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A systematic simulation study of the $n/m=1/1$ instability driven by energetic counter-passing particles in tokamak plasmas has been carried out using the kinetic-MHD (Magnetohydrodynamics) hybrid code M3D-K. The safety factor's radial profile is monotonically increasing with central value $q_0$ less than unity. The linear simulation results show that the instability is either a $m/n=1/1$ energetic particle mode or a $m/n=1/1$ global Alfvén eigenmode depending on the value of the central safety factor. The mode frequencies are close to the tip of Alfvén continuum spectrum at the magnetic axis. The excited modes are radially localized near the magnetic axis well within the safety factor $q=1$ surface. The main wave particle resonance is found to be $\omega _\phi +2\omega _\theta =\omega$ , where ω is the mode frequency. The nonlinear simulation results show that there is a long period of quasi-steady-state saturation phase with frequency chirping up after initial saturation. Correspondingly, the energetic particle distribution with low energies is flattened in the core of the plasma. After this quasi-steady phase, the mode amplitude grows again and frequency jumps down to a low value corresponding to a new mode similar to the energetic co-passing particle-driven low-frequency fishbone while the energetic particle distribution is flattened for higher energies in the core of plasma.

9-cis-epoxy carotenoid dioxygenase (NCED) is a fundamental enzyme, which plays an essential role in the process of organ development and stress resistance by regulating abscisic acid (ABA) synthesis in plant. In this study, a total of 7, 7, 14 and 14 NCED genes were identified from the genomes of G. arboreum, G. raimondii, G. barbadense and G. hirsutum, respectively. Phylogenetic tree showed that all forty-two NCED genes could be classified into three groups in cotton genus. Collinear analysis revealed that the NCED genes in G. hirsutum were not amplified by tandem repeats after polyploidy events. The function of NCED genes was evaluated between two accessions with contrasting plant height. The results showed that expression of the NCED genes in dwarf accession was higher than that in taller ones. GhNCED1-silenced cotton plants confirmed that suppression of NCED genes could increase the plant height, but reduce the resistance abilities to drought and salt stress. Our study systematically identified the homologs of NCED genes and their functions in cotton, which could provide new genetic resources for improving plant height and stress in future cotton breeding.

Background Asian cotton (Gossypium arboreum L.), as a precious germplasm resource of cotton with insect resistance and stress tolerance, possesses a broad spectrum of phenotypic variation related to pigmentation. Flower color affects insect pollination and the ornamental value of plants. Studying flower color of Asian cotton varieties improves the rate of hybridization and thus enriches the diversity of germplasm resources. Meanwhile, it also impacts the development of the horticultural industry. Unfortunately, there is a clear lack of studies concerning intricate mechanisms of cotton flower-color differentiation. Hereby, we report an integrative approach utilizing transcriptome and metabolome concerning flower color variation in three Gossypium arboreum cultivars. Results A total of 215 differentially accumulated metabolites (DAMs) were identified, including 83 differentially accumulated flavonoids (DAFs). Colorless kaempferol was more abundant in white flowers, while gossypetin-fer showed specificity in white flowers. Quercetin and gossypetin were the main contributors to yellow petal formation. Pelargonidin 3-O-beta-D-glucoside and cyanidin-3-O-(6''-Malonylglucoside) showed high accumulation levels in purple petals. Quercetin and gossypetin pigments also promoted purple flower coloration. Moreover, 8178 differentially expressed genes (DEGs) were identified by RNA sequencing. The correlation results between total anthocyanins and DEGs were explored, indicating that 10 key structural genes and 29 transcription factors promoted anthocyanin biosynthesis and could be candidates for anthocyanin accumulation. Ultimately, we constructed co-expression networks of key DAFs and DEGs and demonstrated the interactions between specific metabolites and transcripts in different color flowers. Conclusion This study provides new insights into elucidating the regulatory mechanisms of cotton flower color and lays a potential foundation for generate cotton varieties with highly attractive flowers for pollinators.

An optimized compact stellarator with four simple coils is obtained from direct optimization via a coil shape. The new stellarator consists of two interlocking coils and two vertical field coils similar to those of the Columbia Non-neutral Torus (CNT) (Pedersen et al., Phys. Rev. Lett., vol. 88, 2002, pp. 205002). The optimized configuration has a global magnetic well and a low helical ripple level comparable to that of Wendelstein 7-X (W7-X) (Wolf et al., Nucl. Fusion, vol. 57, 2017, pp. 102020). The two interlocking coils have a smooth three-dimensional shape much simpler than those of advanced stellarators such as W7-X. This result opens up possibilities of future stellarator reactors with simplified coils.

A strong nonlinear saturation mechanism of the reverse shear Alfvén eigenmode (RSAE) induced by thermal electrons is observed in gyrokinetic δ f particle-in-cell simulation. This nonlinear effect occurs at moderate mode amplitude, δ B ⊥ / B < 10 − 3 , and is associated with the electron parallel streaming along the perturbed magnetic field lines, the term v ∥ δ B ⊥ B ⋅ ∇ δ f , in the electron drift-kinetic equation. In the case of an n = 4 RSAE, where n is the toroidal mode number, this magnetic fluttering nonlinearity leads to strong mode coupling and broadening of the saturation spectrum. The nonlinear components, which are highly damped through the interaction between thermal electrons and the parallel electric field, modifies the RSAE mode structure and suppresses energetic particle drive significantly. The split-weight scheme (Chen and Parker 2007 J. Comput. Phys. 220 839–55) is used to simulate kinetic electrons.

