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Experimental measurements of plasma and neutral profiles across the pedestal are used in conjunction with 2D edge modeling to examine pedestal stiffness in Alcator C-Mod H-mode plasmas. Experiments on Alcator C-Mod observed pedestal degradation and loss in confinement below a critical value of net power crossing the separatrix, $P_\mathrm{net} = P_\mathrm{net}^\mathrm{crit} \approx 2.3$ MW. New analysis of ionization and particle flux profiles reveal saturation of the pedestal electron density, $n_{e}^\mathrm{ped}$ despite continuous increases in ionization throughout the pedestal, inversely related to $P_\mathrm{net}$. A limit to the pedestal $\nabla n_{e}$ emerges as the particle flux, $\Gamma_{D}$ continues to grow, implying increases in the effective particle diffusivity, $D_\mathrm{eff}$. This is well-correlated with the separatrix collisionality, $\nu^{*}_\mathrm{sep}$ and a turbulence control parameter, $\alpha_{t}$, implying a possible transition in type of turbulence. The transition is well correlated with the experimentally observed value of $P_\mathrm{net}^\mathrm{crit}$. SOLPS-ITER modeling is performed for select discharges from the power scan, constrained with experimental electron and neutral densities, measured at the outer midplane. The modeling confirms general growth in $D_\mathrm{eff}$, consistent with experimental findings, and additionally suggests even larger growth in $\chi_{e}$ at the same $P_\mathrm{net}^\mathrm{crit}$.

At the high $n_{e}$ proposed for high-field fusion reactors, it is uncertain whether ionization, as opposed to plasma transport, will be most influential in determining $n_{e}$ at the pedestal and separatrix. A database of Alcator C-Mod discharges is analyzed to evaluate the impact of source modification via cryopumping. The database contains similarly-shaped H-modes at fixed $I_{p} =$ 0.8 MA and $B_{t} =$ 5.4 T, spanning a large range in $P_\mathrm{net}$ and ionization. Measurements from an edge Thomson Scattering system are combined with those from a midplane-viewing Ly$_{\alpha}$ camera to evaluate changes to $n_{e}$ and $T_{e}$ in response to changes to ionization rates, $S_\mathrm{ion}$. $n_{e}^\mathrm{sep}$ and $T_{e}^\mathrm{ped}$ are found to be most sensitive to changes to $S_\mathrm{ion}^\mathrm{sep}$, as opposed to $n_{e}^\mathrm{ped}$ and $T_{e}^\mathrm{sep}$. Dimensionless quantities, namely $\alpha_\mathrm{MHD}$ and $\nu^{*}$, are found to regulate attainable pedestal values. Select discharges at different values of $P_\mathrm{net}$ and in different pumping configurations are analyzed further using SOLPS-ITER. It is determined that changes to plasma transport coefficients are required to self-consistently model both plasma and neutral edge dynamics. Pumping is found to modify the poloidal distribution of atomic neutral density, $n_{0}$, along the separatrix, increasing $n_{0}$ at the active X-point. Opaqueness to neutrals from high $n_{e}$ in the divertor is found to play a role in mediating neutral penetration lengths and hence, the poloidal distribution of neutrals along the separatrix. Pumped discharges thus require a larger particle diffusion coefficient than that inferred purely from 1D experimental profiles at the outer midplane.

This work characterizes the core transport physics of SPARC early-campaign plasmas using the PORTALS-CGYRO framework. Empirical modeling of SPARC plasmas with L-mode confinement indicates an ample window of breakeven (Q>1) without the need of H-mode operation. Extensive modeling of multi-channel (electron energy, ion energy and electron particle) flux-matched conditions with the nonlinear CGYRO code for turbulent transport coupled to the macroscopic plasma evolution using PORTALS reveal that the maximum fusion performance to be attained will be highly dependent on the near-edge pressure. Stiff core transport conditions are found, particularly when fusion gain approaches unity, and predicted density peaking is found to be in line with empirical databases of particle source-free H-modes. Impurity optimization is identified as a potential avenue to increase fusion performance while enabling core-edge integration. Extensive validation of the quasilinear TGLF model builds confidence in reduced-model predictions. The implications of projecting L-mode performance to high-performance and burning-plasma devices is discussed, together with the importance of predicting edge conditions.

