A spherical tokamak (ST) with a plasma center column (PCC) can be formed via driven magnetic relaxation of a screw pinch plasma. An ST-PCC could in principle eliminate many problems associated with a material center column, a key weakness of the ST reactor concept. This work summarizes the design space for an ST-PCC in terms of flux amplification, aspect ratio, and elongation, based on the zero-beta Taylor-relaxed analysis of Tang & Boozer [Phys. Plasmas 13, 042514 (2006)]. The paper will discuss (1) equilibrium and stability properties of the ST-PCC, (2) issues for an engineering design, and (3) key differences between the proposed ST-PCC and the ongoing Proto-Sphera effort in Italy.
Turbulence is a major factor limiting the achievement of better tokamak performance as it enhances the transport of particles, momentum and heat which hinders the foremost objective of tokamaks. Hence, understanding and possibly being able to control turbulence in tokamaks is of paramount importance, not to mention our intellectual curiosity of it.
Thermal ions in spherical tokamaks have two adiabatic invariants: the magnetic moment and the longitudinal invariant. For hot ions, variations in magnetic-field strength over a gyro period can become sufficiently large to cause breakdown of the adiabatic invariance. The magnetic moment is more sensitive to perturbations than the longitudinal invariant and there exists an intermediate regime, super-adiabaticity, where the longitudinal invariant remains adiabatic, but the magnetic moment does not. The motion of super-adiabatic ions remains integrable and confinement is thus preserved. However, a…
The parametric instability of upper hybrid wave decay into back scattered upper hybrid wave and lower hybrid wave is considered for conditions of inhomogeneous plasma of spherical tokamaks. The possibility of absolute instability is demonstrated and the corresponding threshold is determined. It is shown that the threshold power increases with pump frequency and electron temperature. Threshold power is estimated for typical parameters of experiment in MAST tokamak. It is shown that in this case parametrical reflection arises, if probing power exceeds 90W/cm^2, which gives 30 kW for a beam of 10…
Recent gyrokinetic stability calculations have revealed that the spherical tokamak is susceptible to tearing parity instabilities with length scales of a few ion Larmor radii perpendicular to the magnetic field lines. Here we investigate this 'micro-tearing' mode in greater detail to uncover its key characteristics, and compare it with existing theoretical models of the phenomenon. This has been accomplished using a full numerical solution of the linear gyrokinetic-Maxwell equations. Importantly, the instability is found to be driven by the free energy in the electron temperature gradient as d…
Understanding generation and mitigation of runaway electrons in disruptions is important for the safe operation of future tokamaks. In this paper we investigate runaway dynamics in reactor-scale spherical tokamaks. We study both the severity of runaway generation during unmitigated disruptions, as well as the effect that typical mitigation schemes based on massive material injection have on runaway production. The study is conducted using the numerical framework DREAM (Disruption Runaway Electron Analysis Model). We find that, in many cases, mitigation strategies are necessary to prevent the r…
The onset and characteristics of Micro-Tearing Modes (MTM) in the core of spherical (NSTX) and conventional tokamaks (ASDEX-UG and JET) are studied through local linear gyrokinetic simulations with gyro [J. Candy and E. Belli, General Atomics Report GA-A26818 (2011)]. For experimentally relevant core plasma parameters in the NSTX and ASDEX-UG tokamaks, in agreement with previous works, we find MTMs as the dominant linear instability. Also, for JET-like core parameters considered in our study an MTM is found as the most unstable mode. In all these plasmas, finite collisionality is needed for MT…
Twisted magnetic flux ropes are ubiquitous in space and laboratory plasmas, and the merging of such flux ropes through magnetic reconnection is an important mechanism for restructuring magnetic fields and releasing free magnetic energy. The merging-compression scenario is one possible start up scheme for spherical tokamaks, which has been used on the Mega Amp Spherical Tokamak MAST. Two current-carrying plasma rings, or flux ropes, approach each other through the mutual attraction of their like currents, and merge, through magnetic reconnection, into a single plasma torus, with substantial pla…
