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Determination of confinement regime boundaries via separatrix parameters on Alcator C-Mod based on a model for interchange-drift-Alfv\'en turbulence

T0 review · 5 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper shows that a separatrix-based turbulence model, built from interchange-drift-Alfvén balances, predicts the L-H transition, the L-mode density limit, and the ideal MHD ballooning limit across a broad range of Alcator C-Mod…

desk verdict First cross-device SepOS validation on C-Mod shows clean L/H/I separation in dimensionless coordinates, but the dimensional boundary curves lean on a self-trained lambda_pe regression that needs a held-out check. read the letter →

arxiv 2412.13100 v1 pith:AKTL2E3K submitted 2024-12-17 physics.plasm-ph

M.A. Miller , J.W. Hughes , T. Eich , G.R. Tynan , P. Manz , T. Body , D. Silvagni , O. Grover
show 8 more authors
A.E. Hubbard A. Cavallaro M. Wigram A.Q. Kuang S. Mordijck B. LaBombard J. Dunsmore D. Whyte
This is my paper · ORCID
classification physics.plasm-ph PACS 52.55.Fa52.35.Ra
keywords separatrixoperationalspaceL-HtransitionL-modedensitylimitidealMHDballooninginterchange-drift-AlfvénturbulenceAlcatorC-ModI-modeSPARC
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to show that the separatrix operational space (SepOS) model, a set of turbulence-balance criteria evaluated at the plasma separatrix, organizes the operational boundaries of Alcator C-Mod the same way it organizes those of the device on which it was originally developed. Using edge Thomson scattering data spanning a wide range of density, toroidal field, and poloidal field, the authors identify the separatrix by a two-point power balance and compute the dimensionless quantities $\alpha_t$ (a collisionality-like turbulence control parameter), $k_{\mathrm{EM}}$ (the electromagnetic wavenumber), and $k_{\mathrm{RBM}}$ (the resistive-ballooning wavenumber). They report that the L-H transition, the L-mode density limit, and the ideal MHD ballooning limit all fall on the model's predicted curves, and that an empirical scaling $\lambda_{p_e} = (1 + C_\alpha \alpha_t^a) C_\rho \rho_{s,p}^r$ captures turbulence-driven widening of the pressure-gradient scale length. In the unfavorable drift direction the same boundaries hold with a reduced Reynolds-stress factor $\alpha_{\mathrm{RS}} < 1$, while I-modes cluster at $\alpha_t \lesssim 0.35$; the Type-I ELMy/EDA transition is better described by $k_{\mathrm{EM}} = k_{\mathrm{RBM}}$ than by a fixed $\alpha_t = 0.55$. The payoff is that dimensionless turbulence balances can be translated into the dimensional $(n_e, T_e)$ space a control room can act on, and projected to the SPARC primary reference discharge.

What carries the argument

The load-bearing object is the SepOS model, a set of identifications between turbulence quantities normalized by the DALF (interchange-drift-Alfvén) equations and evaluated at the separatrix. The L-H criterion is the energy balance of Equation 8, equating the stabilizing Reynolds-stress term $\alpha_{\mathrm{RS}} k_{\mathrm{EM}} \tau_i \Lambda_{p_i}/\bigl(1 + (\alpha_t/\alpha_c k_{\mathrm{EM}})^2\bigr)$ to the destabilizing turbulent energy input $\alpha_t/\alpha_c (k_{\mathrm{EM}}^2 + 1/2) + \tfrac12 k_{\mathrm{EM}}^2 \sqrt{\omega_B \tau_i \Lambda_{p_i}}$. The density limit and the ideal MHD ballooning limit are wavenumber equalities, $k_{\mathrm{EM}} = k_{\mathrm{RBM}}$ and $k_{\mathrm{ideal}} = k_{\mathrm{RBM}}$, where $k_{\mathrm{EM}} = \sqrt{\beta_e/\mu}$ and $k_{\mathrm{RBM}}$ is the resistive-ballooning wavenumber. The fourth ingredient is the empirical scaling $\lambda_{p_e} = (1 + C_\alpha \alpha_t^a) C_\rho \rho_{s,p}^r$, which converts these dimensionless balances into the dimensional $(n_e, T_e)$ space used for the projections. The parameter $\alpha_t$ controls electron adiabaticity and thus the balance between interchange and drift-wave driving, which is why the same parameter appears in the scale-length widening, the I-mode ceiling, and the ELMy/EDA separation.

