ORCID Profile
0000-0002-9550-8776
Current Organisation
Australian National University
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Atomic, Molecular, Nuclear, Particle and Plasma Physics | Power and Energy Systems Engineering (excl. Renewable Power) | Plasma Physics; Fusion Plasmas; Electrical Discharges | Numerical Solution of Differential and Integral Equations | Simulation And Modelling | Plasmas And Electrical Discharges | Dynamical Systems | Harmonic And Fourier Analysis | Space and Solar Physics |
Nuclear Energy | Expanding Knowledge in the Physical Sciences | Expanding Knowledge in the Mathematical Sciences | Physical sciences | Energy transformation not elsewhere classified | Nuclear | Higher education | Mathematical sciences
Publisher: IOP Publishing
Date: 16-04-2018
Publisher: AIP Publishing
Date: 09-2011
DOI: 10.1063/1.3641966
Abstract: We extend existing 2-D analytical high-β equilibrium solutions obtained by Cowley et al. [Phys. Fluids B 3, 2066 (1991)] and Hsu et al. [Phys. Plasmas 3, 266 (1996)] to the case of toroidally flowing plasma, assuming ideal magnetohydrodynamics and isothermal magnetic surfaces. Invoking the ordering βq2& & ε2 and Mφ2q2& & ε, we solve the boundary layer problem, re-obtaining the static solution in the zero flow limit. The phenomenon of extreme plasma diamagnetism in the static solution was found to be reduced due to centrifugal drift currents for significant toroidal flow. Ex le equilibrium calculations are presented using plasma parameters which are approaching attainable values in next generation spherical tokamaks.
Publisher: AIP Publishing
Date: 05-2014
DOI: 10.1063/1.4879802
Abstract: Continuum resonance d ing is an important factor in determining the stability of certain global modes in fusion plasmas. A number of analytic and numerical approaches have been developed to compute this d ing, particularly, in the case of the toroidicity-induced shear Alfvén eigenmode. This paper compares results obtained using an analytical perturbative approach with those found using resistive and complex contour numerical approaches. It is found that the perturbative method does not provide accurate agreement with reliable numerical methods for the range of parameters examined. This discrepancy exists even in the limit where d ing approaches zero. When the perturbative technique is implemented using a standard finite element method, the d ing estimate fails to converge with radial grid resolution. The finite elements used cannot accurately represent the eigenmode in the region of the continuum resonance, regardless of the number of radial grid points used.
Publisher: IOP Publishing
Date: 20-04-2020
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 23-10-2023
Publisher: AIP Publishing
Date: 2012
DOI: 10.1063/1.3677362
Abstract: In this paper, current profiles for plasma discharges on the mega- ere spherical tokamak are directly calculated from pickup coil, flux loop, and motional-Stark effect observations via methods based in the statistical theory of Bayesian analysis. By representing toroidal plasma current as a series of axisymmetric current beams with rectangular cross-section and inferring the current for each one of these beams, flux-surface geometry and q-profiles are subsequently calculated by elementary application of Biot-Savart’s law. The use of this plasma model in the context of Bayesian analysis was pioneered by Svensson and Werner on the joint-European tokamak [Svensson and Werner,Plasma Phys. Controlled Fusion 50(8), 085002 (2008)]. In this framework, linear forward models are used to generate diagnostic predictions, and the probability distribution for the currents in the collection of plasma beams was subsequently calculated directly via application of Bayes’ formula. In this work, we introduce a new diagnostic technique to identify and remove outlier observations associated with diagnostics falling out of calibration or suffering from an unidentified malfunction. These modifications enable a good agreement between Bayesian inference of the last-closed flux-surface with other corroborating data, such as that from force balance considerations using EFIT++ [Appel et al., "A unified approach to equilibrium reconstruction" Proceedings of the 33rd EPS Conference on Plasma Physics (Rome, Italy, 2006)]. In addition, this analysis also yields errors on the plasma current profile and flux-surface geometry as well as directly predicting the Shafranov shift of the plasma core.
Publisher: IOP Publishing
Date: 23-03-2020
Publisher: IOP Publishing
Date: 25-10-2017
Publisher: American Physical Society (APS)
Date: 14-11-2007
Publisher: AIP Publishing
Date: 07-2012
DOI: 10.1063/1.4890847
Abstract: We present an extension of the multi-region relaxed magnetohydrodynamics (MRxMHD) equilibrium model that includes pressure anisotropy and general plasma flows. This anisotropic extension to our previous isotropic model is motivated by Sun and Finn's model of relaxed anisotropic magnetohydrodynamic equilibria. We prove that as the number of plasma regions becomes infinite, our anisotropic extension of MRxMHD reduces to anisotropic ideal MHD with flow. The continuously nested flux surface limit of our MRxMHD model is the first variational principle for anisotropic plasma equilibria with general flow fields.
Publisher: IOP Publishing
Date: 12-04-2012
Publisher: MDPI AG
Date: 14-11-2008
DOI: 10.3390/E10040621
Publisher: American Physical Society (APS)
Date: 04-03-2016
Publisher: Elsevier BV
Date: 02-2022
Publisher: American Physical Society (APS)
Date: 29-01-2020
Publisher: AIP Publishing
Date: 07-2012
DOI: 10.1063/1.4737605
Publisher: AIP Publishing
Date: 05-2007
DOI: 10.1063/1.2722721
Abstract: A generalized energy principle for finite-pressure, toroidal magnetohydrodynamic (MHD) equilibria in general three-dimensional configurations is proposed. The full set of ideal-MHD constraints is applied only on a discrete set of toroidal magnetic surfaces (invariant tori), which act as barriers against leakage of magnetic flux, helicity, and pressure through chaotic field-line transport. It is argued that a necessary condition for such invariant tori to exist is that they have fixed, irrational rotational transforms. In the toroidal domains bounded by these surfaces, full Taylor relaxation is assumed, thus leading to Beltrami fields ∇×B=λB, where λ is constant within each domain. Two distinct eigenvalue problems for λ arise in this formulation, depending on whether fluxes and helicity are fixed, or boundary rotational transforms. These are studied in cylindrical geometry and in a three-dimensional toroidal region of annular cross section. In the latter case, an application of a residue criterion is used to determine the threshold for connected chaos.
