Spherical Torus Research Articles

Mitigation of Alfvénic activity by 3D magnetic perturbations on NSTX

Observations on the National Spherical Torus Experiment (NSTX) indicate that externally applied non-axisymmetric magnetic perturbations (MP) can reduce the amplitude of toroidal Alfvén eigenmodes (TAE) and global Alfvén eigenmodes (GAE) in response to pulsed n = 3 non-resonant fields. From full-orbit following Monte Carlo simulations with the one- and two-fluid resistive MHD plasma response to the magnetic perturbation included, it was found that in response to MP pulses the fast-ion losses increased and the fast-ion drive for the GAEs was reduced. The MP did not affect the fast-ion drive for the TAEs significantly but the Alfvén continuum at the plasma edge was found to be altered due to the toroidal symmetry breaking which leads to coupling of different toroidal harmonics. The TAE gap was reduced at the edge creating enhanced continuum damping of the global TAEs, which is consistent with the observations. The results suggest that optimized non-axisymmetric MP might be exploited to control and mitigate Alfvén instabilities by tailoring the fast-ion distribution function and/or continuum structure.

Resonance in fast-wave amplitude in the periphery of cylindrical plasmas and application to edge losses of wave heating power in tokamaks

Heating magnetically confined plasmas using waves in the ion-cyclotron range of frequencies typically requires coupling these waves over a steep density gradient. This process has produced an unexpected and deleterious phenomenon on the National Spherical Torus eXperiment (NSTX): a prompt loss of wave power along magnetic field lines in front of the antenna to the divertor. Understanding this loss may be key to achieving effective heating and expanding the operational space of NSTX-Upgrade. Here, we propose that a new type of mode, which conducts a significant fraction of the total wave power in the low-density peripheral plasma, is driving these losses. We demonstrate the existence of such modes, which are distinct from surface modes and coaxial modes, in a cylindrical cold-plasma model when a half wavelength structure fits into the region outside the core plasma. The latter condition generalizes the previous hypothesis regarding the occurrence of the edge losses and may explain why full-wave simulations predict these losses in some cases but not others. If valid, this condition implies that outer gap control is a potential strategy for mitigating the losses in NSTX-Upgrade in addition to raising the magnetic field or influencing the edge density.

Progress of the Plasma Centerpost for the PROTO-SPHERA Spherical Tokamak

Plasma properties can be useful in a wide spectrum of applications. Experimental projects on controlled nuclear fusion are the most challenging of these applications and, at the same time, the best way to approach plasma science. Since nuclear fusion reactors can ensure a large-scale, safe, environmentally-friendly and virtually inexhaustible source of energy, several fusion-oriented megaprojects and innovative companies are appearing all over the world. PROTO-SPHERA (Spherical Plasma for HElicity Relaxation Assessment) is the first plasma project with a simply connected configuration, namely not requiring additional objects inside the plasma volume. This is obtained by a plasma arc, shaped as a screw pinch, acting as the centerpost of a spherical torus with minimal aspect ratio. Due to its intrinsic physical, engineering and economic advantages, this new approach is attractive also on an industrial scale and with several developments that still needs to be explored. This paper presents the PROTO-SPHERA basic principles, its first encouraging results and its expected and potential evolutions.

Phase coherence of parametric-decay modes during high-harmonic fast-wave heating in the National Spherical Torus Experiment

Third-order spectral analysis, in particular, the auto bicoherence, was applied to probe signals from high-harmonic fast-wave heating experiments in the National Spherical Torus Experiment. Strong evidence was found for parametric decay of the 30 MHz radio-frequency (RF) pump wave, with a low-frequency daughter wave at 2.7 MHz, the local majority-ion cyclotron frequency. The primary decay modes have auto bicoherence values around 0.85, very close to the theoretical value of one, which corresponds to total phase coherence with the pump wave. The threshold RF pump power for onset of parametric decay was found to be between 200 kW and 400 kW.