What would settle it

Run a dedicated density ramp on a tokamak with directly measured divertor electron temperature: if the plasma disrupts at a separatrix density clearly off the predicted $k_{\mathrm{EM}} = k_{\mathrm{RBM}}$ curve, or if the measured divertor temperature makes the $T_{e,\mathrm{div}} \ll T_{e,\mathrm{sep}}$ assumption fail by more than a few eV, the SepOS boundary identification would be contradicted.

Watch

Extended reading notes

Core claim

The paper's central claim is that the separatrix operational space (SepOS) model predicts three confinement boundaries on Alcator C-Mod: the L-H transition, the L-mode density limit, and the ideal MHD ballooning limit. In the favorable drift direction the L-H transition is described by a balance between Reynolds-stress energy transfer into the shear flow and the total turbulent energy input; the L-mode density limit is identified with the wavenumber equality $k_{\mathrm{EM}} = k_{\mathrm{RBM}}$; and the ideal MHD ballooning limit is identified with $k_{\mathrm{ideal}} = k_{\mathrm{RBM}}$. In the unfavorable drift direction the same three boundaries apply once the Reynolds-stress term is reduced, $\alpha_{\mathrm{RS}} < 1$, and I-modes occupy the low-$\alpha_t$ side of the L-H curve. For the EDA/Type-I ELMy transition, the data support the wavenumber balance $k_{\mathrm{EM}} = k_{\mathrm{RBM}}$ as the better separator. The model is then used to project H-mode access, density-limit avoidance, and ELM-free operating space for the SPARC primary reference discharge.

Load-bearing premise

The entire analysis rests on locating the separatrix with a power-balance formula that assumes a standard collisional heat-conduction law and a fixed electron conduction fraction, with no direct measurement of the divertor temperature; if the inferred separatrix electron temperature is off by even a few electron-volts, the separatrix radius, density, scale lengths, and every boundary curve shift.

Editorial extensions

If this is right

  • If the SepOS boundaries hold, confinement regime access is set by turbulence balances at the separatrix, so a control room could use separatrix density and temperature, rather than core or pedestal quantities, to steer away from disruptive limits.
  • The positive exponents in the $\lambda_{p_e}$ regression imply that near-SOL pressure-gradient scale lengths widen as $\alpha_t$ rises and shrink with increasing $B_p$, a trend consistent with the multi-machine power-width scaling at low $\alpha_t$.
  • In the unfavorable drift direction, a reduced $\alpha_{\mathrm{RS}}$ raises the separatrix temperature required for H-mode and explains both the higher power threshold and the confinement of I-modes to $\alpha_t \lesssim 0.35$.
  • The crossing $k_{\mathrm{EM}} = k_{\mathrm{RBM}}$ provides a wavenumber-based criterion for the EDA/ELMy transition, tying the disappearance of Type-I ELMs to the equilibration of resistive-ballooning and electromagnetic turbulence scales.
  • Projected to the SPARC primary reference discharge, the model predicts a minimum separatrix density for H-mode near $1.5 \times 10^{20}\,\mathrm{m}^{-3}$ and outlines a region where EDA-like ELM-free operation avoids the Type-I ELMy regime.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural next step is to apply the same separatrix procedure to a third tokamak with different aspect ratio and shaping; if the dimensionless curves still separate L/H modes and disruptive density limits, the claim that turbulence physics dominates atomic physics at the separatrix would be substantially strengthened.
  • The apparent dependence of $\alpha_{\mathrm{RS}}$ on $\hat{q}_{\mathrm{cyl}}$ suggests plasma current could be used as a deliberate actuator to favor I-mode access in the unfavorable drift direction, a consequence the paper only notes qualitatively.
  • Because the SPARC density-limit projection depends on an untested value of $\lambda_{p_e}^{\mathrm{LDL}}$, the quickest way to reduce projection uncertainty would be a multi-machine scaling of $\lambda_{p_e}$ against $\alpha_t$ and $\rho_{s,p}$.
  • If the EDA/ELMy boundary is genuinely $k_{\mathrm{EM}} = k_{\mathrm{RBM}}$ rather than a fixed $\alpha_t$, then the transition density should vary with toroidal field and shaping in a way that targeted density scans could check.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 6 minor