Background: Cotton is an important cash crop. The fiber length has always been a hot spot, but multi-factor control of fiber quality makes it complex to understand its genetic basis. Previous reports suggested that OsGASR9 promotes germination, width, and thickness by GAs in rice, while the overexpression of AtGASA10 lead to a reduction in silique length, which is likely to reduce cell wall expansion. Therefore, this study aimed to explore function of GhGASA10 in cotton fibers development.Results: To explore the molecular mechanisms underlying fiber elongation regulation concerning GhGASA10-1, we revealed an evolutionary basis, gene structure, and expression. Our results emphasized the conservative nature of GASA family with its origin in lower fern plants S. moellendorffii. GhGASA10-1 was localized in the cell membrane, which may synthesize and transport secreted protein to the cell wall. Besides, GhGASA10-1 promoted seedling germination and root extension in transgenic Arabidopsis, indicating that GhGASA10-1 promotes cell elongation. Interestingly, GhGASA10-1 was upregulated by IAA at fiber elongation stages. Conclusion: We propose that GhGASA10-1 promotes fiber elongation by regulating the synthesis of cellulose induced by IAA, to lay the foundation for future research on the regulation network of GASA10-1 in cotton fiber development.

Background Cotton is an important cash crop. The fiber length has always been a hot spot, but multi-factor control of fiber quality makes it complex to understand its genetic basis. Previous reports suggested that OsGASR9 promotes germination, width, and thickness by GAs in rice, while the overexpression of AtGASA10 leads to reduced silique length, which is likely to reduce cell wall expansion. Therefore, this study aimed to explore the function of GhGASA10 in cotton fibers development. Results To explore the molecular mechanisms underlying fiber elongation regulation concerning GhGASA10–1, we revealed an evolutionary basis, gene structure, and expression. Our results emphasized the conservative nature of GASA family with its origin in lower fern plants S. moellendorffii. GhGASA10–1 was localized in the cell membrane, which may synthesize and transport secreted proteins to the cell wall. Besides, GhGASA10–1 promoted seedling germination and root extension in transgenic Arabidopsis, indicating that GhGASA10–1 promotes cell elongation. Interestingly, GhGASA10–1 was upregulated by IAA at fiber elongation stages. Conclusion We propose that GhGASA10–1 may promote fiber elongation by regulating the synthesis of cellulose induced by IAA, to lay the foundation for future research on the regulation networks of GASA10–1 in cotton fiber development.

A neoclassically optimized compact stellarator with simple coils has been designed. The magnetic field of the new stellarator is generated by only four planar coils including two interlocking coils of elliptical shape and two circular poloidal field coils. The interlocking coil topology is the same as that of the Columbia Non-neutral Torus (CNT) [Pedersen et al., Phys. Rev. Lett. 88, 205002 (2002)]. The new configuration was obtained by minimizing the effective helical ripple directly via the shape of the two interlocking coils. The optimized compact stellarator has very low effective ripple in the plasma core, implying excellent neoclassical confinement. This is confirmed by the results of the drift-kinetic code SFINCS [Landreman et al., Phys. Plasmas 21, 042503 (2014)], showing that the particle diffusion coefficient of the new configuration is one order of magnitude lower than CNT's.

Large-scale genomic surveys of crop germplasm are important for understanding the genetic architecture of favorable traits. The genomic basis of geographic differentiation and fiber improvement in cultivated cotton is poorly understood. Here, we analyzed 3,248 tetraploid cotton genomes and confirmed that the extensive chromosome inversions on chromosomes A06 and A08 underlies the geographic differentiation in cultivated Gossypium hirsutum. We further revealed that the haplotypic diversity originated from landraces, which might be essential for understanding adaptative evolution in cultivated cotton. Introgression and association analyses identified new fiber quality-related loci and demonstrated that the introgressed alleles from two diploid cottons had a large effect on fiber quality improvement. These loci provided the potential power to overcome the bottleneck in fiber quality improvement. Our study uncovered several critical genomic signatures generated by historical breeding effects in cotton and a wealth of data that enrich genomic resources for the research community.

Neuroblastoma (NB), as a metastatic form of solid tumor, has a high fatality rate found in early childhood. The two anaplastic lymphoma kinase (ALK) neoepitopes nonamer and decamer used in cancer immunotherapy against NB cancer can selectively bind to the human leukocyte antigen (HLA-B*15:01) groove with high affinities, whereas the native self-peptide is unable to interact with the HLA-B*15:01. Here, we performed molecular dynamics (MD) simulations and subsequent molecular mechanics-generalized born surface area (MM-GBSA) binding free energy calculations to explore the selective binding mechanisms of nonamer and decamer to the HLA-B*15:01 against the self-peptide. MD simulations revealed the significant conformational dynamics of the self-peptide in the HLA-B*15:01 groove against the nonamer and decamer. Binding free energy calculations showed that the binding affinities of HLA-B*15:01-neoepitope complexes were followed in the order decamer > nonamer > self-peptide. Detailed analysis of HLA-B*15:01-neoepitope structural complexes showed that compared to the nonamer, the self-peptide tended to move outward to the solvent, whereas the decamer moved deep to the HLA-B*15:01 groove. These different dynamic observations of the ALK neoepitopes can explain the distinct binding affinities of self-peptide, nonamer, and decamer to the HLA-B*15:01. The results may be useful for the design of more selective ALK neoepitopes.