Ion cyclotron emission studies: Retrospects and prospects

Ion cyclotron emission (ICE) studies emerged in part from the papers by A.B. Mikhailovskii published in the 1970s. Among the discussed subjects were electromagnetic compressional Alfvenic cyclotron instabilities with the linear growth rate ~ $\sqrt {n_\alpha /n_e } $ driven by fusion products, -particles which draw a lot of attention to energetic particle physics. The theory of ICE excited by energetic particles was significantly advanced at the end of the 20th century motivated by first DT experiments on TFTR and subsequent JET experimental studies which we highlight. More recently ICE theory was advanced by detailed theoretical and experimental studies on spherical torus (ST) fusion devices where the instability signals previously indistinguishable in high aspect ratio tokamaks due to high toroidal magnetic field became the subjects of experiments. We discuss further prospects of ICE theory applications for future burning plasma (BP) experiments such as those to be conducted in ITER device in France, where neutron and gamma rays escaping the plasma create extremely challenging conditions fusion alpha particle diagnostics.

Evaluation of thermal helium beam and line-ratio fast diagnostic on the National Spherical Torus Experiment-Upgrade

A 1-D kinetic collisional radiative model with state-of-the-art atomic data is developed and employed to simulate line emission to evaluate the Thermal Helium Beam (THB) diagnostic on NSTX-U. This diagnostic is currently in operation on RFX-mod, and it is proposed to be installed on NSTX-U. The THB system uses the intensity ratios of neutral helium lines 667.8, 706.5, and 728.1 nm to derive electron temperature (eV) and density (cm−3) profiles. The purpose of the present analysis is to evaluate the applications of this diagnostic for determining fast (∽4 μs) electron temperature and density radial profiles on the scrape-off layer and edge regions of NSTX-U that are needed in turbulence studies. The diagnostic is limited by the level of detection of the 728.1 nm line, which is the weakest of the three. This study will also aid in future design of a similar 2-D diagnostic system on the divertor.

Quasi-linear gyrokinetic predictions of the Coriolis momentum pinch in National Spherical Torus Experiment

This paper presents quasi-linear gyrokinetic predictions of the Coriolis momentum pinch for low aspect-ratio National Spherical Torus Experiment (NSTX) H-modes where previous experimental measurements were focused. Local, linear calculations predict that in the region of interest (just outside the mid-radius) of these relatively high-beta plasmas, profiles are most unstable to microtearing modes that are only effective in transporting electron energy. However, sub-dominant electromagnetic and electrostatic ballooning modes are also unstable, which are effective at transporting energy, particles, and momentum. The quasi-linear prediction of transport from these weaker ballooning modes, assuming they contribute transport in addition to that from microtearing modes in a nonlinear turbulent state, leads to a very small or outward convection of momentum, inconsistent with the experimentally measured inward pinch, and opposite to predictions in conventional aspect ratio tokamaks. Additional predictions of a low beta L-mode plasma, unstable to more traditional electrostatic ion temperature gradient-trapped electron mode instability, show that the Coriolis pinch is inward but remains relatively weak and insensitive to many parameter variations. The weak or outward pinch predicted in NSTX plasmas appears to be at least partially correlated to changes in the parallel mode structure that occur at a finite beta and low aspect ratio, as discussed in previous theories. The only conditions identified where a stronger inward pinch is predicted occur either in the purely electrostatic limit or if the aspect ratio is increased. As the Coriolis pinch cannot explain the measured momentum pinch, additional theoretical momentum transport mechanisms are discussed that may be potentially important.

Analytical and numerical study of the transverse Kelvin–Helmholtz instability in tokamak edge plasmas

Sheared flows perpendicular to the magnetic field can be driven by the Reynolds stress or ion pressure gradient effects and can potentially influence the stability and turbulent saturation level of edge plasma modes. On the other hand, such flows are subject to the transverse Kelvin–Helmholtz (KH) instability. Here, the linear theory of KH instabilities is first addressed with an analytic model in the asymptotic limit of long wavelengths compared with the flow scale length. The analytic model treats sheared $\boldsymbol{E}\times \boldsymbol{B}$ flows, ion diamagnetism (including gyro-viscous terms), density gradients and parallel currents in a slab geometry, enabling a unified summary that encompasses and extends previous results. In particular, while ion diamagnetism, density gradients and parallel currents each individually reduce KH growth rates, the combined effect of density and ion pressure gradients is more complicated and partially counteracting. Secondly, the important role of realistic toroidal geometry is explored numerically using an invariant scaling analysis together with the 2DX eigenvalue code to examine KH modes in both closed and open field line regions. For a typical spherical torus magnetic geometry, it is found that KH modes are more unstable at, and just outside of, the separatrix as a result of the distribution of magnetic shear. Finally implications for reduced edge turbulence modelling codes are discussed.