Summary. The paper analyzes Alcator C-Mod edge Thomson scattering data to test the separatrix operational space (SepOS) model for three boundaries (L-H transition, L-mode density limit, ideal ballooning MHD limit) in both favorable and unfavorable grad-B drift directions. It constructs a regression for the electron pressure gradient scale length lambda_pe as a function of alpha_t and rho_s,p, uses it to render the SepOS boundaries in (n_e, T_e) space, extends the framework to I-mode access and the ELMy-EDA H-mode transition, and projects the resulting boundaries to the SPARC primary reference discharge. The central claim is that DALF-normalized separatrix parameters organize C-Mod data across a wide range of engineering parameters, supporting a turbulence-based description of operational boundaries.

Significance. This is the first validation of the SepOS model on a device other than ASDEX Upgrade, and it uses a large multi-year C-Mod database with careful edge Thomson scattering analysis and propagated uncertainties on separatrix quantities. If the observed separations are robust, the paper substantially strengthens the case that separatrix DALF parameters control L-H access, the density limit, and the MHD ballooning limit, and it provides useful guidance for SPARC. The dimensionless tests in Figure 4 are the strongest part of the paper because they use measured lambda_pe rather than the fitted regression. However, several load-bearing parameters are selected after the fact (alpha_RS, lambda_LDL_pe), and the dimensional boundary curves rely on a regression trained on the same dataset, so the predictive claims need qualification and additional robustness tests.

major comments (5)
  1. [Section 3.3, Eq. (4), Table 2; Figs. 3, 5, 11] The lambda_pe regression is fit to the same dataset and the same separatrix-identification procedure that is then used to construct the dimensional SepOS boundaries, so Figures 3, 5, and 11 are consistency checks rather than out-of-sample predictions; any systematic bias in T_e,sep or R_sep from Eq. (3) can be partially absorbed by C_alpha, a, C_rho, and r. The authors should add a held-out test (for example, training on one configuration or year and testing on another, or leave-one-shot-out cross-validation) or a perturbation analysis that shifts the fitted coefficients within their covariances and reports how many points change side of each boundary. The footnote in Section 6 already shows that the coefficients change substantially when Type-I ELMy H-modes are added, so this sensitivity is real and should be quantified in the main text.
  2. [Section 5, Figs. 5-6] The unfavorable-drift L-H validation depends on alpha_RS: the value 0.5 is selected because it best separates the C-Mod data in Figure 5, and the alpha_RS(q_cyl) curve in Figure 6 is a manually chosen exponential fit to the same data. Even though the proximity to the AUG value of 0.4 is encouraging, the selection is still post hoc. No quantitative separation metric, uncertainty estimate, or cross-validation is provided, so the claim that the model applies to the unfavorable drift direction is supported only by tuning a free parameter. Please report misclassification rates for fixed alpha_RS values in a plausible range (e.g., 0.4-0.6) and for the empirical alpha_RS(q_cyl) curve, and test on a subset of discharges not used to choose alpha_RS.
  3. [Section 4.2, Fig. 3 caption] The dimensional LDL curve in Figure 3 uses lambda_LDL_pe = 10 mm, described as the empirically observed value for the highest-density L-modes in this dataset; this is an after-the-fact choice, and the SPARC projection in Figure 11 uses the arbitrary values 2.5, 5, and 10 mm. The dimensionless LDL test in the center panel of Figure 4 is more convincing because it uses measured lambda_pe, but the dimensional claim that SepOS predicts the density limit is not supported by an independent parameter. Show how the LDL boundary and the classification of L-modes change over the plausible range of lambda_pe, or construct the curve from the measured lambda_pe of each discharge rather than from a fixed chosen value.
  4. [Section 3.1, Eq. (3)] All SepOS coordinates and lambda_pe values are determined by the two-point-model power balance, which assumes Spitzer-Harm parallel conduction, T_e,div^7/2 much less than T_e,up^7/2, uniform poloidal power flow, f_e,cond = 0.325, and eta_ICRF = 1. The paper propagates +/-20% PSOL uncertainty but does not propagate uncertainty in f_e,cond or the validity of the Spitzer-Harm assumption, which the authors note may fail at high power and low density. Add a sensitivity scan over f_e,cond (and, if possible, a kinetic-correction proxy) and demonstrate that the boundary classifications in Figures 4-6 and 8-9 are stable, or quantify which points change classification.
  5. [Section 6, Figs. 8-10] The claim that k_EM = k_RBM describes the ELMy-EDA transition is not uniquely supported: alpha_t = 0.55 and beta_e = 10^-4 separate the phases equally well in Figure 8, and the values alpha_t = 0.53 and beta_e = 9.9 x 10^-5 obtained by fitting beta_e(alpha_t) and lambda_pe(alpha_t) and solving Eq. (12) are essentially fits to the same transition data. Because k_EM and k_RBM share beta_e and lambda_pe through omega_B, the break in slope in Figure 9 is expected from the correlations in Figure 10. The authors should state that this is an exploratory consistency check rather than a validation, and provide error bars on the fitted transition parameters.
minor comments (6)
  1. [Throughout] The text contains several typos: 'enahnced Dalpha' in Section 3.2, 'ork on AUG' in Section 6, 'T ransition' in the Section 6 heading, and 'denisty' in Reference [33].
  2. [Throughout] Notation for the pressure scale length is inconsistent: lambda_p, lambda_pe, and lambda_p,e are used interchangeably; choose one symbol and define it once.
  3. [Eq. (8)] In Equation (8), alpha_c, tau_i, and Lambda_pi appear without definitions in the main text; define them when first introduced, even if they are defined in the cited references.
  4. [Figs. 4 and 6] The captions of Figure 4 and Figure 6 should state explicitly which equation each panel implements (Eqs. (8), (9), and (10) for Figure 4) and should give the functional form of the empirical alpha_RS(q_cyl) curve shown in Figure 6.
  5. [Section 6, footnote] The regression coefficients in the footnote marked with a dagger are important because they differ strongly from the main H-mode regression; move this discussion into the main text and quantify the comparison.
  6. [Fig. 11] Figure 11 would benefit from a table listing all linestyles and colors and the lambda_pe scaling used for each boundary, since the caption currently describes solid, dashed, and dash-dotted curves without a legend.

