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Predictive simulations of heat and particle fluxes in the plasma boundary are a critical missing capability for magnetic fusion energy power plant design.
A new open source tool for fluid simulation of multi-component plasmas is presented, based on a flexible software design that is applicable to scientific simulations in a wide range of fields. Hermes-3 is built on plasma simulation framework BOUT++, consolidating earlier SD1D and Hermes models into a single code that can be configured at run-time to solve plasma models in 1D, 2D or 3D, either for transport (steady-state) or turbulent (time-evolving) problems, with an arbitrary number of ion and neutral species. Here, we describe the improved numerical algorithms and software design that have been implemented in Hermes-3. To demonstrate the capabilities of this tool, applications relevant to the boundary of tokamak plasmas are presented: 1D simulations of diveror plasmas evolving equations for all charge states of neon and deuterium; 2D transport simulations of tokamak equilibria in single-null X-point geometry with plasma ion and neutral atom species; and simulations of the time-dependent propagation of plasma filaments (blobs). Hermes-3 is publicly available on Github under the GPL-3 open source license. The repository includes documentation and a suite of unit, integrated and convergence tests.
As a promising scenario for fusion reactors, the high poloidal-beta (β P ) scenario is characterized by a strong large radius internal transport barrier (ITB), which significantly enhances the overall confinement quality and the bootstrap current fraction for fully non-inductive operation. It is frequently observed that in the presence of a strong ITB, the pedestal height is lower and is accompanied by small edge localized modes (ELMs), which further improves the compatibility of a high performance core with an edge solution. A mechanism for the formation of the low pedestal is proposed in this paper. It is found that the strong ITB creates an off-axis bootstrap current to clamp the local safety factor q, and thus the magnetic shear in the outer core/pedestal region is increased. Gyrokinetic simulations with the CGYRO code show that the higher magnetic shear brings the experimental profiles into the range where the growth rate of drift-wave instabilities and thus transport is higher, and therefore a lower pedestal gradient is expected. Here, the combination of low pedestal and high magnetic shear further enhances the turbulent transport across the whole pedestal, consistent with power balance analysis. Such a positive feedback mechanism ultimately results in a lower pressure pedestal as observed in experiments. Under such a low pedestal, linear simulations with BOUT++ predict the growth rates of peeling–ballooning modes to be lower across the whole toroidal mode number spectra, and the nonlinear BOUT++ simulation exhibits lower saturated fluctuation intensity as well, consistent with the experimentally observed lower ELM size.
A numerical model that calculates the collisional interactions between the lithium atoms from a lithium pellet and the background plasmas has been upgraded. The ion density ($N_t$), electron temperature ($T_e$), ion temperature ($T_i$) and parallel ion velocity ($V_{∥, i}$) are used to characterize the background plasmas. The lithium atom density ($N^{a}_{Li}$) and parallel velocity ($V_{∥,a}$) of lithium atoms evolve with time. For each lithium ion, the density ($N_{Li^{n+}}$), temperature ($T_{Li^{n+}}$) and parallel velocity ($V_{∥, Li^{n+}}$) are self-consistently calculated. A C-mod lower single null equilibrium is used to generate the grid for the BOUT++ simulation. The lithium atoms can be fully ionized to $Li^{3+}$ in ~2 μs. The rapid radial and poloidal expansion of the lithium ions are found in the simulation. After the collision interaction process, the electron temperature rapidly decreases at the pellet location; then, it rapidly poloidally expands, and the temperature at the pellet location starts to recover. The electron pressure increases at the pellet location despite the decrease in electron temperature because of the extra electrons from the lithium ionization. The ion pressure profile decreases in the pellet location due to the decrease in ion temperature.
Recently the drift-reduced Landau fluid six-field turbulence model within the BOUT++ framework has been upgraded. In particular, this new model employs a new normalization, adds a volumetric flux-driven source option, the Landau fluid closure for parallel heat flux and a Laplacian inversion solver which is able to capture $n$ = 0 axisymmetric mode evolution in realistic tokamak configurations. As we report here, these improvements substantially extended model's capability to study a wider range of tokamak edge phenomena, and are essential to build a fully self-consistent edge turbulence model capable of both transient (e.g., ELM, disruption) and transport time-scale simulations.
