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DOE OSTI2014

Bi-directional Alfvén cyclotron instabilities in the mega-amp spherical tokamak

Alfvén cyclotron instabilities excited by velocity gradients of energetic beam ions were investigated in MAST experiments with super-Alfvénic neutral beam injection over a wide range of toroidal magnetic fields from ∼0.34 T to ∼0.585 T. In MAST discharges with high magnetic field, a discrete spectrum of modes in the sub-cyclotron frequency range is excited toroidally propagating counter to the beam and plasma current (toroidal mode numbers n < 0). At lower magnetic field ≤0.45 T, a discrete spectrum of Compressional Alfvén Eigenmodes (CAEs) with n > 0 arises, in addition to the modes with n < 0. At lowest magnetic fields, the CAEs with n > 0 become dominant, they are observed in frequency range from ∼250 kHz for n=1 to ∼3.5 MHz for n=15, well above the on-axis ion cyclotron frequency (∼2.5 MHz). The data is interpreted in terms of normal and anomalous Doppler resonances modified by magnetic drift terms due to inhomogeneity and curvature of the magnetic field. A Hall MHD model is applied for computing the eigenfrequencies and the spatial mode structure of CAEs and a good agreement with the experimental frequencies is found.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Analytic stability boundaries for compressional and global Alfvén eigenmodes driven by fast ions. II. Interaction via Landau resonance

We report that conditions for net fast ion drive are derived for beam-driven, co-propagating, sub-cyclotron compressional (CAE) and global (GAE) Alfvén eigenmodes driven by the Landau resonance with super-Alfvénic fast ions. Approximations applicable to realistic neutral beam distributions and mode characteristics observed in spherical tokamaks enable the derivation of marginal stability conditions for these modes. Such conditions successfully reproduce the stability boundaries found from numerical integration of the exact expression for local fast ion drive/damping. Coupling between the CAE and GAE branches of the dispersion due to finite ω/ω ci and |k ∥ /k ⊥ | is retained and found to be responsible for the existence of the GAE instability via this resonance. Finally, encouraging agreement is demonstrated between the approximate stability criterion, simulation results, and a database of NSTX observations of co-CAEs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Evaluation of Energy Storage Potential of Unconventional Shale Reservoirs Using Numerical Simulation of Cyclic Gas Injection

Compressed air energy storage (CAES) stores energy as compressed air in underground formations, typically salt dome caverns. When electricity demand grows, the compressed air is released through a turbine to produce electricity. CAES in the US is limited to one plant built in 1991, due in part to the inherent risk and uncertainty of developing subsurface storage reservoirs. As an alternative to CAES, we propose using some of the hundreds of thousands of hydraulically fractured horizontal wells to store energy as compressed natural gas in unconventional shale reservoirs. To store energy, produced or “sales” natural gas is injected back into the formation using excess electricity and is later produced through an expander to generate electricity. To evaluate this concept, we performed numerical simulations of cyclic natural gas injection into unconventional shale reservoirs using cmg-gem commercial reservoir modeling software. We tested short-term (diurnal) and long-term (seasonal) energy storage potential by modeling well injection and production gas flowrates as a function of bottom-hole pressure. First, we developed a conceptual model of a single fracture stage in an unconventional shale reservoir to characterize reservoir behavior during cyclic injection and production. Next, we modeled cyclic injection in the Marcellus shale gas play using published data. Results indicate that Marcellus unconventional shale reservoirs could support both short- and long-term energy storage at capacities of 100–1000 kWe per well. The results indicate that energy storage in unconventional shale gas wells may be feasible and warrants further investigation.

25 ENERGY STORAGE↗

DOE OSTI2017

Density perturbation mode structure of high frequency compressional and global Alfvén eigenmodes in the National Spherical Torus Experiment using a novel reflectometer analysis technique

