Plasma Equilibrium Parameters Research Articles

Helical resonant magnetic perturbation coils for controlling edge localized modes: a robustness study

Abstract Plasma response to helical resonant magnetic perturbation coil current is numerically computed for tokamak plasmas, with optimization results compared with that for conventional window-frame coils. The key aspect of study is the robustness of the proposed new concept against variation of plasma equilibrium parameters including (i) the plasma resistivity, (ii) the toroidal rotation and (iii) the plasma shaping (both elongation and triangularity). Toroidal modeling results yield several important conclusions. First, assuming the same coil current, the optimal helical coils robustly outperform the optimal window-frame coils against variation of the aforementioned plasma equilibrium parameters. Secondly, for a chosen toroidal spectrum, the optimal helical coil geometry including the poloidal location, poloidal coverage and the overall shape, is robust against variation of plasma parameters except the safety factor. Finally, in all cases, optimization based on the plasma response naturally yields a single row of helical coils located near the outboard mid-plane of the torus, ensuring a relatively simple design of the coil geometry.

Athermal pulsational mode dynamics with negative ions

The stability dynamics of the pulsational mode of gravitational collapse (PMGC), excitable in athermal (nonthermal) spherical complex dust molecular clouds (DMCs) in the presence of active role of negative ions, is semi-analytically investigated. The adopted partially ionized DMC model consists of five constitutive plasma species, well-coupled via the gravito-electrostatic Poisson formalism, depicting the corresponding potential-density correlations. The nonthermal uncorrelated lighter (inertialess) species are electrons, positive ions, and negative ions. The thermal correlated heavier (inertial) species are neutral and charged dust grains. The application of a standard spherical wave analysis results in a generalized linear cubic dispersion equation involving a new set of multi-factorial dispersion coefficients dependent on diverse equilibrium plasma parameters. A numerical illustrative platform is broadly created to analyze the DMC stabilization and destabilization factors relative to the non-local inward Newtonian self-gravity. It is interestingly seen that the DMC stabilizing agents are the radial cloud size, dust charge, neutral dust viscoelastic relaxation time, Tribeche thermostatistical parameters, etc. In contrast, the dust mass and equilibrium neutral dust density show destabilizing effects, and so forth. The results systematically explored here are fairly consistent and reliably correlated with the previous results on structure formation mechanism in the DMCs as heretofore reported extensively in the literature.

Magnetic diagnostics layout design for CFETR plasma equilibrium reconstruction

Plasma equilibrium reconstruction provides essential information for tokamak operation and physical analysis. An extensive and reliable set of magnetic diagnostics is required to obtain accurate plasma equilibrium. This study designs and optimizes the magnetic diagnostics layout for the reconstruction of the equilibrium of the plasma according to the scientific objectives, engineering design parameters, and limitations of the Chinese Fusion Engineering Test Reactor (CFETR). Based on the CFETR discharge simulation, magnetic measurement data are employed to reconstruct consistent plasma equilibrium parameters, and magnetic diagnostics’ number and position are optimized by truncated Singular value decomposition, verifying the redundancy reliability of the magnetic diagnostics layout design. This provides a design solution for the layout of the magnetic diagnostics system required to control the plasma equilibrium of CFETR, and the developed design and optimization method can provide effective support to design magnetic diagnostics systems for future magnetic confinement fusion devices.

Interplay of plasma resistivity and rotation on β limits in free boundary diverted tokamaks

A plasma resistivity-β driving mechanism aimed at explaining the appearance of long wavelength global instabilities in free boundary high-β tokamak plasmas with a divertor is presented. These perturbations resemble very closely the resistive wall mode phenomenon. Performing a proper toroidal analysis, we show that the magnetohydrodynamic stability is worsened by the interplay of plasma β and resistivity. By modelling the effect of a magnetic separatrix through a careful positioning of the resonant surfaces, we find that in an ideal plasma wall effects are effectively screened, so that the ideal β limit becomes independent of the wall position/physics. A lower wall dependent critical β is found if plasma resistivity is allowed. We find that global stability can be improved with a toroidal flow, small enough not to induce equilibrium modification. The rotation stabilisation effectiveness depends upon the proximity of the plasma equilibrium parameters to the resistive marginal boundary.