Publisher: IOP Publishing
Date: 05-08-2022
Abstract: The operation of the Instituto Superior Técnico Tokamak (ISTTOK) in the alternating current (AC) regime is characterized by the presence of a residual plasma density during the current transition, i.e. when the plasma current crosses the zero value. Contrary to what has been reported in other AC experiments, the pressure-like profiles obtained by the heavy ion beam diagnostic (the product of plasma density with a known function of plasma temperature) do not show evidence of the co-existence of two anti-parallel currents. This is also confirmed by the fact that in these experiments the plasma current and the V loop both cross the zero value at the same instant. The Murakami–Hugill plots reveal that during the transition the plasma current decays faster than the Hugill limit and that the subsequent r -up phase is sustained by runaway electron (RE) currents. It is hypothesized that during plasma current decay a population of REs can enter the following semi-cycle of the discharge. A trajectory simulation model including the forces at play shows that the retardation effect of the friction and molecular forces can cause the d ening of REs (within 20 μ s) with energy below 1 keV inside the chamber (without external vertical correction magnetic fields), thus ionizing the background gas. Faster REs (above 1 keV) can also contribute to the ionization of the background gas (e.g. within 50 μ s for 3 keV energy electrons) but require a vertical magnetic field to balance the gradB and curvature drifts. This could explain why tuning the vertical field and dosing the background pressure to obtain successful AC discharges is usually challenging.
Publisher: IOP Publishing
Date: 20-01-2009
Publisher: IOP Publishing
Date: 19-11-2004
Publisher: Cambridge University Press (CUP)
Date: 28-09-2021
DOI: 10.1017/S002237782100088X
Abstract: Pressure anisotropy is a commonly observed phenomenon in tokamak plasmas, due to external heating methods such as neutral beam injection and ion-cyclotron resonance heating. Equilibrium models for tokamaks are constructed by solving the Grad–Shafranov equation such models, however, do not account for pressure anisotropy since ideal magnetohydrodynamics assumes a scalar pressure. A modified Grad–Shafranov equation can be derived to include anisotropic pressure and toroidal flow by including drift-kinetic effects from the guiding-centre model of particle motion. In this work, we have studied the mathematical well-posedness of these two problems by showing the existence and uniqueness of solutions to the Grad–Shafranov equation both in the standard isotropic case and when including pressure anisotropy and toroidal flow. A new fixed-point approach is used to show the existence of solutions in the Sobolev space $H_0^1$ to the Grad–Shafranov equation, and sufficient criteria for their uniqueness are derived. The conditions required for the existence of solutions to the modified Grad–Shafranov equation are also constructed.
Publisher: Cambridge University Press (CUP)
Date: 10-2009
DOI: 10.1017/S0022377809008095
Abstract: A unified energy principle approach is presented for analysing the magnetohydrodynamic (MHD) stability of plasmas consisting of multiple ideal and relaxed regions. The gauge a = ξ × B for the vector potential, a , of linearized perturbations is used, with the equilibrium magnetic field B obeying a Beltrami equation, ∇ × B = α B , in relaxed regions. In a region with such a force-free equilibrium Beltrami field we show that ξ obeys the same Euler–Lagrange equation whether ideal or relaxed MHD is used for perturbations, except in the neighbourhood of the magnetic surfaces where B · ∇ is singular. The difference at singular surfaces is analysed in cylindrical geometry: in ideal MHD only Newcomb's small solutions are allowed, whereas in relaxed MHD only the odd-parity large solution and even-parity small solution are allowed. A procedure for constructing global multi-region solutions in cylindrical geometry is presented. Focusing on the limit where the two interfaces approach each other arbitrarily closely, it is shown that the singular-limit problem encountered previously by Hole et al. in multi-region relaxed MHD is stabilized if the relaxed-MHD region between the coalescing interfaces is replaced by an ideal-MHD region. We then present a stable ( k , pressure) phase-space plot, which allows us to determine the form a stable pressure and field profile must take in the region between the interfaces. From this knowledge, we conclude that there exists a class of single-interface plasmas that were found to be stable by Kaiser and Uecker, but are shown to be unstable when the interface is resolved.
Publisher: IOP Publishing
Date: 17-07-2007
Publisher: American Physical Society (APS)
Date: 28-03-2002
Publisher: AIP Publishing
Date: 22-08-2002
DOI: 10.1063/1.1490928
Abstract: Spontaneous transitions from the low “L-mode” to high “H-mode” of tokamak plasma confinement, first observed during neutral beam heating experiments on ASDEX, are now routinely achieved in many tokamak experiments. The H-mode regime is attractive as it offers the possibility of enhanced confinement, and thus a route towards a more “compact” and cost-efficient fusion power-plant. Transition to H-mode is now routinely achievable in the Mega-Amp Spherical Tokamak (MAST) [A. C. Darke et al., Fusion Technology 1994 (Elsevier, Amsterdam, 1995), Vol. 1, p. 799] for both Ohmically and neutral beam injection (NBI) heated plasmas (PNBI∼0.5–1.7 MW). H-mode plasmas can be either center stack limited or X-point erted, exhibiting regular Type III edge localized modes (ELMs). Global confinement in H-mode with low frequency ELMs is consistent with the international IPB(y,2) scaling and exceeds the scaling by a factor ∼1.5–2.0 for high performance discharges. Confinement degrades with increasing ELM frequency (which in turn scales with power and density) as for conventional tokamaks. Densities above the Greenwald limit (G∼1) have been achieved for plasma currents up to 0.8 MA using gas-fueling, and up to 0.9 MA using a low field side multi-pellet injector. High field side fueling, on the other hand, can be supplied via a gas-feed located at the center-column mid-plane, this technique having been found to dramatically enhance H-mode accessibility and quality. When combined with Connected Double Null plasma topology, a significant reduction in Ohmic L–H power threshold can be achieved as a result, power threshold data are now in broad agreement with a number of the latest scaling law predictions. Following the transition to H-mode, power crossing the inner separatrix remains low, resulting in a high recycling scrape-off layer (compared with partial detachment in L-mode). To date, with NBI power limited to 1.7 MW, H-mode MAST plasmas have shown no evidence of having approached a beta limit (βN∼4.5li). High performance H-mode discharges are at sufficient poloidal beta (βp), however, to enable the first studies of the Neoclassical Tearing Mode, the MHD instability responsible for limiting the achievable beta in conventional tokamaks.
Publisher: IOP Publishing
Date: 03-08-2016
DOI: 10.1088/0029-5515/56/11/112017
Abstract: A number of tools have recently been developed to study equilibrium and stability in tokamaks with pressure anisotropy. Here we apply these tools to a Mega Ampere Spherical Tokamak (MAST) discharge to calculate equilibrium, Alfvén continua and eigenmodes, through to linear growth and nonlinear saturation of a toroidal Alfvén eigenmode (TAE) this is the first study of wave growth and saturation for anisotropic equilibria. Comparisons with the standard tools which assume an isotropic pressure reveal various differences in equilibrium and modes: the safety factor profile in the isotropic reconstruction is reversed shear while the anisotropic reconstruction gives normal shear the isotropic TAE gap is much narrower than the anisotropic gap and the TAE radial mode structure is wider in the anisotropic case. These lead to a modification in the resonant regions of fast-ion phase space, and produce a 35% larger linear growth rate and an 18% smaller saturation litude for the TAE in the anisotropic analysis compared to the isotropic analysis.
