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DOE OSTI2026

Power and particle exhaust for the ARC fusion power plant

To successfully show that fusion is an attractive energy source, the ARCTM fusion power plant will need to operate with a robust, integrated power and particle exhaust solution. To maximise ARC’s fusion power output while avoiding excessive erosion of the plasma-facing components, we will need to radiatively dissipate most of the power crossing the last-closed flux surface, injecting radiating impurities such as argon or neon to access divertor detachment. Divertor detachment will need to be integrated with a high-performance core plasma, and with efficient impurity pumping to prevent the accumulation of helium ash in the core. To access and control detachment in high-performance plasmas, we have designed ARC with up–down-symmetric divertors, with secondary X-points in long, tightly baffled outer legs. Using a core-edge modelling workflow, we predict that with this divertor design, ARC will access detachment with modest argon seeding in the divertor (c Ar,div ∼0.9%), which should have minimal impact on the core ( Z eff,core <0.5) for reasonable argon enrichment (c Ar,div /c Ar,core =6). Due to the high predicted divertor neutral pressure (p div ∼20 Pa), we predict that ARC will sufficiently pump helium to limit ash accumulation in the core (c He,core <2%) for a helium enrichment of c He,div /c He,core =0.4. ARC’s divertor design is expected to increase the stability of a detachment front in the outer divertor leg, helping to prevent divertor reattachment during smaller heat-flux transients such as scrape-off-layer filaments associated with the quasi-continuous exhaust regime. However, this buffering will not be sufficient to prevent divertor reattachment during large type-I edge-localised modes (ELMs), and as such these will need to be avoided on ARC. Experiments on SPARC will be used to select an integrated scenario which avoids or mitigates type-I-ELMs while maintaining access to detachment, good core fusion performance and sufficient impurity exhaust. SPARC experiments will also be used to finalise ARC’s divertor design, by studying the impact of magnetic and first-wall geometry on detachment stability, impurity enrichment and neutral baffling under conditions similar to those expected for ARC. In conclusion, our analysis finds that ARC will have a viable power and particle exhaust solution which is compatible with high-power operations, and this solution will be validated in experiments on SPARC.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Development of compact tokamak fusion reactor use cases to inform future transport studies

The OMFIT STEP (Meneghini et al. , Nucl. Fusion , vol. 10, 2020, p. 1088) workflow has been used to develop inductive and steady-state H-mode core plasma scenario use cases for a $B_0 = 8 \, {\rm T}$ , $R_0 = 4 \, {\rm m}$ machine to help guide and inform future higher-fidelity studies of core transport and confinement in compact tokamak reactors. Both use cases are designed to produce 200 MW or more of net electric power in an up-down symmetric plasma with minor radius $a = 1.4 \, {\rm m}$ , elongation $\kappa = 2.0$ , triangularity $\delta = 0.5$ and effective charge $Z_{{\rm eff}} \simeq 2$ . Additional considerations based on the need for compatibility of the core with reactor-relevant power exhaust solutions and external actuators were used to guide and constrain the use case development. An extensive characterization of core transport in both scenarios is presented, the most important feature of which is the extreme sensitivity of the results to the quantitative stiffness level of the transport model used as well as the predicted critical gradients. This sensitivity is shown to arise from different levels of transport stiffness exhibited by the models, combined with the gyroBohm-normalized fluxes of the predictions being an order of magnitude larger than other H-mode plasmas. Additionally, it is shown that although heating in both plasmas is predominantly to the electrons and collisionality is low, the plasmas remain sufficiently well coupled for the ions to carry a significant fraction of the thermal transport. As neoclassical transport is negligible in these conditions, this situation inherently requires long-wavelength ion gyroradius-scale turbulence to be the dominant transport mechanism in both plasmas. These results are combined with other basic considerations to propose a simple heuristic model of transport in reactor-relevant plasmas, along with simple metrics to quantify coupling and core transport properties across burning and non-burning plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Self-consistent modeling of tokamak edge plasma transport with lithium sources