A Doppler backscattering diagnostic for the EXL-50U spherical tokamak: plasma considerations and preliminary quasioptical design
A*STAR Research Entities（新加坡科学研究局）；Imperial College London（帝国理工学院）；Nanyang Technological University（南洋理工大学）；UCLA（加州大学洛杉矶分校）；ENN Science & Technology Development Co., Ltd（新奥科技发展有限公司）
Spherical tokamaks (STs) have been shown to possess properties desirable for a fusion power plant such as achieving high plasma ? and having increased vertical stability. To understand the confinement properties that might be expected in the conceptual design for a high $β$ ST fusion reactor, a 1GW ST plasma equilibrium was analysed using local linear gyrokinetics to determine the type of micro-instabilities that arise. Kinetic ballooning modes (KBMs) and micro-tearing modes (MTMs) are found to be the dominant instabilities. The parametric dependence of these linear modes was determined and fr…
The collisional dynamics of test impurity ions in spherical tokamak plasmas with strongly-sheared radial electric fields is investigated by means of a test particle full orbit simulation code. The strength of the shear is such that the standard drift ordering can no longer be assumed and a full orbit approach is required. The effect of radial electric field shear on neoclassical particle transport is quantified for a range of test particle mass and charge numbers and electric field parameters. It is shown that the effect of a sheared electric field is to enhance the confinement of impurity spe…
Alfvén cyclotron instabilities excited by velocity gradients of energetic beam ions were investigated in MAST experiments with super-Alfvénic NBI over a wide range of toroidal magnetic fields from ~0.34 T to ~0.585 T. In MAST discharges with high magnetic field, a discrete spectrum of modes in the sub-cyclotron frequency range is excited toroidally propagating counter to the beam and plasma current (toroidal mode numbers n < 0).
Recent measurements of microwave and X-ray emission during edge localised mode (ELM) activity in tokamak plasmas provide a fresh perspective on ELM physics. It is evident that electron kinetics, which are not incorporated in standard (fluid) models for the instability that drives ELMs, play a key role in the new observations. These effects should be included in future models for ELMs and the ELM cycle. The observed radiative effects paradoxically imply acceleration of electrons parallel to the magnetic field combined with rapid acquisition of perpendicular momentum. It is shown that this parad…
Neutral-beam-driven, sub-cyclotron compressional (CAE) and global (GAE) \Alfven eigenmodes are routinely excited in spherical tokamaks such as NSTX(-U) and MAST, have been observed on the conventional aspect ratio tokamak DIII-D, and may be unstable in ITER burning plasmas. Their presence has been experimentally linked to the anomalous flattening of electron temperature profiles at high beam power in NSTX, potentially limiting fusion performance. A detailed understanding of CAE/GAE excitation, therefore, is vital to predicting (and ultimately controlling) their effects on plasma confinement. T…
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-beta regimes, in which the usual EC O- and X- modes are cut-off. In this case, EBWs seem to be the only option that can provide features similar to the EC waves---controllable localized H&CD that can be utilized for core plasma heating as well as for accurate plasma stabilization. The EBW is a quasi-electrostatic wave that can be excited by mode conversion from a suita…
The application of non-axisymmetric resonant magnetic perturbations (RMPs) to low current plasmas in the Mega Amp Spherical Tokamak (MAST) was found to be correlated with substantial drops in neutron production, suggesting a significant degradation of fast ion confinement. The effects of such perturbations on fast ions in MAST have been modelled using a revised version of a non-steady-state orbit-following Monte-Carlo code (NSS OFMC), in which the parametrization of fusion reaction rates has been updated and neutron rates have been recalculated. Losses of fast ions via charge-exchange (CX) wit…
In addition to traditional regimes with monotonously increasing magnetic field, regimes with "magnetic wells" also occur in spherical tokamaks (STs). The magnetic field profile inversion modifies significantly the whole picture of the wave propagation and damping. Since the magnetic wells may become quite common with further improvement of ST performance, analysis of such configurations is of interest for assessment of EBW plasma heating an CD perspectives. In this paper the basic features of the EBWs propagation and damping for the second cyclotron harmonic in a slab model are considered.