Publisher: AIP Publishing
Date: 10-2016
DOI: 10.1063/1.4964667
Abstract: The sandpile paradigm is widely used to model aspects of the phenomenology of magnetically confined fusion (MCF) plasmas, including enhanced confinement, edge pedestals and, potentially, the impulsive energy and particle release process known as ELMing. Here we identify new points of contact between ELMing and the systemwide avalanches in a sandpile. We compare the quantified response [Calderon et al., Phys. Plasmas 20, 042306 (2014)] to increased fuelling of the time sequence of edge localised mode events in a series of similar Joint European Torus plasmas with the response to increased fuelling of the time sequence of systemwide avalanches in a sandpile model [Chapman et al., Phys. Rev. Lett. 86, 2814 (2001)] that has well established links to MCF plasma phenomenology. Both the probability density functions of inter-event time intervals, and delay time embeddings of event time sequences, at different fuelling rates, show common features and point to shared underlying physics.
Publisher: AIP Publishing
Date: 12-2009
DOI: 10.1063/1.3272713
Abstract: Over the past two decades, the increase in neutral-beam heating and α particle production in magnetically confined fusion plasmas has led to an increase in energetic particle driven mode activity, much of which has an electromagnetic signature which can be detected by the use of external Mirnov coils. Typically, the frequency and spatial wave number band of such oscillations increase with increasing injection energy, offering new challenges for diagnostic design. In particular, as the frequency approaches the megahertz range, care must be taken to model the stray capacitance of the coil, which limits the resonant frequency of the probe model transmission line effects in the system, which if unchecked can produce system resonances and minimize coil conductive shielding, so as to minimize skin currents which limit the frequency response of the coil. As well as optimizing the frequency response, the coils should also be positioned to confidently identify oscillations over a wide wave number band. This work, which draws on new techniques in stray capacitance modeling and coil positioning, is a case study of the outboard Mirnov array for high-frequency acquisition in the Mega Ampere Spherical Tokamak, and is intended as a roadmap for the design of high frequency, weak field strength magnetic diagnostics.
Publisher: IOP Publishing
Date: 18-05-2011
Publisher: IOP Publishing
Date: 12-2003
Publisher: IOP Publishing
Date: 17-04-2014
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 10-2014
Publisher: Wiley
Date: 19-11-2022
DOI: 10.1111/NPH.18543
Abstract: Multispecies interbreeding networks, or syngameons, have been increasingly reported in natural systems. However, the formation, structure, and maintenance of syngameons have received little attention. Through gene flow, syngameons can increase genetic ersity, facilitate the colonization of new environments, and contribute to hybrid speciation. In this study, we evaluated the history, patterns, and consequences of hybridization in a pinyon pine syngameon using morphological and genomic data to assess genetic structure, demographic history, and geographic and climatic data to determine niche differentiation. We demonstrated that Pinus edulis , a dominant species in the Southwestern US and a barometer of climate change, is a core participant in the syngameon, involved in the formation of two drought‐adapted hybrid lineages including the parapatric and taxonomically controversial fallax ‐type. We found that species remain morphologically and genetically distinct at range cores, maintaining species boundaries while undergoing extensive gene flow in areas of sympatry at range peripheries. Our study shows that sequential hybridization may have caused relatively rapid speciation and facilitated the colonization of different niches, resulting in the rapid formation of two new lineages. Participation in the syngameon may allow adaptive traits to be introgressed across species barriers and provide the changes needed to survive future climate scenarios.
Publisher: AIP Publishing
Date: 10-1997
DOI: 10.1063/1.872246
Abstract: The effect of a variable magnetic field on behavior in the rotation region of a vacuum arc centrifuge is analyzed using a first order perturbation of the fluid equations describing the plasma. It is found that the plasma contracts and rotates more rapidly as it moves into an increasing magnetic field. Under conditions typical of current devices, the separative performance is predicted to improve significantly.
Publisher: IOP Publishing
Date: 26-09-2013
Publisher: IOP Publishing
Date: 03-11-2010
Publisher: IOP Publishing
Date: 08-01-2019
Publisher: IOP Publishing
Date: 25-08-2023
Abstract: An initial investigation into the application of Bayesian inference to the reconstruction of the spatial distribution of current perturbations in tokamaks from diagnostic signals is presented. Previous work in Bayesian equilibrium current tomography is extended to the case of a complex phasor representation of harmonically time varying current distributions. A forward function to predict the response of magnetic diagnostics is constructed using only electrodynamics and not reduced models of ideal MHD. The extension of this forward function to incorporate a fully kinetic model of the plasma state is suggested. The response of soft x-ray diagnostics, and the motional Stark effect diagnostic to the current perturbations are also predicted and the integration of all diagnostics into a single estimate of the current perturbation is proposed. Simulations with synthetic diagnostics in simple geometry demonstrate that the perturbed current distribution can be reconstructed subject to prior assumptions regarding solution smoothness.
Publisher: IOP Publishing
Date: 12-01-2015
Publisher: IOP Publishing
Date: 08-12-2012
Publisher: IOP Publishing
Date: 25-10-2021
Publisher: AIP Publishing
Date: 2021
DOI: 10.1063/5.0032489
Abstract: Nonresonant internal modes can be difficult to anticipate as there is no resonant surface in the plasma. However, equilibria that are unstable to multiple nonresonant magnetohydrodynamic (MHD) modes may be more prone to global loss of confinement since these instabilities generate spatially extended linear displacements, potentially enhancing magnetic field line chaos via nonlinear interactions. Here, we successfully predict the unstable nonresonant pressure-driven modes for equilibria with zero shear in the plasma core, irrational q on axis, and a central pressure gradient, which is consistent with pre-crash profiles in sawtoothing tokamak plasmas in the large-aspect-ratio limit. A criterion for identifying nonresonant modes most likely to be unstable is developed from the convergents of the continued fraction representation of q0. A higher-order analysis of the standard Energy Principle reveals the conditions under which these modes are expected to dominate. Linear growth rate spectra, as a function of toroidal mode number (up to n = 30), calculated using the initial-value extended-MHD code, M3D-C1, recover the characteristic dependence observed for ideal infernal modes. Nonresonant modes have also been invoked in some ideal sawtooth crash models. This work provides a mechanism to predict the mode numbers of infernal modes and, potentially, the width of some post-sawtooth-crash profiles.
Publisher: AIP Publishing
Date: 08-2010
DOI: 10.1063/1.3469580
Publisher: IOP Publishing
Date: 27-04-2021
Abstract: The guiding centre dynamics of fast particles can alter the behaviour of energetic particle (EP) driven modes with chirping frequencies. In this paper, the applicability of an earlier trapped assing locus model (Hezaveh et al 2017 Nucl. Fusion 57 126010) has been extended to regimes where the wave trapping region can expand and trap ambient particles. This extension allows the study of waves with up-ward and down-ward frequency chirping across the full range of EP orbits. Under the adiabatic approximation, the phase-space of EPs is analysed by a Lagrangian contour approach where the islands are discretised using phase-space waterbags. In order to resolve the dynamics during the fast formation of phase-space islands and find an appropriate initialisation for the system, full-scale modelling is implemented using the bump-on-tail code. In addition to investigating the evolution of chirping waves with deepening potentials in a single resonance, we choose specific pitch-angle ranges in which higher resonances can have a relatively considerable contribution to the wave-particle interaction. Hence, the model is also solved in a double-resonance scenario where we report on the significant modifications to the behaviour of the chirping waves due to the 2nd resonance. The model presented in this paper gives a comprehensive 1D paradigm of long range frequency chirping signals observed in experiments with both up-ward and down-ward chirping and multiple resonances.
