Session CO4: C-Mod

Overview of Alcator C-Mod Research

Alcator C-Mod, a compact (R$=$0.68m, a$=$0.21m), high magnetic field, B$_{\mathrm{t}}\le $8T, tokamak accesses a variety of naturally ELM-suppressed high confinement regimes that feature extreme power density into the divertor, q$_{\mathrm{\vert \vert }}\le $3 GW/m$^{\mathrm{2}}$, with SOL heat flux widths $\lambda_{\mathrm{q\thinspace }}$\textless 0.5mm, exceeding conditions expected in ITER and approaching those foreseen in power plants. The unique parameter range provides much of the physics basis of a high-field, compact tokamak reactor. Research spans the topics of core transport and turbulence, RF heating and current drive, pedestal physics, scrape-off layer, divertor and plasma wall interactions. In the last experimental campaign, Super H-mode was explored and featured the highest pedestal pressures ever recorded, p$_{\mathrm{ped}}\approx $90 kPa (90{\%} of ITER target), consistent with EPED predictions. Optimization of naturally ELM-suppressed EDA H-modes accessed the highest volume averaged pressures ever achieved (\textless p\textgreater \textgreater 2 atm), with p$_{\mathrm{ped}}\approx $60 kPa. The SOL heat flux width has been measured at B$_{\mathrm{pol\thinspace }}=$1.25T, confirming the Eich scaling over a broader poloidal field range than before. Multi-channel transport studies focus on the relationship between momentum transport and heat transport with perturbative experiments and new multi-scale gyrokinetic simulation validation techniques were developed.   

Boundary plasma heat flux width measurements for poloidal magnetic fields above 1 Tesla in the Alcator C-Mod tokamak

The boundary heat flux width, along with the total power flowing into the boundary, sets the power exhaust challenge for tokamaks. A multi-machine boundary heat flux width database found that the heat flux width in H-modes scaled inversely with poloidal magnetic field ($B_{\mathrm{p}})$ and was independent of machine size. The maximum $B_{\mathrm{p}}$ in the database was \textasciitilde 0.8 T, whereas the ITER 15 MA, Q$=$10 scenario will be 1.2 T. New measurements of the boundary heat flux width in Alcator C-Mod extend the international database to plasmas with $B_{\mathrm{p}}$ up to \textasciitilde 1.3 T. C-Mod was the only experiment able to operate at ITER-level $B_{\mathrm{p}}$. These new measurements are from over 300 plasma shots in L-, I-, and EDA H-modes spanning essentially the whole operating space in C-Mod. We find that the inverse-$B_{\mathrm{p}}$ dependence of the heat flux width in H-modes continues to ITER-level $B_{\mathrm{p}}$, further reinforcing the empirical projection of \textasciitilde 500 $\mu $m heat flux width for ITER. We find \textasciitilde 50{\%} scatter around the inverse-$B_{\mathrm{p}}$ scaling and are searching for the `hidden variables' causing this scatter. Supported by USDoE award DE-FC02-99ER54512.   

The effect of feedback-controlled divertor nitrogen seeding on the boundary plasma and power exhaust channel width in Alcator C-Mod

The scrape-off layer (SOL) power channel width, $\lambda_{\mathrm{q}}$ , is projected to be \textasciitilde 0.5 mm in power reactors, based on multi-machine measurements of divertor target heat fluxes in H-mode at low levels of divertor dissipation. An important question is: does $\lambda _{\mathrm{q}}$ change with the level of divertor dissipation? We report results in which feedback controlled nitrogen seeding in the divertor was used to systematically vary divertor dissipation in a series of otherwise identical L-mode plasmas at three plasma currents: 0.55, 0.8 and 1.1 MA. Outer midplane profiles were recorded with a scanning Mirror Langmuir Probe; divertor plasma conditions were monitored with `rail' Langmuir probe and surface thermocouple arrays. Despite an order of magnitude reduction in divertor target heat fluxes (q// \textasciitilde 400 MW m$^{\mathrm{-2}}$ to \textasciitilde 40 MW m$^{\mathrm{-2}})$ and corresponding change in divertor regime from sheath-limited through high-recycling to near-detached, the upstream electron temperature profile is found to remain unchanged or to become slightly steeper in the near SOL and to drop significantly in the far SOL. Thus heat in the SOL appears to take advantage of this impurity radiation `heat sink' in the divertor by preferentially draining via the narrow (and perhaps an increasingly narrow) $\lambda_{\mathrm{q}}$ of the near SOL.   

