Pith. sign in

REVIEW 4 major objections 4 minor 53 references

A comparison of low-n Mercier unstable Wendelstein stellarators and quasi-interchange modes in tokamaks

T0 review · 4 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Mercier-unstable stellarators do not automatically settle into the benign flux-pumping state seen in tokamaks.

desk verdict A careful, honest JOREK study of Mercier-unstable stellarators that reproduces the tokamak-like dynamo but finds crash dynamics rather than sustained flux pumping; the W7-AS comparison is credible if you accept the acknowledged profile assumptions. read the letter →

arxiv 2505.03987 v3 pith:XN6JERWO submitted 2025-05-06 physics.plasm-ph

Rohan Ramasamy , Haowei Zhang , Joachim Geiger , Carolin Nührenberg , Håkan M. Smith , Karl Lackner , Valentin Igochine , the JOREK team This is my paper · ORCID
classification physics.plasm-ph PACS 52.30.-q52.35.Py52.55.Hc
keywords Merciercriterionstellaratorfluxpumpinginterchangeinstabilityquasi-interchangemodepartialreconnectionnonlinearMHDW7-AS
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

Mercier's criterion is usually treated as a hard stability limit in stellarator design, but experiments have sometimes operated past it. This paper tests whether the benign nonlinear state that tokamaks reach through flux pumping—where an MHD dynamo redistributes current and keeps the plasma stable—also appears in Mercier-unstable Wendelstein stellarators. In a low-$\iota$, high-mirror W7-X-like configuration, the unstable $(2,3)$ interchange initially produces a dynamo resembling tokamak flux pumping, but the mode does not saturate: overlapping instabilities cause partial reconnection and a core temperature crash within about a millisecond. In reconstructions of W7-AS discharges where a saturated $(1,2)$ mode was observed experimentally, the same simulation approach fails to produce a sustained coherent $(1,2)$ mode even with background flow shear, although the $(1,2)$ mode appears transiently and the plasma can be held at experimental heating power. The authors conclude that a benign flux-pumping state in a stellarator is not automatic; it may require a current source to counterbalance the dynamo and a mode spectrum with a single marginal instability.

What carries the argument

The central object is the MHD dynamo: the $(0,0)$ component of the $\boldsymbol{v}\times\mathbf{B}$ electric field induced by an unstable interchange mode, which in tokamak flux-pumping scenarios redistributes the current profile and keeps the safety factor near a rational value. The simulations are reduced viscoresistive MHD runs that include helical mode coupling and fluid compressibility, which the paper shows are necessary to capture the low-$n$ interchange, and they add a background $\mathbf{E}\times\mathbf{B}$ flow to test shear stabilisation of high-$n$ modes. A second load-bearing concept is partial reconnection: when several interchange instabilities overlap, current sheets break the nested flux surfaces locally, altering the local $\iota$ and ejecting core heat, which cuts off the dynamo before it can self-organise.

What would settle it

A concrete test would be a nonlinear simulation of the W7-X-like configuration with parameters moved close to marginal stability and with a small current-drive source added: if the dynamo then persists over a resistive timescale and the core temperature does not crash, the paper's proposed route to stellarator flux pumping is supported, whereas a persisting crash would falsify the claim that missing current sources and marginality explain the absence of a benign state.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is that Mercier-unstable Wendelstein configurations do not automatically enter the quasi-stationary, dynamo-sustained state seen in flux-pumping tokamaks. Mercier's criterion—the local stability condition for pressure-driven interchange modes in a toroidal plasma—is violated across most of the W7-X-like volume, and the linearly dominant $(2,3)$ interchange creates an $m=0$, $n=0$ dynamo electric field with the same character as the $(1,1)$ quasi-interchange in tokamaks. But the dynamo is not sustained on the resistive timescale: after about $1.15$ ms, current-sheet formation and reconnection partially reconnect the core, the local $\iota$ is modified toward the $2/3$ rational value, and the core temperature crashes despite heating comparable to experimental power. In the W7-AS case, at the experimental Spitzer resistivity and with an equilibrium $\mathbf{E}\times\mathbf{B}$ flow added to suppress high-$n$ modes, the simulations show multiple competing modes and a dominant $(5,10)$ structure rather than the sustained $(1,2)$ mode seen experimentally; a coherent $(1,2)$ mode appears only transiently, depending on initialization, and the stored thermal energy can be maintained when flows are included. The paper argues that the missing ingredients are a current source or current-control mechanism, which in tokamaks counterbalances the dynamo, and operation near marginal stability so that only a single coupled instability is present.

Load-bearing premise

The paper's central negative result for W7-AS rests on an equilibrium reconstruction that assumes a linear pressure profile $p(s)=p_0(1-s)$ and a hand-adjusted radial electric field; if the true profiles are more peaked, the $(1,2)$ mode might saturate as in the experiment and the proposed explanation for the missing flux-pumping state would not apply.