Reflectometry measurements of compressional (CAE) and global (GAE) Alfvén eigenmodes are analyzed to obtain the amplitude and spatial structure of the density perturbations associated with the modes. A novel analysis technique developed for this purpose is presented. The analysis also naturally yields the amplitude and spatial structure of the density contour radial displacement, which is found to be 2–4 times larger than the value estimated directly from the reflectometer measurements using the much simpler ‘mirror approximation’. The modes were driven by beam ions in a high power (6 MW) neutral beam heated H-mode discharge (#141398) in the National Spherical Torus Experiment. The results of the analysis are used to assess the contribution of the modes to core energy transport and ion heating. The total displacement amplitude of the modes, which is shown to be larger than previously estimated (Crocker et al 2013 Nucl. Fusion 53 43017), is compared to the predicted threshold (Gorelenkov et al 2010 Nucl. Fusion 50 84012) for the anomalously high heat diffusion inferred from transport modeling in similar NSTX discharges. The results of the analysis also have strong implications for the energy transport via coupling of CAEs to kinetic Alfvén waves seen in simulations with the Hybrid MHD code (Belova et al 2015 Phys. Rev. Lett. 115 15001). Finally, the amplitudes of the observed CAEs fall well below the threshold for causing significant ion heating by stochastic velocity space diffusion (Gates et al 2001 Phys. Rev. Lett. 87 205003).

Reflectometry↗

DOE OSTI2020

Analytic stability boundaries for compressional and global Alfven eigenmodes driven by fast ions. II. Interaction via Landau resonance.

Conditions for net fast ion drive are derived for beam-driven, co-propagating, sub-cyclotron compressional (CAE) and global (GAE) Alfven eigenmodes driven by the Landau resonance with super-Alfvenic fast ions. Approximations applicable to realistic neutral beam distributions and mode characteristics observed in spherical tokamaks enable the derivation of marginal stability conditions for these modes. Such conditions successfully reproduce the stability boundaries found from numerical integration of the exact expression for local fast ion drive/damping. Coupling between the CAE and GAE branches of the dispersion due to finite \omega/\omega_{ci} and k_\parallel/k_\perp is retained and found to be responsible for the existence of the GAE instability via this resonance. Encouraging agreement is demonstrated between the approximate stability criterion, simulation results, and a database of NSTX observations of co-CAEs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Bottom Fixed Platform Dynamics Models Assessing Surface Ice Interactions for Transitional Depth Structures in the Great Lakes: FAST8 – IceDyn

To create long-term solutions for offshore wind turbines in a variety of environmental conditions, CAE tools are needed to model the design-driving loads that interact with an offshore wind turbine system during operation. This report describes our efforts in augmenting existing CAE tools used for offshore wind turbine analysis with a new module that can provide simulation capabilities for ice loading on the system. This augmentation was accomplished by creating an ice-loading module coupled to FAST8, the CAE tool maintained by the NREL for simulating land-based and offshore wind turbine dynamics. The new module includes both static and dynamic ice loading that can be applied during a dynamic simulation of the response of an offshore wind turbine. The ice forces can be prescribed, or influenced by the structure’s compliant response, or by the dynamics of both the structure and the ice floe. The new module covers ice failure modes of spalling, buckling, crushing, splitting, and bending. The supporting structure of wind turbines can be modeled as a vertical or sloping form at the waterline. The Inward Battered Guide Structure (IBGS) foundation designed by Keystone Engineering for the Great Lakes was used to study the ice models coupled to FAST8. The IBGS foundation ice loading simulations in FAST8 were compared to the baseline simulation case without ice loading. The ice conditions reflecting those from Lake Huron at Port Huron and Lake Michigan at North Manitou were studied under near rated wind speed of 12 m/s for the NREL 5-MW reference turbine. Simulations were performed on ice loading models 1 through 4 and ice model 6 with their respective sub-models. The purpose of ice model 5 is to investigate ice loading on sloping structures such as ice-cones on a monopile and is not suitable for multi-membered jacketed structures like the IBGS foundation. The key response parameters from the simulations, shear forces and moments from the tower base and IBGS foundation base, were compared. Ice models 1 and 6 do not significantly affect the tower fore-aft shear and moment. However, ice model 2 (dynamic analyses), model 3 (random ice loading), and model 4 (multiple ice failure zone loading) show increased effect on the tower fore-aft shear and moment with significant effect from ice model 3.1. In general ice loading creates large reaction forces and moments at the base of the IBGS foundation; the largest occurred in model 1.1 (steady creep ice indentation loading) followed by model 3.1 (random creep ice indentation loading). In general the power production from the ice loading cases had little deviation from the baseline case without ice loading. For ultimate limit state (ULS), ice model 1.1 ice and 3.1 appear to be the ice most critical models to consider at an early stage of design. Ice model 4 is an important tool for assessing structural fatigue.

