-min data for $$\frac{\partial (\rho v)}{\partial t} + \nabla \cdot \left[\rho v v + \left(p + \frac{B^2}{2\mu_0}\right)I - \frac{B B}{\mu_0}\right] = 0 .$$5, $$\frac{\partial (\rho v)}{\partial t} + \nabla \cdot \left[\rho v v + \left(p + \frac{B^2}{2\mu_0}\right)I - \frac{B B}{\mu_0}\right] = 0 .$$6, and IMF components $$\frac{\partial (\rho v)}{\partial t} + \nabla \cdot \left[\rho v v + \left(p + \frac{B^2}{2\mu_0}\right)I - \frac{B B}{\mu_0}\right] = 0 .$$7. The documented sub-Alfvénic interval extends from 12:30 to 14:30 UT on 24 April 2023, with $$\frac{\partial (\rho v)}{\partial t} + \nabla \cdot \left[\rho v v + \left(p + \frac{B^2}{2\mu_0}\right)I - \frac{B B}{\mu_0}\right] = 0 .$$8, $$\frac{\partial (\rho v)}{\partial t} + \nabla \cdot \left[\rho v v + \left(p + \frac{B^2}{2\mu_0}\right)I - \frac{B B}{\mu_0}\right] = 0 .$$9 nT, and $$\frac{\partial B}{\partial t} = \nabla \times (v \times B) .$$0 ramping from negative toward $$\frac{\partial B}{\partial t} = \nabla \times (v \times B) .$$1 nT. The immediately preceding marginally super-Alfvénic interval has $$\frac{\partial B}{\partial t} = \nabla \times (v \times B) .$$2.

These configuration choices are integral to the event interpretation. The enlarged sunward boundary is specifically tied to the sub-Alfvénic regime, in which reflected-wave contamination would be especially problematic. The event design also permits a controlled comparison between two flow states with similar solar-wind conditions but different Alfvén Mach number: before the Alfvén wings formed, solar-wind conditions were similar and $$\frac{\partial B}{\partial t} = \nabla \times (v \times B) .$$3, yet the FAC system extended from 9–18 magnetic local time; after wing formation, the current system reorganized into a much narrower sector (Burkholder et al., 22 Feb 2025).

4. Field-aligned currents in the terrestrial Alfvén-wing state

The key scientific result extracted from the MAGE simulation is a vorticity-driven FAC mechanism operating at the boundary between the Alfvén wings and the unshocked solar wind. During both pre-wing and wing intervals, large vorticity $$\frac{\partial B}{\partial t} = \nabla \times (v \times B) .$$4 localizes at sharp velocity-shear boundaries between magnetosheath flow and slowly convecting lobe or wing flux. The inertial FAC term, proportional to $$\frac{\partial B}{\partial t} = \nabla \times (v \times B) .$$5, is computed along each field line (Burkholder et al., 22 Feb 2025).

Diagnostics reported for the event show a one-to-one spatial correlation between vorticity sign and FAC polarity: positive $$\frac{\partial B}{\partial t} = \nabla \times (v \times B) .$$6 corresponds to negative FAC, described as upward in the Northern Hemisphere, on north lobe edges, while negative $$\frac{\partial B}{\partial t} = \nabla \times (v \times B) .$$7 corresponds to positive FAC on south lobe edges. In the sub-Alfvénic wing state, the magnetospheric wing cross-section is more circular, which concentrates shear, and therefore FAC, over approximately $$\frac{\partial B}{\partial t} = \nabla \times (v \times B) .$$8 in $$\frac{\partial B}{\partial t} = \nabla \times (v \times B) .$$9 rather than approximately $$\frac{\partial E}{\partial t} + \nabla \cdot \left[\left(E + p + \frac{B^2}{2\mu_0}\right)v - \frac{(B \cdot v)B}{\mu_0}\right] = 0 .$$0 for lobe flux.

The resulting FAC morphology differs sharply between the pre-wing and wing states. In the pre-wing super-Alfvénic state, negative FAC extends broadly from the dayside through dusk. In the wing-state sub-Alfvénic interval, negative FAC collapses into a narrow dawn-day sector at 5–11 MLT, with peak currents of approximately $$\frac{\partial E}{\partial t} + \nabla \cdot \left[\left(E + p + \frac{B^2}{2\mu_0}\right)v - \frac{(B \cdot v)B}{\mu_0}\right] = 0 .$$1 at approximately $$\frac{\partial E}{\partial t} + \nabla \cdot \left[\left(E + p + \frac{B^2}{2\mu_0}\right)v - \frac{(B \cdot v)B}{\mu_0}\right] = 0 .$$2 magnetic latitude. Simulation and observations also show that Northern Hemisphere planetward flowing electrons are predominantly at 8–13 MLT.

The geometric interpretation is explicit. Lobe flux is described as having an “aerofoil” cross-section that produces extended shear from $$\frac{\partial E}{\partial t} + \nabla \cdot \left[\left(E + p + \frac{B^2}{2\mu_0}\right)v - \frac{(B \cdot v)B}{\mu_0}\right] = 0 .$$3 to $$\frac{\partial E}{\partial t} + \nabla \cdot \left[\left(E + p + \frac{B^2}{2\mu_0}\right)v - \frac{(B \cdot v)B}{\mu_0}\right] = 0 .$$4 and maps to 5–23 MLT. The Alfvén-wing cross-section is circular, with shear from $$\frac{\partial E}{\partial t} + \nabla \cdot \left[\left(E + p + \frac{B^2}{2\mu_0}\right)v - \frac{(B \cdot v)B}{\mu_0}\right] = 0 .$$5 to $$\frac{\partial E}{\partial t} + \nabla \cdot \left[\left(E + p + \frac{B^2}{2\mu_0}\right)v - \frac{(B \cdot v)B}{\mu_0}\right] = 0 .$$6, mapping to 5–11 MLT. This suggests that, in the documented framework, current morphology is controlled not only by external driving but by the effective obstacle geometry presented to the flow.

