EPED Framework: Tokamak Pedestal Model

• EPED framework is a predictive model for tokamak pedestal structures, defining height and width by intersecting peeling–ballooning and kinetic ballooning limits.
• The model employs a dual-constraint approach using local KBM thresholds (via IBM or GFS) and global MHD stability (ELITE) to determine optimal pedestal conditions.
• Robust across different devices, EPED enhances predictive accuracy for high-confinement regimes and informs next-generation tokamak performance forecasts.

The term "EPED framework" refers principally to a widely used predictive model for the pedestal structure in the edge of high-confinement (H-mode) plasmas in tokamaks. EPED unifies constraints from MHD stability (peeling-ballooning) and kinetic ballooning turbulence to determine the pedestal height and width, forming a cornerstone of modern pedestal theory and predictive modeling. While the acronym "EPED" has appeared in unrelated contexts in epidemic forecast evaluation frameworks, its central significance and technical depth reside in edge plasma physics.

1. The EPED Pedestal Model: Core Concepts

EPED operationalizes pedestal prediction by enforcing two simultaneous constraints on the edge plasma pressure profile $p(\psi)$: (A) global MHD stability enforced by peeling and ballooning mode thresholds, and (B) a constraint motivated by the onset of kinetic ballooning mode (KBM) microinstabilities. In the original EPED1 formulation, these are tied via the following:

• Pedestal height is characterized by the normalized poloidal beta at the pedestal top,

$$\beta_{p,ped} \equiv \frac{2\mu_0 p_{ped}}{(\mu_0 I_p/L)^2},$$

where $p_{ped}$ is pedestal top pressure, $I_p$ the plasma current, and $L$ the in-plane circumference.

• Pedestal width in normalized poloidal flux is parameterized,

$$\Delta_{\psi_N} \equiv \frac{\psi_N(r_{ped})-\psi_N(r_{sep})}{\psi_N(1)-\psi_N(0)} \approx c_1 \beta_{p,ped}^{c_2},$$

with $c_2 \approx 0.5$ empirically.

The key innovation is to find the self-consistent intersection in $(\Delta, \beta_{p,ped})$ space where both the KBM and peeling–ballooning (PB) mode limits are marginally satisfied (Tzanis et al., 15 Sep 2025).

2. Mathematical Formalism and Model Constraints

2.1 Local Constraint: KBM/IBM Limit

The local constraint invokes the critical normalized pressure gradient parameter,

$$\alpha \equiv -\frac{\mu_0}{2\pi^2}\frac{dV}{d\psi}\sqrt{\frac{V}{2\pi^2 R_0}\frac{dp}{d\psi}},$$

where $V$ is the plasma volume, $$\beta_{p,ped} \equiv \frac{2\mu_0 p_{ped}}{(\mu_0 I_p/L)^2},$$0 the major radius, and $$\beta_{p,ped} \equiv \frac{2\mu_0 p_{ped}}{(\mu_0 I_p/L)^2},$$1 the pressure gradient. In EPED1, the KBM threshold is proxied by the ideal ballooning mode (IBM) critical $$\beta_{p,ped} \equiv \frac{2\mu_0 p_{ped}}{(\mu_0 I_p/L)^2},$$2 ($$\beta_{p,ped} \equiv \frac{2\mu_0 p_{ped}}{(\mu_0 I_p/L)^2},$$3), generally computed via the BALOO code.

2.2 Global Constraint: Peeling-Ballooning (PB) Limit

Global ideal-MHD peeling–ballooning stability is computed via the ELITE code, which identifies the boundary in $$\beta_{p,ped} \equiv \frac{2\mu_0 p_{ped}}{(\mu_0 I_p/L)^2},$$4 space where finite-$$\beta_{p,ped} \equiv \frac{2\mu_0 p_{ped}}{(\mu_0 I_p/L)^2},$$5 (typically $$\beta_{p,ped} \equiv \frac{2\mu_0 p_{ped}}{(\mu_0 I_p/L)^2},$$6 3–20) PB modes become unstable.

2.3 Pedestal Prediction

For a given trial $$\beta_{p,ped} \equiv \frac{2\mu_0 p_{ped}}{(\mu_0 I_p/L)^2},$$7, the EPED algorithm:

• Constructs a candidate equilibrium.
• Computes the PB stability boundary $$\beta_{p,ped} \equiv \frac{2\mu_0 p_{ped}}{(\mu_0 I_p/L)^2},$$8.
• Computes the KBM constraint $$\beta_{p,ped} \equiv \frac{2\mu_0 p_{ped}}{(\mu_0 I_p/L)^2},$$9.
• The intersection yields the predicted pedestal ($p_{ped}$0): the largest height and corresponding width where both constraints are marginally satisfied.