Editorial extensions

If this is right

  • Removing the Mercier constraint in stellarator design does not by itself guarantee a benign saturated state; in the W7-X-like simulation the core temperature drops abruptly on a roughly millisecond timescale.
  • A stellarator flux-pumping state is likely to require an external or internal current source to counterbalance the dynamo, since the net toroidal current in a quasi-isodynamic device is negligibly small.
  • Equilibrium $\mathbf{E}\times\mathbf{B}$ flow shear suppresses high-$n$ modes and can allow the plasma to be maintained at experimentally relevant heating power, but it does not automatically recover the experimental $(1,2)$ mode structure.
  • The sustained $(1,2)$ mode observed in W7-AS was not reproduced; the mode is transient and the outcome depends on initialization and on whether the background profiles are maintained.
  • Partial reconnection from overlapping interchange instabilities is a plausible core-crash mechanism for Mercier-unstable stellarators, analogous to the multiple-interchange sawtooth model in tokamaks.

Reading between the lines

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

  • Editorial inference: if a current source is the missing ingredient, then quasi-axisymmetric stellarators, with their substantial bootstrap current, are more natural candidates for a stellarator flux-pumping regime than quasi-isodynamic ones; the paper notes this connection but does not test it.
  • Editorial inference: scanning the W7-AS reconstruction toward more peaked pressure profiles or adding a co-injected current source is the most direct test of whether a sustained $(1,2)$ mode emerges; the paper itself notes that peaked profiles strengthen the low-$n$ signature.
  • Editorial inference: the paper's dichotomy implies that a Mercier-unstable stellarator with many overlapping unstable helicities will tend to crash, while a configuration with a single marginally unstable coupled mode should saturate; this could be checked by a linear scan over rotational-transform and pressure profiles.
  • Editorial inference: if no current source is available, the tokamak flux-pumping picture transfers to stellarators only in modified form, with Pfirsch-Schlüter or bootstrap currents playing the counterbalancing role; whether those currents suffice remains open.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper studies nonlinear evolution of low-n Mercier-unstable stellarator configurations using the JOREK code, with the aim of determining whether benign nonlinear saturation and flux-pumping-like states can arise in stellarators as they do for quasi-interchange modes in tokamaks. Two cases are considered: a low-iota, high-mirror W7-X-like configuration, where a (2,3) interchange mode is found to produce a mean dynamo term but then undergo partial reconnection and a core temperature crash; and a W7-AS intermediate-beta equilibrium reconstructed from experiment, where low-n MHD activity is reproduced only transiently and a sustained (1,2) mode as seen in the experiment is not obtained. The authors argue that the missing ingredients for flux pumping in stellarators are a current source and a single marginal instability, and they discuss several modelling uncertainties, most prominently the assumed linear pressure profile in the W7-AS equilibrium.

Significance. If the results are robust, the paper makes a valuable contribution by showing that Mercier-unstable stellarators do not automatically settle into benign flux-pumping-like states, and by identifying concrete missing ingredients (current source, marginality) for such states. The study is among the first to compare stellarator interchange dynamics with tokamak flux pumping using a common nonlinear MHD framework with experimentally motivated parameters. Strengths include the explicit comparison of the linear (2,3) mode structure between JOREK and CASTOR3D, the use of experimental Spitzer resistivity and heating powers for W7-AS, and the candid, well-documented discussion of modelling limitations. The central negative result for W7-AS, however, rests on an equilibrium reconstruction with an acknowledged uncertain pressure profile and a hand-modified radial electric field, so the significance hinges on the sensitivity of the conclusions to these inputs.