Publisher: IOP Publishing
Date: 30-07-2015
Publisher: AIP Publishing
Date: 03-2013
DOI: 10.1063/1.4795739
Abstract: We show the stepped-pressure equilibria that are obtained from a generalization of Taylor relaxation known as multi-region, relaxed magnetohydrodynamics (MRXMHD) are also generalizations of ideal magnetohydrodynamics (ideal MHD). We show this by proving that as the number of plasma regions becomes infinite, MRXMHD reduces to ideal MHD. Numerical convergence studies illustrating this limit are presented.
Publisher: AIP Publishing
Date: 09-2013
DOI: 10.1063/1.4819250
Abstract: The need to understand the structure of magnetic fluctuations in H-1NF heliac [S. Hamberger et al., Fusion Technol. 17, 123 (1990)] plasmas has motivated the installation of a sixteen former, tri-axis helical magnetic probe Mirnov array (HMA). The new array complements two existing poloidal Mirnov arrays by providing polarisation information, higher frequency response, and improved toroidal resolution. The helical placement is ideal for helical axis plasmas because it positions the array as close as possible to the plasma in regions of varying degrees of favourable curvature in the magnetohydrodynamic sense, but almost constant magnetic angle. This makes phase variation with probe position near linear, greatly simplifying the analysis of the data. Several of the issues involved in the design, installation, data analysis, and calibration of this unique array are presented including probe coil design, frequency response measurements, mode number identification, orientation calculations, and mapping probe coil positions to magnetic coordinates. Details of specially designed digitally programmable pre- lifiers, which allow gains and filters to be changed as part of the data acquisition initialisation sequence and stored with the probe signals, are also presented. The low shear heliac geometry [R. Jiménez-Gómez et al., Nucl. Fusion 51, 033001 (2011)]10.1088/0029-5515/51/3/033001, flexibility of the H-1NF heliac, and wealth of information provided by the HMA create a unique opportunity for detailed study of Alfvén eigenmodes, which could be a serious issue for future fusion reactors.
Publisher: Institution of Engineering and Technology (IET)
Date: 2005
Publisher: IOP Publishing
Date: 16-07-2020
Publisher: AIP Publishing
Date: 04-2011
DOI: 10.1063/1.3581045
Abstract: A two-fluid model developed originally to describe wave oscillations in the vacuum arc centrifuge, a cylindrical, rapidly rotating, low temperature, and confined plasma column, is applied to interpret plasma oscillations in a RF generated linear magnetized plasma [WOMBAT (waves on magnetized beams and turbulence)], with similar density and field strength. Compared to typical centrifuge plasmas, WOMBAT plasmas have slower normalized rotation frequency, lower temperature, and lower axial velocity. Despite these differences, the two-fluid model provides a consistent description of the WOMBAT plasma configuration and yields qualitative agreement between measured and predicted wave oscillation frequencies with axial field strength. In addition, the radial profile of the density perturbation predicted by this model is consistent with the data. Parameter scans show that the dispersion curve is sensitive to the axial field strength and the electron temperature, and the dependence of oscillation frequency with electron temperature matches the experiment. These results consolidate earlier claims that the density and floating potential oscillations are a resistive drift mode, driven by the density gradient. To our knowledge, this is the first detailed physics model of flowing plasmas in the diffusion region away from the RF source. Possible extensions to the model, including temperature nonuniformity and magnetic field oscillations, are also discussed.
Publisher: AIP Publishing
Date: 2006
DOI: 10.1063/1.2154684
Abstract: A stochastic analysis is developed for the superposition of multiple, fully polarized, electric-field vectors. Each vector is described by a polarization ellipse, with fixed axial ratio and polarization angle, and probability distribution functions (pdfs) for the field strength and phase. These wave populations are then superposed in orthonormal modes of polarization, representing the normal modes of a medium. Central results of this work include analytic and Monte Carlo methods to calculate the pdfs of the measurable Stokes parameters I, U, Q, and V, and degrees of polarization, of the superposed waves. Predictions are computed for the superposition of some characteristic wave populations, and several striking and counterintuitive results produced. These include nonzero probabilities for U, Q, and V at U=0, Q=0, and V=0, irrespective of the constituent wave polarizations and field distributions. For wave populations with identical polarization ellipses, a power-law enhancement of the pdf of the intensity I at low I is found, which is independent of the constituent electric-field distributions. Generation of elliptically polarized light from components which each have an opposite sense of polarization is shown to be possible. A description of the asymptotic limits of the pdfs of the Stokes parameters is obtained, and the appearance of fine structure in the pdfs of the degrees of polarization is demonstrated. Together, these results demonstrate the necessity of systematic analysis when predicting pdfs for the Stokes parameters and degrees of polarization: qualitative results cannot be correctly inferred from intuition alone.
Publisher: IOP Publishing
Date: 19-08-2002
Publisher: IOP Publishing
Date: 27-08-2004
Publisher: IOP Publishing
Date: 10-09-2009
DOI: 10.1088/0029-5515/49/10/104017
Abstract: Several improvements to the MAST plant and diagnostics have facilitated new studies advancing the physics basis for ITER and DEMO, as well as for future spherical tokamaks (STs). Using the increased heating capabilities P NBI ⩽ 3.8 MW H-mode at I p = 1.2 MA was accessed showing that the energy confinement on MAST scales more weakly with I p and more strongly with B t than in the ITER IPB98( y , 2) scaling. Measurements of the fuel retention of shallow pellets extrapolate to an ITER particle throughput of 70% of its original designed total throughput capacity. The anomalous momentum diffusion, χ ϕ , is linked to the ion diffusion, χ i , with a Prandtl number close to P ϕ ≈ χ ϕ /χ i ≈ 1, although χ i approaches neoclassical values. New high spatial resolution measurements of the edge radial electric field, E r , show that the position of steepest gradients in electron pressure and E r (i.e. shearing rate) are coincident, but their magnitudes are not linked. The T e pedestal width on MAST scales with rather than ρ pol . The edge localized mode (ELM) frequency for type-IV ELMs, new in MAST, was almost doubled using n = 2 resonant magnetic perturbations from a set of four external coils ( n = 1, 2). A new internal 12 coil set ( n ⩽ 3) has been commissioned. The filaments in the inter-ELM and L-mode phase are different from ELM filaments, and the characteristics in L-mode agree well with turbulence calculations. A variety of fast particle driven instabilities were studied from 10 kHz saturated fishbone like activity up to 3.8 MHz compressional Alfvén eigenmodes. Fast particle instabilities also affect the off-axis NBI current drive, leading to fast ion diffusion of the order of 0.5 m 2 s −1 and a reduction in the driven current fraction from 40% to 30%. EBW current drive start-up is demonstrated for the first time in a ST generating plasma currents up to 55 kA. Many of these studies contributed to the physics basis of a planned upgrade to MAST.