Observation of quasi-coherent edge fluctuations in Ohmic plasmas on National Spherical Torus Experiment

A quasi-coherent edge density mode with frequency fmode ∼ 40 kHz is observed in Ohmic plasmas in National Spherical Torus Experiment using the gas puff imaging diagnostic. This mode is located predominantly just inside the separatrix, with a maximum fluctuation amplitude significantly higher than that of the broadband turbulence in the same frequency range. The quasi-coherent mode has a poloidal wavelength λpol ∼ 16 cm and a poloidal phase velocity of Vpol ∼ 4.9 ± 0.3 km s−1 in the electron diamagnetic direction, which are similar to the characteristics expected from a linear drift-wave-like mode in the edge. This is the first observation of a quasi-coherent edge mode in an Ohmic diverted tokamak, and so may be useful for validating tokamak edge turbulence codes.

Conceptual design of NBI beamline for VEST plasma heating

A 10ms-pulsed NBI (Neutral Beam Injection) system for VEST (Versatile Experiment Spherical Torus) plasma heating is designed to provide a beam power of more than 0.6MW with 20keVH° neutrals. The VEST NBI injector is composed of 2 sets of 20keV/25A magnetic cusp type bucket ion source, neutralizer ducts, residual ion dump, NB vessel with a cryopump, and rotating calorimeter. The position and size of these beamline components are roughly determined with geometric calculation of beam power transmission: the overall length of beamline is 1.8m, spacing between ground grid and neutralizer of 1.0m, and position of residual ion dump is 0.8m downstream from the neutralizer exit. Optimizing the gas feed between ion source and neutralizer can leads to a neutralization efficiency of ∼76%. Finally, the beam power of maximum 0.6 MW can be delivered to the VEST plasma with a beam loss of 10%.

Excitation of ion Bernstein waves as the dominant parametric decay channel in direct X-B mode conversion for typical spherical torus

The electron Bernstein wave (EBW) is typically the only wave in the electron cyclotron (EC) range that can be applied in spherical tokamaks for heating and current drive (H&CD). Spherical tokamaks (STs) operate generally in high-β regimes, in which the usual EC ordinary (O) and extraordinary (X) modes are cut off. As it was recently investigated the existence of EBWs at nonlinear regime thus the next step would be the probable nonlinear phenomena study which are predicted to be occurred within the high levels of injected power. In this regard, parametric instabilities are considered as the major channels for losses at the X-B conversion. Hence, we have to consider their effects at the UHR region which can reduce the X-B conversion efficiency. In the case of EBW heating (EBH) at high power density, the nonlinear effects can arise. Particularly at the UHR position, the group velocity is strongly reduced, which creates a high energy density and subsequently a high amplitude electric field. Therefore, a part of the input wave can decay into daughter waves via parametric instability (PI). Thus, via the present research, the excitations of ion Bernstein waves as the dominant decay channels are investigated and also an estimate for the threshold power in terms of experimental parameters related to the fundamental mode of instability is proposed.

Heating and current drive by fast wave in lower hybrid range of frequency on Versatile Experiment Spherical Torus

An efficient heating and current drive scheme in central or off-axis region is required to realize steady state operation of tokamak fusion reactor. And the fast wave in lower hybrid resonance range of frequency could be a candidate for such an efficient scheme in high density and high temperature plasmas. Its propagation and absorption characteristics including current drive and coupling efficiency are analyzed for Versatile Experiment Spherical Torus and it is shown that it is possible to drive current with considerable current drive efficiency in central region. The RF system for the fast wave experiment including klystron, transmission systems, inter-digital antenna, and RF diagnostics are given as well in this paper.