Intervertebral disc degeneration (IVDD) is a multifactorial pathological process associated with low back pain in which nucleus pulposus cell senescence is disrupted. Increasing evidence reveals that IVDD can be modulated by microRNAs (miRNAs or miRs). In the current study, we set out to elucidate the role of miR-199a-5p in nucleus pulposus cell apoptosis and IVDD progression. After sample collection, we found highly expressed miR-199a-5p in nucleus pulposus tissues of both patients diagnosed with IVDD and in IVDD rat models. Next, normal and degenerated nucleus pulposus cells were isolated and transfected with miR-199a-5p mimic, miR-199a-5p inhibitor, overexpressed sirtuin 1 (oe-SIRT1), and oe-p21, followed by detection of nucleus pulposus cell apoptosis and proliferation. In addition, the binding of miR-199a-5p and SIRT1, the interaction between p21 and SIRT1, and the regulation of p21 acetylation by SIRT1 were analyzed. We found that miR-199a-5p overexpression promoted nucleus pulposus cell apoptosis and IVDD. Overexpression of SIRT1 countered the effect of miR-199a-5p overexpression, while overexpression of p21 reversed the effect of miR-199a-5p silencing. Also, miR-199a-5p inhibited SIRT1, promoted p21 acetylation, and upregulated p21 expression, thus accelerating nucleus pulposus cell apoptosis and IVDD. Overall, miR-199a-5p promotes nucleus pulposus cell apoptosis and IVDD by suppressing SIRT1-dependent deacetylation of p21., Graphical Abstract, miR-199a-5p, found to be highly expressed in nucleus pulposus tissues, promoted nucleus pulposus cell apoptosis and aggravated the progression of IVDD by disrupting SIRT1-dependent deacetylation of targeted p21. Thus, targeting the miR-199a-5p/SIRT1/p21 axis would shed light on the development of new therapeutic strategies for IVDD.

A new linked mirror device for magnetic confinement experiment is proposed. The new linked mirror device consists of two straight magnetic mirrors connected by two half-torus. The structure of the configuration as a whole is three dimensional because the two linear mirror sections are not parallel. The angle between the two mirror sections generates rotational transform which results in good magnetic confinement of toroidally processing passing particles. In this way the usual loss cone of the traditional linear mirror machines is eliminated. The single particle confinement is similar to that of tokamaks with most of particles well confined. The calculated neoclassical confinement is very good and is even better than that of an equivalent tokamak. Potentially the proposed linked mirror configuration can allow MHD stable high beta equilibria with good plasma confinement suitable for neutron sources and magnetic fusion reactors.

Significant variations in MHD activity and fast-ion transport are observed in the DIIID high-beta, steady-state hybrid discharges with a mixture of Electron Cyclotron (EC) waves and Neutral Beam Injection (NBI). When Electron Cyclotron Heating (ECH) or Current Drive (ECCD) is applied, Alfven Eigenmodes (AEs) are usually suppressed and replaced by low-frequency bursting modes. The analysis of a recently compiled database of hybrid discharges suggests that the change of the fast-ion pressure especially the perpendicular pressure is the main factor responsible for the instability transition although the transition in some discharges can also be explained by a slight drop of the safety factor qmin. The lower ratio of fast-ion injection speed vinj to Alfven speed valfven and slight drop of safety factor qmin during ECCD may also facilitate the transition. The database shows that AEs mainly occur when the fast-ion fraction Pf/Ptotal is less than 0.53 and vinj/valfven is greater than 0.50, while low-frequency bursting modes appear in the opposite regime. Here, Pf and Ptotal are the central fast-ion pressure from classical prediction and total plasma pressure, respectively. The correlation with qmin is weaker and qmin is around unity in all the cases. The reason why the instability transition correlates with Pf/Ptotal and vinj/valfven is that they can significantly modify the drive of low-frequency bursting modes and AEs. The explanation is supported by the observation that low-frequency bursting modes are rarely seen in the hybrids with NBI only, with EC waves and counter-NBI, or with high plasma density. A careful check of the low-frequency bursting modes suggests that they are mainly chirping (neoclassical) tearing modes [referred to as chirping (N)TM], i.e. the mode frequency firstly jumps up from the steady (N)TM frequency, then chirps down, and finally returns to the steady (N)TM frequency. Occasionally, the (N)TMs are fully stabilized and replaced with pure fishbones. The resonance condition calculation and 'Kick' model simulations suggest that (N)TMs and fishbones can interact through modification of the fast ion distribution in phase space, which influences the drive.