Numerical study of alpha particle loss with toroidal field ripple based on CFETR steady-state scenario

Abstract Effects of plasma equilibrium parameters on the alpha particle loss with the toroidal field ripple based on the CFETR steady-state scenario have been numerically investigated by the orbit-following code GYCAVA. It is found that alpha particle losses decrease and loss regions become narrower with the plasma current increasing or with the magnetic field decreasing. It is because the ripple stochastic transport and the ripple well loss of alpha particle are reduced with the safety factor decreasing. Decrease of the plasma density and temperature can reduce alpha particle losses due to enhancement of the slowing-down effect. The direction of the toroidal magnetic field can significantly affect heat loads induced by lost alpha particle. The vertical asymmetry of heat loads induced by the clockwise and counter-clockwise toroidal magnetic fields are due to the fact that the ripple distribution is asymmetric about the mid-plane, which can be explained by the typical orbits of alpha particle. The maximal heat load of alpha particle for the clockwise toroidal magnetic field is much smaller than that for the counter-clockwise one.

Propagatory dynamics of nucleus-acoustic waves excited in gyrogravitating degenerate quantum plasmas electrostatically confined in curved geometry

A theoretic model to investigate the dynamics of the longitudinal nucleus-acoustic waves (NAWs) in gyrogravitating electrostatically confined degenerate quantum plasma (DQP) system in spherically symmetric geometry is constructed. The model setup consists of non-degenerate heavy nuclear species (HNS), lighter nuclear species (LNS), and quantum degenerate electronic species (DES). It specifically considers the influences of the Bohm potential, Coriolis rotation, viscoelasticity, and electrostatic confinement pressure (ECP, scaling quadratically in density). A standard normal spherical mode analysis gives a generalized dispersion relation (septic). It highlights the dependency of various atypical instability response on the equilibrium plasma parameters. A numerical illustrative platform portrays that the relative nuclear charge-to-mass coupling parameter (beta) acts as a destabilizing agency and the heavy-to-light nuclear charge density ratio (mu) acts as a stabilizing agency in both the non-relativistic (NR) and ultra-relativistic (UR) limits. Another interesting conjuncture is that the Coriolis rotation introduces a destabilizing influence on the system in both the limits. The progressive analysis presented herein has correlations and consistencies in the dynamic growth backdrop of various compact astro objects and their circumvent atmospheres, such as white dwarfs, neutron stars, etc.

Estimation of plasma equilibrium parameters via a neural network approach**Project supported by the National Magnetic Confinement Fusion Energy R&D Program of China (Grant No. 2018YFE0302100), the National Key Research and Development Program of China (Grant Nos. 2017YFE0300500 and 2017YFE0300501), the National Natural Science Foundation of China (Grant Nos. 11575245, 11805236, and 11905256), and Young and Middle-aged Academic Back-bone Finance Fund

Plasma equilibrium parameters such as position, X-point, internal inductance, and poloidal beta are essential information for efficient and safe operation of tokamak. In this work, the artificial neural network is used to establish a non-linear relationship between the measured diagnostic signals and selected equilibrium parameters. The estimation process is split into a preliminary classification of the kind of equilibrium (limiter or divertor) and subsequent inference of the equilibrium parameters. The training and testing datasets are generated by the tokamak simulation code (TSC), which has been benchmarked with the EAST experimental data. The noise immunity of the inference model is tested. Adding noise to model inputs during training process is proved to have a certain ability for maintaining performance.

Experimental validation of coil phase parametrisation on ASDEX Upgrade, and extension to ITER