Modeling and control of plasma rotation for NSTX using neoclassical toroidal viscosity and neutral beam injection

A model-based feedback system is presented to control plasma rotation in a magnetically confined toroidal fusion device, to maintain plasma stability for long-pulse operation. This research uses experimental measurements from the National Spherical Torus Experiment (NSTX) and is aimed at controlling plasma rotation using two different types of actuation: momentum from injected neutral beams and neoclassical toroidal viscosity generated by three-dimensional applied magnetic fields. Based on the data-driven model obtained, a feedback controller is designed, and predictive simulations using the TRANSP plasma transport code show that the controller is able to attain desired plasma rotation profiles given practical constraints on the actuators and the available measurements of rotation.

Development of wall conditioning and impurity monitoring systems in Versatile Experiment Spherical Torus (VEST)

Wall conditioning and impurity monitoring systems are developed in Versatile Experiment Spherical Torus (VEST). As a wall conditioning system, a baking system covering the vacuum vessel wall partially and a glow discharge cleaning (GDC) system using two electrodes with dc and 50kHz power supplies are installed. The GDC system operates with hydrogen and helium gases for both chemical and physical desorption. The impurity monitoring system with residual gas analyzer (RGA), operating at <10−5Torr with a differential pumping system, is installed along with the optical emission spectroscopy (OES) system to monitor the hydrogen and impurity radiation lines. Effects of these wall conditioning techniques are investigated with the impurity monitoring system for ohmic discharges of VEST. The partial baking and He GDC show limited effects on plasma characteristics but sufficient H2 GDC above 4h enables the longer plasma current duration up to ∼15ms within 3h from the end of treatment.

Evolution patterns and parameter regimes in edge localized modes on the National Spherical Torus Experiment

We implement unsupervised machine learning techniques to identify characteristic evolution patterns and associated parameter regimes in edge localized mode (ELM) events observed on the National Spherical Torus Experiment. Multi-channel, localized measurements spanning the pedestal region capture the complex evolution patterns of ELM events on Alfvén timescales. Some ELM events are active for less than 100 μs, but others persist for up to 1 ms. Also, some ELM events exhibit a single dominant perturbation, but others are oscillatory. Clustering calculations with time-series similarity metrics indicate the ELM database contains at least two and possibly three groups of ELMs with similar evolution patterns. The identified ELM groups trigger similar stored energy loss, but the groups occupy distinct parameter regimes for ELM-relevant quantities like plasma current, triangularity, and pedestal height. Notably, the pedestal electron pressure gradient is not an effective parameter for distinguishing the ELM groups, but the ELM groups segregate in terms of electron density gradient and electron temperature gradient. The ELM evolution patterns and corresponding parameter regimes can shape the formulation or validation of nonlinear ELM models. Finally, the techniques and results demonstrate an application of unsupervised machine learning at a data-rich fusion facility.

Implementation of a 3D halo neutral model in the TRANSP code and application to projected NSTX-U plasmas

A 3D halo neutral code developed at the Princeton Plasma Physics Laboratory and implemented for analysis using the TRANSP code is applied to projected National Spherical Torus eXperiment-Upgrade (NSTX-U plasmas). The legacy TRANSP code did not handle halo neutrals properly since they were distributed over the plasma volume rather than remaining in the vicinity of the neutral beam footprint as is actually the case. The 3D halo neutral code uses a ‘beam-in-a-box’ model that encompasses both injected beam neutrals and resulting halo neutrals. Upon deposition by charge exchange, a subset of the full, one-half and one-third beam energy components produce first generation halo neutrals that are tracked through successive generations until an ionization event occurs or the descendant halos exit the box. The 3D halo neutral model and neutral particle analyzer (NPA) simulator in the TRANSP code have been benchmarked with the Fast-Ion D-Alpha simulation (FIDAsim) code, which provides Monte Carlo simulations of beam neutral injection, attenuation, halo generation, halo spatial diffusion, and photoemission processes. When using the same atomic physics database, TRANSP and FIDAsim simulations achieve excellent agreement on the spatial profile and magnitude of beam and halo neutral densities and the NPA energy spectrum. The simulations show that the halo neutral density can be comparable to the beam neutral density. These halo neutrals can double the NPA flux, but they have minor effects on the NPA energy spectrum shape. The TRANSP and FIDAsim simulations also suggest that the magnitudes of beam and halo neutral densities are relatively sensitive to the choice of the atomic physics databases.