The effects of kinetic whistler wave instabilities on the runaway-electron (RE) avalanche is investigated. With parameters from experiments at the DIII-D National Fusion Facility, we show that RE scattering from excited whistler waves can explain several poorly understood experimental results. We find an enhancement of the RE avalanche for low density and high electric field, but for high density and low electric field the scattering can suppress the avalanche and raise the threshold electric field, bringing the present model much closer to observations. The excitation of kinetic instabilities and the scattering of resonant electrons are calculated self-consistently using a quasilinear model and local approximation. We also explain the observed fast growth of electron cyclotron emission signals and excitation of very low-frequency whistler modes observed in the quiescent RE experiments at DIII-D tokamak. Simulations using ITER parameters show that by controlling the background thermal plasma density and temperature, the plasma waves can also be excited spontaneously in tokamak disruptions and the avalanche generation of runaway electrons may be suppressed.

An optimization study of Quasi-Axisymmetric (QA) stellarators with varied elongation has been carried out using the optimization code STELLOPT. The starting point of our optimization is a previously obtained QA stellarator with three field periods and an aspect ratio of 6. A series of QA stellarators are obtained at zero plasma beta with the varied elongation value ranging from 2.5 to 3.7. A good quasi-symmetry is kept when the elongation value is reduced from the original value of 3.7. The rotational transform profile and aspect ratio are kept fixed. The plasma volume is ether kept fixed or varied linearly with elongation. Furthermore, finite beta QA stellarators are considered. The corresponding bootstrap currents are calculated using the kinetic code SFINCS. A series of kink-stable QA stellarators are obtained via optimization with varied plasma beta up to 5% and self-consistent bootstrap current. This work demonstrates that good QA stellarators with finite beta and varied elongation exist that are stable to external kink modes.

It was shown that asymmetric vertical displacement event disruptions in JET and ITER do not produce a large asymmetric force on conducting structures surrounding the plasma, provided that the current quench (CQ) time is less than the resistive wall penetration time. This is verified with JET data. In ITER, the CQ is expected to be comparable to the resistive wall penetration time, which gives a small wall force. It is shown that runaway electrons (REs) in JET do not produce a large wall force, and this is verified with JET data. This occurs if the RE current is about half of the initial plasma current. In ITER, the RE current might be comparable to the initial current, and REs might lengthen the CQ time sufficiently to produce a large wall force.

Motivated by the fact that geomagnetic field inhomogeneity is weak close to the chorus generation region and the observational evidence that falling-tone chorus tend to have large oblique angles of propagation, we propose that falling-tone chorus start as a marginally unstable mode. The marginally unstable mode requires the presence of a relatively large damping, which has its origins in the Landau damping of oblique waves in this collisionless environment. A marginally unstable mode produces phase-space structures that release energy and produce wave chirping. We show that the present model produces results in reasonable agreement with observations.

A systematic study of the global Energetic particle-induced Geodesic Acoustic Mode (EGAM) has been carried out for bump-on-tail energetic distribution in tokamak plasmas using linear kinetic-fluid hybrid simulation. The stability threshold of EGAM in energetic particle pressure is found to be very low. The eigenmode structure becomes more and more radially extended as energetic particle distribution evolves from bump-on-tail distribution to fully slowing-down distribution. The mode radial scale length increases with the energetic particle orbit width.

In DIII-D hybrid discharges, the intense Alfven eigenmode (AE) activity driven by Neutral Beam Injection that is typically observed can be suppressed and replaced by fishbone modes when Electron Cyclotron Current Drive (ECCD) is centrally applied. Simulations have been carried out with the kinetic-magnetohydrodynamic hybrid code M3D-K based on DIII-D discharges #161401 without ECCD and #161403 with ECCD, respectively. In both cases, unstable modes are found—the mode frequency and the mode structure indicate that the instability excited in #161403 is of fishbone type, while that in #161401 is identified as the beta-induced Alfven eigenmode-like mode. Moreover, we find that the calculated mode frequencies of these two shots are consistent with experimental observations. A systematic scan has been performed to study the instability region of n=1,2,3 modes in (q0,βhot) parameter space, where n is the toroidal mode number, q0 is the safety factor value at the magnetic axis, and βhot is the energetic particle beta. It is found that the transition between AEs and fishbone modes can occur when q0 is changed. In addition, the modes of n=1,2,3 are stable or weakly unstable in the region of Phot/Ptotal≤0.5 and 1.2

It is shown that nonlinear self-interaction of energetic particle-driven geodesic acoustic mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second-order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second-order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low fluctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.

A new pair of linear operators is introduced into the partially implicit but largely explicit time advance algorithm for the MHD equations in the M3D code. These operators jointly render the algorithm implicit with respect to propagation of the shear Alfven wave to leading order. As a result, the maximum stable time step is increased by up to a factor of three for many practical applications. The additional computational cost is trivial for the linear mode of operation and adds only approximately 30% additional execution time per step for nonlinear calculations.

The ideal magnetohydrodynamic (MHD) stability of the National Compact Stellarator Experiment (NCSX) is extensively analyzed using the most advanced three-dimensional MHD codes. It is shown that the NCSX is stable to finite-n MHD modes, including the vertical mode, external kink modes and ballooning modes. However, high-n external kink modes that peak near the plasma edge are found to be weakly unstable. A global calculation shows that finite-n ballooning modes are significantly more stable than the local infinite-n modes.

Based on numerical simulations with the magnetohydrodynamic code NOVA, reversed shear Alfven eigenmodes (RSAE) associated with the ellipticity-induced and non-circular triangularity-induced Alfven eigenmode gaps were found. An analytical model for large aspect ratio plasmas confirms the existence of those modes with a pressure gradient threshold that agrees very well with the NOVA calculations. It is predicted that these higher gap RSAEs might be observed in existing large tokamaks in the early phase of reversed shear discharges when the minimum value of the magnetic safety factor is high (larger than two) and in ITER advanced scenario discharges.

