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At least 235 records · Page 13

Error-Field Penetration Thresholds in Ohmically Heated ITER and SPARC Plasmas

The critical n=1, n=2, and n=3 error-field amplitudes needed to trigger error-field penetration in ITER and SPARC, steady-state, ohmically heated plasmas are calculated using a standard asymptotic matching approach. The calculation incorporates plasma impurities, trapped particles, the bootstrap current, and neoclassical poloidal flow-damping. The energy confinement time is specified by the neo-Alcator scaling law in the low-density linear ohmic confinement (LOC) regime, and by the ITER-89P L-mode scaling law in the high-density saturated ohmic confinement regime (SOC) regime. The response of the plasma in the inner region is calculated using a linearized version of the four-field model. At the normal operating electron number density, diamagnetic levels of rotation are found to be sufficient to protect ITER and SPARC ohmically heated plasmas from m=2/n=1 error-field penetration. On other hand, SPARC, and especially ITER, ohmically heated plasmas may be vulnerable to n>1 error-field penetration. ITER and SPARC ohmically heated plasmas are also slightly more susceptible to error-field penetration when the electron fluid at the rational surface rotates in the ion diamagnetic direction, rather than the electron diamagnetic direction. At electron number densities that are sufficiently low that the plasma lies in the LOC confinement regime, the error-field penetration threshold increases with increasing density. However, as soon as the electron number density becomes large enough that the plasma enters the SOC regime, the increase in the error-field penetration threshold with increasing density levels off.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Asymptotic vacuum solution at tokamak X-point tip

In the H-mode regime of diverted tokamaks, the presence of strong pressure gradients in the pedestal gives rise to a sizable bootstrap current, together with the Ohmic and Pfirsch–Schlueter currents, close to the separatrix. For such equilibria, the presence of finite current density close to the separatrix requires the reexamination of equilibrium properties. It is almost universally assumed that the two branches of the separatrix (the stable and unstable manifolds) are straight as they cross at the X-point. However, the opposite angles of the plasma-filled segment and vacuum one cannot be equal if the current density does not vanish at the separatrix on the plasma side. We solve this difficulty by chipping off a thin layer of plasma edge so that the sharp corner of the plasma-filled segment becomes a hyperbola. Using the conformal transformation, we found that in the assumption of a hyperbolic boundary, the X point moves beyond the plasma boundary to fall in the vacuum region. An acute angle of the plasma-filled segment leads to an obtuse opposite angle of vacuum segment and vice versa. In the case of an acute angle of the plasma-filled segment, the new X point shifts inside the X point formed by the asymptotes of a hyperbolic boundary; in the case of an obtuse angle of the plasma-filled segment, the new X point shifts outside the X point formed by the asymptotes of a hyperbolic plasma boundary. Furthermore, the results are important for understanding the X point features, which affect the tokamak edge stability and transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A review on charged-particle transport modeling for laser direct-drive fusion

Inertial confinement fusion (ICF) with the laser-indirect-drive scheme has recently made a tremendous breakthrough recently after decades of intensive research effort. Taking this success to the next step, the ICF community is coming to a general consensus that laser direct-drive (LDD) fusion might be the viable way for enabling inertial fusion energy (IFE) and high-gain targets for other applications. Designing and understanding LDD fusion targets heavily rely on radiation-hydrodynamic code simulations, in which charged-particle transport plays an essential role in modeling laser-target energy coupling and bootstrap heating of fusion-produced α-particles. To better simulate charged-particle transport in LDD targets, over the past four decades the plasma physics community has advanced transport calculations from simple plasma physics models to sophisticated computations based on first-principles methods. In this review, we give an overview of the current status of charged-particle transport modeling for LDD fusion, including what challenges we still face and the possible paths moving forward to advance transport modeling for ICF simulations. We hope this review will provide a summary of exciting challenges to stimulate young minds to enter the field, facilitate further progress in understanding warm-dense matter physics, and ultimately bridge toward the success of reliable LDD fusion designs for IFE and other high-gain ICF applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Inverse aspect-ratio expanded tokamak equilibria