It has been previously demonstrated in Li et al (2016 Nucl. Fusion 56 126007) that the optimum upper/lower coil phase shift ΔΦopt for alignment of RMP coils for ELM mitigation depends sensitively on q95, and other equilibrium plasma parameters. Therefore, ΔΦopt is expected to vary widely during the current ramp of ITER plasmas, with negative implications for ELM mitigation during this period. A previously derived and numerically benchmarked parametrisation of the coil phase for optimal ELM mitigation on ASDEX Upgrade (Ryan et al 2017 Plasma Phys. Control. Fusion 59 024005) is validated against experimental measurements of ΔΦopt, made by observing the changes to the ELM frequency as the coil phase is scanned. It is shown that the parametrisation may predict the optimal coil phase to within 32° of the experimental measurement for n = 2 applied perturbations. It is explained that this agreement is sufficient to ensure that the ELM mitigation is not compromised by poor coil alignment. It is also found that the phase which maximises ELM mitigation is shifted from the phase which maximizes density pump-out, in contrast to theoretical expectations that ELM mitigation and density pump out have the same ΔΦul dependence. A time lag between the ELM frequency response and density response to the RMP is suggested as the cause. The method for numerically deriving the parametrisation is repeated for the ITER coil set, using the baseline scenario as a reference equilibrium, and the parametrisation coefficients given for future use in a feedback coil alignment system. The relative merits of square or sinusoidal toroidal current waveforms for ELM mitigation are briefly discussed.

Marginal stability, characteristic frequencies, and growth rates of gradient drift modes in partially magnetized plasmas with finite electron temperature

The detailed analysis of stability of azimuthal oscillations in partially magnetized plasmas with crossed electric and magnetic fields is presented. The instabilities are driven by the transverse electron current which, in general, is due to a combination of E×B and electron diamagnetic drifts. Marginal stability boundary is determined for a wide range of the equilibrium plasma parameters. It is shown that in some regimes near the instability threshold, only the low-frequency long-wavelength oscillations are unstable, while the short-wavelength high-frequency modes are stabilized by the finite Larmor radius effects. Without such stabilization, the high-frequency modes have much larger growth rates and dominate. A new regime of the instability driven exclusively by the magnetic field gradient is identified. Such instability takes place in the region of the weak electric field and for relatively large gradients of plasma density (ρs/ln>1, where ρs is the ion-sound Larmor radius and ln is the scale length of plasma density inhomogeneity).

The GOL-NB program: further steps in multiple-mirror confinement research

Physical and technical details of the GOL-NB project are presented. GOL-NB is a medium-scale multiple-mirror trap that is under development in the Budker Institute, Novosibirsk, Russia. This device will be created in several years as a deep conversion of the existing GOL-3 facility. It will consist of a central trap with two 0.75 MW neutral beams, two multiple-mirror solenoids, two expander tanks and a plasma gun that creates the start plasma. The central trap with the neutral beam injection-heated plasma is a compact gas-dynamic system. The multiple-mirror sections should decrease the power and particle losses along the magnetic field. The confinement improvement factor depends on plasma parameters and on the magnetic configuration in the multiple mirrors. The main physical task of GOL-NB is direct demonstration of the performance of multiple-mirror sections that will change equilibrium plasma parameters in the central trap. In this paper we discuss results of the scenario modeling and progress in the hardware.

Magnetic measurement based methods in determination of plasma equilibrium parameters in Damavand tokamak

Determination of plasma equilibrium parameters such as poloidal beta (βp) with half of plasma internal inductance (li) known as Shafranov parameter (asymmetry factor) (βp+\U0001d521li2) and edge safety factor plays very important role in primary equilibrium and stability analysis and control of tokamak plasma. In this study, the well known Shafranov semi-empirical model, based on external magnetic measurements is used to extract Shafranov parameter and effective edge safety factor in low-β operating regime of Damavand tokamak. The well known integral representation of βp+\U0001d521li2 was modified for non-circular tokamaks with ellipse-like cross section. After calibration of magnetic pick-up coils, Shafranov parameter was estimated with respect to the first and second Fourier harmonic of radial and poloidal components of magnetic field. The results were compared with approximate, semi-analytical determination of Shafranov parameter which is based on analytical solution of Grad-Shafranov equation (GSE). Founding evolution of Shafranov parameter, effective edge safety factor was obtained in terms of Shafranov parameter and compared with semi-empirical description. It was found that between the ramp-up and ramp-down domain of the plasma current, the result from Shafranov model is approximately in good agreement with the semi-analytical and semi-empirical benchmarks and the integral model provides more reliable trace of the Shafranov parameter in out of ramp domains of the discharge.