Measurements of Heat-flux Footprints at the Inner Divertor Target of Alcator C-Mod

IR thermography has been used to measure the footprints of heat-flux onto the inner high-field side divertor target in C-Mod in a variety of discharge conditions. These include different magnetic-configurations (LSN, near-DN, and USN, with particular attention to near-DN configurations) and different confinement modes (I-mode, EDA H-mode, and ELM-free H-mode). Heat-fluxes and heat-flux widths during I-mode are especially of interest because of the enhanced power to the inner target that occurs in the ``reversed'' toroidal field condition that is favorable for I-mode. We find that under LSN conditions the footprints can be described by an ``Eich-fit'' function, with a characteristic length for heat-flux spreading into the SOL ($\lambda _{\mathrm{q}})$ and a characteristic width for heat-flux spreading along the divertor leg. We find that the minimum values of $\lambda _{\mathrm{q}}$ in I-mode are consistent with the multi-machine observations that the H-mode $\lambda_{\mathrm{q}}$ on the outer target scales inversely with B$_{\mathrm{pol}}$, with $\lambda_{\mathrm{q}}$ between 1 and 2 mm over the 0.6 \textless B$_{\mathrm{pol}}$ \textless 1.0T range. However, we also measure widths that are significantly larger, both within a single discharge and between discharges that are nominally similar. We will continue to search for ``hidden'' variables that might lead to the scatter of the widths above the observed minimum.   

Investigation of parameter space for fully detached long-legged divertor operation

Recently it was found in numerical modeling that passively-stable fully detached divertor regimes exist in a broad range of input power from the core, for divertor configurations with radially or vertically extended, tightly baffled, outer divertor legs, with or without a secondary X-point in the leg volume [1]. This report presents a comparative computational study of detached divertor operation carried out for a variety of divertor configurations, expanding on the initial work reported in Ref. [1]. The parameters are based on those of the ADX tokamak design [2], and the simulations are carried out with the tokamak edge transport code UEDGE [3]. The simulations show that long-legged divertors have a large increase of the peak power handling capability, by up to an order of magnitude, compared to conventional divertors. For the detached divertor regime in these simulations, important physics combines interplay of strong convective plasma transport to the outer wall, confinement of neutral gas in the divertor volume, geometric effects including secondary X-point, and atomic radiation. As the power from the core is varied, the detachment front merely shifts up or down in the leg but remains stable. The present work addresses sensitivity of the detached divertor regime to various parameters used in the model, including the anomalous plasma transport, neutral transport, impurity radiation, and geometry of plasma-facing material surfaces. [1] Umansky et al., Phys. Plasmas 24, 056112 (2017); [2] LaBombard et al., Nucl. Fusion 55, 053020 (2015); [3] Rognlien et al., J. Nuc. Mat. 196, 347--123 (1992).   

Implementation of a long leg X-point target divertor in the ARC fusion pilot plant

A long leg X-point target divertor geometry in a double null geometry has been implemented in the ARC pilot plant design [1], exploiting ARC's demountable toroidal field (TF) coils and FLiBe immersion blanket, which allow superconducting poloidal field coils to be located inside the TF coils, adequately shielded from neutrons. This new design maintains the original TF coil size, core plasma shape, and attains a tritium breedin ratio $\approx $1.08. The long leg divertor geometry provides significant advantages. Neutron transport computations indicate a factor of 10 reduction in divertor material neutron damage rate compared to the first wall, easing requirements for high heat flux components. Simulations have shown that long legged divertors are able to maintain a passively stable detachment front that stays in the divertor leg over a wide power window [2], in principle, responding immediately to fast changes in power exhaust. The ARC design exploits this new paradigm for divertor heat flux control: fewer concerns about coping with fast transients and a focus on neutron-tolerant diagnostics to measure and adjust detachment front locations in the outer divertor legs over long timescales. [1] Sorbom, B. N., et al. \textit{Fusion Engineering and Design} 100 (2015) 378-405; [2] Umansky, M. V., et al. \textit{Physics of Plasmas} 24 (2017) 056112.   