Following Greene et al. [Phys. Fluids 14, 671 (1971)] and Connor et al. [Phys. Plasmas 31, 577 (1988); Plasma Phys. Control. Fusion 34, 161 (1992); and Nucl. Fusion 33, 1533 (1993)], the Grad-Shafranov equation for an axisymmetric tokamak plasma equilibrium is solved via an expansion in the, supposedly small, inverse aspect-ratio of the plasma, ϵ. The displacements of equilibrium magnetic flux-surfaces due to plasma shaping are assumed to be $\mathcal{O}$(ϵ) smaller than the minor radii of the surfaces, but no other restriction is placed on the nature of the shaping. The solution of the Grad-Shafranov equation is matched to a vacuum solution that extends to infinity, and consists of an expansion in toroidal functions. The external poloidal magnetic field generated by a finite set of discrete external poloidal magnetic field-coils is calculated, and incorporated into the toroidal function expansion. In this manner, the shape of a large aspect-ratio tokamak plasma is directly related to the currents flowing in the external poloidal field-coils. Finally, a pedestal in the plasma pressure, and the associated spike in the bootstrap current, are incorporated into the model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Investigating nonlinear magnetohydrodynamics in an optimized, reactor-scale quasi-axisymmetric stellarator

We use the new simulation capabilities of the extended-magnetohydrodynamic (MHD) code, M3D-C1, to investigate the nonlinear MHD properties of a reactor-scale quasisymmetric stellarator equilibrium. Our model captures the self-consistent evolution of the magnetic field, temperature, density, and flow profiles without imposing restrictions on the structure of the first. We include the effects of resistivity using a realistic temperature-dependent Spitzer model, along with a model for heat transport that captures the key physical characteristic, namely, strongly anisotropic diffusion in directions perpendicular and parallel to the magnetic field. We consider a quasi-axisymmetric, finite-pressure equilibrium that was optimized for self-consistent bootstrap current, quasi-symmetry, and energetic particle confinement. Our assessment finds that the equilibrium is highly unstable to interchange-like pressure-driven instabilities near the plasma edge. The initially unstable modes rapidly destabilize other modes in the direction of the N-fold rotational symmetry (toroidal, in this case). For this equilibrium, N = 2, meaning destabilization of a large number of even-numbered toroidal Fourier modes. Thus, field-periodicity is likely to be an important factor in the nonlinear MHD stability characteristics of optimized stellarators.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A high-frequency, low-power resonant radio-frequency neutron spin flipper for high-resolution spectroscopy

Here, we present a resonant-mode, transverse-field, radio-frequency (rf) neutron spin flipper design that uses high-temperature superconducting films to ensure sharp transitions between uniform magnetic field regions. Resonant mode allows for low-power, high-frequency operation but requires strict homogeneity of the magnetic fields inside the device. This design was found to efficiently flip neutrons at 96.6 ± 0.6% at an effective frequency of 4 MHz in bootstrap configuration with a beam size of 2.4 × 2.5 cm 2 and a wavelength of 0.4 nm. The high frequency and efficiency enable this device to perform high-resolution neutron spectroscopy with comparable performance with currently implemented rf flipper designs. The limitation of the maximum frequency was found due to the field homogeneity of the device. We numerically analyze the maximum possible efficiency of this design using a Bloch solver simulation with magnetic fields generated from finite-element simulations. We also discuss future improvements of the efficiency and frequency to the design based on the experimental and simulation results.

47 OTHER INSTRUMENTATION↗

Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator

Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as optimization and satisfiability. Here, we report the implementation of a low-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator. We estimate the ground-state energy of the Transverse Field Ising Model with long-range interactions with tunable range, and we optimize the corresponding combinatorial classical problem by sampling the QAOA output with high-fidelity, single-shot, individual qubit measurements. We execute the algorithm with both an exhaustive search and closed-loop optimization of the variational parameters, approximating the ground-state energy with up to 40 trapped-ion qubits. We benchmark the experiment with bootstrapping heuristic methods scaling polynomially with the system size. We observe, in agreement with numerics, that the QAOA performance does not degrade significantly as we scale up the system size and that the runtime is approximately independent from the number of qubits. We finally give a comprehensive analysis of the errors occurring in our system, a crucial step in the path forward toward the application of the QAOA to more general problem instances.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Role of fast ions in spontaneous neoclassical tearing mode instabilities in NSTX

Spontaneous neoclassical tearing modes (spontaneous NTMs) have been observed in the National Spherical Torus Experiment (NSTX). Recently, a TRANSP based model for the modified Rutherford equation analysis was developed to accurately predict the effect of fast ions on the growth of magnetic islands. The goal of this paper is to utilize the TRANSP NTM model to understand the role of fast ions in NSTX spontaneous NTMs. Our analysis shows that when the passing fast ion driven kinetic neoclassical polarization current term is larger than 1% of the bootstrap current term in the modified Rutherford equation, fast ions play a decisive role in the early growth phase of spontaneous NTM. This result is applicable to any tokamak plasmas with a fast ion drift orbit width, or the fast ion poloidal Larmor radius, comparable to the magnetic island width.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Verification of gyrokinetic particle simulations of neoclassical tearing modes in fusion plasmas