Characteristics of Plasma Current Start-Up by Transient Coaxial Helicity Injection on HIST

Transient coaxial helicity injection (T-CHI) was successfully demonstrated in the Helicity Injected Spherical Torus (HIST) device for non-inductive plasma current start-up. The spherical torus (ST) requires no central solenoid coil. The characteristics of the T-CHI start-up discharges on the HIST were investigated in detail. The toroidal plasma current reached 60 - 80 kA, and the current density profile was significantly modified by variations in the bias poloidal coil flux. The Doppler ion temperature and electron temperatures reached 10 - 15 eV, and the electron density of 1 × 1020 m−3, depending on the bias flux. Internal magnetic field measurements using a two-dimensional magnetic probe array verified that closed flux surfaces formed after fast magnetic reconnection during the current rising phase. The amount of closed flux was quantitatively related to the bias flux. We also present the first experimental measurements of helicity balance during the T-CHI process. These results validate the capability of T-CHI for higher current generation in the ST.

Particle-in-cell δf gyrokinetic simulations of the microtearing mode

The linear stability properties of the microtearing mode are investigated in the edge and core regimes of the National Spherical Torus Experiment (NSTX) using the particle-in-cell method based gyrokinetic code GEM. The dependence of the mode on various equilibrium quantities in both regions is compared. While the microtearing mode in the core depends upon the electron-ion collisions, in the edge region, it is found to be weakly dependent on the collisions and exists even when the collision frequency is zero. The electrostatic potential is non-negligible in each of the cases. It plays opposite roles in the core and edge of NSTX. While the microtearing mode is partially stabilized by the electrostatic potential in the core, it has substantial destabilizing effect in the edge. In addition to the spherical tokamak, we also study the microtearing mode for parameters relevant to the core of a standard tokamak. The fundamental characteristics of the mode remain the same; however, the electrostatic potential in this case is destabilizing as opposed to the core of NSTX. The velocity dependence of the collision frequency, which is crucial for the mode to grow in slab calculations, is not required to destabilize the mode in toroidal devices.

Full wave simulations of fast wave efficiency and power losses in the scrape-off layer of tokamak plasmas in mid/high harmonic and minority heating regimes**This article is dedicated to the memory of Cynthia K. Phillips

Several experiments on different machines and in different fast wave (FW) heating regimes, such as hydrogen minority heating and high harmonic fast waves (HHFW), have found strong interaction between radio-frequency (RF) waves and the scrape-off layer (SOL) region. This paper examines the propagation and the power loss in the SOL by using the full wave code AORSA, in which the edge plasma beyond the last closed flux surface (LCFS) is included in the solution domain and a collisional damping parameter is used as a proxy to represent the real, and most likely nonlinear, damping processes. 2D and 3D AORSA results for the National Spherical Torus eXperiment (NSTX) have shown a strong transition to higher SOL power losses (driven by the RF field) when the FW cut-off is removed from in front of the antenna by increasing the edge density. Here, full wave simulations have been extended for ‘conventional’ tokamaks with higher aspect ratios, such as the DIII-D, Alcator C-Mod, and EAST devices. DIII-D results in HHFW regime show similar behavior found in NSTX and NSTX-U, consistent with previous DIII-D experimental observations. In contrast, a different behavior has been found for C-Mod and EAST, which operate in the minority heating regime.

Geodesic acoustic mode investigation in the spherical Globus-M tokamak using multi-diagnostic approach

The results of a multi-diagnostic approach for geodesic acoustic mode (GAM) studies in the spherical torus Globus-M are presented. The GAM oscillations of radial electric field, plasma density and magnetic field were simultaneously observed. The spatial structures of crucial plasma parameters are exhibited and discussed. The intermittent character of the GAM manifests itself as a modulation at two time-scales: equilibrium time scale and the characteristic time for limit-cycle oscillations. The mutual influence of GAM oscillations and turbulence is demonstrated by bicoherence analysis.