Here, the Electron Cyclotron Emission Imaging (ECEI) diagnostic was used to observe a finite-n interchange mode structure in the edge of negative triangularity shaped plasmas on DIII-D. At a small negative triangularity (δ u = -0.2), the plasma is in the H-mode with ELMs that are triggered by a low-n interchange mode. At a larger negative triangularity (δ u = -0.4) and low NBI power (2 MW), a dithering oscillation is observed that is triggered by a low-n interchange mode, whereas at higher NBI power (>2 MW), the edge reverts to L-mode and the low-n interchange mode is present continuously. In all cases, the edge pressure gradient is clamped when the interchange mode is present. It is concluded that the low-n interchange mode prevents the plasma from transitioning to H-mode at a large negative triangularity. This agrees with linear BOUT++ simulations which suggest that the interchange-type MHD can be a resistive ballooning mode whereby resistivity can significantly increase the finite-n ballooning mode growth rate. The absence of H-mode at large negative triangularity can, thus, be explained by the excitation of low-n pressure driven resistive ballooning modes in the plasma edge.
Edge-localized modes (ELMs) eject intense bursts of heat and particles that threaten plasma-facing components in fusion reactors. Nonlinear full-torus BOUT++ simulations show that turbulence-driven zonal magnetic fields (ZMFs) play an essential role in nonlinear ELM evolution by maintaining self-consistent force balance. Zonal flows mitigate the initial crash through shear but do not prevent continued radial transport. When ZMFs are self-consistently included, turbulence-driven zonal currents modify the parallel current distribution and magnetic tension and are associated with a reduction of the axisymmetric (𝑛 = 0) perturbed radial force imbalance. This coincides with a transition from convective, bursty propagation to more localized, diffusive transport. Similar behavior is observed across the regimes considered, including both resistive-ballooning and peeling-ballooning cases. Finally, associated signatures, including radial electric field shear and parallel current redistribution, provide experimentally accessible diagnostics for present devices and ITER-relevant conditions.
A new integrating model has been developed to couple tokamak edge multiscale magnetohydrodynamic (MHD) events and transport simulations, such as edge-localized mode (ELM) cycles. As a proof of principle, we first start from a set of three-field two-fluid model equations, which includes the pressure, current, and vorticity. Here, the equations are separated into the slowly evolving part of the axisymmetric component by taking a time average of the axisymmetric component. The time-averaged fluxes, which are quadratic in fluctuating quantities, act as driven terms for the time-averaged axisymmetric quantities that determine the plasma transport, and therefore the large-scale evolution of the plasma profiles. Then the HL-2A's ELM cycles are simulated using the model. Good agreements of ELM size and pedestal recovery time have been achieved for the solutions obtained from the coupled simulation compared with experiment. For one ELM cycle simulation, the coupled code can achieve a speedup of a factor of up to 30 over standalone code.
For tokamak edge plasma simulation, a plasma simulation framework BOUT++ employs a dual coordinate system to simulate moderate-n and high-n plasma instability with reasonable computational cost, where n is the toroidal mode number. This coordinate system however limits the computational domain to the toroidal wedge (full torus divided into N parts in the toroidal direction) for computational efficiency and the use of flute-ordering approximation in the field solver calculating the flow potential from the vorticity which may not be valid for low-n modes. Improving numerical treatment of low-n modes is however indispensable to address simulations of low-n current-driven edge localized mode (ELM), ELM control by resonant magnetic perturbations (RMPs), edge turbulence with RMPs and so on. In this work, BOUT++ is extended to simulate the interplay between $n=0$, low-n and high-n plasma components in a full annular tokamak edge domain through hybrid modeling of the flow potential and the vorticity. Low-n modes of flow potential are calculated in an orthogonal flux surface coordinate and high-n modes in the dual coordinate system separately in Fourier space. Finally, the proposed scheme can capture an interplay between $n=1$ global modes and high-n turbulence during pedestal collapse in a full annular torus domain with a circular cross section.