major comments (4)
  1. [Section 3.1 and Appendix C] The W7-AS equilibrium is constructed with the assumed pressure profile p(s)=p0(1-s), which the authors themselves state in Section 4 is 'likely incorrect given observations of peaked profiles in experimental diagnostics of similar discharges'. Since the central claim that no sustained (1,2) mode appears in simulations is based on this equilibrium, and since Section 3.2 reports that more peaked pressure profiles make low-n MHD signatures more prominent, the possibility that the experimental profile is peaked directly undermines the paper's main experimental counterexample. The authors should quantify this risk, for example by performing linear stability scans with CASTOR3D (as they themselves suggest is appropriate) or by running a nonlinear case with a more peaked initial profile, before concluding that the (1,2) mode cannot saturate.
  2. [Section 3.1, Figure 7] The radial electric field used in the W7-AS simulations is modified by hand from the neoclassical calculation to enforce subsonic poloidal flow and zero boundary electric field, an inconsistency the authors acknowledge. This input directly controls which mode families are stabilised: the paper reports that without the modified E×B flow the high-n branch dominates, and with it the (5,10) mode dominates. Because the result is so sensitive to this profile, the paper should demonstrate how the nonlinear outcome changes under plausible variations of the Er profile (e.g., amplitude, radial transition location, boundary value). Without such a sensitivity scan, the claim that E×B flow shear is a necessary ingredient for matching the experiment remains unsupported.
  3. [Section 2.1 and 2.2] The W7-X-like case is initialised by freezing the Nf=0 and Nf=1 mode families for t<0.85 ms so that the low-n (2,3) mode can lead the dynamics. This is an artificial intervention that prevents the high-n branch from naturally competing during the linear phase, and the later observation of partial reconnection and crash may depend on this scheduling. The paper states that this is done to investigate the case where low-n modes lead, but it should be made explicit that the conclusion 'the MHD dynamo cannot be followed over a resistive timescale' (Section 4) applies only to this specific initialization protocol. A test relaxing the freeze time, or a demonstration that the crash is robust to the freeze interval, is needed to support the more general statement.
  4. [Section 3.2, Figure 9] The nonlinear dynamics in the W7-AS case are highly sensitive to the mode-family initialization schedule: with Nf=0 evolved longer the (5,10) mode dominates and causes a crash, while allowing Nf=1 to grow early leads to a dominant (1,2) structure at t=3 ms (bottom-right panel of Figure 9). Given this, the statement in Section 4 that 'a coherent sustained (1,2) mode like the one observed in the experiment has not been found in any of the simulations' is not fully transparent. The authors should clarify whether the t=3 ms (1,2) structure persists or subsequently breaks up, and should provide the time trace beyond 3 ms. If the mode is only transient, that should be stated explicitly with evidence; if it persists, the central claim needs revision.
minor comments (4)
  1. [Acknowledgements] The declaration reads 'The authors report not conflict of interest' and should be 'no conflict of interest'.
  2. [Section 1] The notation s = sqrt(psi_t) is introduced in the text but the definition of psi_t itself is not given; a one-line definition of the normalised toroidal flux would help readers.
  3. [Appendix B, Equation B5] The parallel momentum equation contains a time-derivative term involving partial B^2/partial t that is not discussed; a brief comment on why this term is retained in the reduced MHD ordering would improve readability.
  4. [Figure 3] The colour scale for the iota value in the Poincare plots is not defined in the caption; adding a colourbar or describing the range of colours would make the claimed local iota modification visible to the reader.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; central simulation results are externally benchmarked, and acknowledged profile assumptions are modeling limitations rather than circular inputs.

full rationale

The paper is a nonlinear MHD simulation study. Its two central results — the dynamo followed by partial reconnection in the W7-X-like case, and the absence of a sustained (1,2) mode in the W7-AS simulations — are outputs of JOREK runs whose inputs are the VMEC/GVEC equilibrium, Spitzer resistivity, DKES/Neotransp neoclassical radial electric field, and experimental heating and diffusive parameters. These inputs are not fitted to the simulated outputs, so no fitted parameter is renamed as a prediction. The W7-X-like run intentionally isolates the Nf=2 mode family so that low-n dynamics can lead; this conditioning is explicitly disclosed and makes the conclusions scenario-specific rather than tautological. The W7-AS comparison rests on an assumed linear pressure profile and a hand-modified Er profile; the authors explicitly acknowledge this, writing that the linear pressure assumption 'is likely incorrect' and that the Er modification 'introduces an inconsistency' between the neoclassical prediction and the enforced field. These are external reconstruction uncertainties, not circular reductions. Citations to prior work by the same group (Ramasamy et al. 2024, Zhang et al. 2025, Nührenberg 1996) provide a target equilibrium, motivation, and an AUG flux-pumping benchmark, but the present claims are independently checked against CASTOR3D linear stability calculations and against W7-AS experimental observations. No uniqueness theorem is invoked to forbid alternatives, no ansatz is smuggled in solely via self-citation, and no derivation step reduces to its own input by definition. The paper is self-contained against external benchmarks and discloses its modeling limitations, so the appropriate finding is no significant circularity.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The central claims rest on the JOREK reduced MHD model, reconstructed equilibria, and several hand-tuned transport and flow profiles; these are inputs chosen to approximate the experiment or improve numerical stability, not outputs of the underlying theory.