Magnetic confinement fusion devices require effective heat and particle exhaust solutions on the divertor plates to operate sustainably, especially under reactor-relevant conditions. Liquid lithium divertors have been proposed to address two major challenges: control of excessive heat flux to plasma-facing components through vapor shielding and minimization of core plasma contamination from impurities. The National Spherical Torus Experiment-Upgrade (NSTX-U) will explore lithium as a divertor material due to its potential to meet both objectives. We present a self-consistent coupling framework between the plasma boundary transport code UEDGE and the lithium wall transport code Wall–Li to evaluate the feasibility and operational limits of lithium-based divertors. The model aims to optimize lithium sourcing levels to prevent core plasma contamination via fuel dilution while ensuring divertor protection through vapor shielding. This integrated framework, applicable to any tokamak with lithium sources, dynamically adjusts lithium sourcing based on local plasma conditions and surface temperature. The coupled model is tested using NSTX-like geometry and plasma conditions to assess its performance and reliability. Wall–Li calculates lithium fluxes from plasma-facing components, incorporating physical sputtering, thermally enhanced sputtering, and evaporation driven by surface temperature and ion flux. These fluxes are reintroduced into UEDGE as neutral lithium atoms, enabling simulation of their transport and distribution within the plasma. UEDGE computes plasma and neutral transport, surface heat flux, and iteratively feeds this information back to Wall–Li. A small time step is employed to ensure numerical stability and convergence, enabling accurate simulations over typical tokamak discharge durations. This integrated modeling approach provides a robust tool for identifying operational regimes that balance effective lithium sourcing with minimal core plasma contamination, offering critical insights for optimizing lithium-based divertor systems in current and future fusion devices.

Magnetic confinement fusion↗

DOE OSTI2021

First evidence of dominant influence of E × B drifts on plasma cooling in an advanced slot divertor for tokamak power exhaust

Addressing power exhaust in tokamaks is presently recognized as one of the major remaining open issues for the development of fusion reactors. At the forefront of this endeavor is the effort to develop an advanced divertor by maximizing dissipation of plasma power and momentum inside the divertor. Here, we demonstrate, for the first time, that the electromagnetic (E × B) drifts exert a key influence on plasma and gas dynamics in a new advanced slot divertor in the DIII-D tokamak, named the small angle slot (SAS). SAS leverages the effect of drifts to achieve a highly dissipative divertor with electron temperature T e ≲ 10 eV over a wide range of plasma densities, for ion B × ∇B away from the divertor, as used for advanced tokamak operation on DIII-D. Modeling with the SOLPS-ITER code shows that for this drift direction, the E × B flow carries particles toward the outer common flux region (CFR) via the private flux region (PFR), reinforcing neutral recycling and enhancing divertor dissipation. In contrast, for the opposite field direction, the E × B flow carries particles away from the outer CFR into the PFR, offsetting the anticipated SAS geometric effects. Furthermore, this finding is an important step in the understanding of the behavior of advanced divertors for achieving a power exhaust solution for fusion reactors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Development of an integrated core–edge scenario using the super H-mode

An optimized pedestal regime called the super-H (SH) mode is leveraged to couple a fusion relevant core plasma with a high density scrape-off layer appropriate for realistic reactor power exhaust solutions. Recent DIII-D experiments have expanded the operating space of the SH regime using advanced control algorithms and investigated optimization of impurity seeding, deuterium gas puffing, and 3D magnetic perturbations. Simultaneous real-time control of the pedestal density and radiated power with in-vessel coils and nitrogen seeding enable optimal coupled divertor and pedestal conditions. Four case studies are analysed with varied levels of radiated power in the divertor volume ranging from 0 (no seeding) to 8.5 MW radiated from carbon and nitrogen emission. Plasmas with a 4.5 MW radiated power target establish a radiative mantle, leading to divertor temperatures of ~16 eV while maintaining SH-mode, and with only marginal impact on the pedestal and core performance. Increased levels of N 2 seeding with a 7.5 MW radiated power target facilitate detachment onset and divertor temperatures <5 eV, with no degradation in stored energy and the operational point remaining inside the SH-mode channel for $ > 2.5{\tau }_{\text{E}}$. Finally, a 8.5 MW radiated power target leads to partial detachment, which is so far associated with the loss of access to SH-mode pedestal conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Toroidal modeling of 3D perturbations generated by current filaments in scrape-off layer in tokamak with biased divertor targets