The wide-pedestal quiescent high confinement mode discovered on DIII-D in recent years is a stationary and quiescent H-mode (QH-mode) with the pedestal width exceeding EPED prediction by at least 25%. Its characteristics, such as low rotation, high energy confinement and edge localized mode-free operation, make it an attractive operation mode for future reactors. Linear and nonlinear simulations using BOUT++ reduced two fluid MHD models and awere carried out to investigate the bursty broadband turbulence often observed in the edge of wide-pedestal QH-mode plasmas. Two kinds of MHD-scale instabilities in different spatial locations within the pedestal were found in the simulations: one mild peeling–ballooning (PB) mode γ PB < 0.04ω A ) located near the minimum in E r</:sub> well propagating in ion diamagnetic drift direction; and one drift-Alfvén wave locates at smaller radius compared to E r</:sub> well propagating in the electron diamagnetic drift direction and unstable only when the parallel electron dynamics is included in the simulation. The coupling between drift wave and shear Alfvén wave provides a possible cause of the experimentally observed local profile flattening in the upper-pedestal. The rotation direction, mode location, as well as the wavenumber of these two modes from BOUT++ simulations agree reasonably well with the experimental measurements, while the lack of quantitative agreement is likely due to the lack of trapped electron physics in current fluid model. This work presents improved physics understanding of the pedestal stability and turbulence dynamics for wide-pedestal QH-mode.
We report BOUT++ turbulence simulations are conducted for a 60 s steady-state long pulse high β p EAST grassy ELM discharge. BOUT++ linear simulations show that the unstable mode spectrum covers a range of toroidal mode numbers from low-n (n = 10–15) peeling–ballooning modes (P–B) to high-n (n = 40–80) drift-Alfvén instabilities. Nonlinear simulations show that the ELM crash is triggered by low-n peeling modes and fluctuation is generated at the peak pressure gradient position and radially spread outward into the scrape-off-layer, even though the drift-Alfvén instabilities dominate the linear growth phase. However, drift-Alfvén turbulence delays the onset of the grassy ELM and enhances the energy loss with the fluctuation extending to pedestal top region. Simulations further show that if the peeling drive is removed, the fluctuation amplitude drops by an order of magnitude and the ELM crashes disappear. The divertor heat flux width is ~2 times larger than the estimates based on the HD model and the Eich's ITPA multi-tokamak scaling (or empirical Eich scaling) due to the strong radial turbulence transport.
A study of the effects of drifts on the particle flow pattern and in–out divertor plasma density asymmetry for L-mode and H-mode plasmas is carried out for EAST discharges by the edge plasma transport codes SOLPS and BOUT++. The simulation of L-mode plasmas is done by SOLPS while the simulation of H-mode plasmas is done by BOUT++. The toroidal magnetic field direction for the simulated discharge is artificially reversed in the codes to study the effects of different drift directions on the divertor particle flow pattern and the in–out asymmetry of divertor plasma density. The divertor particle flows induced by diamagnetic and E × B drifts are found to have similar directions in the divertor region for the same discharge. The directions of the flows induced by drifts would be reversed with the reverse of toroidal magnetic field direction. The diamagnetic drift seems to have no effect on the in–out asymmetry of divertor plasma density due to its divergence-free nature. However, the E × B drift could result in a pronounced asymmetry of plasma density between the inner and outer divertor targets. The density in–out asymmetry caused by E × B drift is reversed with the reverse of E × B drift flow direction. Detailed analysis shows that the radial component of the E × B drift flow is the main cause of density asymmetry. The results from the simulation of H-mode plasmas with BOUT++ are similar to those of the L-mode plasmas with SOLPS except that the drift effects seem to be slightly larger in the H-mode plasmas compared to the L-mode plasmas.