17 WIND ENERGY↗

DOE OSTI2019

Earth Battery: Storing Energy with Compressed Air and Heated Brine in Porous Rock (Final Technical Report)

Cost-effective reductions in greenhouse gas (GHG) emissions are best achieved when all lowcarbon energy resources are fully utilized. This includes base-load power: nuclear energy (NE) and fossil energy (FE), integrated with CO 2 capture, use, and storage (CCUS), and variable renewable energy (VRE) (wind and solar); but, current CCUS options don’t justify CO 2 -capture costs and existing energy-storage approaches lack the capacity and storage duration needed to fully utilize all forms of low-carbon energy without curtailment. The Earth Battery is designed to meet these challenges by synergistically integrating conventional- and renewable-energy resources, allowing each to contribute more efficiently to the grid than if operated independently. The Earth Battery stores energy underground as pressure and heat, using compressed air and/or CO 2 , together with heated brine. These fluids are stored in either saline aquifers used for CO 2 or natural gas (NG) storage or in oil and gas reservoirs, making deployment possible over much of the U.S. We can provide enormous energy-storage capacity and duration. The main goal of this study was to assess the techno-economic feasibility of the versions of the Earth Battery that use compressed air energy storage (CAES). Current CAES systems use NG turbines and store air in salt caverns, which limits geographic deployment. Conventional CAES wastes much of the heat of air compression, comprising half of the compression energy. Our technology addresses these deficiencies by using permeable sedimentary rock to store air and the heat of compression as heated brine. When electricity is needed, air and hot brine are produced, with hot brine used to pre-heat air before it is fed into the expanders. Key factors affecting round-trip efficiency are (1) pressure loss in the air-storage reservoir, which depends on permeability (> 100 mD being needed for efficient operations) and (2) temperature loss in the hot-brine storage reservoir, which decreases with time as the storage formation heats up.

25 ENERGY STORAGE↗

DOE OSTI2023

Techno-Economic Analysis and Optimization of a Compressed-Air Energy Storage System Integrated with a Natural Gas Combined-Cycle Plant

To address the rising electricity demand and greenhouse gas concentration in the environment, considerable effort is being carried out across the globe on installing and operating renewable energy sources. However, the renewable energy production is affected by diurnal and seasonal variability. To ensure that the electric grid remains reliable and resilient even for the high penetration of renewables into the grid, various types of energy storage systems are being investigated. In this paper, a compressed-air energy storage (CAES) system integrated with a natural gas combined-cycle (NGCC) power plant is investigated where air is extracted from the gas turbine compressor or injected back into the gas turbine combustor when it is optimal to do so. First-principles dynamic models of the NGCC plant and CAES are developed along with the development of an economic model. The dynamic optimization of the integrated system is undertaken in the Python/Pyomo platform for maximizing the net present value (NPV). NPV optimization is undertaken for 14 regions/cases considering year-long locational marginal price (LMP) data with a 1 h interval. Design variables such as the storage capacity and storage pressure, as well as the operating variables such as the power plant load, air injection rate, and air extraction rate, are optimized. Results show that the integrated CAES system has a higher NPV than the NGCC-only system for all 14 regions, thus indicating the potential deployment of the integrated system under the assumption of the availability of caverns in close proximity to the NGCC plant. The levelized cost of storage is found to be in the range of 136–145 $/MWh. Roundtrip efficiency is found to be between 74.6–82.5%. A sensitivity study with respect to LMP shows that the LMP profile has a significant impact on the extent of air injection/extraction while capital expenditure reduction has a negligible effect.

25 ENERGY STORAGE↗

NASA NTRS2011

A Quasi-Steady Flexible Launch Vehicle Stability Analysis Using Steady CFD with Unsteady Aerodynamic Enhancement