Circularity Check

2 steps flagged · score 5.0 of 10

Partial circularity: the ELMy-EDA transition values are obtained by fitting the same data they claim to explain, and the dimensional SepOS curves inherit the in-sample lambda_pe regression; the dimensionless Figure 4 tests are independent.

  1. fitted input called prediction [Section 6, Equation 12 and Figure 10]
    "Parameterizing the parameters plotted here by the curves of best fit with αt, i.e. βe = βe(αt) and λpe = λpe(αt), substituting into Equation 12, and solving numerically yields αt = 0.53, βe = 9.9 × 10−5, and λpe = 2.0 mm. This procedure yields transition values of αt and βe close to those manually identified in [15] and in this dataset."

    The transition values are not independent predictions: βe(αt) and λpe(αt) are nonlinear least-squares fits to the same EDA/ELMy discharge set whose classification is being explained. Substituting those empirical fits into Equation 12 and solving returns a crossing that is determined by the fitted data, so the 'close' agreement with the αt = 0.55 and βe = 10^-4 thresholds is in-sample by construction; those thresholds were also read off the same dataset. The k_EM = k_RBM criterion is therefore not tested out-of-sample in this section.

  2. fitted input called prediction [Section 3.3, Eq. 4; Figure 3 caption and Section 4]
    "For the H-modes in the large, favorable drift direction dataset ... a multi-variable non-linear least squares regression is performed for λpe, using both αt and ρs,p as the regression variables ... λp = (1 + Cααa_t )Cρρr_s,p ... The L-H and IBML curves use the scaling for λp from the first column in Table 2."

    The dimensional L-H and IBML curves in Figures 3 and 5 are constructed with the λpe(αt, ρs,p) regression fitted to H-modes from the same C-Mod database that is then plotted against those curves. Because λpe enters the boundary criteria through ω_B = λpe/Rgeo and k_ideal, any systematic error in the two-point-model separatrix identification that is absorbed into the regression coefficients shifts the curves and the plotted H-mode points coherently; the resulting separation is not an out-of-sample prediction. The dimensionless comparisons in Figure 4, which use measured λpe, are independent of this regression and provide the main non-circular support.