free parameters (8)
  • Perpendicular viscosity mu_perp = 1.55e-7 kg m-1 s-1 (W7-X-like), 6.46e-9 (W7-AS)
    Chosen high to improve numerical stability; affects saturation amplitude, current-sheet formation, and crash dynamics.
  • Numerical dissipation eta_num and mu_num = 1.93e-14 Ohm m3 and 1.55e-13 kg m s-1 (W7-X-like); 3.49e-13 and 6.46e-15 (W7-AS)
    Numerical hyper-resistivity and hyper-viscosity introduced for stability; can affect reconnection onset and mode competition.
  • Anomalous heat and particle diffusivities (kappa_perp, D_perp) = kappa_perp=0.231 m2/s, D_perp=0.154 m2/s (W7-X-like); kappa_perp=0.924, D_perp=0.231 (W7-AS)
    Increased in W7-AS to approximate experimental transport; directly determines whether stored energy can be sustained.
  • Core-localized heat source profile = Sum of two Gaussians with variances 0.125 and 0.33; power up to 3.2 MW (W7-AS) or 20 MW (W7-X-like)
    Chosen to mimic NBI deposition; affects pressure peaking and mode drive.
  • Modified E×B flow profile = Not specified as formula; Er adjusted to keep flow subsonic and zero at boundary
    Neoclassical Er from DKES/Neotransp is modified by hand; the resulting shear stabilizes high-n modes and changes the dominant mode from (1,2) to (5,10).
  • Mode-family initialization schedule = Nf=2 evolved alone until t=0.85 ms (W7-X-like); Nf=1 grown early in some W7-AS runs
    Freezing Nf=0/1 lets the low-n mode lead; the observed low-n-led dynamics are partly imposed by this choice.
  • Toroidal harmonic truncation ntor = 30 in most runs, 50 in one check
    Limited by computational cost; higher harmonics can change nonlinear dynamics, acknowledged in the text.
  • Initial pressure profile p(s)=p0(1-s) = Linear profile for both cases; W7-AS p0 corresponds to 8 kPa core pressure
    Assumed in equilibrium reconstructions; authors state it is likely incorrect and affects low-n mode visibility.
assumptions (6)
  • domain assumption Single-fluid viscoresistive reduced MHD as implemented in JOREK captures the nonlinear evolution of low-n interchange modes in stellarators.
    All simulations use this model; kinetic effects such as finite Larmor radius are absent, which may suppress high-n modes in experiments.
  • domain assumption The reconstructed VMEC/GVEC equilibria, including the W7-AS linear pressure profile and 8 kPa core pressure, approximate the experimental discharges.
    Section 3.1; authors acknowledge the linear pressure profile is likely incorrect.
  • ad hoc to paper The modified subsonic E×B flow profile, rather than the raw neoclassical Er, is representative of the experimental background flow.
    Section 3.1, Fig. 7; the modification is justified by sonic-shock avoidance and boundary conditions, but it is an inconsistency with the neoclassical calculation.
  • domain assumption The vacuum magnetic field direction approximates the total magnetic field when projecting the dynamo electric field.
    Section 2.2: 'The vacuum magnetic field direction is used for this projection... assumed to be a suitable approximation.'
  • domain assumption Classical Spitzer resistivity with Zeff=1 is appropriate for the W7-AS plasma.
    Section 3.1; justified by high collisionality and low impurity content.
  • standard math The linear MHD stability results from CASTOR3D and JOREK agree and identify the relevant ideal interchange mode.
    Section 2.1; agreement is shown for the (2,3) mode structure.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A comparison of low-n Mercier unstable Wendelstein stellarators and quasi-interchange modes in tokamaks." pith.science (2026). https://pith.science/paper/XN6JERWO

@misc{pith2026250503987,
  author       = {Pith},
  title        = {Pith review of: A comparison of low-n Mercier unstable Wendelstein stellarators and quasi-interchange modes in tokamaks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XN6JERWO}},
  note         = {Machine review of arXiv:2505.03987}
}
abstract

Mercier's criterion is typically enforced as a hard operational limit in stellarator design. At the same time, past experimental and numerical studies have shown that this limit may often be surpassed, though the exact mechanism behind this nonlinear stability is not well understood. This work aims to contribute to our current understanding by comparing the nonlinear evolution of Mercier unstable Wendelstein stellarators to that of nonlinearly stable quasi-interchange modes in tokamaks. A high mirror, very low $\iota$, W7-X-like configuration is first simulated. A second case is then considered using experimental reconstructions of intermediate $\beta$ W7-AS discharges, where saturated low-n modes were observed experimentally, with sustained MHD signatures over tens of milliseconds. The possible reasons for the discrepancies between experiment and simulation, and the observation of partial reconnection in contrast to flux pumping are discussed, in view of reproducing and designing for operation of stellarators beyond the Mercier stability limit.

Figures

Figures reproduced from arXiv: 2505.03987 by the authors.