BOUT++ turbulence simulations are conducted to capture the underlying physics of small ELM characteristics achieved by increasing separatrix density via controlling strike points from vertical to horizontal divertor plates for three EAST discharges. BOUT++ linear simulations show that the most unstable modes change from high-n ideal ballooning modes to intermediate-n peeling–ballooning modes and eventually to peeling–ballooning stable plasmas in the pedestal. Nonlinear simulations show that the fluctuation is saturated at a high level for the lowest separatrix density. The ELM size decreases with increasing separatrix density, until the fraction of this energy lost during the ELM crash becomes less than 1% of the pedestal stored energy, leading to small ELMs. Simulations indicate that small ELMs can be triggered either by the marginally peeling–ballooning instability near the peak pressure gradient position inside the pedestal or by a local instability in the pedestal foot with a larger separatrix density gradient. The pedestal collisionality scan for type-I ELMs with steep pedestal density gradient shows that both linear growth rate and ELM size decrease with increasing collisionality. On the contrary, the pedestal collisionality and pedestal density width scan with a weak pedestal density gradient indicate small ELMs can either be triggered by a high-n ballooning mode or by a low-n peeling mode in a low collisionality region 0.04–0.1. We report the simulations indicate the weaker the linear unstable modes near marginal stability with small linear growth rate, the lower nonlinearly saturated fluctuation intensity and the smaller turbulence spreading from the linear unstable zone to stable zone in the nonlinear saturation phase, leading to small ELMs.
BOUT++ turbulence simulations were performed to investigate the impact of turbulence spreading on the edge localized mode (ELM) size and divertor heat flux width (λ q ) broadening in small ELM regimes. Here, this study is motivated by EAST experiments. BOUT++ linear simulations of a pedestal radial electric field (E r ) scan show that the dominant toroidal number mode (n) shifts from high-n to low-n, with a narrow mode spectrum, and the maximum linear growth rate increases as the pedestal E r well deepens. The nonlinear simulations show that as the net E × B pedestal flow increases, the pressure fluctuation level and its inward penetration beyond the top of the pedestal both increase. This leads to a transition from small ELMs to large ELMs. Both inward and outward turbulence spreading are sensitive to the scrape-off-layer (SOL) plasma profiles. The inward turbulence spreading increases for the steep SOL profiles, leading to increasing pedestal energy loss in the small ELM regime. The SOL width (λ q ) is significantly broadened progressing from the ELM-free to small ELM regime, due to the onset of strong radial turbulent transport. The extent of the SOL width (λ q ) broadening depends strongly on outward turbulence spreading. The fluctuation energy intensity flux Γ ε at the separatrix can be enhanced by increasing either pedestal E r flow shear or local SOL pressure gradient. The λ q is broadened as the fluctuation energy intensity flux Γ ε at the last close flux surface (LCFS) increases. Local SOL E × B flow shear will restrain outward turbulence spreading and the associated heat flux width broadening. Operating in H-mode with small ELMs has the potential to solve two critical problems: reducing the ELM size and broadening the SOL width.
The scrape-off layer of a tokamak fusion reactor carries the plasma exhaust from the hot core plasma to the material surfaces of the reactor vessel. The heat loads imposed by the exhaust are a critical limit on the performance of fusion power plants. Turbulent transport of the plasma regulates the width of the scrape-off layer plasma and must be modelled to understand the intensity of these heat loads. STORM is a plasma turbulence code capable of simulating three dimensional turbulence across the full scrape-off layer of a tokamak fusion reactor, using a drift reduced, collisional fluid model. STORM uses mostly finite difference schemes, with a staggered grid in the direction parallel to the magnetic field. We describe the model, geometry and initialisation options used by STORM, as well as the numerical methods, which are implemented using the BOUT++ plasma simulation framework. BOUT++ has been enhanced alongside the development of STORM, providing better support for staggered grid methods. We summarise these enhancements, including a detailed explanation of the parallel derivative methods, which underwent a major update for version 4 of BOUT++.