The divertor biasing technique offers a promising alternative to control the edge localized mode (ELM) as well as the divertor heat load in tokamaks, as compared to the resonant magnetic perturbation (RMP) generated by magnetic coils. The linear resistive MHD code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) is employed to study the plasma response to the n = 2 (n is the toroidal mode number) field perturbation in HL-2A, produced by the divertor biasing current filaments flowing in the scrape-off layer region. The response field due to biasing currents is compared with the RMP field utilized for ELM control in HL-2A. The strength of the radial resonant field perturbation, produced by the biasing currents of 100 A level, is found to be comparable with RMP generated by several kA of ELM control coil currents for the reference plasma. The plasma normal displacement near the X-point and the associated neoclassical toroidal viscosity torque are also computed to be similar between these two techniques. The modeling results thus strongly suggest that the biasing technique can be applied to control ELMs. Moreover, the biasing currents produce field perturbations, including the plasma response, that are localized more near the plasma edge (compared to the RMP counterpart), thus reducing the chance of mode locking associated with core perturbations. Particle orbit tracing also reveals that the biasing current produced magnetic perturbation tends to widen the heat deposition region and induce the strike point splitting of the ion saturation flow on the outer divertor surface, consistent with experimental observations in HL-2A. These toroidal modeling results confirm the possibility of ELM control and plasma exhaust solution by the divertor biasing technique.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

A Novel Approach to Quantum Circuit Partitioning

Quantum synthesis presents an effective method of circuit optimization, but scales exponentially with the number of qubits in the circuit. This problem can be addressed by partitioning the circuit into blocks with a limited number of qubits. Existing partitioning algorithms make large trade-offs to achieve either high speed or quality. We propose a method of circuit partitioning which is competitive with existing algorithms for both metrics. The proposed method is compared with two existing methods across common circuit architectures, matching an exhaustive solution in performance and a fast solution on time.

Clark, Joseph↗

DOE OSTI2025

Divertor shaping with neutral baffling as a solution to the tokamak power exhaust challenge

Exhausting power from the hot fusion core to the plasma-facing components is one fusion energy’s biggest challenges. The MAST Upgrade tokamak uniquely integrates strong containment of neutrals within the exhaust area (divertor) with extreme divertor shaping capability. By systematically altering the divertor shape, this study shows the strongest evidence to date to our knowledge that long-legged divertors with a high magnetic field gradient (total flux expansion) deliver key power exhaust benefits without adversely impacting the hot fusion core. These benefits are already achieved with relatively modest geometry adjustments that are more feasible to integrate in reactor designs. Benefits include reduced target heat loads and improved access to, and stability of, a neutral gas buffer that ‘shields’ the target and enhances power exhaust (detachment). Analysis and model comparisons shows these benefits are obtained by combining multiple shaping aspects: long-legged divertors have expanded plasma-neutral interaction volume that drive reductions in particle and power loads, while total flux expansion enhances detachment access and stability. Containing the neutrals in the exhaust area with physical structures further augments these shaping benefits. These results demonstrate strategic variation in the divertor geometry and magnetic topology is a potential solution to one of fusion’s power exhaust challenge.

magnetically confined plasmas↗

DOE OSTI2024

A semi-automated algorithm for designing stellarator divertor and limiter plates and application to HSX

We present a semi-automated algorithm for designing three-dimensional divertor or limiter plates targeting low heat loads. The algorithm designs the plates in two stages: firstly, the parallel heat flux distribution is caught on vertically-inclined plates at one or several toroidal locations. Secondly, the power per unit area is reduced by stretching, tilting and bending the plates toroidally. Heat transport is modelled using the EMC3-Lite code, which uses an anisotropic diffusion model. We apply this scheme to HSX, a medium-sized stellarator located at the University of Wisconsin–Madison. Starting from the current machine with an extended vessel wall, we construct plates which are able to effectively catch and spread the heat for three different magnetic configurations. The scheme has a computational cost in the order of tens of CPU-minutes, making it a powerful tool for semi-automated plasma-facing component design in three-dimensional environments.

anisotropic diffusion↗

DOE OSTI2020

Challenges and Practical Solutions for Conducting Structural MARSSIM Surveys in Elevated Radon Environments - 20413