Stable and unstable manifolds, and the structure of magnetic footprints

The generic analytic formulae of the stable and unstable manifolds near the separatrix and on the divertor plates in tokamaks in the presence of resonant magnetic perturbations are derived. The stable (unstable) manifolds on the divertor plates describe the form of the magnetic footprint boundaries. They are derived using the separatrix mapping. The analytical formulae depend on a few of the equilibrium plasma parameters and the magnetic perturbations.

Magnetic-Based Measurements of Tokamak Plasma Equilibrium Parameters

The main purpose of this paper is the determination of plasma equilibrium parameters, as well as current density and safety factor profiles, in IR-T1 tokamak. For this purpose, a diamagnetic loop with its compensation coil and an array of magnetic probes were designed, constructed, and installed on the outer surface of the IR-T1 chamber, and then, the poloidal beta and poloidal and radial magnetic fields were measured. Moreover, a few approximate values of the internal inductance for different possible profiles of the plasma current density were also calculated. Then, from these two techniques results, the plasma horizontal displacement was determined. In addition, from the results, the current density and q-profiles were obtained.

Dynamic simulator of RWM control for fusion devices: modelling and experimental validation on RFX-mod

A new integrated simulator for experiments of resistive wall mode (RWM) closed-loop control and its benchmark against experimental data are presented. The numerical tool couples in a self-consistent way a full 3D finite element description of the machine boundaries (Cariddi code), a 2D toroidal model of RFP plasma stability (MARS-F code) and a realistic representation of the RFX-mod control system producing an overall dynamic model cast in the state variable space. In this way a full dynamic ‘flight simulator’ of RWM control experiments has been implemented where the interaction of proportional–integral–derivative controller gains and plasma equilibrium parameters can be explored.As an application of the new integrated tool, closed-loop RWM stability analyses have been benchmarked against experimental data. In this way it was possible to experimentally prove that the control simulator correctly reproduces closed-loop RWM growth rates under different control conditions. Time domain simulations were also run to assess the overall accuracy of the model including the presence of non-linear blocks. The achieved results are discussed in connection with the broader international effort towards an effective control of RWMs in both tokamak and RFP configurations.

Stabilization of magnetic curvature-driven Rayleigh–Taylor instabilities

AbstractThe finite ion Larmor radius (FLR) stabilization of the magnetic curvature-driven Rayleigh–Taylor (MCD RT) instability in a low beta plasma with nonzero ion temperature gradient is investigated. Finite electron temperature effects and ion temperature perturbations are incorporated. A new set of nonlinear equations for flute waves with arbitrary wavelengths as compared with the ion Larmor radius in a plasma with curved magnetic field lines is derived. Particular attention is paid to the waves with spatial scales of the order of the ion Larmor radius. In the linear limit, a Fourier transform of these equations yields an improved dispersion relation for flute waves. The dependence of the MCD RT instability growth rate on the equilibrium plasma parameters and the wavelengths is studied. The condition for which the instability cannot be stabilized by the FLR effects is found.

Influence of Negative Ions on Drift Waves in a Low‐Density Ar/O2‐Plasma

AbstractThe effect of negative ions on the drift wave instability has been studied in detail in a linear device by means of Langmuir probes and cross‐correlation analysis. Drift waves are excited in low‐density (5 × 1014 m–3) and strongly magnetized (0.5 T) pure argon plasmas and in the presence of an oxygen admixture. The radial density profile of negative ions is hollow. For increasing concentration of negative ions the wave frequency decreases by about 25%. Despite of an axial density gradient, a global wave frequency is established for the entire column length. While for the noble gas case the drift wave frequency is given by the equilibrium plasma parameters in the mid‐plane, there is no such relationship for the argon plasma with oxygen admixture. This different finding is attributed to the inhomogeneous distribution of the negative ions (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Theory of nonaxisymmetric vertical displacement events in tokamaks