The major objective of the National Spherical Torus Experiment (NSTX) is to understand basic toroidal confinement physics at low aspect ratio and high βT in order to advance the spherical torus (ST) concept. In order to do this, NSTX utilizes up to 7.5 MW of neutral beam injection, up to 6 MW of high harmonic fast waves (HHFWs), and it operates with plasma currents up to 1.5 MA and elongations of up to 2.6 at a toroidal field up to 0.45 T. New facility, and diagnostic and modelling capabilities developed over the past two years have enabled the NSTX research team to make significant progress towards establishing this physics basis for future ST devices. Improvements in plasma control have led to more routine operation at high elongation and high βT (up to ~40%) lasting for many energy confinement times. βT can be limited by either internal or external modes. The installation of an active error field (EF) correction coil pair has expanded the operating regime at low density and has allowed for initial resonant EF amplification experiments. The determination of the confinement and transport properties of NSTX plasmas has benefitted greatly from the implementation of higher spatial resolution kinetic diagnostics. The parametric variation of confinement is similar to that at conventional aspect ratio but with values enhanced relative to those determined from conventional aspect ratio scalings and with a BT dependence. The transport is highly dependent on details of both the flow and magnetic shear. Core turbulence was measured for the first time in an ST through correlation reflectometry. Non-inductive start-up has been explored using PF-only and transient co-axial helicity injection techniques, resulting in up to 140 kA of toroidal current generated by the latter technique. Calculated bootstrap and beam-driven currents have sustained up to 60% of the flat-top plasma current in NBI discharges. Studies of HHFW absorption have indicated parametric decay of the wave and associated edge thermal ion heating. Energetic particle modes, most notably toroidal Alfven eigenmodes and fishbone-like modes result in fast particle losses, and these instabilities may affect fast ion confinement on devices such as ITER. Finally, a variety of techniques has been developed for fuelling and power and particle control.

Extended MHD effects are important in the nonlinear behavior of magnetically confined plasmas, even at the simplest level represented by the self-consistent diamagnetic (B × ∇p) drifts. Allowing the electrons and ions to move independently, even as fluids, breaks certain geometrical symmetries preserved by the MHD equations that can be important for toroidal fusion burning plasmas. These symmetries are also broken by certain experimental designs and high temperature plasma conditions. Results are shown from the two-fluid and hybrid particle/fluid models in the M3D MPP code, part of the SciDAC CEMM (Center for Extended Magnetohydrodynamic Modeling) project.

An overview of the research capabilities and the future plans on the MA-class National Spherical Torus Experiment (NSTX) at Princeton is presented. NSTX research is exploring the scientific benefits of modifying the field line structure from that in more conventional aspect ratio devices, such as the tokamak. The relevant scientific issues pursued on NSTX include energy confinement, MHD stability at high beta, non-inductive sustainment, solenoid-free start-up, and power and particle handling. In support of the NSTX research goal, research tools are being developed by the NSTX team. In the context of the fusion energy development path being formulated in the US, an ST-based Component Test Facility (CTF) and, ultimately a high beta Demo device based on the ST, are being considered. For these, it is essential to develop high performance (high beta and high confinement), steady-state (non-inductively driven) ST operational scenarios and an efficient solenoid-free start-up concept. We will also briefly describe the Next-Step-ST (NSST) device being designed to address these issues in fusion-relevant plasma conditions.

The coefficient matrices in M3D are reformed here to have symmetric structures. They are further categorized into 3 types: weak diagonally-dominant matrix, moderate diagonally-dominant matrix, and strong diagonally-dominant matrix. The weak diagonally-dominant matrix corresponds to the solution of auxiliary quantity F of the perturbed toroidal flux Ĩ with Neumann boundary conditions. The moderate diagonally-dominant matrix corresponds to the solution of the toroidal current C and the scalar potential Φ with Dirichlet boundary conditions. The strong diagonally-dominant matrix corresponds to the solution of the perturbed toroidal flux Ĩ , the poloidal flux ψ , the pressure p , and the 3 components of velocity: χ , U , and v ϕ with Dirichlet boundary conditions, respectively. We compare LU, GMRES, and ICCG algorithms for linear equation with these 3 types of matrices. It is observed that ICCG greatly accelerates the solution process as compared to GMRES, especially for the weak diagonally-dominant matrix. In this case we achieved 4 to 44 times speedup when the matrix order ranges from ∼10 1 to ∼10 4 . For the moderate diagonally-dominant case, there is a 4 to 24 times speedup. For the strong diagonally-dominant case, an average 2 times speedup is observed. It is also shown that the GMRES algorithm is much slower for the weak diagonally-dominant type than for the other 2 types: 4.4 times slower than the moderate diagonally-dominant case, 333 times slower than the strong diagonally-dominant case. The LU algorithm is faster than GMRES for the weak diagonally-dominant matrix since the matrix is strong ill-conditioned, but GMRES outperforms LU for the strong diagonally-dominant matrix since the matrix is well-conditioned. However, the ICCG algorithm outperforms both ILU and GMRES for all matrix types.

