arXiv subjects

T. Eich

Publications and source records attributed to T. Eich.

13 recordsLinked to original sources

arXiv2026

First step toward multi machine ELM energy scalings and extrapolations to SPARC and ITER

It is shown that the ELM energy loss normalized by the plasma stored energy ({\Delta}EELM/Wplasma) for high-density small/QCE ELM regimes scales inversely with the separatrix turbulence parameter a_t. In contrast, the neoclassical electron collisionality at the pedestal top, nu*e,neo, expected to regulate {\Delta}EELM/Wplasma according to the Loarte scaling (Plasma Phys. Control. Fusion 2003 45 1549), does not adequately capture {\Delta}EELM/Wplasma data for peeling-ballooning-limited type-I ELMs and ballooning-limited small/QCE ELMs, limiting its applicability for extrapolation to one scenario window. A multi-machine database including seven tokamaks and with {\Delta}EELM/Wplasma ranging from 0.5% to 14%, has been analyzed. A regression analysis on only type-I ELMs yields (({\Delta}E_ELM)/W_plasma )_(Type-I ) [%]=6.8*T_(e,ped)^0.03 n_(e,ped)^(-0.4) \k{appa}^(-0.4) R_major^0.4, corresponding to {\Delta}EELM/Wplasma =4.5% for nominal SPARC pedestal parameters and 12% for the ITER D-T Q=10 scenario. For the small/QCE ELM class, however, as a_t increases, the pedestal moves toward a ballooning-limited boundary, the toroidal mode number increases, the ELM frequency rises following the scaling f_ELM=46e^((2.25*a_t)), and {\Delta}EELM/Wplasma decreases via the relation ({\Delta}E_ELM)/W_plasma [%]=1.6e^(-({\alpha}_t/2)). For SPARC QCE-relevant a_t=0.86 and ITER high-fueling scenario a_t = 0.64, the scaling favorably predicts {\Delta}EELM/Wplasma of 1.0% and 1.2%, respectively, with values below 1% if the small/QCE ELM regime is pushed beyond a_t >1. The small/QCE ELM-fitted results represent an initial step toward future analysis on broader datasets, which will be necessary to improve the accuracy of projections for future reactor-relevant scenarios.

physics.plasm-ph↗

arXiv2026

The power exhaust constrained SPARC separatrix operational space

In this work we extrapolate the separatrix operational space (SepOS) projections to SPARC and introduce detachment access criteria, thus formulating the combined power exhaust constrained SepOS (i.e., PE-SepOS) to evaluate integrated power exhaust solutions at scale. Through the interpretation of SPARC SOLPS-ITER datasets and foundational work already demonstrated in experiments we formulate an as simple as possible description of the SOL net power and momentum losses in dissipative regimes to link the main power exhaust quantities with the SepOS parameters. Through this framework, we demonstrate the utility of a normalized PE-SepOS framework in identifying accessible operational points for given exhaustible Psep requirements. In applying the PE-SepOS framework to project the SPARC operational space, we find inherent trade-offs, namely: i) accessing high impurity radiation scenarios leads to pronounced reductions in ne,sep (e.g., 50% reductions at 2% Ne concentration) as a consequence of power limitation, and ii) given present understanding of access criteria to the quasi-continuous exhaust regime (QCE), a compromise between high radiative fraction and high density/neutral pressure is required for QCE access at sufficiently high density, high alpha_t conditions, with the divertor dissipative regime transitioning to pronounced detachment. Taking advantage of universal trends enabling projections of density and impurity seeding scans, the PE-SepOS thus provides a framework for mapping out the edge plasma operational space in a scalable manner, subject to validation during early SPARC operations with suitable divertor and edge plasma observables.

physics.plasm-ph↗

arXiv2026

Experimental Evidence for Increased Particle Fluxes Due to a Change in Transport at the Separatrix near Density Limits on Alcator C-Mod

Experimental inferences of cross-field particle flux at the separatrix, $\Gamma_{\perp}^\mathrm{sep}$, show rapid growth near H-mode and L-mode density limits at high magnetic field on Alcator C-Mod. Increases in $\Gamma_{\perp}^\mathrm{sep}$ correlate well with proximity to high density operational boundaries as proposed by the separatrix operational space model. $\Gamma_{\perp}^\mathrm{sep}$ grows as the L-mode density limit and the H-L-mode back transition boundaries are approached, consistent with expectations of plasma instability-driven turbulence suggested by theory, confirming the power dependence of density limits. $\Gamma_{\perp}^\mathrm{sep}$ is well-organized by the characteristic wavenumber for resistive ballooning mode turbulence, $k_\mathrm{RBM}$, from interchange-drift-Alfv\'en fluid turbulence theory, with additional dependence on the cylindrical safety factor, $\hat{q}_\mathrm{cyl}$, yielding an empirical limit to plasma operation of $k_\mathrm{RBM}^{2}\hat{q}_\mathrm{cyl} = 1$. This limit corresponds to the point where the perpendicular heat flux, $Q_{\perp}$, reaches the level of the parallel heat flux, $Q_{\parallel}$, i.e. $Q_{\perp} \approx Q_{\parallel}$, beyond which point thermal equilibrium is not satisfied, resulting in a fold catastrophe.