Launch vehicles frequently experience a reduced stability margin through the transonic Mach number range. This reduced stability margin is caused by an undamping of the aerodynamics in one of the lower frequency flexible or rigid body modes. Analysis of the behavior of a flexible vehicle is routinely performed with quasi-steady aerodynamic lineloads derived from steady rigid computational fluid dynamics (CFD). However, a quasi-steady aeroelastic stability analysis can be unconservative at the critical Mach numbers where experiment or unsteady computational aeroelastic (CAE) analysis show a reduced or even negative aerodynamic damping. This paper will present a method of enhancing the quasi-steady aeroelastic stability analysis of a launch vehicle with unsteady aerodynamics. The enhanced formulation uses unsteady CFD to compute the response of selected lower frequency modes. The response is contained in a time history of the vehicle lineloads. A proper orthogonal decomposition of the unsteady aerodynamic lineload response is used to reduce the scale of data volume and system identification is used to derive the aerodynamic stiffness, damping and mass matrices. The results of the enhanced quasi-static aeroelastic stability analysis are compared with the damping and frequency computed from unsteady CAE analysis and from a quasi-steady analysis. The results show that incorporating unsteady aerodynamics in this way brings the enhanced quasi-steady aeroelastic stability analysis into close agreement with the unsteady CAE analysis.

Bartels, Robert E.↗

DOE OSTI2017

Challenges in the UK Generic Design Assessment Process - 17062

In the UK, Generic Design Assessment (GDA) is a voluntary step-wise joint assessment process undertaken by the Office for Nuclear Regulation (ONR) and the Environment Agency (EA) of a generic reactor design. The process focuses purely on the reactor design and does not consider any site specific issues. The key objective of GDA is for the regulators to consider the adequacy of claims, arguments and evidence (CAE) put forward by a requesting party (RP) to demonstrate the safety of its design in the UK context. This includes all CAE relating to management of spent fuel and radioactive waste. The CAE are generally applied to a reference design put forward by the RP that is substantially complete in terms of the overall concepts and functions of the major systems, having already been deployed elsewhere. GDA assessment encompasses a broad range of topic areas which include fuel and core design, management of spent fuel, radioactive waste management and decommissioning. Other technical disciplines also have valid interests in particular aspects of the management of spent fuel. This paper summarises the UK GDA process and the types of issues raised; in particular aspects of the proposed operation of liquid waste management systems and Spent Fuel Interim Storage are presented and the instructive resolution of the RP's original limited design scope to allow the regulators to carry out a meaningful assessment. Some examples are presented and useful lessons learned for future GDAs are discussed. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2017

Synthesis of new N-(pyridin-3-ylmethyl)-2-aminothiazoline derivatives possessing anticholinesterase and antiradical activity as potential multifunctional agents for the treatment of neurodegenerative diseases

New N-(pyridin-3-ylmethyl)-2-aminothiazolines containing various substituents at the 5 position of the thiazoline ring and the 4-tert-butylbenzyl, 4-isopropylbenzyl, or 4-fluorobenzyl moiety at the nitrogen atom of the amino group were synthesized. The inhibitory activity of the synthesized compounds against human erythrocyte acetylcholinesterase (AChE, EC 3.1.1.7), equine serum butyrylcholinesterase (BChE, EC 3.1.1.8), and porcine liver carboxylesterase (CaE, EC 3.1.1.1) was evaluated and their antioxidant properties were studied by ABTS assay. N-(Pyridin-3-ylmethyl)-2-aminothiazolines proveded to be very weak AChE inhibitors, while their inhibitory activity against BChE and CaE was structure-dependent. 2-Aminothiazolines containing the 4-tert-butylbenzyl moiety are more efficient BChE inhibitors compared to the derivatives containing the 4-isopropylbenzyl or 4-fluorobenzyl substituent. An analysis of the dependence of the esterase profile of N-(pyridin-3-ylmethyl)-2-aminothiazolines on the structure of the substituent at the 5 position of the thiazoline ring of these compounds demonstrated that the derivatives containing the iodomethyl substituent possess the highest anti-BChE activity, the compounds with R{sup 2} = H and R{sup 3} = CH{sub 2}I have the optimal esterase profile. Regardless of the structure of the substituents in the benzyl moiety, all N-(pyridin-3-ylmethyl)-2-aminothiazolines containing the iodomethyl substituent at the 5 position of the thiazoline ring exhibited high radical scavenging activity comparable with that of the standard antioxidant Trolox. N-(Pyridin-3-ylmethyl)-2-aminothiazolines were shown to be a new promising class of compounds for the design of multifunctional agents for the treatment of neurodegenerative diseases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Numerical modeling study of a man-made low-permeability barrier for the compressed air energy storage in high-permeability aquifers