Publisher: IOP Publishing
Date: 03-02-2022
Abstract: We present a procedure to examine energetic particle phase-space during long range frequency chirping phenomena in tokamak plasmas. To apply the proposed method, we have performed self-consistent simulations using the MEGA code and analyzed the simulation data. We demonstrate a traveling wave in phase-space and that there exist specific slices of phase-space on which the resonant particles lie throughout the wave evolution. For non-linear evolution of an n = 6 toroidicity-induced Alfvén eigenmode (TAE), our results reveal the formation of coherent phase-space structures (holes/clumps) after coarse-graining of the distribution function. These structures cause a convective transport in phase-space which implies a radial drift of the resonant particles. We also demonstrate that the rate of frequency chirping increases with the TAE d ing rate. Our observations of the TAE behavior and the corresponding phase-space dynamics are consistent with the Berk–Breizman theory.
Publisher: Cambridge University Press (CUP)
Date: 04-2021
Publisher: IOP Publishing
Date: 23-02-2004
Publisher: IOP Publishing
Date: 17-10-2014
Publisher: IOP Publishing
Date: 23-05-2023
Abstract: We show that the variational energy principle of the multi-region relaxed magnetohydrodynamic (MRxMHD) model can be used to predict finite-pressure linear tearing instabilities. In this model, the plasma volume is sliced into sub-volumes separated by ‘ideal interfaces’, and in each volume the magnetic field relaxes to a Taylor state, where the pressure gradient ∇ p = 0 . The MRxMHD model is implemented in the Stepped-Pressure Equilibrium Code (SPEC) so that the equilibrium solution in each region is computed while preserving the force balance across the interfaces. As SPEC computes the Hessian matrix (a discretized stability matrix), the stability of an MRxMHD equilibrium can also be computed with SPEC. In this article, using SPEC, we investigate the effect of local pressure gradients and the ∇ p = 0 in the vicinity of the resonant surface of a tearing mode. For low-beta plasma, we have been able to illustrate a relationship between the resistive singular-layer theory (Coppi et al 1966 Nucl. Fusion 6 101 Glasser et al 1975 Phys. Fluids 18 875–88) and the MRxMHD model. Within the singular layer, the volume-averaged magnetic helicity and the flux-averaged toroidal flux are shown to be the invariants for the linear tearing modes in SPEC simulations. Our technique to compute MRxMHD stability is first tested numerically in a cylindrical tokamak and its application in toroidal geometry is demonstrated. We demonstrate an agreement between the stability boundary obtained with SPEC simulation and the resistive inner-layer theories.
Publisher: IOP Publishing
Date: 17-04-2013
Publisher: IOP Publishing
Date: 10-2005
Publisher: IOP Publishing
Date: 03-11-2020
Abstract: The numerical solution of the stepped pressure equilibrium (Hudson et al 2012 Phys. Plasmas 19 112502) requires a fast and robust solver to obtain the Beltrami field in three-dimensional geometry such as stellarators. The spectral method implemented in the stepped pressure equilibrium code (SPEC) is efficient when the domain is a hollow torus, but ill-conditioning of the discretised linear equations occurs in the (solid) toroid due to the artificially singular coordinate parameterisation near the axis. In this work, we propose an improved choice for the reference axis to prevent coordinates surfaces from overlapping. Then, we examine the parity and asymptotics of the magnetic vector potential near the axis and suggest the use of recombined and rescaled Zernike radial basis functions. The maximum relative error in the magnetic field of the Wendelstein 7-X geometry is shown to reach 10 −9 at high resolution in a series of convergence tests and benchmarks against the boundary integral equation solver for Taylor states. The new method is also reported to significantly improve the accuracy of multi-volume SPEC calculations. A comparison between free-boundary SPEC and the analytical Dommaschk potential is presented with higher-than-usual Fourier resolution. It is illustrated that we are able to resolve low litude current sheets when an interface is placed where there is no flux surface in the analytic solution. This was previously concealed because of insufficient numerical resolution.
Publisher: IOP Publishing
Date: 10-07-2020
Publisher: AIP Publishing
Date: 06-2013
DOI: 10.1063/1.4811378
Abstract: A unified, Bayesian inference of midplane electron temperature and density profiles using both Thomson scattering (TS) and interferometric data is presented. Beyond the Bayesian nature of the analysis, novel features of the inference are the use of a Gaussian process prior to infer a mollification length-scale of inferred profiles and the use of Gauss-Laguerre quadratures to directly calculate the depolarisation term associated with the TS forward model. Results are presented from an application of the method to data from the high resolution TS system on the Mega-Ampere Spherical Tokamak, along with a comparison to profiles coming from the standard analysis carried out on that system.
Publisher: AIP Publishing
Date: 09-2005
DOI: 10.1063/1.2009107
Abstract: The increasing reservoirs of energetic particles which drive high-frequency modes, together with advances in the understanding of magnetohydrodynamics, have led to a need for higher-frequency (50 kHz to & MHz) measurements of magnetic field fluctuations in magnetic fusion devices such as tokamaks. This article uses transmission line equations to derive the voltage response of a Mirnov coil at the digitizer end of a transmission line of length ℓ. It is shown that, depending on the terminations of the line, resonances can occur even for ℓ∕λ⪡1, with λ the wavelength of a fluctuation in the transmission line. A lumped-circuit model based on the approach of Heeter et al. [R. F. Heeter, A. F. Fasoli, S. Ali-Arshad, and J. M. Moret. Rev. Sci. Instrum. 71, 4092 (2000)] is extended to enable the inclusion simultaneously of both serial resistance and parallel conductance elements. As originally proposed by Heeter et al. the lumped-circuit model offers the advantage of remote calibration this may be of particular value when upgrading existing systems to operate at frequencies above the original design specification. It is formally shown that the transmission line equations for the transfer function and measured impedance reduce to those of the lumped circuit model of Heeter et al. under specific conditions. The result extends the use of the lumped-circuit model of Heeter et al., which can be used to extract the transfer function from measurement of the impedance, beyond the case of an open-circuit termination. Although the numerical procedure does exhibit some problems associated with non-uniqueness, it provides a simple calibration method for systems that are not well defined. Using typical parameters for a high-frequency Mirnov coil installed on the Joint European Torus (JET) tokamak, the lumped-circuit approximation agrees with the steady-state transmission line model to within 0.015° in phase and 22% in litude for frequencies up to 1 MHz. A matched termination, though eliminating line resonances and reducing the length of time for the system to reach steady state, is inappropriate for the JET-type coils which exhibit significant temperature-dependent resistance. Finally, for fluctuations of finite duration, a method of computing the discrepancy due to the simplifying assumption of Fourier-stationary conditions is described.