Figure 1
Figure 1. Equilibrium flux surfaces (a) and ι profile (b) of an ASDEX upgrade discharge characteristic of flux pumping, reconstructed using VMEC. The contributions to Mercier’s criterion (c) computed in VMEC imply that the plasma is Mercier unstable in the core of the device. (DMerc < 0). The VMEC computation was carried out with 1001 radial points. using the JOREK code (Huysmans et al. 2009; Hoelzl et al. 2021). The paper is… view at source ↗
Figure 2
Figure 2. Equilibrium and linear stability properties of a very low ι, high mirror W7-X-like configuration. The ι profile (a) shows a 2/3 resonance is close to the ι value on the magnetic axis. The equilibrium is linearly MHD unstable to a (2, 3) interchange mode in both JOREK and CASTOR3D (b). Mercier’s criterion shows that the configuration is interchange unstable over most of the plasma volume (c). The velocity vector plot… view at source ↗
Figure 3
Figure 3. Evolution of magnetic (a) and kinetic (b) energies during the initial nonlinear phase of a (2, 3) interchange mode in a W7-X-like configuration. The initial dynamics of the dominant (2, 3) perturbation is ideal (c-d), as illustrated by the nested compression of flux surfaces. Only in the late nonlinear phase (e-g), the local ι value changes due to reconnection of local current sheets. The pressure profile deformatio… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Radial profile of the (0, 0) component of the electric field (a) induced along ∇χ, the vacuum magnetic field as described in Appendix B, due to the dynamo voltage. This profile is plotted over time (b) to show that the dynamo is not sustained on the resistive timescale…
Figure 5
Figure 5. Figure 5: Time trace of the core temperature for simulations at different heating power show a crash of the temperature profile. must therefore remain a subdominant process if the mode is to be sustained over resistive time scales. This is more likely to occur for modes closer t…
Figure 6
Figure 6. Figure 6: W7-AS experimental equilibrium reconstruction with 8 kP a core pressure. The ι profile (a) shows the presence of a low order 1/2 resonance. Flux surfaces in the ϕ = 0.0, π 10 and π 5 planes (b) show the basic magnetic topology of the five field period stellarator. The …
Figure 7
Figure 7. Figure 7: Computed and modified radial electric field (a) from neoclassical transport calculations. Comparing the approximate timescales of poloidal and parallel flow dynamics (b), the computed radial electric field implies the formation of shocks in the plasma periphery. The mo…
Figure 8
Figure 8. Figure 8: Early in the simulation, before the Nf > 0 modes are initialised, the high n modes belonging to the Nf = 0 mode family grow more slowly than in the case without flows, where the nonlinear saturation and stochastisation of the outer plasma is rapid, occurring within the…
Figure 8
Figure 8. Figure 8: Magnetic (a, d) and kinetic (b, e) energies of W7-AS cases without flows using a gaussian heating profile (top row) and artificially maintaining the initial equilibrium profiles (bottom row). The pressure is shown in the ϕ = 0 and ϕ = π poloidal planes (c) and (f) at t…
Figure 9
Figure 9. Figure 9: It can be seen that the Nf = 0 and 2 mode families are allowed to evolve while the Nf = 1 mode family is still subdominant. The subsequent evolution of the Nf = 1 mode family shows that the n = 4 mode saturates first at a subdominant value, before the n = 1 mode overta…
Figure 9
Figure 9. Figure 9: Magnetic (a, d) and kinetic (b, e) energies of W7-AS case with the background flow profile shown in [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: Integrated thermal energy over the plasma volume (a) and applied heating power (b) in cases with (dashed) and without (solid) flows. Without flows, the degradation in confinement is too significant to sustain the plasma at the experimental heat source. With flows, the…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

53 extracted references · 51 canonical work pages

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address author booktitle chapter edition editor howpublished institution journal key month note number organization pages publisher school series title type volume year eprint label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 'mid.sentence ...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

  3. [3]

    Plasma Physics and Controlled Fusion 40 (6), 967

    Baldzuhn, J , Kick, M , Maassberg, H & the W7-AS Team 1998 Measurement and calculation of the radial electric field in the stellarator W7-AS . Plasma Physics and Controlled Fusion 40 (6), 967

    work page 1998

  4. [4]

    Physics of Plasmas 7 (6), 2439--2448

    Betti, R & Freidberg, JP 2000 Radial discontinuities in tokamak magnetohydrodynamic equilibria with poloidal flow . Physics of Plasmas 7 (6), 2439--2448

    work page 2000

  5. [5]

    Nuclear Fusion 64 (12), 124005

    Boyes, W , Turco, F , Hanson, J , Navratil, GA , Turnbull, A , Hyatt, A , Luce, T , Meyer, W , Nelson, AO , Odstrcil, T & others 2024 Novel intrinsic helical cores and MHD dynamo flux pumping evidence in DIII-D . Nuclear Fusion 64 (12), 124005

    work page 2024

  6. [6]

    Physical review letters 122 (15), 155003

    Brunetti, D , Graves, JP , Lazzaro, E , Mariani, A , Nowak, S , Cooper, Wilfred Anthony & Wahlberg, Christer 2019 Excitation mechanism of low-n edge harmonic oscillations in edge localized mode-free, high performance, tokamak plasmas . Physical review letters 122 (15), 155003

    work page 2019

  7. [7]

    u tterich, T , Stober, J , G \

    Burckhart, A , Bock, A , Fischer, R , P \"u tterich, T , Stober, J , G \"u nter, S , Gude, A , Hobirk, J , H \"o lzl, M , Igochine, V & others 2023 Experimental evidence of magnetic flux pumping in ASDEX upgrade . Nuclear Fusion 63 (12), 126056

    work page 2023

  8. [8]

    Plasma Physics and Controlled Fusion 64 (5), 054011

    Cathey, A , Hoelzl, M , Harrer, Georg , Dunne, MG , Huijsmans, GTA , Lackner, K , Pamela, SJP , Wolfrum, Elisabeth , G \"u nter, S , team, JOREK & others 2022 MHD simulations of small ELMs at low triangularity in ASDEX Upgrade . Plasma Physics and Controlled Fusion 64 (5), 054011

    work page 2022

Show all 53 references
  1. [9]

    Nuclear Fusion 56 (7), 076011

    Chen, Xi , Burrell, Keith H , Ferraro, Nathaniel M , Osborne, Thomas H , Austin, Max E , Garofalo, Andrea M , Groebner, Richard J , Kramer, Gerrit J , Luhmann, NC , McKee, George R & others 2016 Rotational shear effects on edge harmonic oscillations in DIII-D quiescent H-mode ...