MHD and resistive MHD are inadequate to understand the stability of stellarators properly. Ideal MHD ballooning mode theory predicts β limits substantially below the values that can be expected in experiments. Resistive MHD is even more pessimistic, predicting that many stellarators are completely unstable. Including two fluid effects, ideally and resistively stable stellarator equilibria can be obtained. It may be possible to completely stabilize ballooning modes. The two fluid computations are done with a realistic value of the Hall parameter, the ratio of the ion skin depth to the major radius. Hybrid gyrokinetic simulations with energetic particles indicate that global shear Alfven TAE modes can be more stable in stellarators than in tokamaks. Computations in a two-period compact stellarator obtained a predominantly n = 1 toroidal mode with the expected TAE frequency. The TAE modes are more stable in the two-period compact stellarator than in a tokamak with the same q and pressure profiles. The cause for the stabilization is believed to be the increased damping rate due to 3D geometry. Simulations were performed with the M3D extended MHD code.

Second ballooning stability is examined in quasipoloidally symmetric, compact stellarator configurations. These high-β (volume-average β>4%) free-boundary equilibria are calculated using a reference Quasi-Poloidal Stellarator (QPS) configuration. QPS plasmas have low-shear, stellarator-like rotational transform profile with |B| that is approximately poloidally symmetric. The high-β QPS equilibria are similar in their magnetic configuration to previously studied tokamak-stellarator hybrids which have a high-shear, tokamak-like rotational transform profile. Both types of configurations have strong magnetic wells and consequently high interchange stability β limits. Free-boundary QPS equilibria have regions of second stability at high β. For infinite-n ballooning modes in QPS plasmas, the boundary for first instability is 〈β〉∼2% and the boundary for second stability is 〈β〉∼6%. Finite-n ballooning mode calculations show higher β limits, 〈β〉>5%. Increasing plasma current (for fixed plasma pressure) can lower t...

For the (non-axisymmetric) stellarator class of plasma confinement devices to be feasible candidates for fusion power stations it is essential that, to a good approximation, the magnetic field lines lie on nested flux surfaces; however, the inherent lack of a continuous symmetry implies that magnetic islands responsible for breaking the smooth topology of the flux surfaces are guaranteed to exist. Thus, the suppression of magnetic islands is a critical issue for stellarator design, particularly for small aspect ratio devices. Pfirsch–Schluter currents, diamagnetic currents and resonant coil fields contribute to the formation of magnetic islands, and the challenge is to design the plasma and coils such that these effects cancel.Magnetic islands in free-boundary high-pressure full-current stellarator magnetohydrodynamic equilibria are suppressed using a procedure based on the Princeton Iterative Equilibrium Solver (Reiman and Greenside 1986 Comput. Phys. Commun. 43 157) which iterates the equilibrium equations to obtain the plasma equilibrium. At each iteration, changes to a Fourier representation of the coil geometry are made to cancel resonant fields produced by the plasma. The changes are constrained to preserve certain measures of engineering acceptability and to preserve the stability of ideal kink modes. As the iterations continue, the coil geometry and the plasma simultaneously converge to an equilibrium in which the island content is negligible, the plasma is stable to ideal kink modes, and the coils satisfy engineering constraints. The method is applied to a candidate plasma and coil design for the National Compact Stellarator eXperiment (Reiman et al 2001 Phys. Plasma 8 2083).

Spherical tokamaks have relatively low toroidal field which means that the fast-ion Larmor radius is relatively large (ρfi>0.04 ap) and the fast ion velocity is much greater than the Alfven speed (Vfi>2 VAlfven). This regime of large Larmor radius and low Alfven speed is a regime in which fast ion driven instabilities are potentially virulent. It is therefore an important goal of the present proof-of-principle spherical tokamaks to evaluate the role of fast ion driven instabilities in fast ion confinement. This paper presents the first observations of fast ion losses in a spherical tokamak resulting from energetic particle driven modes. Two classes of instabilities are responsible for the losses. Multiple, simultaneously bursting modes in the toroidal Alfven eigenmode frequency gap cause neutron drops of up to 15%. A bursting, chirping mode identified as precession and/or bounce resonance fishbone also causes significant neutron drops. Both modes are usually present when the losses are observed.

The stability of α-particle driven shear Alfven eigenmodes (AE) for nominal burning plasma (BP) parameters in the proposed international tokamak experimental reactor (ITER), fusion ignition research experiment (FIRE) and IGNITOR tokamaks is studied. JET plasma, where fusion αs were generated in tritium experiments, is also studied to compare the numerical predictions with the existing experiments. An analytic assessment of toroidal AE (TAE) stability is first presented, where the α-particle β due to the fusion reaction rate and electron drag is simply and accurately estimated in plasmas with central temperature in the range of 7–20 keV. In this assessment the hot particle drive is balanced against ion-Landau damping of the background deuterons, and electron collision effects and stability boundaries are determined. Then two numerical studies of AE instability are presented. In one, the HIgh-n STability (HINST) code is used to predict the instabilities of low and moderately high frequency Alfven modes. HINST computes the non-perturbative solutions of the AE including effects of ion finite Larmor radius, orbit width, trapped electrons etc. The stability calculations are repeated using the global code NOVAK. We show that for these plasmas the spectrum of the least stable AE modes is at medium-/high-n numbers. In HINST, TAEs are locally unstable due to the α pressure gradient in all the devices under consideration except IGNITOR. However, NOVAK calculations show that the global mode structure enhances the damping mechanisms and produces stability for the nominal FIRE proposal and near-marginal stability for the nominal ITER proposal. NBI ions produce a strong stabilizing effect for JET. However, in ITER, the beam energies needed to penetrate to the core must be high (~1 MeV) so that a diamagnetic drift frequency comparable to that of α-particles is produced by the beam ions which induces a destabilizing effect. A serious question remains whether the perturbation theory used in NOVAK overestimates the stability predictions, so that it is premature to conclude that the nominal operation of all three BP proposals without neutral beam injection are stable (or marginally stable) to AEs.

