Zonal shear layer collapse and the power scaling of the density limit: old L-H wine in new bottles

Singh, Rameswar; Diamond, P. H.

doi:10.1088/1361-6587/ac7972

Cited by 6 publications

(16 citation statements)

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“…The Singh-Diamond model 2 [34] (equations (4.2) and (4.3)) is a zero-dimensional model evolving turbulence energy E = q 2 y ρ 2 s I q /q 2 y ρ 2 s ρ 2 * , zonal flow energy v 2 z , mean temperature gradient ∇T (T ) and mean density n. In this model, time is normalized by the gyro-Bohm diffusion time, i.e. t ≡ tD GB /a 2 , where D GB = c i ρ i ρ * is the gyro-Bohm diffusivity, a is the minor radius.…”

Section: Appendix a Singh-diamond Modelmentioning

confidence: 99%

“…Existing understanding and modelling results developed to address the L false→ H transition are useful to this end. In 2022, Singh and Diamond (hereafter SD2) [34] developed an extension of the Kim–Diamond model [7,8,12], of the L false→ H transition, and used this to investigate the evolution of zonal shears (as present in L-mode) at high density, with auxiliary power. SD2 solved coupled evolution equations for edge fluctuation energy E, edge zonal shear energy vz2, edge density n and edge ion temperature gradient, written as T for simplicity.…”

Section: Density Limit Scaling Theorymentioning

confidence: 99%

“…

Figure 15Evolution of zonal flow energy with various edge heat flux (Q) and edge density fuelling source (S). Different colours refer to different power Q and ultimately to different shear layer collapse densities [34]. (Online version in colour.…”

Section: Density Limit Scaling Theorymentioning

confidence: 99%

“…for ion temperature gradient (ITG) turbulence [34]. Here, n crit is the critical edge density for zonal flow collapse and Q i is the edge ion heat flux.…”

Section: Introductionmentioning

confidence: 99%

“…We identify a dimensionless parameter that characterizes the collapse onset. By exploiting and extending the Kim–Diamond model of the L false→ H transition, we derive the scaling relation ncrit∼Qi1/3 for ion temperature gradient (ITG) turbulence [34]. Here, nnormalcrit is the critical edge density for zonal flow collapse and Qi is the edge ion heat flux.…”

Section: Introductionmentioning

confidence: 99%

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How the birth and death of shear layers determine confinement evolution: from the L → H transition to the density limit

Diamond

Singh

Long

et al. 2023

Phil. Trans. R. Soc. A.

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Electric field profile structure—especially its shear—is a natural order parameter for the edge plasma, and characterizes confinement regimes ranging from the H-mode (Wagner et al. 1982 Phys. Rev. Lett. 49 , 1408–1412 ( doi:10.1103/PhysRevLett.49.1408 )) to the density limit (DL) (Greenwald et al. 1988 Nucl. Fusion 28 , 2199–2207 ( doi:10.1088/0029-5515/28/12/009 )). The theoretical developments and lessons learned during 40 years of H-mode studies (Connor & Wilson 1999 Plasma Phys. Control. Fusion 42 , R1–R74 ( doi:10.1088/0741-3335/42/1/201 ); Wagner 2007 Plasma Phys. Control. Fusion 49 , B1–B33 ( doi:10.1088/0741-3335/49/12b/s01 )) are applied to the shear layer collapse paradigm (Hong et al. 2017 Nucl. Fusion 58 , 016041 ( doi:10.1088/1741-4326/aa9626 )) for the onset of DL phenomena. Results from recent experiments on edge shear layers and DL phenomenology are summarized and discussed in the light of L → H transition physics. The theory of shear layer collapse is then developed. We demonstrate that shear layer physics captures both the well known current (Greenwald) scaling of the DL (Greenwald 2002 Plasma Phys. Control. Fusion 44 , R27–R53 ( doi:10.1088/0741-3335/44/8/201 ); Greenwald et al. 2014 Phys. Plasmas 21 , 110501 ( doi:10.1063/1.4901920 )), as well as the emerging power scaling (Zanca, Sattin, JET Contributors 2019 Nucl. Fusion 59 , 126011 ( doi:10.1088/1741-4326/ab3b31 )). The derivation of the power scaling theory exploits an existing model, originally developed for the L → H transition (Diamond, Liang, Carreras, Terry 1994 Phys. Rev. Lett. 72 , 2565–2568 ( doi:10.1103/PhysRevLett.72.2565 ); Kim & Diamond 2003 Phys. Rev. Lett. 90 , 185006 ( doi:10.1103/PhysRevLett.90.185006 )). We describe the enhanced particle transport events that occur following shear layer collapse. Open problems and future directions are discussed. This article is part of a discussion meeting issue ‘H-mode transition and pedestal studies in fusion plasmas’.