The transport of heat out of tokamak plasmas by turbulence is the dominant mechanism limiting the performance of fusion reactors. Turbulence can be driven by the ion temperature gradient (ITG) and suppressed by toroidal sheared flows. Numerical simulations attempting to understand turbulence are crucial for guiding the design of future reactors. We investigate ion-scale turbulence via gyrokinetic simulations in the outer core of the Mega Ampere Spherical Tokamak (MAST). We perform a parameter scan in the values of the ITG and the flow shear. We show that nonlinear simulations reproduce the exp…
Reinforcement learning for vertical position control on the EXL-50U spherical tokamak
Beijing ENN Fusion Energy Science and Technology Co., Ltd.（北京恩诺聚变能源科技有限公司）；Beijing Key Laboratory of High Magnetic Field Spherical Torus Fusion Energy（北京市高磁场球形托卡马克聚变能重点实验室）；Hebei Key Laboratory of Compact Fusion（河北省紧凑型聚变重点实验室）；School of Nuclear Science and Engineering, East China University of Technology（华东理工大学核科学与技术学院）；Institute of Robotics and Automatic Information System, Nankai University（南开大学机器人与自动化信息系统研究所）；Key Laboratory of Materials Modification by Beams of the Ministry of Education, School of Physics, Dalian University of Technology（大连理工大学物理学院教育部 beam 材料改性重点实验室）；Dalian University of Technology（大连理工大学）
Anti-dynamo modes are usually found in spheromaks plasma devices experiments due to the fact that Cowling anti-dynamo theorem is naturally applied to axisymmetric devices and flows. In this paper full consideration is given to the existence of slow dynamo modes in the case of compact Riemannian plasma devices without boundaries, such as tokamaks, stellarators and torsatrons. It is shown that a perturbed untwisted flow given by a decaying mode magnetic field is able to generate a slow twisted dynamo plasma flow where the unperturbed flow is also a steady flow. When the slow dynamo limit is obta…
Edge localised modes (ELMs) are a concern for future devices as they can limit the operational lifetime of the divertor. The mitigation of ELMs can be performed by the application of resonant magnetic perturbations (RMPs) which act to degrade the pressure gradient in the edge of the plasma. Investigations of the effect of RMPs on MAST have been performed in a range of plasmas using perturbations with toroidal mode numbers of n=3, 4 and 6. It has been seen that the RMPs increase the ELM frequency, which gives rise to a corresponding decrease in the ELM energy. The reduced ELM energy decreases t…
Using the recently-installed Fast-Ion Deuterium Alpha (FIDA) spectrometer, the effects of low-frequency (20-50 kHz) chirping energetic particle modes with toroidal mode number n \geq 1 on the fast-ion population in MAST plasmas are considered. Results from the FIDA diagnostic are presented and discussed in the light of the present theoretical understanding of these modes, known as fishbones, in plasmas with reversed shear. Measurements of the fast-ion population reveal strong redistribution of fast ions in both real and velocity space as a result of the fishbones. Time-resolved measurements th…
The effectiveness of multiple electron cyclotron resonance (ECR) harmonics has been thoroughly investigated in context of high current drive efficiency, generally observed in fully non-inductive operation of the low aspect ratio EXL-50 spherical tokamak (ST) powered by electron cyclotron (EC) waves. The Fokker-Plank equation is numerically solved to obtain electron distribution function, under steady state of the relativistic nonlinear Coulomb collision and quasi-linear diffusion operators, for calculating plasma current driven by the injected EC wave. For the extra-ordinary EC wave, simulatio…
The results of a comprehensive investigation into the effects of various MHD modes on the NBI-generated fast-ion population in MAST plasmas are reported. Fast-ion redistribution due to low-frequency (20-50 kHz) chirping energetic particle modes known as fishbones, as well as the long-lived internal kink mode, is observed with the Fast-Ion Deuterium Alpha (FIDA) spectrometer and radially-scanning collimated neutron camera. In addition, strongly-driven chirping toroidicity-induced Alfven eigenmodes are observed to cause fast-ion redistribution, as are sawteeth and large edge-localised modes. In …