    2016

  2. [10]

    Nuclear Fusion 55 (11), 113014

    De Aguilera, Adriana M , Castej \'o n, Francisco , Ascas \' bar, Enrique , Blanco, Emilio , De la Cal, Eduardo , Hidalgo, Carlos , Liu, Bing , L \'o pez-Fraguas, Antonio , Medina, Francisco , Ochando, Mar \' a Antonia & others 2015 Magnetic well scan and confinement in the TJ-...

    2015

  3. [11]

    Physics of Plasmas 27 (2), 022502

    Feng, Zhichen , Gates, David A , Lazerson, Samuel A , Landreman, Matt , Pomphrey, Neil & Fu, GuoYong 2020 Optimization of quasi-axisymmetric stellarators with varied elongation . Physics of Plasmas 27 (2), 022502

    2020

  4. [12]

    In 30th European Physical Society Conference on Plasma Physics and Controlled Fusion\/

    Geiger, J , Marushchenko, NB , Maassberg, H , Dinklage, A , Werner, A , Team, W7-AS & others 2003 Analysis of high- equilibria with toroidal net-current densities for W7-AS . In 30th European Physical Society Conference on Plasma Physics and Controlled Fusion\/ . European Phys...

    2003

  5. [13]

    PRX Energy 3 (2), 023010

    Goodman, Alan G , Xanthopoulos, Pavlos , Plunk, Gabriel G , Smith, H kan , N \"u hrenberg, Carolin , Beidler, Craig D , Henneberg, Sophia A , Roberg-Clark, Gareth , Drevlak, Michael & Helander, Per 2024 Quasi-isodynamic stellarators with low turbulence as fusion reactor candid...

    2024

  6. [14]

    In 25th International Conference on Numerical Simulation of Plasmas (ICNSP 2017)\/

    Hindenlang, Florian , Hoelzl, Matthias & Sonnendr \"u cker, Eric 2017 A Parallel 3D DG Framework for Resistive MHD Simulations in Tokamak and Stellarator Geometries . In 25th International Conference on Numerical Simulation of Plasmas (ICNSP 2017)\/

    2017

  7. [15]

    , van Rij, W

    Hirshman, Steven P. , van Rij, W. I. & Merkel, P. 1986 Three-dimensional free boundary calculations using a spectral G reens's function method . Comput. Phys. Commun. 43 (1), 143

    1986

  8. [16]

    Nuclear Fusion 61 (6), 065001

    Hoelzl, Matthias , Huijsmans, GTA , Pamela, SJP , Becoulet, Marina , Nardon, Eric , Artola, Francisco Javier , Nkonga, Boniface , Atanasiu, CV , Bandaru, Vinodh , Bhole, Ashish & others 2021 The JOREK non-linear extended MHD code and applications to large-scale instabilities a...

    2021

  9. [17]

    Plasma Physics and Controlled Fusion 51 (12), 124012

    Huysmans, GTA , Pamela, Stanislas , Van Der Plas, Emiel & Ramet, Pierre 2009 Non-linear MHD simulations of edge localized modes (ELMs) . Plasma Physics and Controlled Fusion 51 (12), 124012

    2009

  10. [18]

    Plasma physics and controlled fusion 37 (11), 1287

    Itoh, K , Itoh, S-I & Fukuyama, A 1995 A sawtooth model based on the transport catastrophe . Plasma physics and controlled fusion 37 (11), 1287

    1995

  11. [19]

    Physics of Plasmas 27 (3)

    Jardin, Stephen C , Krebs, I & Ferraro, N 2020 A new explanation of the sawtooth phenomena in tokamaks . Physics of Plasmas 27 (3)

    2020

  12. [20]

    Physics of Plasmas 24 (10)

    Krebs, I , Jardin, SC , G \"u nter, S , Lackner, K , Hoelzl, M , Strumberger, E & Ferraro, N 2017 Magnetic flux pumping in 3D nonlinear magnetohydrodynamic simulations . Physics of Plasmas 24 (10)

    2017

  13. [21]

    Journal of Plasma Physics 88 (6), 905880616

    Landreman, Matt 2022 Mapping the space of quasisymmetric stellarators using optimized near-axis expansion . Journal of Plasma Physics 88 (6), 905880616

    2022

  14. [22]

    Physics of Plasmas 31 (3)

    Liu, Dingyun , Fox, William , Bose, Sayak , Ji, Hantao , Jardin, Stephen & Ferraro, Nathaniel 2024 On discriminating tokamak sawtooth crash models via localized density and temperature measurements . Physics of Plasmas 31 (3)

    2024

  15. [23]

    arXiv preprint arXiv:2402.00458

    McGibbon, Bridget 2024 Simulations of poloidal flow stabilization of ballooning modes in a classical l= 2 stellarator using JOREK . arXiv preprint arXiv:2402.00458

    2024 arXiv

  16. [24]

    Nuclear Fusion 4 (3), 213

    Mercier, Claude 1964 Equilibrium and stability of a toroidal magnetohydrodynamic system in the neighbourhood of a magnetic axis . Nuclear Fusion 4 (3), 213

    1964

  17. [25]

    o nies, Axel , N \

    Mishchenko, Alexey , Borchardt, Matthias , Hatzky, Roman , Kleiber, Ralf , K \"o nies, Axel , N \"u hrenberg, Carolin , Xanthopoulos, Pavlos , Roberg-Clark, Gareth & Plunk, Gabriel G 2023 Global gyrokinetic simulations of electromagnetic turbulence in stellarator plasmas . Jou...