The Multi-Agency Radiation Survey and Site Investigation Manual (MARSSIM) [1] provides comprehensive guidance for the development and implementation of radiological surveys conducted to demonstrate compliance with a dose- or risk-based cleanup goal during final status survey. The MARSSIM methodology follows an integrated strategy combining direct measurements and sampling to assess uniform residual contamination, and scanning surveys to identify localized areas of elevated activity. Building surveys assessing residual surface contamination present unique challenges from reliance on field measurements that may be subject to less than ideal environmental conditions. Additionally, limited characterization and excessive conservatism incorporated into the conceptual site model may result in derived concentration guideline levels (DCGL) and, as a consequence of relatively inefficient field instrumentation, corresponding attributable count rates generally comparable to background. The presence of elevated ambient radon concentrations and associated progeny deposition both exacerbate these intrinsic survey challenges and introduce a series of technical, logistic, and administrative obstacles that can wreak havoc on the statistical legitimacy of each component of the MARSSIM process. Short-lived radon progeny including polonium-218, lead-214, bismuth-214, and polonium-214 produce excessive alpha and beta radiation that may decrease instrument sensitivity through an increase in background count rates, and, at worst, may result in incorrect survey unit failure through the simulation of residual surface activity. Aside from the obvious solution of exhaustive radon mitigation, the primary objectives are to distinguish between radon progeny deposition and actual surface activity, and collect sufficient defensible data. The following is a technical discussion of the consequences of performing building MARSSIM surveys in the presence of elevated ambient radon atmospheres, conceptual examples, and an overview of practical strategies to minimize the effects of radon interference while collecting sufficient defensible data to complete the survey. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2024

Investigation of Ammonia Carrier Materials for Next Generation Ammonia Dosing System - CRADA 334 (Abstract)

Lean-burn gasoline and diesel engines can offer substantially higher fuel efficiency, good driving performance, and reduced carbon dioxide emission compared to stoichiometric gasoline engines. Various catalyst technologies have been developed to remove the pollutants from these engines. For example, a three-way catalyst (TWC) is used to remove hydrocarbons (HC), carbon monoxide (CO), and nitrogen oxides (NOx) from gasoline engines during the stoichiometric conditions. During the lean-burn conditions, a TWC or a diesel oxidation catalyst (DOC) is used to control HC and CO emissions. NOx is removed by either lean NOx trap catalyst (LNT) that can store NOx under lean conditions and reduce NOx under rich conditions, or selective catalytic reduction catalyst (SCR) that can selectively remove NOx with a reducing agent. Among the NOx reduction catalyst technologies, SCR offers a number of advantages, including excellent NOx reduction efficiency over a wide range of temperatures and overall lower system cost. In fact, the SCR technology using ammonia (NH3) as reductant has been proven effective and used commercially for the removal of NOx emissions from stationary sources since the 1970s. Currently, SCR is being used to meet the NOx emission standards for diesel engines in Europe and North America, and also being considered for meeting the future NOx emission standards for lean-burn gasoline engines. Because of the challenges associated with storage, handling and transportation of ammonia on a vehicle, aqueous urea solution (e.g., Diesel Exhaust Fluid, AdBlue) has been developed as ammonia storage compound for mobile applications. When the aqueous urea solution is sprayed into exhaust gas stream, urea is decomposed to release ammonia, which then reduces NOx over the downstream SCR catalyst. Although aqueous urea solution technology has enabled automakers and engine manufacturers to meet the current NOx emission standards, this process of releasing ammonia requires a hot exhaust gas and sufficient mixing, creating challenges for low temperature NOx emission control and aftertreatment system packaging. For these reasons, alternative technologies have been developed as ammonia sources (e.g., solid urea, ammonium carbamate, metal ammine chloride) during the past few years. These technologies promise more convenient handling and distribution of ammonia sources, and help maximize the low-temperature performance of SCR catalysts and reduce the overall system volume and weight. However, none of these alternative technologies can be successfully implemented without the industry consensus. Therefore, the USCAR SCR work group, which is comprised of representatives from GM, Ford, and Chrysler, has decided to investigate the potential alternative ammonia carriers, define common standard vehicle interfaces, and address personal and environmental safety concerns with part suppliers and chemical companies. Under this CRADA Project, USCAR and Battelle will investigate alternative ammonia carrier materials that are currently under development. Based on the data and information derived under the CRADA project, the USCAR SCR work group plans to build the consensus and make recommendations for the industry.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