Compressed air energy storage (CAES) is a grid-scale energy storage technology for intermittent energy, as proven by the decades-long successful operation of two existing compressed air energy storage in cavern (CAESC) power plants. Because of the limited availability of salt domes appropriate for CAESC, the more widely available aquifers (compressed air energy storage in aquifers, CAESA) have recently attracted considerable attention as candidates for CAES. An ideal aquifer for CAESA is highly permeable around the well to facilitate easy injection and withdrawal of air, but the high-permeability region is surrounded by low-permeability zones to minimize the loss of injected air and decrease in energy efficiency. However, such ideal geological structures are not always available in nature. Therefore, the potential of creating man-made low-permeability barrier in high-permeability aquifers is very interesting. In this paper, we investigate the feasibility of man-made low-permeability barriers in high-permeability aquifers using the numerical simulator TOUGH2/Gel to calculate the three-component flow (including a miscible gelling liquid). The simulation results show that an expected low-permeability barrier can be created by injecting grout with certain properties, and the altered aquifer performs well for CAESA. Additional sensitivity studies are also performed to reveal the effects of the various factors on the success of the low-permeability barrier creation, including the critical solidification concentration, the scale factor of the time dependence of the grout viscosity, the relative density of the grout, and the volume of the follow-up water injection. The results indicate that, in a horizontal aquifer, low critical solidification concentrations, and small scale factors are generally preferred and the density of grout should be close to that of the in situ water. For the given volume of the injected grout, there is an optimal follow-up water injection that will create the largest storage space without damaging the barrier. Furthermore, these results may help to extend the candidate sites for CAESA and the prospect of large scale energy storage.

25 ENERGY STORAGE↗

DOE OSTI2026

Covalent adaptable networks for electrolyte–binder integration in recyclable lithium metal batteries

Lithium-metal batteries (LMBs) are considered a promising next-generation energy storage technology due to their exceptionally high energy density. However, the development of solid polymer electrolytes and cathode binders for LMBs faces critical challenges, including interfacial instability, poor recyclability, and growing environmental concerns. In particular, current systems often rely on non-recyclable components featuring permanently crosslinked networks and polyfluoroalkyl substances (PFAS), such as poly(vinylidene fluoride) (PVDF), which cause battery waste and environmental harm. Herein, we introduce a multifunctional covalent adaptable network (CAN) platform based on thermally reversible Diels–Alder (DA) chemistry, designed for dual functionality as a CAN-based electrolyte (CAE) and a CAN-based cathode binder. The CAE achieves high ionic conductivity and strong storage modulus (1.4 mS cm −1 and ∼ 10 5 Pa at room temperature, respectively) and enables stable long-term cycling in symmetric Li||Li cells for over 2000 h with low overpotential. When it is applied as a cathode binder in LiFePO 4 (LFP) composite electrodes (C-LFP), the CAN matrix significantly reduces interfacial resistance and enhances discharge capacity compared to conventional PVDF-based systems. Thermal treatment induces self-healing at the cathode–electrolyte interface, further improving contact and yielding a discharge capacity of 150 mAh g −1 at 0.5 C. Moreover, the dynamic CAN architecture allows efficient recovery and reuse of lithium salts from spent electrolytes through retro-DA reactions under mild conditions (∼80 °C), establishing a low-energy, cost-effective recycling pathway. In conclusion, this work presents a scalable and sustainable strategy for high-performance LMBs by integrating recyclability, interfacial healing, and PFAS-free design, offering a holistic solution aligned with circular economy principles and next-generation battery demands.

Diels–Alder↗

DOE OSTI2016

Thermodynamic analysis of a compressed carbon dioxide energy storage system using two saline aquifers at different depths as storage reservoirs

Compressed air energy storage (CAES) is one of the leading large-scale energy storage technologies. However, low thermal efficiency and low energy storage density restrict its application. To improve the energy storage density, we propose a two-reservoir compressed CO 2 energy storage system. We present here thermodynamic and parametric analyses of the performance of an idealized two-reservoir CO 2 energy storage system under supercritical and transcritical conditions using a steady-state mathematical model. Results show that the transcritical compressed CO 2 energy storage system has higher round-trip efficiency and exergy efficiency, and larger energy storage density than the supercritical compressed CO 2 energy storage. However, the configuration of supercritical compressed CO 2 energy storage is simpler, and the energy storage densities of the two systems are both higher than that of CAES, which is advantageous in terms of storage volume for a given power rating.