    2023

  18. [26]

    PhD thesis, Technische Universit\"at M\"unchen

    Nikulsin, Nikita 2021 Models and methods for nonlinear magnetohydrodynamic simulations of stellarators . PhD thesis, Technische Universit\"at M\"unchen

    2021

  19. [27]

    Physics of Plasmas 3 (6), 2401--2410

    N \"u hrenberg, Carolin 1996 Global ideal magnetohydrodynamic stability analysis for the configurational space of Wendelstein 7-X . Physics of Plasmas 3 (6), 2401--2410

    1996

  20. [28]

    Contributions to Plasma Physics 50 (6-7), 552--557

    Ohdachi, S , Sakamoto, R , Miyazawa, J , Morisaki, T , Masuzaki, S , Yamada, H , Watanabe, KY , Jacobo, VR , Nakajima, N , Watanabe, F & others 2010 Density collapse events observed in the large helical device . Contributions to Plasma Physics 50 (6-7), 552--557

    2010

  21. [29]

    Nuclear Fusion 57 (6), 066042

    Ohdachi, S , Watanabe, KY , Tanaka, K , Suzuki, Y , Takemura, Y , Sakakibara, S , Du, XD , Bando, T , Narushima, Y , Sakamoto, R & others 2017 Observation of the ballooning mode that limits the operation space of the high-density super-dense-core plasma in the LHD . Nuclear Fu...

    2017

  22. [30]

    Physical review letters 102 (4), 045005

    Petty, CC , Austin, ME , Holcomb, CT , Jayakumar, RJ , La Haye, RJ , Luce, TC , Makowski, MA , Politzer, PA & Wade, MR 2009 Magnetic-flux pumping in high-performance, stationary plasmas with tearing modes . Physical review letters 102 (4), 045005

    2009

  23. [31]

    Nuclear Fusion 57 (7), 076014

    Piovesan, P , Bonfiglio, Daniele , Cianciosa, M , Luce, TC , Taylor, NZ , Terranova, D , Turco, F , Wilcox, RS , Wingen, A , Cappello, S & others 2017 Role of a continuous MHD dynamo in the formation of 3D equilibria in fusion plasmas . Nuclear Fusion 57 (7), 076014

    2017

  24. [32]

    , Aleynikova, K

    Ramasamy, R. , Aleynikova, K. , Nikulsin, N. , Hindenlang, F. , Holod, I. , Strumberger, E. , Hoelzl, M. & the JOREK team 2024 Nonlinear MHD modeling of soft limits in W7-AS . Nuclear Fusion 64 (8), 086030

    2024

  25. [33]

    Journal of Plasma Physics 90 (3), 175900301

    Roberg-Clark, GT , Xanthopoulos, P & Plunk, GG 2024 Reduction of electrostatic turbulence in a quasi-helically symmetric stellarator via critical gradient optimization . Journal of Plasma Physics 90 (3), 175900301

    2024

  26. [34]

    Fusion Science and Technology 58 (1), 176--185

    Sakakibara, S , Watanabe, KY , Ohdachi, S , Narushima, Y , Toi, K , Tanaka, K , Narihara, K , Ida, K , Tokuzawa, T , Kawahata, K & others 2010 Study of MHD Stability in LHD . Fusion Science and Technology 58 (1), 176--185

    2010

  27. [35]

    Plasma physics and controlled fusion 44 (5A), A217

    Sakakibara, S , Yamada, H , Watanabe, KY , Narushima, Y , Toi, K , Ohdachi, S , Yamamoto, S , Narihara, K , Tanaka, K , Komori, A & others 2002 Effect of MHD activities on pressure profile in high- plasmas of LHD . Plasma physics and controlled fusion 44 (5A), A217

    2002

  28. [36]

    Nuclear Fusion 61 (11), 116012

    Sato, M & Todo, Y 2021 Kinetic thermal ion effects on maintaining high beta plasmas above the Mercier criterion in the Large Helical Device . Nuclear Fusion 61 (11), 116012

    2021

  29. [37]

    Physics of Fluids B: Plasma Physics 5 (9), 3195--3206

    Schwab, Carolin 1993 Ideal magnetohydrodynamics: Global mode analysis of three-dimensional plasma configurations . Physics of Fluids B: Plasma Physics 5 (9), 3195--3206

    1993

  30. [38]