We use a new gyrokinetic threshold model to predict a bifurcation in tokamak pedestal width-height scalings that depends strongly on plasma shaping and aspect-ratio. The bifurcation arises from the first and second stability properties of kinetic-ballooning-modes that yields wide and narrow pedestal branches, expanding the space of accessible pedestal widths and heights. The wide branch offers potential for edge-localized-mode-free pedestals with high core pressure. For negative triangularity, low-aspect-ratio configurations are predicted to give steeper pedestals than conventional-aspect-ratio. Both wide and narrow branches have been attained in tokamak experiments., Comment: 7 pages, 7 figures

The role of turbulence in setting boundary plasma conditions is presently a key uncertainty in projecting to fusion energy reactors. To robustly diagnose edge turbulence, we develop and demonstrate a technique to translate brightness measurements of HeI line radiation into local plasma fluctuations via a novel integrated deep learning framework that combines neutral transport physics and collisional radiative theory for the $3^3 D - 2^3 P$ transition in atomic helium. The tenets for experimental validity are reviewed, illustrating that this turbulence analysis for ionized gases is transferable to both magnetized and unmagnetized environments with arbitrary geometries. Based upon fast camera data on the Alcator C-Mod tokamak, we present the first 2-dimensional time-dependent experimental measurements of the turbulent electron density, electron temperature, and neutral density revealing shadowing effects in a fusion plasma using a single spectral line., Comment: 16 pages, 14 figures

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.

We present experimental inferences of cross-field impurity transport coefficients for Alcator C-Mod plasmas using a novel forward model for the entire Ca K-alpha spectrum, including satellite lines within the spectral range, to compare to high-resolution X-ray Imaging Crystal Spectroscopy (XICS). These measurements are complemented by Extreme Ultra-Violet (EUV) spectroscopy that constrains transport closer to the edge. Using new atomic data sets for both XICS and EUV analysis has enabled consideration of line ratios across both spectral ranges and has increased the accuracy of inferred transport coefficients. Inclusion of charge exchange between edge thermal neutrals and impurities is shown to be extremely important in C-Mod pedestals. We obtain D atomic neutral densities from experimental D Ly-alpha measurements at the midplane and compare these to SOLPS-ITER simulations, finding good agreement. Bayesian inferences of impurity transport coefficients are presented for L-, EDA H-, and I-mode discharges, making use of the Aurora package for forward modeling and combining our spectroscopic constraints. Experimentally inferred diffusion profiles are found to match turbulent transport models at midradius within uncertainties, using both quasilinear gyro-fluid TGLF SAT-1 and nonlinear ion-scale gyrokinetic CGYRO simulations. Significant discrepancies in convection are observed in some cases, suggesting difficulties in predictions of flat or hollow impurity profiles., Comment: 23 pages of main body; 38 pages including appendices. 17 figures. Submitted to Nuclear Fusion

We present a fully Bayesian approach for the inference of radial profiles of impurity transport coefficients and compare its results to neoclassical, gyrofluid and gyrokinetic modeling. Using nested sampling, the Bayesian Impurity Transport InferencE (BITE) framework can handle complex parameter spaces with multiple possible solutions, offering great advantages in interpretative power and reliability with respect to previously demonstrated methods. BITE employs a forward model based on the pySTRAHL package, built on the success of the well-known STRAHL code [Dux, IPP Report, 2004], to simulate impurity transport in magnetically-confined plasmas. In this paper, we focus on calcium (Ca, Z=20) Laser Blow-Off injections into Alcator C-Mod plasmas. Multiple Ca atomic lines are diagnosed via high-resolution X-ray Imaging Crystal Spectroscopy and Vacuum Ultra-Violet measurements. We analyze a sawtoothing I-mode discharge for which neoclassical and turbulent (quasilinear and nonlinear) predictions are also obtained. We find good agreement in diffusion across the entire radial extent, while turbulent convection and density profile peaking are estimated to be larger in experiment than suggested by theory. Efforts and challenges associated with the inference of experimental pedestal impurity transport are discussed., Comment: 38 pages, 19 figures, submitted for publication in Nuclear Fusion

Naturally stable to ELMs, and with widths larger than EPED predictions, the I-modes are an excellent laboratory for investigating the role of drift micro-instabilities in pedestals since I-mode pedestal are not "limited" by MHD instabilities. We present here a study based on gyrokinetic simulations (using GENE) to model fluctuations and heat transport in the I-mode pedestals in C-Mod. We find the Weakly Coherent Mode observed on C-Mod I-mode to be an electrostatic Ion Temperature Gradient/Impurity density gradient (ITG/Impurity) driven mode. The ITG/Impurity mode match frequency and the impurity confinement time observed on the I-mode. Nonlinear ETG simulations, can match experimental heat flux with profile adjustment well within experimental error bars. Simulations, varying impurity level (Zeff) and temperature and density profiles (within experimental error bars), are used to probe the sensitivity of fluctuations and transport.