The damping rate of the n = 1 toroidal Alfven eigenmodes (TAE) mode in Ohmic-heated JET plasmas has been measured and compared with the prediction of the kinetic NOVA-K code, which includes electron and ion Landau damping of the global shear-Alfven wave field, collisional damping, and radiative damping. It was found that the calculated damping rate is too small to account for the measured value under these experimental conditions. A relatively weak dependence of the damping rate on the normalized Larmor radius is observed experimentally.

The multilevel physics, massively parallel plasma simulation code, M3D has been used to study spherical toris (STs) and tokamaks. The magnitude of outboard shift of density profiles relative to electron temperature profiles seen in NSTX under strong toroidal flow is explained. Internal reconnection events in ST discharges can be classified depending on the crash mechanism, just as in tokamak discharges; a sawtooth crash, disruption due to stochasticity, or high-β disruption. Toroidal shear flow can reduce linear growth of internal kink. It has a strong stabilizing effect nonlinearly and causes mode saturation if its profile is maintained, e.g. through a fast momentum source. Normally, however, the flow profile itself flattens during the reconnection process, allowing a complete reconnection to occur. In some cases, the maximum density and pressure spontaneously occur inside the island and cause mode saturation. Gyrokinetic hot particle/MHD hybrid studies of NSTX show the effects of fluid compression on a fast-ion driven n = 1 mode. MHD studies of recent tokamak experiments with a central current hole indicate that the current clamping is due to sawtooth-like crashes, but with n = 0.

Hybrid simulations with the global kinetic-magnetohydrodynamic (MHD) code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of beam-driven fishbone in the experimental advanced superconducting tokamak (EAST) experiment. Linear simulations show that a low frequency fishbone instability is excited at experimental value of beam ion pressure. The mode is mainly driven by low energy beam ions via precessional resonance. The results are consistent with the experimental measurement with respect to mode frequency and mode structure. When the beam ion pressure is increased to exceed a critical value, the low frequency mode transits to a beta-induced Alfven eigenmode (BAE) with much higher frequency. This BAE is driven by higher energy beam ions. Nonlinear simulations show that the frequency of the low frequency fishbone chirps up and down with corresponding hole-clump structures in phase space, consistent with the Berk–Breizman theory. In addition to the low frequency mode, the high frequency BAE is excited during the nonlinear evolution. For the transient case of beam pressure fraction where the low and high frequency modes are simultaneously excited in the linear phase, only one dominant mode appears in the nonlinear phase with frequency jumps up and down during nonlinear evolution.

Linear and nonlinear simulations of high-order harmonics q = 1 energetic particle modes excited by trapped energetic particles in tokamaks are carried out using kinetic/magnetohydrodynamic hybrid code M3D-K. It is found that with a flat safety factor profile in the core region, the linear growth rate of high-order harmonics ( m = n > 1) driven by energetic trapped particles can be higher than the m / n = 1 / 1 component. The high m = n > 1 modes become more unstable when the pressure of energetic particles becomes higher. Moreover, it is shown that there exist multiple resonant locations satisfying different resonant conditions in the phase space of energetic particles for the high-order harmonics modes, whereas there is only one precessional resonance for the m / n = 1 / 1 harmonics. The fluid nonlinearity reduces the saturation level of the n = 1 component, while it hardly affects those of the high n components, especially the modes with m = n = 3 , 4. The frequency of these modes does not chirp signifi...

Compact optimized stellarators offer novel solutions for confining high-beta plasmas and developing magnetic confinement fusion. The three-dimensional plasma shape can be designed to enhance the magnetohydrodynamic (MHD) stability without feedback or nearby conducting structures and provide drift-orbit confinement similar to tokamaks. These configurations offer the possibility of combining the steady-state low-recirculating power, external control, and disruption resilience of previous stellarators with the low aspect ratio, high beta limit, and good confinement of advanced tokamaks. Quasi-axisymmetric equilibria have been developed for the proposed National Compact Stellarator Experiment (NCSX) with average aspect ratio 4-4.4 and average elongation similar to 1.8. Even with bootstrap-current consistent profiles, they are passively stable to the ballooning, kink, vertical, Mercier, and neoclassical-tearing modes for beta > 4%, without the need for external feedback or conducting walls. The bootstrap current generates only 1/4 of the magnetic rotational transform at beta = 4% (the rest is from the coils); thus the equilibrium is much less non-linear and is more controllable than similar advanced tokamaks. The enhanced stability is a result of 'reversed' global shear, the spatial distribution of local shear, and the large fraction of externally generated transform. Transport simulations show adequate fast-ion confinement and thermal neoclassical transport similar to equivalent tokamaks. Modular coils have been designed which reproduce the physics properties, provide good flux surfaces, and allow flexible variation of the plasma shape to control the predicted MHD stability and transport properties.