full rationale

The paper's strongest independent content is the dimensionless validation in Figure 4: the L-H, LDL, and IBML criteria are evaluated with measured separatrix n_e, T_e, and λ_pe, and the y=x separations are not constructed from any fit to the regime labels. That part is not circular. However, two parts of the paper reduce partially to their own inputs. First, the Section 6 inference that k_EM = k_RBM describes the ELMy/EDA transition is supported by fitting β_e(α_t) and λ_pe(α_t) to the same 50 ms phases that are labeled EDA or ELMy, then solving Equation 12; the resulting α_t = 0.53 and β_e = 9.9e-5 are in-sample intersections of empirical curves, so their agreement with the manually identified α_t = 0.55 and β_e = 1e-4 thresholds is not an independent confirmation. Second, the dimensional SepOS boundaries in Figures 3 and 5 are translated using the λ_pe(α_t, ρ_s,p) regression of Equation 4, which is fit to the same H-mode database shown against those curves; this makes the dimensional boundary plots semi-empirical rather than first-principles predictions. The manual choice of α_RS = 0.5 for the unfavorable-drift L-H correction is an openly fitted adjustment and is not claimed as a prediction, so I do not count it as a separate circular step. The self-citations to Eich and Manz and to the AUG papers are normal prior-work citations and are not load-bearing in a way that forbids alternatives. Overall, the dimensionless core is self-contained, but the dimensional projections and the ELMy-EDA transition claim contain in-sample fitted inputs, giving a partial circularity score of 5.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central dimensionless balances in Figure 4 use measured separatrix values and are not fits to the outcome labels, which is genuine independent evidence. Nonetheless, the dimensional boundaries in Figures 3 and 5, the unfavorable-drift L-H test, and the SPARC projections depend on fitted inputs: the lambda_pe regression, the chosen lambda_LDL_pe, and a data-adjusted alpha_RS. No new physical entities are introduced.

free parameters (4)
  • fe_cond and eta_ICRF = 0.325 and 1
    Fixed inputs to the two-point model power balance in Section 3.1. They set T_sep and therefore the separatrix position and all derived gradient scale lengths.
  • alpha_RS (Reynolds stress factor, unfavorable drift) = 0.5 for typical C-Mod M; empirical alpha_RS(q_cyl) curve in Fig. 6; AUG used 0.4
    Chosen after inspecting data to best separate the unfavorable-drift L- and H-modes. The same values are used for the SPARC L-H projections in Figure 11.
  • lambda_pe regression coefficients (C_alpha, a, C_rho, r) = C_alpha=1.1, a=0.82, C_rho=3.6e-3, r=0.18 for C-Mod lambda_p; dataset with ELMy H-modes gives {1.1, 2.6, 1.3e-2, 0.3}
    These come from a multi-variable nonlinear least squares fit of Eq. (4) to H-mode Thomson data. They are used to draw the L-H, IBML, and ELMy-EDA boundary curves and to extrapolate to SPARC.
  • lambda_LDL_pe = 10 mm for C-Mod LDL curves; 2.5, 5.0, and 10.0 mm for SPARC LDL curves
    No L-mode scaling is derived, so the LDL curve uses an empirically observed scale length from non-disruptive points near the boundary. The SPARC LDL projection is shown as a band over three assumed values.
assumptions (6)
  • domain assumption Two-point model separatrix identification: Spitzer-Harm parallel conduction, T_e,div^7/2 much less than T_e,up^7/2, uniform poloidal power flow, fe_cond = 0.325, eta_ICRF = 1.
    Used in Section 3.1, Eq. (3) to compute T_sep and locate the separatrix from Thomson profiles. Every SepOS coordinate in Figures 3-6 depends on this location. The paper flags kinetic corrections and divertor temperature as potential issues.
  • domain assumption The perpendicular turbulence length scale lambda_perp is identified with the electron pressure gradient scale length lambda_pe.
    Section 2.2 states lambda_perp has no closed-form parametrization and is replaced by lambda_pe, which then requires an empirical scaling. If this identification fails, the dimensional boundary curves shift.
  • domain assumption tau_i * Lambda_pi = 1, where tau_i = T_i/T_e and Lambda_pi = lambda_pi/lambda_pe.
    Set in Section 4.1 because no ion temperature or ion gradient measurements are available near the separatrix. This product enters the L-H criterion in Eq. (8).
  • domain assumption Z_eff = 1.4 for all low-impurity plasmas.
    Used in the definition of alpha_t in Section 1. A different Z_eff changes alpha_t and all alpha_t-based boundaries; the value is not measured here.
  • ad hoc to paper The Reynolds stress factor alpha_RS is 1 in favorable drift and below 1 in unfavorable drift, with 0.5 chosen for C-Mod and an empirical alpha_RS(q_cyl) fit.
    Section 5 selects alpha_RS = 0.5 to best separate L- and H-modes, and Fig. 6 contains a manually fitted alpha_RS(q_cyl). This is a fitted premise for the unfavorable-drift L-H prediction, not a derived quantity.
  • domain assumption The DALF equation set of Scott and the SepOS parameter definitions of Eich and Manz are accepted as the turbulence model.
    The paper derives all boundaries from balances of DALF-normalized wavenumbers and energy transfer rates but does not rederive the model. It cites references 10-12 and 18-19 for the background.