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Section: Appendix a Singh-diamond Modelmentioning

confidence: 99%

Section: Density Limit Scaling Theorymentioning

confidence: 99%

“…

Section: Density Limit Scaling Theorymentioning

confidence: 99%

“…for ion temperature gradient (ITG) turbulence [34]. Here, n crit is the critical edge density for zonal flow collapse and Q i is the edge ion heat flux.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

How the birth and death of shear layers determine confinement evolution: from the L → H transition to the density limit

Diamond

Singh

Long

et al. 2023

Phil. Trans. R. Soc. A.

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Investigation on the edge cooling threshold of the density limit in the J-TEXT tokamak with limiter and divertor configurations

Xu,

Chen,

Yang

et al. 2024

Plasma Phys. Control. Fusion

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The cooling of the plasma edge is widely considered to be a key element in the density limit of tokamak. This paper investigates the critical edge cooling threshold of the density limit, exploring various plasma configurations in the J-TEXT tokamak. Notably, significant differences in edge electron temperature in the vicinity of last closed flux surface (LCFS) were observed between limiter and divertor configuration. However, the electron temperature dropped to a similar level in the vicinity of q = 3 surface close to density limit, independent of the magnetic field configurations. In addition, to evaluate the reliability of critical edge cooling threshold, experiments were implemented by increasing the carbon impurity content for enhancing the edge cooling rate. These experiments involved two approaches to increase the carbon impurity content: methane injection and penetration of a graphite solid source. Results from these experiments indicate that the temperature threshold of the q = 3 surface remains consistent even with the stronger edge cooling rate. The consistency observed in the electron temperature threshold near the q=3 surface, regardless of magnetic configuration and edge cooling rate, could help to refine existing theoretical and simulation work and improve the prediction accuracy of the density limit disruption.

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The power dependence of the maximum achievable H-mode and (disruptive) L-mode separatrix density in ASDEX Upgrade

2023

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In future fusion reactors disruptions must be avoided at all costs. Disruptions due to the density limit are typically described by the power-independent Greenwald scaling. Recently, a power dependence of the disruptive density limit was predicted by several authors. In future fusion reactors disruptions must be avoided at all costs. Disruptions due to the density limit are typically described by the power-independent Greenwald scaling. Recently, a power dependence of the disruptive density limit was predicted by several authors (P. Zanca et al. Nuclear Fusion 59, 126011 (2019), M. Giacomin et al. Phys. Rev. Lett. 128, 185003 (2022), R. Singh and P.~H. Diamond Plasma Physics and Controlled Fusion 64, 084004 (2022), U. Stroth et al. Nuclear Fusion 62, 076008 (2022), A.O. Brown and R.J. Goldston Nuclear Materials and Energy 27, 101002 (2021)). It is investigated whether this increases the operational range of the tokamak. Increasing the heating power in the L-mode can induce an L-H transition, and therefore a power-dependent density limit and the L-H transition cannot be considered independently. The different models are tested on a data base for separatrix parameters at the separatrix of ASDEX Upgrade and compared with the concept (SepOS) presented in T.Eich, P. Manz Nuclear Fusion 61 (2021) 086017. The disruptive separatrixdensity scales with the power ne ∝ P0.38±0.08 in good agreement to all models. Also the back transition from high to low (H-L) confinement shows an approximately Greenwald scaling with an additional power dependence ne ∝ P0.4 according to the SepOS concept. For future devices operating at much higher heating power such a power scaling may allow operation at much higher separatrix densities as common in H-Mode operation. Preconditions to extrapolation for future devices are discussed.

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Zonal shear layer collapse and the power scaling of the density limit: old L-H wine in new bottles

Cited by 6 publications

References 70 publications

How the birth and death of shear layers determine confinement evolution: from the L → H transition to the density limit

How the birth and death of shear layers determine confinement evolution: from the L → H transition to the density limit

Investigation on the edge cooling threshold of the density limit in the J-TEXT tokamak with limiter and divertor configurations

The power dependence of the maximum achievable H-mode and (disruptive) L-mode separatrix density in ASDEX Upgrade

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