    Nuclear fusion 44 (9), 1008

    Strauss, HR , Sugiyama, LE , Fu, GY , Park, W & Breslau, J 2004 Simulation of two fluid and energetic particle effects in stellarators . Nuclear fusion 44 (9), 1008

    2004

  31. [39]

    & Günter, S

    Strumberger, E. & Günter, S. 2017 CASTOR3D: linear stability studies for 2D and 3D tokamak equilibria . Nuclear Fusion 57 (1), 016032

    2017

  32. [40]

    Physics of Fluids B: Plasma Physics 1 (3), 563--569

    Van Rij, WI & Hirshman, SP 1989 Variational bounds for transport coefficients in three-dimensional toroidal plasmas . Physics of Fluids B: Plasma Physics 1 (3), 563--569

    1989

  33. [41]

    Frontiers in Physics 12 , 1422411

    Varela, J , Spong, Donald , Garcia, Luis , Ghai, Yashika , Ortiz, Juan & project collaborators, FAR3d 2024 Stability optimization of energetic particle driven modes in nuclear fusion devices: the FAR3d gyro-fluid code . Frontiers in Physics 12 , 1422411

    2024

  34. [42]

    Plasma and Fusion Research 6 , 1403013--1403013

    Varela, Jacobo , Watanabe, Kiyomasa Y , Nakajima, Noriyoshi , Ohdachi, Satoshi , Garcia, Luis & Mier, Jose A 2011 Ballooning modes instabilities in outward LHD configurations . Plasma and Fusion Research 6 , 1403013--1403013

    2011

  35. [43]

    Plasma physics and controlled fusion 45 (12A), A285

    Weller, A , Geiger, J , Werner, A , Zarnstorff, MC , N \"u hrenberg, C , Sallander, E , Baldzuhn, J , Brakel, R , Burhenn, R , Dinklage, A & others 2003 Experiments close to the beta-limit in w7-as . Plasma physics and controlled fusion 45 (12A), A285

    2003

  36. [44]

    In 19^ th IAEA fusion energy conference, Lyon (France), 14-19 Oct 2002\/

    Weller, A , Geiger, J & Zarnstorff, M 2002 Investigation of the -limit in the W7-AS stellarator. In 19^ th IAEA fusion energy conference, Lyon (France), 14-19 Oct 2002\/

    2002

  37. [45]

    Fusion science and technology 50 (2), 158--170

    Weller, Arthur , Sakakibara, S , Watanabe, KY , Toi, K , Geiger, J , Zarnstorff, MC , Hudson, SR , Reiman, A , Werner, A , N \"u hrenberg, C & others 2006 Significance of MHD effects in stellarator confinement . Fusion science and technology 50 (2), 158--170

    2006

  38. [46]

    Plasma physics and controlled fusion 28 (1A), 243

    Wesson, John A 1986 Sawtooth oscillations . Plasma physics and controlled fusion 28 (1A), 243

    1986

  39. [47]

    Physics of Plasmas 31 (8)

    Wright, AM & Ferraro, NM 2024 a\/ Investigating nonlinear magnetohydrodynamics in an optimized, reactor-scale quasi-axisymmetric stellarator . Physics of Plasmas 31 (8)

    2024

  40. [48]

    Physics of Plasmas 31 (10)

    Wright, AM & Ferraro, NM 2024 b\/ MHD-induced beta limits in the Large Helical Device . Physics of Plasmas 31 (10)

    2024

  41. [49]

    Nuclear Fusion 64 (8), 086053

    Yu, Q , G \"u nter, S & Lackner, K 2024 Numerical modelling of sawteeth and sawtooth-free regime . Nuclear Fusion 64 (8), 086053

    2024

  42. [50]

    In 20^ th IAEA fusion energy conference 2004, Villamoura (Portugal), 1-6 Nov 2004\/

    Zarnstorff, MC , Fredrickson, E , Hudson, S , Reiman, A , Fu, G-Y , Ku, LP , Monticello, D , Weller, A , Geiger, J , Knauer, JP & others 2004 Equilibrium and stability of high- plasmas in Wendelstein 7-AS . In 20^ th IAEA fusion energy conference 2004, Villamoura (Portugal), 1...

    2004

  43. [51]

    Nuclear Fusion

    Zhang, Haowei , Hoelzl, Matthias , Krebs, Isabel , Burckhart, Andreas , Bock, Alexander , G \"u nter, Sibylle , Igochine, Valentin , Lackner, Karl , Ramasamy, Rohan & Zohm, Hartmut 2025 Quantitative magnetohydrodynamic modelling of flux pumping in ASDEX Upgrade . Nuclear Fusion

    2025

  44. [52]

    Physical Review Letters 133 (13), 135102

    Zhou, Yao , Aleynikova, K , Liu, Chang & Ferraro, NM 2024 Benign saturation of ideal ballooning instability in a high-performance stellarator . Physical Review Letters 133 (13), 135102

    2024

  45. [53]

    John Wiley & Sons

    Zohm, Hartmut 2014 Magnetohydrodynamic stability of tokamaks\/ . John Wiley & Sons

    2014

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.