Abstract The ability to simulate neoclassical tearing modes (NTMs) in the gyrokinetic toroidal code (GTC) has been developed and verified, in which ions are treated with a gyrokinetic model and electrons are treated as a resistive fluid. The simulation results demonstrate that the neoclassical bootstrap current effect can destabilize an otherwise stable classical tearing mode. In the cylindrical geometry, GTC simulations in the magnetohydrodynamic limit show quantitative agreement with the modified Rutherford theory, both in terms of the scaling law in the small island limit and in terms of the saturation level and pressure flattening effect in the large island limit. The toroidal effects are slightly destabilizing for the NTM, while the kinetic effects of thermal ions are stabilizing for the NTM and increase its excitation threshold.

Physics↗

Measurement of small island characteristics using high resolution ECE and CER at DIII-D

Abstract The measurements using the high resolution electron cyclotron emission radiometry and the charge exchange and recombination spectroscopy are processed using analytic formulas to allow for the detection of islands as small as 1.9 cm. In contrast to large, saturated magnetic islands which are relatively well understood to be governed by the loss of bootstrap current inside the island, small islands are less well understood due to the difficulty of their accurate measurement in tokamaks. Here, ‘small’ islands are islands comparable in size to the ion banana width, which can be as small as 0.8 cm at DIII-D. The new measurement methods allow for the detection of small island widths when the predicted increase of mode frequency to match the Doppler shifted ion diamagnetic frequency is observed. Therefore, for the first time, the mode frequency increase can be unambiguously associated to the acceleration of the magnetic island propagation. Such association allows for a further development and validation of the much-debated theory of ion polarization currents, which is thought to govern the small island growth.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Assessing the numerical stability of physics models to equilibrium variation through database comparisons on DIII-D

High fidelity kinetic equilibria are crucial for tokamak modeling and analysis. Manual workflows for constructing kinetic equilibria are time consuming and subject to user error, motivating development of automated equilibrium reconstruction tools to provide accurate and consistent reconstructions for downstream physics analysis. These automated tools also provide access to kinetic equilibria at large database scales, which enables the quantification of general uncertainties arising from equilibrium reconstruction techniques. In this paper, we compare a large database of DIII-D kinetic equilibria generated manually by physics experts to equilibria from automated kinetic reconstruction tools, assessing the impact of reconstruction method on equilibrium parameters and resulting magnetohydrodynamic stability calculations. We find agreement among scalar parameters, whereas profile quantities, such as the bootstrap current, show larger disagreements. We analyze ideal kink and classical tearing stability with DCON and STRIDE respectively, finding that the kink stability calculation is generally more robust than the tearing index Δ' calculation. We find that in 90% of cases, both kink stability classifications are unchanged between the manual expert and automated kinetic equilibria.

CAKE↗

Achieving a robust grassy-ELM operation regime in CFETR

We have identified a robust grassy-edge localized mode (ELM) operation regime for future tokamak reactors. The regime exists within a pedestal top electron collisionality (ν*) window at high global poloidal beta (β p ). The existence of an upper ν* limit for grassy-ELMs is consistent with results previously reported in experiments (Oyama et al 2010 Nucl. Fusion 50 064014), while the existence of a lower ν* limit has not been reported previously. Using EPED and BOUT++, a theoretical model that quantitatively explains the physics of the grassy-ELMs within the window, which distinguishes them from the small mixed-ELMs at lower ν*, is presented for the first time. A peeling-ballooning stability boundary is obtained by scanning the operating density space. The change in density corresponds to a change in ν* that affects the pedestal bootstrap current. High β p leads to a strong Shafranov shift, which affects the flux surface averaged pressure drive. The two effects combine to create a peeling-dominated window in intermediate ν* buffered by ballooning-dominated regimes. Only the peeling-dominated regime shows a cyclic behavior in the perturbed pressure during the nonlinear simulation of an ELM crash, reminiscent of grassy-ELM dynamics. Similarly, the energy released across the separatrix is demonstrated to be significantly smaller. The quick recovery of the ELM crash is explainable by the rapid rise of a low n kink-peeling instability when the pedestal current I ped exceeds a threshold at high β p . It minimizes the excursion beyond marginal stability and is absent in the ballooning-dominated regime. Comparison with recent experiments over a range of β p and ν* strongly supports the physical picture proposed by the modeling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The advanced tokamak path to a compact net electric fusion pilot plant