physics.plasm-ph↗

arXiv2026

Empirical impact of near-separatrix plasma and neutral transport on the pedestal in the transition between EDA and ELMy H-modes on Alcator C-Mod

The transition between the ELMy H-mode and the EDA H-mode is studied on Alcator C-Mod using an experimental database and predictive pedestal models. High-resolution Thomson scattering measurements are used to compare the pedestal density, $n_{e}^\mathrm{ped}$, and the separatrix density, $n_{e}^\mathrm{sep}$ with main chamber neutral measurements. $n_{e}^\mathrm{ped}$ is sensitive to neutral sources only in the ELMy H-mode regime and not in the EDA H-mode regime. Density fluctuation spectra reveal that quasi-coherent structures become stronger at higher densities and more coherent in the EDA relative to the inter-ELM phases of ELMy H-modes, before weakening again at the highest values of $n_{e}^\mathrm{ped}$. The Saarelma-Connor pedestal density prediction model is validated for ELMy H-modes up to $n_{e}^\mathrm{ped} = 2.0 \times 10^{20}$ m$^{-3}$. An additional transport channel driven by resistive ballooning modes (RBM), $D_\mathrm{RBM}$, scaling directly with $\alpha_{t}$ and inversely with $k_\mathrm{RBM}^{2}\hat{q}_\mathrm{cyl}$ is shown to improve the prediction for EDA H-modes, finding good model agreement up to $n_{e}^\mathrm{ped} = 3.0 \times 10^{20}$ m$^{-3}$. EPED scans in $n_{e}^\mathrm{ped}$ are then performed at three values of $n_{e}^\mathrm{sep}/n_{e}^\mathrm{ped}$. Increasing this ratio moves the peeling-ballooning branch transition to lower $n_{e}^\mathrm{ped}$, increasing $p^\mathrm{ped}$ in the peeling branch and decreasing it in the ballooning branch. Agreement is found for large ELM H-modes. SPARC pedestal density predictions for an ELMy and an EDA/QCE-like H-mode are performed and found consistent with assumptions used in previous EPED modeling. Inclusion of $D_\mathrm{RBM}$ significantly weakens the density gradient near the separatrix, lowering $n_{e}^\mathrm{ped}$ by approximately 20%.

physics.plasm-ph↗

arXiv2024

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

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.

physics.plasm-ph↗

arXiv2023

Reduced model for H-mode sustainment in unfavorable $\mathbf{ \nabla B}$ drift configuration in ASDEX Upgrade

A recently developed reduced model of H-mode sustainment based on interchange-drift-Alfv\'en turbulence description in the vicinity of the separatrix matching experimental observations in ASDEX Upgrade has been extended to experiments with the unfavorable $\nabla B$ drift. The combination with the theory of the magnetic-shear-induced Reynolds stress offers a possibility to quantitatively explain the phenomena. The extension of the Reynolds stress estimate in the reduced model via the magnetic shear contribution is able to reproduce the strong asymmetry in the access conditions depending on the ion $\nabla B$ drift orientation in agreement with experimental observations. The Reynolds stress profile asymmetry predicted by the magnetic shear model is further extended by comparison with GRILLIX and GENE-X simulations matched with comparable experiments in realistic X-point geometry. The predictions of the radial electric field well depth and its difference between the favorable and unfavorable configurations at the same heating power from the extended model also show consistency with experimental measurements.

physics.plasm-ph↗

arXiv2022

First-principles density limit scaling in tokamaks based on edge turbulent transport and implications for ITER

A first-principles scaling law, based on turbulent transport considerations, and a multi-machine database of density limit discharges from the ASDEX Upgrade, JET and TCV tokamaks, show that the increase of the boundary turbulent transport with the plasma collisionality sets the maximum density achievable in tokamaks. This scaling law shows a strong dependence on the heating power, therefore predicting for ITER a significantly larger safety margin than the Greenwald empirical scaling (Greenwald et al, Nucl. Fusion, 28(12), 1988) in case of unintentional H-L transition.

physics.plasm-ph↗

arXiv2021

A quasi-continuous exhaust scenario for a fusion reactor: the renaissance of small edge localized modes

Tokamak operational regimes with small edge localized modes (ELMs) could be a solution to the problem of large transient heat loads in future fusion reactors because they provide quasi-continuous exhaust while keeping a good plasma confinement. A ballooning mode mechanism near the last closed flux surface (LCFS) governed by an interplay of the pressure gradient and the magnetic shear there has been proposed for small ELMs in high density ASDEX Upgrade and TCV discharges. In this manuscript we explore different factors relevant for plasma edge stability in a wide range of edge safety factors by changing the connection length between the good and the bad curvature side. Simultaneously this influences the stabilizing effect of the local magnetic shear close to the LCFS as well as the $E \times B$ flow shear. Ideal ballooning stability calculations with the HELENA code reveal that small ELM plasmas are indeed unstable against ballooning modes very close to the LCFS but can exhibit second ballooning stability in the steep gradient region which correlates with enhanced confinement. We also present first non-linear simulations of small ELM regimes with the JOREK code including the $E \times B$ shear which indeed develop ballooning like fluctuations in the high triangularity limit. In the region where the small ELMs originate the dimensionless parameters are very similar in our investigated discharges and in a reactor, making this regime the ideal exhaust scenario for a future reactor.