Recently-proposed tokamak concepts use magnetic fields up to 12 T, far higher than in conventional devices, to reduce size and cost. Theoretical and computational study of trends in plasma behavior with increasing field strength is critical to such proposed devices. This paper considers trends in Alfv\'en eigenmode (AE) stability. Energetic particles, including alphas from D-T fusion, can destabilize AEs, possibly causing loss of alpha heat and damage to the device. AEs are sensitive to device magnetic field via the field dependence of resonances, alpha particle beta, and alpha orbit width. We describe the origin and effect of these dependences analytically and by using recently-developed numerical techniques (Rodrigues et al. 2015 Nucl. Fusion 55 083003). The work suggests high-field machines where fusion-born alphas are sub-Alfv\'enic or nearly sub-Alfv\'enic may partially cut off AE resonances, reducing growth rates of AEs and the energy of alphas interacting with them. High-field burning plasma regimes have non-negligible alpha particle beta and AE drive, but faster slowing down time, provided by high electron density, and higher field strength reduces this drive relative to low-field machines with similar power densities. The toroidal mode number of the most unstable modes will tend to be higher in high magnetic field devices. The work suggests that high magnetic field devices have unique, and potentially advantageous, AE instability properties at both low and high densities., Comment: Accepted to Nuclear Fusion

Transport barrier formation and its relation to sheared flows in fluids and plasmas are of fundamental interest in various natural and laboratory observations and of critical importance in achieving an economical energy production in a magnetic fusion device. Here we report the first observation of an edge transport barrier formation event in a gyrokinetic simulation carried out in a realistic tokamak edge geometry. The results show that turbulent Reynolds stress driven sheared ExB flows act in concert with neoclassical orbit loss to quench turbulent transport and form a transport barrier just inside the last closed magnetic flux surface., Comment: Accepted, Physical Review Letter

The guiding-center kinetic neoclassical transport code, XGC0, [C.S. Chang et. al, Phys. Plasmas 11, 2649 (2004)] is used to compute the heat fluxes and the heat-load width in the outer divertor plates of Alcator C-Mod and DIII-D tokamaks. The dependence of the width of heat-load fluxes on neoclassical effects, neutral collisions and anomalous transport is investigated using the XGC0 code. The XGC0 code includes realistic X-point geometry, a neutral source model, the effects of collisions, and a diffusion model for anomalous transport. It is observed that width of the XGC0 neoclassical heat-load is approximately inversely proportional to the total plasma current $I_{\rm p}$. The scaling of the width of the divertor heat-load with plasma current is examined for an Alcator C-Mod discharge and four DIII-D discharges. The scaling of the divertor heat-load width with plasma current is found to be weaker in the Alcator C-Mod discharge compared to scaling found in the DIII-D discharges. The effect of neutral collisions on the $1/I_{\rm p}$ scaling of heat-load width is shown not to be significant. Although inclusion of poloidally uniform anomalous transport results in a deviation from the $1/I_{\rm p}$ scaling, the inclusion of the anomalous transport that is driven by ballooning-type instabilities results in recovering the neoclassical $1/I_{\rm p}$ scaling. The Bohm or Gyro-Bohm scalings of anomalous transport does not strongly affect the dependence of the heat-load width on plasma current. The inclusion of anomalous transport, in general, results in widening the width of neoclassical divertor heat-load and enhances the neoclassical heat-load fluxes on the divertor plates. Understanding heat transport in the tokamak scrape-off layer plasmas is important for strengthening the basis for predicting divertor conditions in ITER., Comment: Submitted to Physics of Plasmas

To study finite-dimensional modules of the Lie superalgebras, Kac introduced the Kac-modules and divided them into typical or atypical modules according as they are simple or not. For Lambda being atypical, Hughes et al have an algorithm to determine all the composition factors of a Kac-module; they conjectured that there exists a bijection between the composition factors of a Kac-module and the so-called permissible codes. The aim of this paper is to prove this conjecture. We give a partial proof here, i.e., to any unlinked code, by constructing explicitly the primitive vector, we prove that there corresponds a composition factor of the Kac-module. We will give a full proof of the conjecture in another paper., Comment: 25 pages, Latex