Abstract Physics-based simulations project a compact net electric fusion pilot plant with a nuclear testing mission is possible at modest scale based on the advanced tokamak concept, and identify key parameters for its optimization. These utilize a new integrated 1.5D core-edge approach for whole device modeling to predict performance by self-consistently applying transport, pedestal and current drive models to converge fully non-inductive stationary solutions, predicting profiles and energy confinement for a given density. This physics-based approach leads to new insights and understanding of reactor optimization. In particular, the levering role of high plasma density is identified, which raises fusion performance and self-driven ‘bootstrap currents’, to reduce current drive demands and enable high pressure with net electricity at a compact scale. Solutions at 6–7 T, ∼4 m radius and 200 MW net electricity are identified with margins and trade-offs possible between parameters. Current drive comes from neutral beam and ultra-high harmonic (helicon) fast wave, though other advanced approaches are not ruled out. The resulting low recirculating power in a double null configuration leads to a divertor heat flux challenge that is comparable to ITER, though reactor solutions may require more dissipation. Strong H-mode access (x2 margin over L–H transition scalings) and ITER-like heat fluxes are maintained with ∼20%–60% core radiation, though effects on confinement need further analysis. Neutron wall loadings appear tolerable. The approach would benefit from high temperature superconductors, as higher fields would increase performance margins while potential for demountability may facilitate nuclear testing. However, solutions are possible with conventional superconductors. An advanced load sharing and reactive bucking approach in the device centerpost region provides improved mechanical stress handling. The prospect of an affordable test device which could close the loop on net-electric production and conduct essential nuclear materials and breeding research is compelling, motivating research to validate the techniques and models employed here.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Advances in the long-pulse steady-state high beta H-mode scenario with active controls of divertor heat and particle fluxes in EAST

Since the last IAEA-Fusion Energy Conference, the Experimental Advanced Superconducting Tokamak (EAST) research program has been, in support of ITER and CFETR, focused on development in terms of the long-pulse steady-state (fully noninductive) high beta H-mode scenario with active controls of the stationary and transient divertor heat and particle fluxes. The operational domain of the steady-state H-mode plasma scenario has been significantly extended with ITER-like tungsten mono-block divertor, plasma control and heating schemes. EAST has achieved several important milestones in the development of high β p H-mode scenario and its key physics and technologies. A 60 s-scale long-pulse steady-state high β p H-mode discharge with the major normalized plasma parameters similar to the designed performance of the CFETR 1GW fusion power operation scenario has been successfully established and sustained by pure RF heating and current drive. Several feedback control schemes have been developed for a sustained detachment with good core confinement. This includes control of the total radiation power, target electron temperature, and particle flux measured using divertor Langmuir probes or a combination of the control of target electron temperature and AXUV radiation near the X point. The detachment feedback control schemes have been integrated with small-ELM regimes and high β p scenario via neon seeding, enabling a core and edge compatible integrated high-beta scenario applicable to long-pulse operations. ELM suppression has been achieved using various methods, including resonant magnetic perturbations and impurity seeding. Full suppression of ELMs by using n=4 RMPs has been demonstrated for ITER for the first time in low input torque plasmas in EAST. Finally, EAST has been operated with helium to support the ITER research requirements for the first time. For a long-pulse, high bootstrap current fraction operation, a new lower tungsten divertor with active water-cooling has been installed, along with improvements in the heating and current drive capability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NSTX-U theory, modeling and analysis results

Here, the mission of the low aspect ratio spherical tokamak NSTX-U is to advance the physics basis and technical solutions required for optimizing the configuration of next-step steady-state tokamak fusion devices. NSTX-U will ultimately operate at up to 2 MA of plasma current and 1 T toroidal field on axis for 5 s, and has available up to 15 MW of neutral beam injection power at different tangency radii and 6 MW of high harmonic fast wave heating. With these capabilities NSTX-U will develop the physics understanding and control tools to ramp-up and sustain high performance fully non-inductive plasmas with large bootstrap fraction and enhanced confinement enabled via the low aspect ratio, high beta configuration. With its unique capabilities, NSTX-U research also supports ITER and other critical fusion development needs. Super-Alfvénic ions in beam-heated NSTX-U plasmas access energetic particle (EP) parameter space that is relevant for both α-heated conventional and low aspect ratio burning plasmas. NSTX-U can also generate very large target heat fluxes to test conventional and innovative plasma exhaust and plasma facing component solutions. This paper summarizes recent analysis, theory and modelling progress to advance the tokamak physics basis in the areas of macrostability and 3D fields, EP stability and fast ion transport, thermal transport and pedestal structure, boundary and plasma material interaction, RF heating, scenario optimization and real-time control.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Comparison of MHD stability properties between QH-mode and ELMy H-mode plasmas by considering plasma rotation and ion diamagnetic drift effects