Publisher: IOP Publishing
Date: 08-05-2014
Publisher: IOP Publishing
Date: 21-12-2013
Publisher: IOP Publishing
Date: 09-04-2020
Abstract: A theoretical framework has been developed for an NBI scenario to model the hard non-linear evolution of global Alfvén eigenmodes (GAEs) where the adiabatic motion of phase-space structures (holes and clumps), associated with frequency chirping, occurs in generalised phase-space of slowing down energetic particles. The radial profile of the GAE is expanded using finite elements which allows update of the mode structure as the mode frequency chirps. Constants of motion are introduced to track the dynamics of energetic particles during frequency chirping by implementing proper action-angle variables and canonical transformations which reduce the dynamics essentially to 1D. Consequently, we specify whether the particles are drifting inward/outward as the frequency deviates from the initial MHD eigenfrequency. Using the principle of least action, we have derived the non-linear equation describing the evolution of the radial profile by varying the total Lagrangian of the system with respect to the weights of the finite elements. For the choice of parameters in this work, it is shown that the peak of the radial profile is shifted and also broadens due to frequency chirping. The time rate of frequency change is also calculated using the energy balance and we show that the adiabatic condition remains valid once it is satisfied. This model clearly illustrates the theoretical treatment to study the long range adiabatic frequency sweeping events observed for Alfvén gap modes in real experiments.
Publisher: AIP Publishing
Date: 10-2010
DOI: 10.1063/1.3491044
Abstract: Recently, Bayesian probability theory has been used at a number of experiments to fold uncertainties and interdependencies in the diagnostic data and forward models, together with prior knowledge of the state of the plasma, to increase accuracy of inferred physics variables. A new probabilistic framework, MINERVA, based on Bayesian graphical models, has been used at JET and W7-AS to yield predictions of internal magnetic structure. A feature of the framework is the Bayesian inversion for poloidal magnetic flux without the need for an explicit equilibrium assumption. Building on this, we discuss results from a new project to develop Bayesian inversion tools that aim to (1) distinguish between competing equilibrium theories, which capture different physics, using the MAST spherical tokamak, and (2) test the predictions of MHD theory, particularly mode structure, using the H-1 Heliac. Specifically, we report on correction of the motional Stark effect, pickup coils, flux-loop constrained Bayesian inferred equilibrium for varying toroidal flux.
Publisher: AIP Publishing
Date: 04-2014
DOI: 10.1063/1.4870008
Abstract: We present an extension of the multi-region relaxed magnetohydrodynamics (MRxMHD) equilibrium model that includes plasma flow. This new model is a generalization of Woltjer's model of relaxed magnetohydrodynamics equilibria with flow. We prove that as the number of plasma regions becomes infinite, our extension of MRxMHD reduces to ideal MHD with flow. We also prove that some solutions to MRxMHD with flow are not time-independent in the laboratory frame, and instead have 3D structure which rotates in the toroidal direction with fixed angular velocity. This capability gives MRxMHD potential application to describing rotating 3D MHD structures such as "snakes" and long-lived modes.
Publisher: IOP Publishing
Date: 09-12-2017
Publisher: AIP Publishing
Date: 02-2015
DOI: 10.1063/1.4907792
Abstract: D ing due to continuum resonances can be calculated using dissipation-less ideal magnetohydrodynamics provided that the poles due to these resonances are properly treated. We describe a singular finite element technique for calculating the continuum d ing of Alfvén waves. A Frobenius expansion is used to determine appropriate finite element basis functions on an inner region surrounding a pole due to the continuum resonance. The location of the pole due to the continuum resonance and mode frequency is calculated iteratively using a Galerkin method. This method is used to find the complex frequency and mode structure of a toroidicity-induced Alfvén eigenmode in a large aspect ratio circular tokamak and is shown to agree closely with a complex contour technique.
Publisher: IOP Publishing
Date: 15-10-2008
Publisher: IOP Publishing
Date: 22-02-2013
Publisher: Informa UK Limited
Date: 09-1995
Publisher: IOP Publishing
Date: 12-08-2015
Publisher: Jenny Stanford Publishing
Date: 02-12-2014
DOI: 10.1201/B17705
Publisher: IOP Publishing
Date: 19-05-2009
DOI: 10.1088/0029-5515/49/6/065019
Abstract: We calculate the stability of a multiple relaxation region MHD (MRXMHD) plasma, or stepped-Beltrami plasma, using both variational and tearing mode treatments. The configuration studied is a periodic cylinder. In the variational treatment, the problem reduces to an eigenvalue problem for the interface displacements. For the tearing mode treatment, analytic expressions for the tearing mode stability parameter Δ′, being the jump in the logarithmic derivative in the helical flux across the resonant surface, are found. The stability of these treatments is compared for m = 1 displacements of an illustrative reverse field pinch-like configuration, comprising two distinct plasma regions. For pressureless configurations, we find the marginal stability conclusions of each treatment to be identical, confirming the analytical results in the literature. The tearing mode treatment also resolves ideal MHD unstable solutions for which Δ′ → ∞: these correspond to displacement of a resonant interface. Wall stabilization scans resolve the internal and external ideal kink. Scans with increasing pressure are also performed: these indicate that both variational and tearing mode treatments have the same stability trends with β, and show destabilization in configurations with increasing core pressure. Combined, our results suggest that variational stability of MRXMHD configurations is sufficient for both ideal and tearing (Δ′ 0) stability. Such configurations, and their stability properties, are of emerging importance in the quest to find mathematically rigorous solutions of ideal MHD force balance in 3D geometry.
Publisher: AIP Publishing
Date: 2018
DOI: 10.1063/1.4998793
Abstract: We present modifications to the sandpile model [Chapman, Phys. Rev. E 62, 1905 (2000)] (Classic Model). A feedback loop is added to the Classic Model, elements of which may have relevance to the behaviour of a fusion plasma. Those elements include variation of the total energy of the system in proportion to a proxy for the Larmor radius, ρ, and resulting variations in mass loss event (MLE) size and waiting times between MLEs. We also show other variants of the Classic Model which produce pedestals, without introducing feedback. The modifications produce a pedestal similar to that seen in a fusion plasma, as well as feedback effects. We observe that maximum MLE sizes, and maximum waiting times between MLEs, grow with pedestal size only in the presence of feedback. If, as we purport, the edge localised mode (ELM) process is captured by an MLE model with feedback, then a conclusion is that ELMs can be reduced if feedback effects are reduced.