The ion temperature behavior in the plasma core of the spherical tokamak Globus-M (major radius 0.36 m, minor radius 0.24 m, torus aspect ratio 1.5, toroidal magnetic field near the plasma axis 0.4 T, plasma current up to 0.3 MA) was studied by means of 12-channels neutral particle analyzer (NPA) ACORD-12. The experiments were performed in ohmic regimes as well as in regimes with the ion cyclotron resonance heating (ICRH) in the vicinity of fundamental harmonic for hydrogen minority in deuterium bulk plasma and the neutral beam injection (NBI). The total auxiliary power exceeded the magnitude …
We present recent results and technical breakthroughs for the Bayesian inference of tokamak equilibria using force-balance as a prior constraint. Issues surrounding model parameter representation and posterior analysis are discussed and addressed. These points motivate the recent advancements embodied in the Bayesian Equilibrium Analysis and Simulation Tool (BEAST) software being presently utilised to study equilibria on the Mega-Ampere Spherical Tokamak (MAST) experiment in the UK (von Nessi \emph{et. al.} 2012 \emph{J. Phys. A} \textbf{46} 185501). State-of-the-art results of using BEAST to …
The high-k ($7 \lesssim k_{\bot} ρ_i \lesssim 11$) wavenumber spectrum of density fluctuations has been measured for the first time in MAST [B. Lloyd et al, Nucl. Fusion 43, 1665 (2003)]. This was accomplished with the first implementation of Doppler backscattering (DBS) for core measurements in a spherical tokamak. DBS has become a well-established and versatile diagnostic technique for the measurement of intermediate-k ($k_{\bot} ρ_i \sim 1$, and higher) density fluctuations and flows in magnetically confined fusion experiments. A novel implementation with 2D steering was necessary to enable…
Observer-Based Model Predictive Control for Isoflux Regulation in the EXL-50U Spherical Tokamak
Institute of Robotics and Automatic Information System, Nankai University（南开大学机器人与自动化信息研究所）；Beijing ENN Fusion Energy Science and Technology Co., Ltd.（北京新奥聚变能源科技有限公司）
A comprehensive numerical study has been conducted in order to investigate the stability of beam-driven, sub-cyclotron frequency compressional (CAE) and global (GAE) Alfvén Eigenmodes in low aspect ratio plasmas for a wide range of beam parameters. The presence of CAEs and GAEs has previously been linked to anomalous electron temperature profile flattening at high beam power in NSTX experiments, prompting further examination of the conditions for their excitation. Linear simulations are performed with the hybrid MHD-kinetic initial value code HYM in order to capture the general Doppler-shifted…
In the merging-compression method of plasma start-up, two flux-ropes with parallel toroidal current are formed around in-vessel poloidal field coils, before merging to form a spherical tokamak plasma. This start-up method, used in the Mega-Ampere Spherical Tokamak (MAST), is studied as a high Lundquist number and low plasma-beta magnetic reconnection experiment. In this paper, 2D fluid simulations are presented of this merging process in order to understand the underlying physics, and better interpret the experimental data. These simulations examine the individual and combined effects of tight…
Development of a Reduced Multi-Fluid Equilibrium Model and Its Application to Proton-Boron Spherical Tokamaks
ENN Science and Technology Development Co., Ltd.（恩能科技发展有限公司）；School of Physics, Dalian University of Technology（大连理工大学物理学院）；Southwestern Institute of Physics（西南核物理与化学研究所）；Institute for Fusion Theory and Simulation, Zhejiang University（浙江大学聚变理论与模拟研究所）；Forschungszentrum Jülich GmbH, Institute of Fusion Energy and Nuclear Waste Management Plasmaphysik（于利希有限公司聚变能与核废料管理等离子体物理研究所）
A kinetic model for studying the time evolution of the distribution function for microwave start-up is presented. The model for the distribution function is two dimensional in momentum space, but, for simplicity and rapid calculations, has no spatial dependence. Experiments on the Mega Amp Spherical Tokamak have shown that the plasma current is carried mainly by electrons with energies greater than $70$ keV, and effects thought to be important in these experiments are included, i.e. particle sources, orbital losses, the loop voltage and microwave heating, with suitable volume averaging where n…