physics.plasm-ph↗

arXiv2021

I-mode pedestal relaxation events in the Alcator C-Mod and ASDEX Upgrade tokamaks

In some conditions, I-mode plasmas can feature pedestal relaxation events (PREs) that transiently enhance the energy reaching the divertor target plates. To shed light into their appearance, characteristics and energy reaching the divertor targets, a comparative study between two tokamaks $-$ Alcator C-Mod and ASDEX Upgrade $-$ is carried out. It is found that PREs appear only in a subset of I-mode discharges, mainly when the plasma is close to the H-mode transition. Also, the nature of the triggering instability is discussed by comparing measurements close to the separatrix in both devices. The PRE relative energy loss from the confined region increases with decreasing pedestal top collisionality $\nu_{\mathrm{ped}}^*$. In addition, the relative electron temperature drop at the pedestal top, which is related to the conductive energy loss, rises with decreasing $\nu_{\mathrm{ped}}^*$. Finally, the peak parallel energy fluence due to the PRE measured on the divertor in both devices is compared to the model introduced in [1] for type-I ELMs. The model is shown to provide an upper boundary for PRE energy fluence data, while a lower boundary is found by dividing the model by three. These two boundaries are used to make projections to future devices such as DEMO and ARC.

physics.plasm-ph↗

arXiv2020

I-mode pedestal relaxation events at ASDEX Upgrade

The I-mode confinement regime can feature small edge temperature drops that can lead to an increase in the energy deposited onto the divertor targets. In this work, we show that these events are associated with a relaxation of both electron temperature and density edge profiles, with the largest drop found at the pedestal top position. Stability analysis of edge profiles reveals that the operational points are far from the ideal peeling-ballooning boundary. Also, we show that these events appear close to the H-mode transition in the typical I-mode operational space in ASDEX Upgrade, and that no further enhancement of energy confinement is found when they occur. Moreover, scrape-off layer transport during these events is found to be very similar to type-I ELMs, with regard to timescales ($\approx$ 800 $\mu$s), filament propagation, toroidally asymmetric energy effluxes at the midplane and asymmetry between inner and outer divertor deposited energy. In particular, the latter reveals that more energy reaches the outer divertor target. Lastly, first measurements of the divertor peak energy fluence are reported, and projections to ARC - a reactor designed to operate in I-mode - are drawn.

physics.plasm-ph↗

arXiv2014

Effect of resonant magnetic perturbations on low collisionality discharges in MAST and a comparison with ASDEX Upgrade

Sustained ELM mitigation has been achieved on MAST and AUG using RMPs with a range of toroidal mode numbers over a wide region of low to medium collisionality discharges. The ELM energy loss and peak heat loads at the divertor targets have been reduced. The ELM mitigation phase is typically associated with a drop in plasma density and overall stored energy. In one particular scenario on MAST, by carefully adjusting the fuelling it has been possible to counteract the drop in density and to produce plasmas with mitigated ELMs, reduced peak divertor heat flux and with minimal degradation in pedestal height and confined energy. While the applied resonant magnetic perturbation field can be a good indicator for the onset of ELM mitigation on MAST and AUG there are some cases where this is not the case and which clearly emphasise the need to take into account the plasma response to the applied perturbations. The plasma response calculations show that the increase in ELM frequency is correlated with the size of the edge peeling-tearing like response of the plasma and the distortions of the plasma boundary in the X-point region.

physics.plasm-ph↗

arXiv2014

Contrasting H-mode behaviour with deuterium fuelling and nitrogen seeding in the all-carbon and metallic versions of JET

The former all-carbon wall on JET has been replaced with beryllium in the main torus and tungsten in the divertor to mimic the surface materials envisaged for ITER. Comparisons are presented between Type I H-mode characteristics in each design by examining respective scans over deuterium fuelling and impurity seeding, required to ameliorate exhaust loads both in JET at full capability and in ITER.

physics.plasm-ph↗

arXiv2009

Observation of confined current ribbon in JET plasmas

we report the identification of a localised current structure inside the JET plasma. It is a field aligned closed helical ribbon, carrying current in the same direction as the background current profile (co-current), rotating toroidally with the ion velocity (co-rotating). It appears to be located at a flat spot in the plasma pressure profile, at the top of the pedestal. The structure appears spontaneously in low density, high rotation plasmas, and can last up to 1.4 s, a time comparable to a local resistive time. It considerably delays the appearance of the first ELM.

physics.plasm-ph↗