Publisher: AIP Publishing
Date: 06-2019
DOI: 10.1063/1.5099354
Abstract: As a step toward understanding 3D magnetohydrodynamic (MHD) equilibria, for which smooth solutions may not exist, we develop a simple cylindrical model to investigate the resistive stability of MHD equilibria with alternating regions of constant and nonuniform pressure, producing states with continuous total pressure (i.e., no singular current sheets) but discontinuities in the parallel current density. We examine how the resistive stability characteristics of the model change as we increase the localization of pressure gradients at fixed radii, which approaches a discontinuous pressure profile in the zero-width limit. Equilibria with continuous pressure are found to be unstable to moderate/high-m modes and apparently tend toward ideal instability in some cases. We propose that additional geometric degrees of freedom or symmetry breaking via island formation may increase the parameter space on which equilibria of our model are physically realizable, while preserving the radial localization of pressure gradients. This is consistent with the possibility of realizing, in practice, 3D MHD equilibria which support both continuously nested flux surfaces (where ∇p ≠ 0) and chaotic field regions (where ∇p = 0).
Publisher: AIP Publishing
Date: 09-2015
DOI: 10.1063/1.4930209
Abstract: In an ideal magnetohydrodynamic (MHD) plasma, shear Alfvén eigenmodes may experience dissipationless d ing due to resonant interaction with the shear Alfvén continuum. This continuum d ing can make a significant contribution to the overall growth/decay rate of shear Alfvén eigenmodes, with consequent implications for fast ion transport. One method for calculating continuum d ing is to solve the MHD eigenvalue problem over a suitable contour in the complex plane, thereby satisfying the causality condition. Such an approach can be implemented in three-dimensional ideal MHD codes which use the Galerkin method. Analytic functions can be fitted to numerical data for equilibrium quantities in order to determine the value of these quantities along the complex contour. This approach requires less resolution than the established technique of calculating d ing as resistivity vanishes and is thus more computationally efficient. The complex contour method has been applied to the three-dimensional finite element ideal MHD Code for Kinetic Alfvén waves. In this paper, we discuss the application of the complex contour technique to calculate the continuum d ing of global modes in tokamak as well as torsatron, W7-X and H-1NF stellarator cases. To the authors' knowledge, these stellarator calculations represent the first calculation of continuum d ing for eigenmodes in fully three-dimensional equilibria. The continuum d ing of global modes in W7-X and H-1NF stellarator configurations investigated is found to depend sensitively on coupling to numerous poloidal and toroidal harmonics.
Publisher: IOP Publishing
Date: 28-08-2020
Publisher: IOP Publishing
Date: 28-10-2013
Publisher: IOP Publishing
Date: 09-10-2001
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 04-1999
DOI: 10.1109/27.772294
Publisher: AIP Publishing
Date: 06-2020
DOI: 10.1063/5.0005740
Abstract: A phase-space version of the ideal magnetohydrodynamic (MHD) Lagrangian is derived from first principles and shown to give a relabeling transformation when a cross-helicity constraint is added in Hamilton's Action Principle. A new formulation of time-dependent “relaxed” magnetohydrodynamics is derived using microscopic conservation of mass and macroscopic constraints on total magnetic helicity, cross helicity, and entropy under variations of density, pressure, fluid velocity, and magnetic vector potential. This gives Euler–Lagrange equations consistent with previous work on both ideal and relaxed MHD equilibria with flow, but generalizes the relaxation concept from statics to dynamics. The application of the new dynamical formalism is illustrated for short-wavelength linear waves, and the interface connection conditions for Multiregion Relaxed MHD (MRxMHD) are derived. The issue of whether E+u×B=0 should be a constraint is discussed.
Publisher: AIP Publishing
Date: 08-2012
DOI: 10.1063/1.4748874
Abstract: A radio frequency field solver based on Maxwell's equations and a cold plasma dielectric tensor is employed to describe wave phenomena observed in a cylindrical non-uniform helicon discharge. The experiment is carried out on a recently built linear plasma-material interaction machine: The magnetized plasma interaction experiment [Blackwell et al., Plasma Sources Sci. Technol. (submitted)], in which both plasma density and static magnetic field are functions of axial position. The field strength increases by a factor of 15 from source to target plate, and the plasma density and electron temperature are radially non-uniform. With an enhancement factor of 9.5 to the electron-ion Coulomb collision frequency, a 12% reduction in the antenna radius, and the same other conditions as employed in the experiment, the solver produces axial and radial profiles of wave litude and phase that are consistent with measurements. A numerical study on the effects of axial gradient in plasma density and static magnetic field on wave propagations is performed, revealing that the helicon wave has weaker attenuation away from the antenna in a focused field compared to a uniform field. This may be consistent with observations of increased ionization efficiency and plasma production in a non-uniform field. We find that the relationship between plasma density, static magnetic field strength, and axial wavelength agrees well with a simple theory developed previously. A numerical scan of the enhancement factor to the electron-ion Coulomb collision frequency from 1 to 15 shows that the wave litude is lowered and the power deposited into the core plasma decreases as the enhancement factor increases, possibly due to the stronger edge heating for higher collision frequencies.
Publisher: IOP Publishing
Date: 05-03-2005
Publisher: AIP Publishing
Date: 11-2012
DOI: 10.1063/1.4765691
Abstract: We describe the construction of stepped-pressure equilibria as extrema of a multi-region, relaxed magnetohydrodynamic (MHD) energy functional that combines elements of ideal MHD and Taylor relaxation, and which we call MRXMHD. The model is compatible with Hamiltonian chaos theory and allows the three-dimensional MHD equilibrium problem to be formulated in a well-posed manner suitable for computation. The energy-functional is discretized using a mixed finite-element, Fourier representation for the magnetic vector potential and the equilibrium geometry and numerical solutions are constructed using the stepped-pressure equilibrium code, SPEC. Convergence studies with respect to radial and Fourier resolution are presented.
Publisher: American Physical Society (APS)
Date: 30-07-2013
Publisher: IOP Publishing
Date: 28-04-2022
Abstract: In this work, the stepped pressure equilibrium code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502), which computes the equilibria of the multi-region relaxed magnetohydrodynamic energy principle (MRxMHD), has been upgraded to determine the MRxMHD stability in toroidal geometry. A theoretical formalism for SPEC is obtained by relating the second variation of the MRxMHD energy functional to the Hessian matrix, enabling the prediction of magnetohydrodynamic (MHD) linear instabilities. Negative eigenvalues of this matrix imply instability. Further, we demonstrate our method on simplified test scenarios in both tokamak and stellarator magnetic topologies, with a systematic comparison study between the marginal stability prediction of the SPEC with the ideal MHD stability code packages CAS3D and MISHKA-1.