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Pith. "Pith review of Determination of confinement regime boundaries via separatrix parameters on Alcator C-Mod based on a model for interchange-drift-Alfv\'en turbulence." pith.science (2026). https://pith.science/paper/AKTL2E3K

@misc{pith2026241213100,
  author       = {Pith},
  title        = {Pith review of: Determination of confinement regime boundaries via separatrix parameters on Alcator C-Mod based on a model for interchange-drift-Alfv\'en turbulence},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AKTL2E3K}},
  note         = {Machine review of arXiv:2412.13100}
}
abstract

The separatrix operational space (SepOS) model [Eich \& Manz, \emph{Nuclear Fusion} (2021)] is shown to predict the L-H transition, the L-mode density limit, and the ideal MHD ballooning limit in terms of separatrix parameters for a wide range of Alcator C-Mod plasmas. The model is tested using Thomson scattering measurements across a wide range of operating conditions on C-Mod, spanning $\overline{n}_{e} = 0.3 - 5.5 \times 10^{20}$m$^{-3}$, $B_{t} = 2.5 - 8.0$ T, and $B_{p} = 0.1 - 1.2$ T. An empirical regression for the electron pressure gradient scale length, $\lambda_{p_{e}}$, against a turbulence control parameter, $\alpha_{t}$, and the poloidal fluid gyroradius, $\rho_{s,p}$, for H-modes is constructed and found to require positive exponents for both regression parameters, indicating turbulence widening of near-SOL widths at high $\alpha_{t}$ and an inverse scaling with $B_{p}$, consistent with results on AUG. The SepOS model is also tested in the unfavorable drift direction and found to apply well to all three boundaries, including the L-H transition as long as a correction to the Reynolds energy transfer term, $\alpha_\mathrm{RS} < 1$ is applied. I-modes typically exist in the unfavorable drift direction for values of $\alpha_{t} \lesssim 0.35$. Finally, an experiment studying the transition between the type-I ELMy and EDA H-mode is analyzed using the same framework. It is found that a recently identified boundary at $\alpha_{t} = 0.55$ excludes most EDA H-modes but that the balance of wavenumbers responsible for the L-mode density limit, namely $k_\mathrm{EM} = k_\mathrm{RBM}$, may better describe the transition on C-Mod. The ensemble of boundaries validated and explored is then applied to project regime access and limit avoidance for the SPARC primary reference discharge parameters.

Figures

Figures reproduced from arXiv: 2412.13100 by the authors.

Figure 1
Figure 1. Typical profiles measured by edge Thomson Scattering on C-Mod, for both an L-mode (left) and an H-mode (right). [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Scaling of λp normalized to its dependence on ρs,p against αt (left) and result of joint ρs,p and αt regression plotted against experimentally measured value (right). The coefficients used in this scaling are shown in the first column of table 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Separatrix operational space in terms of [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: The three primary boundaries in the SepOS model in dimensionless terms. Data are from the dataset introduced in [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Separatrix operational space in the unfavorable drift [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Ratio of Reynolds energy transfer rate to turbulent energy input rate plotted against [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 8
Figure 8. Figure 8: As an additional check on Equations 5 and 8 of the [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]
Figure 7
Figure 7. Figure 7: Measurements from outermost channel of the electron cyclotron emission (top) and the 15th chord of the phase contrast [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: The separatrix operational space for the experiment [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 10
Figure 10. Figure 10: Plasma beta (top) and electron pressure gradient scale [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: Projected boundaries for the separatrix operational space of SPARC based on PRD parameters, using the SepOS for both [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]

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    2024

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.