Investigation of Ammonia Carrier Materials for Next Generation Ammonia Dosing System - CRADA 334 (Abstract)

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

Overview of the EUROfusion Tokamak Exploitation programme in support of ITER and DEMO

Within the 9th European Framework programme, since 2021 EUROfusion is operating five tokamaks under the auspices of a single Task Force called ‘Tokamak Exploitation’. The goal is to benefit from the complementary capabilities of each machine in a coordinated way and help in developing a scientific output scalable to future largre machines. The programme of this Task Force ensures that ASDEX Upgrade, MAST-U, TCV, WEST and JET (since 2022) work together to achieve the objectives of Missions 1 and 2 of the EUROfusion Roadmap: i) demonstrate plasma scenarios that increase the success margin of ITER and satisfy the requirements of DEMO and, ii) demonstrate an integrated approach that can handle the large power leaving ITER and DEMO plasmas. The Tokamak Exploitation task force has therefore organized experiments on these two missions with the goal to strengthen the physics and operational basis for the ITER baseline scenario and for exploiting the recent plasma exhaust enhancements in all four devices (PEX: Plasma EXhaust) for exploring the solution for handling heat and particle exhaust in ITER and develop the conceptual solutions for DEMO. The ITER Baseline scenario has been developed in a similar way in ASDEX Upgrade, TCV and JET. Key risks for ITER such as disruptions and run-aways have been also investigated in TCV, ASDEX Upgrade and JET. Experiments have explored successfully different divertor configurations (standard, super-X, snowflakes) in MAST-U and TCV and studied tungsten melting in WEST and ASDEX Upgrade. The input from the smaller devices to JET has also been proven successful to set-up novel control schemes on disruption avoidance and detachment.

ASDEX upgrade↗

DOE OSTI2024

Targeted Adaptive Design

Modern advanced manufacturing and advanced materials design often require searches of relatively high-dimensional process control parameter spaces for settings that result in optimal structure, property, and performance parameters. The mapping from the former to the latter must be determined from noisy experiments or from expensive simulations. Here, we abstract this problem to a mathematical framework in which an unknown function from a control space to a design space must be ascertained by means of expensive noisy measurements, which locate control settings generating desired design features within specified tolerances, with quantified uncertainty. We describe targeted adaptive design (TAD), a new algorithm that performs this sampling task efficiently. TAD creates a Gaussian process surrogate model of the unknown mapping at each iterative stage, proposing a new batch of control settings to sample experimentally and optimizing the updated expected log-predictive probability density of the target design. TAD either stops upon locating a solution with uncertainties that fit inside the tolerance box or uses a measure of expected future information to determine that the search space has been exhausted with no solution. TAD thus embodies the exploration-exploitation tension in a manner that recalls, but is essentially different from, Bayesian optimization and optimal experimental design.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

DIII-D's role as a national user facility in enabling the commercialization of fusion energy

The path to fusion in the United States requires partnership between public and private sector. While the private sector provides the vigor to take some of the major steps necessary, there is a depth of expertise and capability in the public sector that is vital to resolving feasible approaches. As an open national user facility, DIII-D provides a crucial testbed to develop the required new technologies and approaches in relevant conditions. It has unparalleled potential to meet this challenge, thanks to its extreme flexibility and world leading diagnostics. This provides a basis to rapidly develop solutions that project to future reactors with confidence. The program has thus been redeveloped to enable public and private sector engagement and testing of new concepts. A new technology program has been launched to resolve plasma interacting technologies. With modest heating upgrades, the facility can confront the crucial “Integrated Tokamak Exhaust and Performance” gap, to resolve core, exhaust and technology solutions together. The device is also being redeveloped as a training facility, with dedicated student run time, a mentorship program, and open access to all opportunity roles, part of wider efforts to diversify and open pathways through inclusion, access, and equity. This exciting agenda is enabling scientists and technology researchers to pioneer the solutions needed for a Fusion Pilot Plant (FPP) and ITER this decade. As a national user facility, DIII D has singular potential to provide the tools, teams, and insight necessary, to do its part in moving the United States rapidly toward the commercialization of fusion energy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Selective Sampling for Sensor Type Classification in Buildings