5. Auroral precipitation, conductance, and mapping

MAGE predicts auroral precipitation by mapping precipitation energy flux $$\frac{\partial E}{\partial t} + \nabla \cdot \left[\left(E + p + \frac{B^2}{2\mu_0}\right)v - \frac{(B \cdot v)B}{\mu_0}\right] = 0 .$$7 from GAMERA footpoints to $$\frac{\partial E}{\partial t} + \nabla \cdot \left[\left(E + p + \frac{B^2}{2\mu_0}\right)v - \frac{(B \cdot v)B}{\mu_0}\right] = 0 .$$8, then to 110 km. Monoenergetic and diffuse electron precipitation formulas yield the differential flux $$\frac{\partial E}{\partial t} + \nabla \cdot \left[\left(E + p + \frac{B^2}{2\mu_0}\right)v - \frac{(B \cdot v)B}{\mu_0}\right] = 0 .$$9 from local plasma properties, and the integrated energy flux is

$$\Sigma_P = f(\Phi_e), \qquad \Sigma_H = \alpha \Sigma_P ,$$0

Conductance closure is then imposed through the Robinson et al. (1987) conversion

$$\Sigma_P = f(\Phi_e), \qquad \Sigma_H = \alpha \Sigma_P ,$$1

with $$\Sigma_P = f(\Phi_e), \qquad \Sigma_H = \alpha \Sigma_P ,$$2 following Kaeppler et al. (2015); these conductances feed back to REMIX and close the FAC loop (Burkholder et al., 22 Feb 2025).

Within the April 2023 event, the simulated auroral precipitation pattern follows the FAC morphology closely. The simulated energy-flux contour exceeding $$\Sigma_P = f(\Phi_e), \qquad \Sigma_H = \alpha \Sigma_P ,$$3 localizes to 8–10 MLT, matching the dawn-side FAC. The study further states that pre-wing aurora, analogous to lobe flux, would have been more extended across MLT but is difficult to observe due to sunlight.

This precipitation treatment is significant because it embeds auroral energetics directly into the electrodynamic solution rather than treating aurora as a purely diagnostic visualization. In the documented application, precipitating electron energy flux determines conductance, conductance determines ionospheric potential structure, and ionospheric closure feeds back on the current system. A plausible implication is that MAGE is intended to capture morphology and energetics simultaneously, not merely one as a byproduct of the other.

6. Validation against AMPERE and scientific implications

Validation against AMPERE is a central part of the documented use of MAGE. The total Northern Hemisphere Birkeland current is defined as

$$\Sigma_P = f(\Phi_e), \qquad \Sigma_H = \alpha \Sigma_P ,$$4

with the MAGE radius at $$\Sigma_P = f(\Phi_e), \qquad \Sigma_H = \alpha \Sigma_P ,$$5 and AMPERE at $$\Sigma_P = f(\Phi_e), \qquad \Sigma_H = \alpha \Sigma_P ,$$6. The simulated $$\Sigma_P = f(\Phi_e), \qquad \Sigma_H = \alpha \Sigma_P ,$$7 tracks AMPERE within approximately 10% over 00:00 UT on 23 April through 24 April. Hourly MLT profiles of FAC strength, expressed as $$\Sigma_P = f(\Phi_e), \qquad \Sigma_H = \alpha \Sigma_P ,$$8 versus MLT, show excellent agreement in shape and magnitude, especially during the sub-Alfvénic interval, which is characterized by 5–11 MLT dominance. Magnetic-latitude keograms for the 8–10 MLT and 14–16 MLT sectors reproduce the simulated localization of negative FAC around $$\Sigma_P = f(\Phi_e), \qquad \Sigma_H = \alpha \Sigma_P ,$$9 magnetic latitude and the suppression in dusk (Burkholder et al., 22 Feb 2025).

The documented discrepancies are also specific. There is a slight shift of the pre-wing peak negative FAC, with the simulation at MLT 18 versus AMPERE near 15. Southern Hemisphere FAC in AMPERE shows more asymmetry than the nearly mirrored simulation, which is described as possibly reflecting observational artifact or southern cusp dynamics.

The broader implications identified in the study extend beyond terrestrial space weather. Earth’s Alfvén wings are presented as a natural laboratory for sub-Alfvénic coupling regimes relevant to Europa and other moons in sub-Alfvénic plasma, and to exoplanets inside stellar Alfvén surfaces, where a constant Alfvén-wing state and persistent dawn-sector aurora are suggested. The study further states that the vorticity-driven FAC mechanism should generalize to any magnetized obstacle in sub-Alfvénic flow, with auroral signatures directly mapping the flow-shear geometry. This should be understood as a generalization advanced within the paper rather than as a settled universal result. Within that framing, MAGE’s validated ability to reproduce global FACs and energetics in an extreme regime is presented as support for cross-planetary application and for predicting storm-time space weather effects (Burkholder et al., 22 Feb 2025).