A semi-analytic sharp-boundary model of a nonaxisymmetric vertical displacement event (VDE) in a large aspect-ratio, high-beta (i.e. β ∼ ϵ), vertically elongated tokamak plasma is developed. The model is used to simulate nonaxisymmetric VDEs with a wide range of different plasma equilibrium and vacuum vessel parameters. These simulations yield poloidal halo current fractions and toroidal peaking factors whose magnitudes are similar to those seen in experiments, and also reproduce the characteristic inverse scaling between the halo current fraction and the toroidal peaking factor. Moreover, the peak poloidal halo current density in the vacuum vessel is found to correlate strongly with the reciprocal of the minimum edge safety factor attained during the VDE. In addition, under certain circumstances, the ratio of the net sideways force acting on the vacuum vessel to the net vertical force is observed to approach unity. Finally, the peak vertical force per unit area acting on the vessel is found to have a strong correlation with the equilibrium toroidal plasma current at the start of the VDE, but is also found to increase with increasing vacuum vessel resistivity relative to the scrape-off layer plasma.

The linear model and experimentally observed resonant field amplification in tokamaks and reversed field pinches

A review is given of the experimentally observed effects related to the resonant field amplification (RFA) and the Resistive Wall Mode (RWM) instability in tokamaks and reversed field pinches (RFPs). This includes the feedback rotation of RWM in RFX-mod RFP, dependence of the RWM growth rate on the plasma-wall separation observed in JT-60U, appearance of the slowly growing RWM precursors in JT-60U and similar phenomena in other devices. The experimental results are compared with theoretical predictions based on the model comprising the Maxwell equations, Ohm’s law for the conducting wall, the boundary conditions and assumption of linear plasma response to the external magnetic perturbations. The model describes the plasma reaction to the error field as essentially depending on two factors: the plasma proximity to the RWM stability threshold and the natural rotation frequency of the plasma mode. The linear response means that these characteristics are determined by the plasma equilibrium parameters only. It is shown that the mentioned effects in different devices under different conditions can be described on a common basis with only assumption that the plasma behaves as a linear system. To extend the range of the model validation, some predictions are derived with proposals for experimental studies of the RFA dynamics.

Magnetic drift kinetic damping of the resistive wall mode in large aspect ratio tokamaks

An analytical, large aspect ratio, calculation of the drift-kinetic energy perturbation is carried out for the resistive wall mode, due to the mode resonance with the magnetic precession drifts of trapped thermal ions and electrons. Four asymptotic cases are identified and analyzed in detail. Generally, a partial stabilization of the mode is possible thanks to the kinetic correction to the perturbed plasma energy. A complete stabilization can occur only in a narrow space of the plasma equilibrium parameters. Kinetic destabilization of the mode is also possible due to a finite pressure correction to the precession drift frequency.

Chapter 3: Microwave Diagnostics

Microwave-based diagnostics have found broad application in magnetic fusion plasma diagnostics and are expected to be widely employed in future burning plasma experiments (BPXs). Most of these techniques are based directly on the dispersive properties of the plasma medium that, as shown in the body of the paper, results in the microwave/millimeter wave portion of the electromagnetic spectrum being particularly well suited for a variety of measurements of both magnetic fusion plasma equilibrium parameters and their fluctuations. Electron cyclotron emission provides a measurement of electron temperature and its fluctuations while electron cyclotron absorption potentially can provide a measurement of electron pressure (the product of electron density and temperature) as well as information on the suprathermal electron distribution. Electron Bernstein wave emission is also employed for electron temperature radiometric measurements in devices including reversed field pinches, spherical tori, and higher-aspect-ratio tokamaks and stellarators that operate at high β. The radar-based microwave reflectometry technique measures the electron density profile and its fluctuations by means of the reflection of electromagnetic waves at the plasma cutoff layer. Coherent Thomson scattering in the microwave region yields information on the fast ion population. Wave number resolved microwave collective scattering is also widely employed for measuring nonthermal (turbulent) density fluctuations or coherent electrostatic waves. The approach taken in this review is to address each technique separately beginning with the physical principles followed by representative implementations on magnetic fusion devices. In each case, the applicability to future BPXs is discussed. It is impossible in a short review to capture fully the numerous significant accomplishments of the many clever scientists and engineers who have advanced microwave plasma diagnostics technology over many decades. Therefore, in this paper, we can reveal only the basic principles together with some of the most exciting highlights while outlining the major trends, and we hope it will serve as an exciting introduction to this rich field of plasma diagnostics.