A key barrier to applying any smart technology to a building is the requirement of locating and connecting to the necessary resources among the thousands of sensing and control points, i.e., the metadata mapping problem. Existing solutions depend on exhaustive manual annotation of sensor metadata --- a laborious, costly, and hardly scalable process. To reduce the amount of manual effort required, this paper presents a multi-oracle selective sampling framework to leverage noisy labels from information sources with unknown reliability such as existing buildings, which we refer to as weak oracles, for metadata mapping. This framework involves an interactive process, where a small set of sensor instances are progressively selected and labeled for it to learn how to aggregate the noisy labels as well as to predict sensor types. Two key challenges arise in designing the framework, namely, weak oracle reliability estimation and instance selection for querying. To address the first challenge, we develop a clustering-based approach for weak oracle reliability estimation to capitalize on the observation that weak oracles perform differently in different groups of instances. For the second challenge, we propose a disagreement-based query selection strategy to combine the potential effect of a labeled instance on both reducing classifier uncertainty and improving the quality of label aggregation. We evaluate our solution on a large collection of real-world building sensor data from 5 buildings with more than 11,000 sensors of 18 different types. The experiment results validate the effectiveness of our solution, which outperforms a set of state-of-the-art baselines.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

DOE OSTI2024

Breakup dynamics in a pressure-swirl injector for urea-water solution applications: A computational study

The co-optimization of in-cylinder combustion and after-treatment technology has become a major aspect in engine design and development, with the goal of meeting the increasingly restrictive emission regulations in the transportation industry. Selective Catalytic Reduction is a robust technology to control the emission of NO x , and the injection of urea in water solution is the exhaust tailpipe is a key aspect of its operation. The proposed work uses high-fidelity Computational Fluid Dynamics to characterize the atomization dynamics of the liquid jet in relevant cross-flow conditions. The study focuses on a commercial low-pressure (9 bar) pressure-swirl injector which is characterized in its internal geometry through high-resolution X-ray micro-computational tomography. The internal two-phase flow has been modeled according to the volume-of-fluid approach in a large eddy simulation framework and validated against near-nozzle X-ray radiography measurement. Moreover, characterizing the breakup dynamics for the swirling hollow cone formation, and assessing the influence of the cross-flow in the breakup dynamics was completed. The results have been reported proposing Re-Oh maps and probability density functions of the spray kinematics. Higher cross-flow momentum generates an increase in the jet intact length and a reduction of the liquid droplet diameters. The axial momentum of the jet is affected by the cross-flow already in the near-nozzle region, determining a relevant deviation of the spray velocities. In conclusion, this work aims to inform the initialization of Eulerian-Lagrangian spray models through the assignment of droplet kinematics and static one-way coupling between volume-of-fluid results and Lagrangian spray parcels, to be used for system-size domain simulations.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2020

Instantons in chiral magnets

In this work, we exhaustively construct instanton solutions and elucidate their properties in one-dimensional antiferromagnetic chiral magnets based on the $\textit{O}(3)$ nonlinear sigma model description of spin chains with the Dzyaloshinskii-Moriya (DM) interaction. By introducing an easy-axis potential and a staggered magnetic field, we obtain a phase diagram consisting of ground-state phases with two points (or one point) in the easy-axis dominant cases, a helical modulation at a fixed latitude of the sphere, and a tricritical point allowing helical modulations at an arbitrary latitude. We find that instantons (or skyrmions in two-dimensional Euclidean space) appear as composite solitons in different fashions in these phases: temporal domain walls or wall-antiwall pairs (bions) in the easy-axis dominant cases, dislocations (or phase slips called merons) with fractional instanton numbers in the helical state, and isolated instantons and calorons living on the top of the helical modulation at the tricritical point. We also show that the models with DM interaction and an easy-plane potential can be mapped into those without them, providing a useful tool to investigate the model with the DM interaction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