Non-axisymmetric stationary magnetic perturbations lead to the formation of homoclinic tangles near the divertor magnetic saddle in tokamak discharges. These tangles intersect the divertor plates in static helical structures that delimit the regions reached by open magnetic field lines reaching the plasma column and leading the charged particles to the strike surfaces by parallel transport. In this article we introduce a non-axisymmetric rotating magnetic perturbation to model the time development of the three-dimensional magnetic field of a single-null DIII-D tokamak discharge developing a ro…
Plasma equilibria reconstructed from the Mega-Amp Spherical Tokamak (MAST) have sufficient resolution to capture plasma evolution during the short period between edge-localized modes (ELMs). Immediately after the ELM steep gradients in pressure, P, and density, ne, form pedestals close to the separatrix, and they then expand into the core. Local gyrokinetic analysis over the ELM cycle reveals the dominant microinstabilities at perpendicular wavelengths of the order of the ion Larmor radius. These are kinetic ballooning modes (KBMs) in the pedestal and microtearing modes (MTMs) in the core clos…
A Novel Numerical Algorithms Optimization Method with Machine Learning Frameworks: Application on Real-time Plasmas Equilibrium Reconstruction in EXL-50U Spherical Torus
Nankai University（南开大学）；ENN Science and Technology Development Co., Ltd.（新奥科技发展有限公司）；Southwestern Institute of Physics（西南物理研究院）
Tokamak turbulence, driven by the ion-temperature gradient and occurring in the presence of flow shear, is investigated by means of local, ion-scale, electrostatic gyrokinetic simulations (with both kinetic ions and electrons) of the conditions in the outer core of the Mega-Ampere Spherical Tokamak (MAST). A parameter scan in the local values of the ion-temperature gradient and flow shear is performed. It is demonstrated that the experimentally observed state is near the stability threshold and that this stability threshold is nonlinear: sheared turbulence is subcritical, i.e. the system is fo…
In order to identify complicated systems, more prominent and promising methods are needed among which we may refer to fractional order differential equations. The aim of this paper is to propose a fractional order nonlinear model to predict the vertical position of a plasma column system in a Tokamak by using real data from Damavand Tokamak. The system is identified based on a newly introduced fractional order dynamic neural network. The proposed fractional order dynamic neural network (FODNN) is an extension of the integer order dynamic neural network that employs the so called fractional-ord…
Understanding of the transport in a Tokamak plasma is an important issue. Various mechanisms have been reported in the literature to relate the core phenomenon to edge phenomenon. Sawtooth and Mirnov oscillations caused by MHD instabilities are generally observed in Tokamak discharges. Observation of these effects in the visible radiation from outer edge may offer a possible means to understand the transport.Oscillations in the visible radiation from outer region of the plasma have been observed during recent Aditya discharges. Percentage modulation of these oscillations vary with the Lines of…
Tokamak plasmas rotate even without external injection of momentum. A Doppler backscattering system installed at MAST has allowed this intrinsic rotation to be studied in Ohmic L-mode and H-mode plasmas, including the first observation of intrinsic rotation reversals in a spherical tokamak. Experimental results are compared to a novel 1D model, which captures the collisionality dependence of the radial transport of toroidal angular momentum due to the effect of neoclassical flows on turbulent fluctuations. The model is able to accurately reproduce the change in sign of core toroidal rotation, …
Magnetohydrodynamic equilibrium and neutronics study on MAST-U using Jenga framework
Pranos Fusion Private Limited（普拉诺斯融合私人有限公司）；Indian Institute of Science（印度科学学院）；Jawaharlal Nehru Centre for Advanced Scientific Research（贾瓦哈拉尔·尼赫鲁高级科学研究中心）