Magnetohydrodynamic (MHD) stability at tokamak edge pedestal in a quiescent H-mode (QH-mode) and type-I ELMy H-mode plasmas in DIII-D experiment was analyzed by considering plasma rotation and ion diamagnetic drift effects. QH-mode plasma is marginally stable to kink/peeling mode (K/PM), but ELMy H-mode one is almost unstable to peeling-ballooning mode (PBM). It was identified that there are three physics features responsible for the difference in the MHD stability properties between QH-mode plasma and ELMy H-mode one. These are the distance of pedestal foot from the last closed flux surface (LCFS), the amount of the ion diamagnetic drift frequency at pedestal, and impact of coupled rotation and ion diamagnetic drift effects. These features were confirmed through the numerical experiments that the stability properties of the QH-mode plasma can be changed to that of the ELMy H-mode one by shifting the plasma profiles inward in the radial direction and halving the ion diamagnetic drift frequency. The reasons of the change in the stability properties are thought as that K/PM is stabilized due to the inward shift of the bootstrap current profile, and PBM is destabilized due to the reduction of the coupled rotation and ion diamagnetic drift stabilizing effect. Importance of these features was validated through numerical experiments with experimental data of other QH-mode plasmas in DIII-D. All the results show that MHD stability properties of QH-mode plasma can be obtained in case that pedestal foot is close to LCFS, ion diamagnetic drift frequency is large due to high ion temperature, and strong rotation shear exists near pedestal.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Direct preemptive stabilization of $m,n$ = 2,1 neoclassical tearing modes by electron cyclotron current drive in the DIII-D low-torque ITER baseline scenario

We report the first preemptive direct stabilization of $m,n$ = 2,1 neoclassical tearing modes (NTMs) in DIII-D low-torque ITER baseline scenario plasmas by electron cyclotron waves. These experiments strongly support that the observed stabilization is achieved by replacing the missing bootstrap current in the island by electron cyclotron current drive (ECCD). These plasmas (with and without ECCD) are stable to 2,1 NTMs when the differential rotation between the q = 1 and q = 2 surfaces (Δf 1,2 ) is sustained above a critical value (Δf CRIT ≈ 1 kHz), but those evolving to low differential rotation (Δf 1,2 < Δf CRIT ) routinely develop a disruptive 2,1 island at the time and frequency of a sawtooth precursor. Preemptive, local and direct stabilization by ECCD is tested by scanning the current drive amplitude and location inside and outside of the q = 2 rational surface shot by shot. Analysis of only low differential rotation time windows, i.e. when stabilization from Δf 1,2 is absent, shows focused ECCD at q = 2 prevents the onset of 2,1 NTMs. These results are important, as they give the first demonstration of disruptive NTM control by ECCD in the plasma scenario planned for ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Plasma rotation and diamagnetic drift effects on the resistive wall modes in the negative triangularity tokamaks

Abstract It was found previously that the negative triangularity (NT) configuration is more MHD-unstable for low n modes than the positive triangularity (PT) case, although the situation is reversed for intermediate n modes and the NT configuration becomes more stable for intermediate n modes ( n = 3 − 10 ) (Zheng et al 2021 Nucl. Fusion 61 116014). Here, n is the toroidal mode number. In this work, we extend the studies to include the rotation effects, as well as the diamagnetic drift effects, to see how the resistive wall modes (RWMs) in the NT configuration are affected as compared with the PT configuration. This is particularly motivated by noting that the wall interface with the plasma is quite different between the NT and PT configurations. It affects the plasma rotation and diamagnetic drift effects on the low n RWM. We consider the DIII-D-NT-experiment equilibrium reconstructed by the EFIT code. Based on the equilibrium g-file, the extended equilibria are constructed with the VMEC code by varying the beta values while keeping the pressure and poloidal current flux profiles basically unchanged. The bootstrap current contribution to the equilibria is taken into account with the Sauter formula. The MHD stability is then computed using the AEGIS code with the rotation and diamagnetic drift effects taken into account. We found that, although the NT configuration is less stable for n = 1 MHD modes, the rotation and diamagnetic drift stabilization effects on RWMs are more effective in the NT configuration than in the PT one. Note that even in the PT case, the stabilization of RWMs by the rotation and kinetic effects is critical. Because the low-n RWMs in the regular NT case are more unstable, the rotation and diamagnetic drift stabilization effects found in this research are important for the NT tokamak concept.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