Global Core Plasma Model (GCPM)

• Global Core Plasma Model is a physics-based, empirical framework that provides spatially-resolved electron density profiles essential for understanding both fusion plasmas and geospace navigation.
• It integrates empirical submodels with MHD formalisms and kinetic resonance analyses to simulate ionospheric, plasmaspheric, and fusion plasma behaviors under various solar and geomagnetic conditions.
• The model supports low-frequency eigenmode analysis in tokamak plasmas and accurate correction of GNSS signal delays, enhancing both fusion research and spaceborne navigation systems.

The Global Core Plasma Model (GCPM) is a physics-based, empirical framework developed to provide accurate descriptions of plasma characteristics in planetary environments, specifically focusing on electron density distributions in the Earth’s ionosphere and plasmasphere. It serves dual roles: as a predictive tool for linear kinetic effects in core fusion plasmas—crucially informing low-frequency eigenmode stability analyses—and as the standard for characterizing spaceborne propagation delays in geospace navigation systems, including lunar GNSS (Global Navigation Satellite System) applications. The model integrates plasma physics submodels, magnetohydrodynamic (MHD) formalisms, and kinetic resonances, enabling robust simulations and analyses across laboratory and space plasma contexts.

1. Construction and Components of the Global Core Plasma Model

GCPM integrates several empirical and theoretical submodels to provide spatially resolved electron density profiles ($n_e$) as functions of geographic location, altitude, time, solar activity, and geomagnetic indices (Iiyama et al., 11 Oct 2025). It draws upon established lower-atmosphere and ionospheric models (such as IRI for the ionosphere), and includes specific treatments of the plasmasphere, plasmapause boundary, and related regimes. Key inputs driving the model’s output include the F10.7 and R12 solar activity indices and the %%%%1%%%% geomagnetic disturbance index.

A central goal of GCPM is to encapsulate the cumulative effects of high-density ionospheric regions and low-density but spatially extended plasmaspheric regions, both of which significantly influence the total electron content (TEC) along relevant physical paths (e.g., electromagnetic ray traces for navigation signals or field-aligned particle dynamics in fusion plasmas). The model also provides the spatial and temporal variation of magnetic field parameters needed for comprehensive wave–particle interaction and propagation analyses.

2. GCPM in Low-Frequency Eigenmode Analysis in Fusion Plasmas

In the framework of tokamak plasmas, GCPM enables first-principles treatment of core kinetic effects on low-frequency eigenmodes such as Beta-induced Alfvén Acoustic Eigenmodes (BAAEs) and Kinetic Ballooning Modes (KBMs) (Chavdarovski et al., 2022). The model’s capacity to self-consistently incorporate core plasma parameters—particularly the diamagnetic frequency ($\omega_{*i}$) and trapped particle precession frequencies—enables accurate predictions of eigenmode excitation, polarization, and damping.

The generalized fishbone-like dispersion relation (GFLDR) is used as the overarching mathematical formalism:

$i \Lambda(\omega) = \delta W_{f} + \delta W_{k}$

Here, $\Lambda(\omega)$ generalizes mode inertia (including both inertial layer dynamics and ideal MHD region response), $\delta W_f$ captures the non-resonant background MHD potential (including non-resonant energetic particle contributions), and $\delta W_k$ incorporates resonant drives from thermal ions, electrons, and energetic particles.

Core plasma properties fundamentally determine the excitation and coupling of BAAEs and KBMs, as reflected in:

• Dominance of diamagnetic and precession resonance terms for BAAE excitation over energetic particle effects
• Coupling of BAAEs and KBMs by the diamagnetic frequency, modifying polarization and damping
• Reduced BAAE damping due to diamagnetic effects, allowing mode frequencies below the energetic particle resonance threshold
• Enhanced KBM damping and modified polarization as coupling to BAAEs intensifies

This approach captures both resonant and non-resonant drives in the low-frequency branch, offering a unified basis for systematic analysis of mode frequency, growth rates, and polarization in tokamak plasmas.

3. Modeling Signal Propagation Delays for Lunar GNSS Receivers

In space environment applications, GCPM provides the empirically validated electron density maps required for quantitative analysis of electromagnetic signal propagation, particularly for lunar GNSS navigation (Iiyama et al., 11 Oct 2025). Signal propagation through Earth’s ionosphere and plasmasphere leads to measurable phase and group delays, as well as excess path length due to ray bending. Analytical treatment utilizes expansions for the phase ($n$) and group ($n_\mathrm{gr}$) refractive indices for right-hand circularly polarized waves: $$n = 1 - \frac{f_p^2}{2f^2} - \frac{f_p^2 f_g \cos\theta}{2f^3} - \frac{f_p^2}{4f^4} \left( \frac{f_p^2}{2} + f_g^2(1+\cos^2\theta) \right)$$

$$n_\mathrm{gr} = 1 + \frac{f_p^2}{2f^2} + \frac{f_p^2 f_g \cos\theta}{f^3} + \frac{3f_p^2}{4f^4} \left( \frac{f_p^2}{2} + f_g^2(1+\cos^2\theta) \right)$$

where $f_p = \sqrt{n_e e^2 / (4\pi\varepsilon_0 m)}$ is the plasma frequency, $f_g = eB / (2\pi m)$ the gyro frequency, $f$ is the radio frequency, and $\theta$ the angle with the magnetic field.