Studies of Lower Hybrid Range of Frequencies Actuators in the ARC Device

High field side (HFS) placement of lower hybrid range of frequencies (LHRF) actuators is attractive from both the standpoint of a more quiescent scrape off layer (SOL) and from the improved LH wave accessibility and penetration to higher electron temperature that results from the higher magnetic field on the HFS [1]. The resulting profiles of LH current drive (LHCD) are also more suitable for advanced tokamak (AT) operation where it is most desirable to provide a significant (\textasciitilde 20-30{\%}) contribution to the total current density with a broad profile extending from r/a \textasciitilde 0.5-0.85. Here we re-assess HFS LHCD in the ARC device [2] using a hierarchy of LHCD models that include a combined adjoint plus ray tracing calculation, a ray tracing plus 3D Fokker Planck calculation, and a full-wave plus Fokker Planck simulation. [1] B. LaBombard et al, Nucl. Fusion 55, 053020 (2015). [2] B. Sorbom et al, Fus. Eng. Design 100, 378 (2015).   

Cross Machine Comparison of Turbulence and Transport Measurements on Alcator C-Mod and ASDEX Upgrade

Experimental turbulence and transport measurements aid in the effort to validate gyrokinetic codes such as GYRO and GENE. There seems to be some discrepancy between the ability of ion-scale simulations to match experimental heat fluxes on Alcator C-Mod [A.J. Creely, PoP 2017] and ASDEX Upgrade (AUG) [D. Told, PoP 2013], motivating additional experimental measurements, such as perturbative thermal diffusivity and electron temperature fluctuations. The perturbative thermal diffusivity is measured on both machines using partial sawtooth crashes [A.J. Creely, NF 2016] and cross machine parametric trends are investigated. Calculations based on partial sawteeth heat pulses are compared to modulated ECH heat pulses on AUG for the first time, and agree within uncertainty. Electron temperature fluctuations are measured with correlation ECE. Comparisons of total temperature fluctuation levels between gyrokinetic codes and experiment seem to show similar trends to electron heat flux, in that they are under-predicted on C-Mod, but matched or even over-predicted on AUG. This implies possible differences in the dominant plasma turbulence, but further study is needed.   

On the $\rho_{\mathrm{\ast }}$ Scaling of Intrinsic Rotation in C-Mod Plasmas with Edge Transport Barriers

Changes in the core intrinsic toroidal rotation velocity following L- to H- and L- to I-mode transitions have been investigated in Alcator C-Mod tokamak plasmas. The magnitude of the co-current rotation increments is found to increase with the pedestal temperature gradient and q$_{\mathrm{95}}$, and to decrease with toroidal magnetic field. These results are captured quantitatively by a model of fluctuation entropy balance which gives the Mach number M$_{\mathrm{i}}$ \textasciitilde $\rho_{\mathrm{\ast }}$/2 L$_{\mathrm{s}}$/L$_{\mathrm{T}}$ \textasciitilde gradT q$_{\mathrm{95}}$/B$_{\mathrm{T}}$ in an ITG turbulence dominant regime. The agreement between experiment and theory gives confidence for extrapolation to future devices in similar operational regimes. Core thermal Mach numbers of \textasciitilde 0.07 and \textasciitilde 0.2 are expected for ITER and ARC, respectively.   

Observations of Rotation Reversal and Fluctuation Hysteresis in Alcator C-Mod L-Mode Plasmas

Intrinsic core toroidal rotation in Alcator C-Mod L-mode plasmas has been observed to spontaneously reverse direction when the minimum value of the normalized collisionality \(\nu^*\), crosses around 0.4. In Ohmic plasmas, the rotation is co-current in the low density linear Ohmic confinement (LOC) regime and counter-current in the higher density saturated Ohmic confinement (SOC) regime. The reversal manifests a hysteresis loop in \(\nu^*\), where the critical collisionalities for the forward and reverse transitions differ by 10-15\%. Temperature and density profiles of the two rotation states are observed to be indistinguishable to within experimental error estimated with Gaussian process regression. However, qualitative differences between the two rotation states are observed in fluctuation spectra, including the broadening of reflectometry spectra and, under certain conditions, the appearance of high-k features in phase contrast imaging (PCI) spectra (\(k_\theta \rho_s\) up to 1). These results suggest that the turbulent state can decouple from local profiles, and that turbulent self-regulation may play a role in the LOC/SOC transition.   