25 ENERGY STORAGE↗

DOE OSTI2020

Interference of chiral Andreev edge states

The search for topological excitations such as Majorana fermions has spurred interest in the boundaries between distinct quantum states. Here, we explore an interface between two prototypical phases of electrons with conceptually different ground states: the integer quantum Hall insulator and the s-wave superconductor. We find clear signatures of hybridized electron and hole states similar to chiral Majorana fermions, to which we refer as chiral Andreev edge states (CAES). They propagate along the interface in the direction determined by magnetic field and their interference can turn an incoming electron into an outgoing electron or a hole, depending on the phase accumulated by the CAES along their path. Our results demonstrate that these excitations can propagate and interfere over a significant length, opening future possibilities for their coherent manipulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Analytic stability boundaries for compressional and global Alfvén eigenmodes driven by fast ions. I. Interaction via ordinary and anomalous cyclotron resonances

Conditions for net fast ion drive are derived for beam-driven, sub-cyclotron compressional (CAE) and global (GAE) Alfvén eigenmodes, such as those routinely observed in spherical tokamaks such as NSTX(-U) and MAST. Both co- and counter-propagating CAEs and GAEs are investigated, driven by the ordinary and anomalous Doppler-shifted cyclotron resonance with fast ions. Whereas prior results were restricted to vanishingly narrow distributions in velocity space, broad parameter regimes are identified in this work which enable an analytic treatment for realistic fast ion distributions generated by neutral beam injection. The simple, approximate conditions derived in these regimes for beam distributions of realistic width compare well to the numerical evaluation of the full analytic expressions for fast ion drive. Additionally, previous results in the very narrow beam case are corrected and generalized to retain all terms in ω/ω ci and |k ∥ /k ⊥ |, which are often assumed to be small parameters but can significantly modify the conditions of drive and damping when they are non-negligible. Lastly, favorable agreement is demonstrated between the approximate stability criterion, simulation results, and a large database of NSTX observations of cntr-GAEs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders

A common strategy for the dimensionality reduction of nonlinear partial differential equations (PDEs) relies on the use of the proper orthogonal decomposition (POD) to identify a reduced subspace and the Galerkin projection for evolving dynamics in this reduced space. However, advection-dominated PDEs are represented poorly by this methodology since the process of truncation discards important interactions between higher-order modes during time evolution. In this study, we demonstrate that encoding using convolutional autoencoders (CAEs) followed by a reduced-space time evolution by recurrent neural networks overcomes this limitation effectively. We demonstrate that a truncated system of only two latent space dimensions can reproduce a sharp advecting shock profile for the viscous Burgers equation with very low viscosities, and a six-dimensional latent space can recreate the evolution of the inviscid shallow water equations. Additionally, the proposed framework is extended to a parametric reduced-order model by directly embedding parametric information into the latent space to detect trends in system evolution. Furthermore, our results show that these advection-dominated systems are more amenable to low-dimensional encoding and time evolution by a CAE and recurrent neural network combination than the POD-Galerkin technique.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Compressional Alfvén eigenmodes in rotating spherical tokamak plasmas

Spherical tokamaks often have a considerable toroidal plasma rotation of several tens of kHz. Compressional Alfvén eigenmodes in such devices therefore experience a frequency shift, which if the plasma were rotating as a rigid body, would be a simple Doppler shift. However, since the rotation frequency depends on minor radius, the eigenmodes are affected in a more complicated way. The eigenmode solver CAE3B (Smith et al 2009 Plasma Phys. Control. Fusion 51 075001) has been extended to account for toroidal plasma rotation. The results show that the eigenfrequency shift due to rotation can be approximated by a rigid body rotation with a frequency computed from a spatial average of the real rotation profile weighted with the eigenmode amplitude. To investigate the effect of extending the computational domain to the vessel wall, a simplified eigenmode equation, yet retaining plasma rotation, is solved by a modified version of the CAE code used in Fredrickson et al (2013 Phys. Plasmas 20 042112). Lastly, both solving the full eigenmode equation, as in the CAE3B code, and placing the boundary at the vessel wall, as in the CAE code, significantly influences the calculated eigenfrequencies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