Publisher: IOP Publishing
Date: 04-04-2017
Publisher: IOP Publishing
Date: 16-08-2011
DOI: 10.1088/0029-5515/51/10/103005
Abstract: In recent years, Bayesian probability theory has been used in a number of experiments to fold uncertainties and interdependences in the diagnostic data and forward models, and together with prior knowledge of the state of the plasma, thus increase accuracy of inferred physics variables. Key developments include the application to current and flux surface tomography, effective charge, the electron energy distribution function, neutron spectrometry and density. Virtual observations have also been introduced to better constrain inferred quantities in current tomography. In this work we present Bayesian inference results of toroidal and poloidal current and flux surface tomography. Whilst the uncertainty in these profiles, as well as the uncertainty in inferred parameters such as the safety factor profile is small ( %), the inference can change substantially depending on the physics model used. We also present Bayesian inference results for Thomson scattering and charge-exchange recombination spectroscopy. In separate work we have computed radial force balance components on the midplane in the Mega Ampére Spherical tokamak. Our aim is to establish a validation framework for different equilibrium physics models. We find that in the overlapping region of the core (normalized poloidal flux less than 0.4) and motional Stark effect (MSE) chords, the plasma is consistent with static Grad–Shafranov force balance to within two standard deviations. In the outboard edge region, where MSE data are also available, the pressure gradient exceeds the Lorentz force. Most likely, this is because the poloidal current is not constrained to zero at the plasma edge. To lowest order, the results suggest computing components of force balance are useful to assess data-consistency, independent of any equilibrium solution. To first order, we have integrated the residue to force balance to infer an energetic particle pressure.
Publisher: IOP Publishing
Date: 23-06-2011
Publisher: Cambridge University Press (CUP)
Date: 12-2006
Publisher: IOP Publishing
Date: 17-12-2012
Publisher: IOP Publishing
Date: 17-12-2013
Publisher: American Physical Society (APS)
Date: 30-09-2004
Publisher: IOP Publishing
Date: 12-09-2017
Publisher: IOP Publishing
Date: 25-10-2007
Publisher: IOP Publishing
Date: 19-12-2023
Abstract: The shear Alfvén continuum spectrum is studied for a tokamak with a single island chain using the ideal magnetohydrodynamics theory. We have taken into account the toroidal geometry and toroidal mode coupling with the island considered as a highly-shaped stellarator. Various new frequency gaps open up inside the island due to its asymmetry both poloidally and toroidally, such as the mirror-induced Alfvén eigenmode (MAE) gap and the helicity-induced Alfvén eigenmode (HAE) gap. We have shown that the MAE gap acts as the continuation of the outside toroidal Alfvén eigenmode (TAE) gap into the island. However, the combined TAE/MAE gap is getting narrower as the island grows, leaving only half of its original width with a moderate island size as much as 3.2% of the minor radius. In addition, the two-dimensional eigenfunction of the continuum mode on the lower tip of the MAE gap now has highly localised structures around the island’s long axis, contrary to the usual oscillatory global solutions found with no or a low level of toroidal asymmetry—an indication of the continuous spectrum becoming discrete and dense. These results have implications for the frequency, mode structure and continuum d ing of global TAEs residing in the gap.
Publisher: IOP Publishing
Date: 22-07-2004
Publisher: IOP Publishing
Date: 02-2017
Publisher: IOP Publishing
Date: 14-08-2020
Publisher: AIP Publishing
Date: 12-2015
DOI: 10.1063/1.4939026
Abstract: We extend previous analytical calculations of 2D high-β equilibria in order-unity aspect ratio tokamaks with toroidal flow to include pressure anisotropy, assuming guiding-center theory for a bi-Maxwellian plasma and the ideal MHD Ohm's law. Equilibrium solutions are obtained in the core region (which fills most of the plasma volume) and the boundary layer. We find that pressure anisotropy with p∥& ⊥ (p∥& ⊥) reduces (enhances) the plasma diamagnetism relative to the isotropic case whenever an equilibrium solution exists. Sufficiently fast toroidal flows (Ω& Ωmin) were previously found to suppress the field-free region (diamagnetic hole) that exists in static isotropic high-β equilibria. We find that all equilibrium solutions with pressure anisotropy suppress the diamagnetic hole. For the static case with a volume-averaged toroidal beta of 70%, plasmas with max(p∥ ⊥)& α1=1.07 have equilibrium solutions. We find that α1 decreases with increasing toroidal flow speed, and above the flow threshold Ωmin we find α1=1, so that all p∥& ⊥ plasmas have equilibrium solutions. On the other hand, for p∥& ⊥ there are no equilibrium solutions below Ωmin. Above Ωmin (where there is no diamagnetic hole in the isotropic case), equilibrium solutions exist for α2& min(p∥ ⊥)& , where α2 decreases from unity with increasing flow speed. The boundary layer width increases and the Shafranov shift decreases for p∥& ⊥, while the converse is true for p∥& ⊥.
Publisher: IOP Publishing
Date: 11-02-2021
Abstract: Over the last decade, a variational principle based on a generalisation of Taylor’s relaxation, referred to as multi-region relaxed magnetohydrodynamics (MRxMHDs) has been developed. The numerical solutions of the MRxMHD equilibria have been constructed using the Stepped Pressure Equilibrium Code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502). In principle, SPEC could also be established to describe the MRxMHD stability of an equilibrium. In this work, a theoretical framework is developed to relate the second variation of the energy functional to the so-called Hessian matrix, enabling the prediction of MHD linear instabilities of cylindrical plasmas, and is implemented in SPEC. The negative and positive eigenvalues of the Hessian matrix predict the stability of an equilibrium. Verification studies of SPEC stability results with the M3D- C 1 code and the tearing mode Δ ′ criterion have been conducted for ideal and resistive MHD instabilities, respectively, in a pressureless cylindrical tokamak, and have shown good agreement. Our stability analysis is a critical step towards understanding the MHD stability of three-dimensional MHDs where nested flux surfaces, magnetic islands and stochastic regions co-exist.
Start Date: 2020
End Date: 2021
Funder: Australian National University
View Funded ActivityStart Date: 2006
End Date: 2007
Funder: Department of Industry, Innovation, Science, Research and Tertiary Education, Australian Government
View Funded ActivityStart Date: 2020
End Date: 2021
Funder: Australian Academy of Science
View Funded ActivityStart Date: 2011
End Date: 2013
Funder: Australian Research Council
View Funded ActivityStart Date: 2014
End Date: 2016
Funder: Australian Research Council
View Funded ActivityStart Date: 2017
End Date: 2019
Funder: Australian Research Council
View Funded ActivityStart Date: 2010
End Date: 12-2013
Amount: $285,000.00
Funder: Australian Research Council
View Funded ActivityStart Date: 2011
End Date: 12-2014
Amount: $255,000.00
Funder: Australian Research Council
View Funded ActivityStart Date: 02-2010
End Date: 02-2014
Amount: $686,400.00
Funder: Australian Research Council
View Funded ActivityStart Date: 2014
End Date: 05-2018
Amount: $270,000.00
Funder: Australian Research Council
View Funded ActivityStart Date: 2017
End Date: 12-2021
Amount: $353,500.00
Funder: Australian Research Council
View Funded Activity