Investigating the Mode Structure of the Weakly Coherent Mode

The Weakly Coherent Mode (WCM, 200-500 kHz, $k_{\perp} \rho_s < 0.1$) is an edge phenomenon associated with I-mode, a steady state, ELM-free confinement regime that has been observed on the Alcator C-Mod, ASDEX-Upgrade, and DIII-D tokamaks. I-mode is characterized by high particle flux, creating a separation of transport channels that leads to the development of a temperature pedestal, but not a density pedestal. The WCM is thought to contribute to this increased particle flux, though its precise role in regulating edge transport is not well-understood. Here, we investigate the structure of the WCM, particularly regarding poloidal asymmetry, using data from poloidally- and toroidally-arrayed Mirnov coils, as well as phase contrast imaging, with radial profiles of $T_e$, $n_e$, and $\Phi$ in the scrape-off layer provided by the Mirror Langmuir Probe. The WCM phenomenology is then compared to that of the Quasi-Coherent Mode, the edge fluctuation responsible for exhausting impurities in the Enhanced D$_{\alpha}$ H-mode.   

Application of a deconvolution method for identifying burst amplitudes and arrival times in Alcator C-Mod far SOL plasma fluctuations

In the far scrape-off layer (SOL), radial motion of filamentary structures leads to excess transport of particles and heat. Amplitudes and arrival times of these filaments have previously been studied by conditional averaging in single-point measurements from Langmuir Probes and Gas Puff Imaging (GPI). Conditional averaging can be problematic: the cutoff for large amplitudes is mostly chosen by convention; the conditional windows used may influence the arrival time distribution; and the amplitudes cannot be separated from a background. Previous work has shown that SOL fluctuations are well described by a stochastic model consisting of a super-position of pulses with fixed shape and randomly distributed amplitudes and arrival times. The model can be formulated as a pulse shape convolved with a train of delta pulses. By choosing a pulse shape consistent with the power spectrum of the fluctuation time series, Richardson-Lucy deconvolution can be used to recover the underlying amplitudes and arrival times of the delta pulses. We apply this technique to both L and H-mode GPI data from the Alcator C-Mod tokamak. The pulse arrival times are shown to be uncorrelated and uniformly distributed, consistent with a Poisson process, and the amplitude distribution has an exponential tail.   

Comparison of measured and modeled gas-puff emissions on Alcator C-Mod

Understanding neutral transport in tokamak boundary plasmas is important because of its possible effects on the pedestal and scrape-off layer (SOL). On Alcator C-Mod, measured neutral line emissions from externally-puffed deuterium and helium gases are compared with the synthetic results of a neutral transport code, DEGAS 2. The injected gas flow rate and the camera response are absolutely calibrated. Time-averaged SOL density and temperature profiles are input to a steady-state simulation. An updated helium atomic model is employed in DEGAS2. Good agreement is found for the D$\alpha $ peak brightness and profile shape. However, the measured helium I line brightness is found to be lower than that in the simulation results by a roughly a factor of three over a wide range of density particularly in the far SOL region. Two possible causes for this discrepancy are reviewed. First, local cooling due to gas puff may suppress the line emission. Second, time-dependent turbulence effect may impact the helium neutral transport. Unlike deuterium atoms that gain energy from charge exchange and dissociation processes, helium neutrals remain cold and have a relatively short mean free path, known to make them prone to turbulence based on the Kubo number criterion.   

New investigation of reconnection time scale of the m/n$=$1/1 sawtooth instability in tokamak plasmas

The condition of magnetic shear and reconnection time scale of the m/n$=$1/1 flux rope (sawtooth instability) in the core of tokamak plasma have been disputed for more than four decades. Recent validation of the condition of the core magnetic shear (i.e., the core safety factor ($q_{0} )$ is below $\sim 1.0$ before the crash and above $\sim 1$ after the crash) in KSTAR [1] encouraged to investigate the observed crash time scale which is known to be one or two order of magnitude faster than the critical reconnection time ($\tau_{c} \cong \sqrt {\tau_{A} \tau_{s} } )$ proposed by the Kadomtsev model [2] where $\tau_{A} $ and $\tau_{s} $ are Alfven and resistive time, respectively. It has been universal that the experimentally observed reconnection time scale is indeed faster than $\tau_{c} $. It is rare but there are cases in which the reconnection time is comparable to $\tau_{c} $. This paper investigates the role of the symmetry (poloidal and toroidal) of the 1/1 flux rope inside the $q\sim 1$ surface in determining the reconnection time. [1] Nam, Y., PhD Thesis, POSTECH (2017). [2] Kadomtsev, B., Sov. J. Plasma Phys. 1, 389 (1975).