Total phase and group delays over a path $s$ are then computed as integrals with coefficients: $$d_\mathrm{Igr} = \int (n_\mathrm{gr} - 1) ds = \frac{p}{f^2} + \frac{q}{f^3} + \frac{u}{f^4}$$ where:

• $p = 40.3 \int n_e ds$
• $$q = -2.2566 \times 10^{12} \int n_e B \cos\theta ds$$
• $$u = 2437 \int n_e^2 ds + 4.74 \times 10^{22} \int n_e B^2 (1 + \cos^2\theta) ds$$

Delays are decomposed into first-order ($p/f^2$, dominant and directly proportional to TEC), second-order ($q/f^3$), and third-order ($u/f^4$) terms. Numerical results demonstrate that mean group delays can be $\sim$1 m, but may exceed 100 m for low-altitude, high-density ray paths during periods of high solar activity.

Ray bending further introduces an excess delay: $d_\mathrm{len} = \int ds - \rho$ with $\rho$ the geometric (straight-line) distance. This “bending delay” is typically smaller in magnitude than the first-order group delay, yet becomes non-negligible for horizontal or low-altitude propagation.

4. Sensitivity to Environmental Parameters and Frequency Dependence

GCPM's output and the propagation delays derived from it are strongly functionals of:

• Signal frequency: Delays scale as $f^{-2}$, $f^{-3}$, and $f^{-4}$. Lower-frequency signals like L5 (1176.45 MHz) experience larger group delays than L1 (1575.42 MHz). For low-altitude plasma-dense paths, L1 is preferable due to its reduced delay, while L5 is advantageous geometrically in tangent propagation where noise dominates.
• Geomagnetic activity ($K_p$ index): Higher $K_p$ values cause the plasmapause to contract, reducing the column-integrated electron density and leading to smaller group delays.
• Solar activity (R12 index): Higher R12 (increased solar UV flux) elevates ionospheric and plasmaspheric electron densities, directly increasing all orders of delay. The range and statistical percentiles of group delays for lunar GNSS propagation widen significantly as R12 increases.

These dependencies are critical for the design and operation of spaceborne navigation and timing systems, as compensation or mitigation of these variable error sources is key for reliable lunar GNSS (Iiyama et al., 11 Oct 2025).

5. Applications and Experimental Validation

GCPM informs a variety of research and engineering applications:

• Tokamak experiments: Measurements in DIII-D and HL-2A tokamaks show low-frequency modes scaling with thermal core plasma parameters and featuring nonlinear couplings (e.g., “Christmas lights” patterns as rational surfaces are crossed in reversed-shear profiles). Experimental evidence confirms that BAAE damping and excitation is dominated by core plasma effects, rather than energetic particle drive, directly validating GCPM-based kinetic models (Chavdarovski et al., 2022).
• GNSS lunar navigation: By integrating GCPM-based delay characterizations into positioning algorithms, significant group and bending delays associated with horizontal lunar ray paths can be correctly modeled or filtered. Design rules emerging from these studies include the application of altitude- or geometry-based filters, optimized dual-frequency strategies, and dynamic correction models responsive to real-time $K_p$ and R12 data (Iiyama et al., 11 Oct 2025).

6. Implications for Model-Based System Design

GCPM’s detailed physical treatment—accounting for diamagnetic, precession resonance, and ray propagation effects—enables the development of:

• GNSS navigation/timing algorithms with real-time correction for ionospheric and plasmaspheric delays, using profile forecasts from GCPM as model-driven corrections or quality masks
• Advanced kinetic/MHD stability analyses in tokamak plasmas, where all resonant and non-resonant effects are systematically included through the GFLDR formalism, crucially improving the prediction of eigenmode thresholds, growth/damping rates, and cross-branch couplings.

A plausible implication is that the wide parameter coverage and physical completeness of GCPM allows its use as both an interpretive and predictive tool across domains where global plasma density and kinetic effects are significant contributors to system behavior.

7. Outlook and Ongoing Developments

Continued integration of empirical data, improved physics submodels (e.g., for suprathermal particle effects or extreme geomagnetic events), and higher-resolution measurement grids are expected to further enhance the predictive fidelity and operational utility of GCPM. Ongoing space and fusion plasma experiments continue to provide benchmarks for validation, particularly as new operational regimes (such as cislunar navigation or advanced burning plasma states) are probed using these models.