3. Model Enhancements: GFS-KBM and Global High-$p_{ped}$1 Constraints

EPED has evolved through successive enhancements, critically including:

3.1 Gyro-Fluid System (GFS) for Local KBM Limit (EPED3)

The EPED3 variant integrates a reduced gyro-fluid system (GFS) to compute the KBM threshold directly. GFS retains electromagnetic, finite-Larmor-radius, and trapped particle physics via fluid moment equations. It solves for the critical $p_{ped}$2 by root-finding the dispersion relation,

$p_{ped}$3

tracking the most unstable electromagnetic root. Compared to the IBM/BALOO proxy, GFS yields a systematically lower $p_{ped}$4 (by 10–30% at low aspect ratio or strong shaping), producing a stricter local ballooning limit (Tzanis et al., 15 Sep 2025).

3.2 Global High-$p_{ped}$5 Ballooning Mode Constraint

When both local IBM and GFS-KBM suggest access to a 2nd-stable region, experimental observations reveal that pedestal width remains finite, implying global effects remain relevant. ELITE computes stability for high toroidal mode number, approximating $p_{ped}$6, which provides a boundary $p_{ped}$7 beyond which global ballooning modes become marginally unstable. This high-$p_{ped}$8 boundary often intersects the local KBM curve, restoring the empirical square-root scaling,

$p_{ped}$9

3.3 Intersection Logic

EPED2 (ELITE/ELITE) and EPED3 (GFS/ELITE) apply the same logic, seeking the $I_p$0 pair that maximizes

$I_p$1

4. Benchmarking, Empirical Performance, and Applications

Comparison on DIII-D and Alcator C-Mod databases demonstrates:

EPED Variant	$I_p$2 (fractional error, $I_p$3)	$I_p$4 (fractional error, width)
EPED1	0.14	0.21
EPED1.63	0.17	0.26
EPED2	0.12	0.20
EPED3	0.08	0.15

EPED3 reduces scatter in comparison to earlier models by a factor $I_p$5 (Tzanis et al., 15 Sep 2025). In Alcator C-Mod, EPED captures the bifurcation between "peeling" and "ballooning" limited branches. Increasing the separatrix-to-pedestal density ratio $I_p$6 shifts the critical $I_p$7 for PB transition, consistent with large-ELM H-mode operation (Miller et al., 17 Mar 2026).

In coupled density-pedestal modeling for contemporary and next-generation devices (e.g., SPARC), EPED-derived predictions for $I_p$8 and $I_p$9 are found consistent with empirical and first-principles neutral transport model outputs, particularly when additional resistive ballooning transport channels are included (Miller et al., 17 Mar 2026).

5. Significance, Robustness, and Ongoing Developments

Key strengths of the EPED framework:

• Ab initio pedestal prediction: No empirical fitting to local profile data is required; model is predictive given only global parameters and the input density.
• Unified treatment of global and microinstability physics: By combining PB stability and KBM (local or global), EPED avoids overestimation of pedestal width in the 2nd-stable regime.
• Device independence: Empirical coefficients show limited scatter (10–20%) across devices from spherical tokamaks to conventional aspect ratios.

Ongoing refinements include systematic benchmarking of the global high-$L$0 constraint via gyrokinetic simulations at lower aspect ratios and higher collisionalities, inclusion of additional micro-instability channels (e.g., micro-tearing, trapped-electron modes), and improved parametrization of critical $L$1 beyond single-exponent scaling.

6. Limitations and Future Directions

While EPED is broadly validated for large-ELM H-modes in machines such as DIII-D, NSTX, and Alcator C-Mod, several outstanding questions remain:

• Fidelity in strongly shaped or low-aspect-ratio regimes is not fully established; global mode constraints need benchmarking against nonlinear gyrokinetic computation (Tzanis et al., 15 Sep 2025).
• Additional transport channels such as resistive ballooning modes must be included for regimes (e.g., high-density EDA H-mode) where conventional PB/KBM limits are exceeded (Miller et al., 17 Mar 2026).
• Parameter sensitivity: Predictions are most sensitive to neutral boundary conditions and the critical $L$2 for KBM onset, less so to neoclassical transport coefficients.
• Role of other micro-instabilities: Quantification of micro-tearing and trapped electron mode effects on pedestal stiffness in specific conditions is needed for comprehensive closure.

A plausible implication is that future pedestal models will require dynamic integration of neutral transport, evolving kinetic stability analysis, and incorporation of higher-$L$3 and additional mode spectra to extend the predictive capacity established by EPED.

7. Broader Usage of "EPED" Acronym

While "EPED" most commonly designates the tokamak pedestal model, the same acronym has appeared in unrelated domains:

• Epidemic Forecast Evaluation: The "EPED Framework" for epidemic prediction (Epidemic-Features + Error-measures + rAnking + Forecast-Evaluation) modularizes prescriptive evaluation of epidemic models by collecting epidemiologically relevant time-series features, quantifying forecast errors with complementary metrics, and computing feature-wise and global consensus rankings (Tabataba et al., 2017).
• Epidemic Intelligence System Comparison: A distinct "EPED" evaluation framework compares Event-Based Surveillance (EBS) systems for epidemic intelligence, employing multi-granular event normalization, cross-document fusion, and spatial, temporal, thematic, and source-centered evaluation metrics (Arinik et al., 2023).

These unrelated frameworks share only the acronym and represent no technical or conceptual connection to the EPED pedestal modeling framework in plasma physics. In each context, the acronym expansion and usage are wholly distinct.