A series of BOUT++ turbulence simulations are performed for two Pre-Fusion Power Operation (PFPO-1,2) phases of the ITER Research plan proclaimed in 2019. Linear simulation results show that PFPO-1 is unstable to Peeling-ballooning modes (PB), while the PFPO-2 is unstable to the coupling of PB and Drift-Alfvén wave (DAW) instabilities. The linear results are qualitatively consistent with the dispersion relation of DAW. To study the influence of the DAW on the edge-localized mode (ELM) crash, the PFPO-2 is adopted in this section. Different from the grassy ELM in [Li et al 2022 Nucl. Fusion 62, 096030], nonlinear simulations show that the ELM size of PFPO-2 is almost one-third of the grassy ELM, representing a distinct small ELM. However, simulations then show that if the PB instability is removed, the fluctuation amplitude drops by an order of magnitude and the ELM crash disappears, which is in accord with the theory in [Xu et al 2010 Physical Review Letters, Vol. 105, 175005] and the results in [Li et al 2022 Nucl. Fusion 62, 096030], confirming that the PB instability is a necessary condition for an ELM crash. Furthermore, removing the DAW drive also suppresses ELM crashes, implying that PB instability is necessary but insufficient for PFPO-2 ELM and that DAW could amplify PB-driven turbulence. In addition, by integrating results of both PFPO phases by BOUT++ turbulence analysis with heat flux width (λ q ) and electron thermal diffusivity (χ e ), these simulations establish a predictive framework for heat flux width and its dominant mechanisms, thereby providing a comprehensive scheme for the prediction of the heat flux width. Moreover, simulations indicate that DAW driving can increase the transport coefficient by enhancing the turbulent transport, leading to a broadened heat flux width once the transport coefficient exceeds
Here a linear plasma device (LPD) module based on the 2D transport module under the BOUT++ framework is developed in this paper to simulate plasma transport in the LPD. The LPD module includes three parts, i.e. magnetic field calculation, simulation mesh generation and plasma transport setup. The magnetic field is calculated with the circular current loop using the location and current information of each coil. The mesh generation code can produce a simulation mesh for LPD by employing the magnetic field. The plasma transport model is based on the reduced Braginskii equations, which consist of the continuity equation, momentum equation, and energy equation. The fluid neutral model is applied for neutral particle simulation. Deuterium (D) and helium (He) ions and atoms can be simulated by the model. The first attempt to simulate plasma transport in the new LPD, called multiple plasma simulation linear plasma device (MPS-LD), is presented using the developed model. The D plasma transport in the MPS-LD is simulated and benchmarked against the two-point model, showing the validation of the BOUT++ simulation. The effects of radial transport on the heat load to the target are studied, which illustrates the significant impact of the radial diffusivities $D_⟂$ and $\mathcal{X}_{⟂i,e}$ on the plasma. Moreover, the He impurity injection process during the discharge is studied with emphasis on plasma–impurity interactions. The simulation results show that He injection can reduce the plasma energy load to the target significantly, and the efficiency depends on the He source density and injection velocity. The present work provides an alternative and flexible simulation tool for plasma transport in LPDs.
In this work, we report the observation of a quasi-coherent density fluctuation (QCF) by the Doppler backscattering system in the scrape-off layer (SOL) region of the DIII-D tokamak. This QCF is observed in high power, high performance hybrid plasmas with near double-null divertor (DND) shape during the electron cyclotron heating period. This mode is correlated with a steepened SOL density profile, and leads to significantly elevated particle and heat fluxes between ELMs. The SOL QCF is a long-wavelength ion-scale fluctuation (k θ ρ s ≈0.2-0.4 and k r ρ s ≈0.03), and propagates in the ion diamagnetic direction in the plasma frame. Its radial expanse is about 1.5–2 cm, well beyond the typical width of heat flux λ q on DIII-D. Also, the SOL QCF does not show any clear dependence on the effective SOL collisionality, and thus may raise issues on the control of plasma-material interactions in low collisionality plasmas in which the blob-induced transport is reduced. A linear simulation using BOUT++ with a 5-field reduced model is performed and compared with experimental observations. In simulation results, an interchange-like density perturbation can be driven by the SOL density gradient, and its peak location and the radial width of the density perturbation are in agreement with the experimental observations.