The internal structure of the toroidicity-induced Alfven eigenmode (TAE) is studied by comparing soft x-ray profile and beam ion loss data taken during TAE activity in the DIII-D tokamak [W. W. Hei ...

Physics issues are discussed for compact stellarator configurations which achieve good confinement by the fact that the magnetic field modulus |B| in magnetic co-ordinates is dominated by poloidally symmetric components. Two distinct configuration types are considered: (1) those which achieve their drift optimization and rotational transform at low β and low bootstrap current by appropriate plasma shaping; and (2) those which have a greater reliance on plasma β and bootstrap currents for supplying the transform and obtaining quasi-poloidal symmetry. Stability analysis of the latter group of devices against ballooning, kink and vertical displacement modes has indicated that stable β values on the order of 15% are possible. The first class of devices is being considered for a low β near term experiment that could explore some of the confinement features of the high β configurations.

Instabilities with frequency chirping in the frequency range of Alfven eigenmodes have been found in the domain 0.1% < βh < 1% and vb||/vA ~1 with high energy neutral beam injection in JT-60U. One instability with a frequency inside the Alfven continuum spectrum appears and its frequency increases slowly to the toroidicity induced Alfven eigenmode (TAE) gap on the timescale of an equilibrium change ( ≈ 200 ms). Other instabilities appear with a frequency inside the TAE gap and their frequencies change very quickly by 10-20 kHz in 1-5 ms. During the period when these fast frequency sweeping (fast FS) modes occur, abrupt large amplitude events (ALEs) often appear with a drop of neutron emission rate and an increase in fast neutral particle fluxes. The loss of energetic ions increases with a peak fluctuation amplitude of θ/Bθ. An energy dependence of the loss ions is observed and suggests a resonant interaction between energetic ions and the mode.

Toroidicity-induced Alfven eigenmode (TAE) stability in the National Spherical Torus Experiment (NSTX) [S. M. Kaye, M. Ono, Y.-K. M. Peng et al., Fusion Technol. 36, 16 (1999)] is analyzed using the improved NOVA-K code [N. N. Gorelenkov, C. Z. Cheng, and G. Y. Fu, Phys. Plasmas 6, 2802 (1999)], which includes finite orbit width and Larmor radius effects and is able to predict the saturation amplitude for the mode using the quasilinear theory. A broad spectrum of unstable global TAEs with different toroidal mode numbers is predicted. Due to the strong poloidal field and the presence of the magnetic well in NSTX, better particle confinement in the presence of TAEs in comparison with tokamaks is illustrated making use of the ORBIT code [R. B. White and M. S. Chance, Phys. Fluids 27, 2455 (1984)].

Recent stability results of external kink modes and vertical modes in compact stellarators are presented. The vertical mode is found to be stabilized by externally generated poloidal flux. A simple stability criterion is derived in the limit of large aspect ratio and constant current density. For a wall at infinite distance from the plasma, the amount of external flux needed for stabilization is given by F-i = (kappa(2) - kappa)/(kappa(2) + 1), where kappa is the axisymmetric elongation and F-i is the fraction of the external rotational transform. A systematic parameter study shows that the external kink mode in a quasiaxisymmetric stellarator (QAS) can be stabilized at high beta (similar to 5%) without a conducting wall by magnetic shear via three-dimensional (3D) shaping. It is found that external kinks are driven by both parallel current and pressure gradient. The pressure contributes significantly to the overall drive through the curvature term and the Pfirsch-Schluter current. (C) 2000 American Institute of Physics. [S1070-664X(00)91005-X].

Physics knowledge (theory and experiment) in energetic particles relevant to design of a reactor scale tokamak is reviewed, and projections for ITER are provided in this Chapter of the ITER Physics Basis. The review includes single particle effects such as classical alpha particle heating and toroidal field ripple loss, as well as collective instabilities that might be generated in ITER plasmas by energetic alpha particles. The overall conclusion is that fusion alpha particles are expected to provide an efficient plasma heating for ignition and sustained burn in the next step device. The major concern is localized heat loads on the plasma facing components produced by alpha particle loss, which might affect their lifetime in a tokamak reactor.

Key physics issues in the design of a high- quasi-axisymmetric stellarator configuration are discussed. The goal of the design study is a compact stellarator configuration with aspect ratio comparable to that of tokamaks and good transport and stability properties. Quasi- axisymmetry has been used to provide good drift trajectories. Ballooning stabilization has been accomplished by strong axisymmetric shaping, yielding a stellarator configuration whose core is in the second stability regime for ballooning modes. A combination of externally generated shear and non-axisymmetric corrugation of the plasma boundary provides stability to external kink modes even in the absence of a conducting wall. The resulting configuration is also found to be robustly stable to vertical modes, increasing the freedom to perform axisymmetric shaping. Stability to neoclassical tearing modes is conferred by a monotonically increasing profile. A gyrokinetic f code has been used to confirm the adequacy of the neoclassical confinement. Neutral beam losses have been evaluated with Monte Carlo codes.