Current Profile Control Research Articles

Development of pulsed plasma operation scenario and required conditions in JA DEMO

We have developed the pulsed plasma operation scenarios for JA DEMO, a design concept of the steady-state tokamak demonstration reactor, to clarify controls of the current profile and power required for the operation. We compare the scenarios when injecting electron cyclotron waves only and both neutral beam and electron cyclotron waves for external heating and current drive. We demonstrate current profile control that maintains the minimum value of the safety factor above one and avoids creating the local minima in the safety factor profile and power control by argon seeding that maintains the fusion power constant at the desired value and reduces the heat load on the divertor, performing long-time integrated modeling simulations. We clarify the conditions of the heating and current drive system and impurity injection system required for such control. The dependence of power control on argon anomalous transport coefficients is investigated. We have the prospect of maintaining the fusion power of 1 GW for more than two hours, i.e. obtaining the required plasma performance determined using a systems code.

Model predictive current profile control in tokamaks by exploiting spatially moving electron cyclotron current drives

The plasma control systems in next-generation tokamaks like ITER will balance competing control objectives to achieve the desired level of performance in advanced scenarios while preventing magnetohydrodynamic instabilities and disruptions. During normal tokamak operation, the points of incidence of the electromagnetic waves generated by the electron cyclotron heating and current drives (EC H&CDs) are usually fixed in space. However, the points of incidence can be modified in real-time by changing the angles of the mirrors that reflect the EC H&CD waves. Altering the points of incidence, in turn, varies the ability of the plasma control system to regulate a plasma property. For instance, changing the EC H&CD wave incidence location may place the power demands necessary to achieve a particular plasma target within saturation limits. Therefore, using the EC H&CD deposition location, which is related to the EC H&CD mirror angle, as a supplementary controllable variable may facilitate access to a given target scenario. However, active scenario-control algorithms have not been designed so far to fully exploit this capability in real time. In this work, a model predictive controller that can handle actuation locations as control inputs is developed. In particular, the controller is designed to regulate both the auxiliary powers and the EC H&CD deposition locations in a pre-defined optimal sense to achieve the control objective of attaining and sustaining a target current profile. The proposed controller is tested for a DIII-D tokamak scenario in nonlinear simulations using the Control Oriented Transport SIMulator (COTSIM).

Electron beam shaping via laser heater temporal shaping

Active longitudinal beam optics can help FEL facilities achieve cutting edge performance by optimizing the beam to: produce multi-color pulses, suppress caustics, or support attosecond lasing. As the next generation of superconducting accelerators comes online, there is a need to find new elements which can both operate at high beam power and which offer multiplexing capabilities at Mhz repetition rate. Laser heater shaping promises to satisfy both criteria by imparting a programmable slice-energy spread on a shot-by-shot basis. We use a simple kinetic analysis to show how control of the slice energy spread translates into control of the bunch current profile, and then we present a collection of start-to-end simulations at LCLS-II in order to illustrate the technique.

Real-time signal processing system based on FPGA for motional Stark effect diagnostic on EAST.

The plasma current density profile plays a key role in the development of a high poloidal beta scenario, which is essential for long-pulse and high-performance plasma operation on a tokamak. Based on the polarimetry technique, a Motional Stark Effect (MSE) diagnostic has been built on the Experimental Advanced Superconducting Tokamak. To be prepared for real-time (RT) feedback control of the plasma current density profile in the future, a RT signal processing system has been developed. The RT signal processing system is composed of three functional modules: analog-to-digital conversion (ADC) module, polarization information extraction module, and digital-to-analog conversion (DAC) module. The final objective of this system is to acquire the polarization information of the MSE. Based on the field-programmable gate array unit, fast Fourier transformation is adopted to process the Photoelastic Modulator (PEM) digital signal, which was converted from a PEM signal via the ADC module. By means of frequency spectrum separation, the components around double modulating frequencies are restored through inverse fast Fourier transformation. Furthermore, the two amplitudes of their corresponding components can be obtained through a digital harmonic analyzer technique. Afterward, the ratio of the two amplitudes is calculated by arc tangent so that the polarization angle is obtained. Finally, the information of this polarization angle is converted into a voltage signal by the DAC module and then output in RT. The test results based on the RT signal processing system are in good agreement with those based on the phase lock-in amplifiers. The working cycle of this system is shorter than 10ms, which meets the requirements of the MSE diagnostic as a RT controller. The algorithm of RT signal processing and the relevant technology applied for building this system are presented in the main body of this paper in detail.

Robust control of q-profile and βp using data-driven models on EAST

• A novel H ∞ robust control scheme is developed for the current profile control using data-driven models. • A decoupling technique enables the control scheme to exhibit multi-functional characteristics. • An anti-windup technique can compensate the effects from moderate time-delays and actuator dynamics. • An efficient procedure is provided to support the H-mode steady-state operation on EAST. • Three general performance indexes are proposed to characterize the current profile control performance. A new robust feedback controller for the safety factor profile and poloidal plasma pressure parameter has been developed using a two-time-scale data-driven model. The model describes the linear plasma responses of the ι profile and β p with respect to auxiliary heating & current drive (H&CD) powers, around a typical plasma equilibrium in an H-mode steady-state plasma discharge on EAST. The feedback controller comprises a carefully designed low-pass filter for the timescale separation, a decoupling module and three local controllers synthesized from the H ∞ norm optimization and the singular value decomposition. The actuators are the lower hybrid current drive (LHCD) system at 4.6 GHz and the ion cyclotron resonance heating (ICRH) system at 33 MHz. Taking into account the actuation dynamics, an anti-windup technique is employed to condition the controller online aiming to attenuate the negative effects from moderate time delays and power saturations. Extensive nonlinear closed-loop simulations with the METIS code suggest that high β p and negative central magnetic shear that characterize advanced tokamak plasma scenarios can be achieved and sustained on EAST with good tracking performance and reasonable robustness via the proposed control scheme. The feedback control of the core ι profile and β p with a range of time delays, power saturations and varying weighting functions are evaluated numerically, compared and discussed. The control robustness to plasma parameter uncertainties including the line-averaged plasma density 〈 n ¯ e 〉 , the H-mode enhancement factor H factor and the effective charge number Z eff are assessed and analyzed.

Plasma Profiles Modifications by Upgraded Power of IBW Heating System in HT-7 Tokamak

The enhancement in local and globalized electron heating has been observed after upgrading of ion Bernstien waves (IBWs) heating system in HT-7 tokamak. The overall capability of injection power has been upgraded from 350 to 600 kW (15–30 MHz) for best and active control of pressure and current density profiles, and to discover the new phenomena of plasma heating for good energy and particle confinement. A new quadruple T-type IBWs coupling antenna has been utilized which has been mounted in the toroidal direction on low field side in the device. The electron heating on both on-axis and off-axis electrons not delete has been observed. Not delete The change in direct electron heating via electron Landau damping (ELD) from IBWs has been investigated, while the bulk electron temperature showed a large rise with a heating factor, ∆(Tene)/Prf, up to 9.3 × 1019 eV m–3 kW–1 with central electron density (ne) 3.7 × 1019 m–3. The particle confinement has also been achieved with IBW injection power of 550 kW at frequency of 27 MHz and with toroidal magnetic field of 1.92 T. The modifications observed in electron temperature and other plasma profiles are discussed under various plasma conditions. The improved energy confinement has also been observed in this scenario.

Integrated current profile, normalized beta and NTM control in DIII-D

There is an increasing need for integrating individual plasma-control algorithms with the ultimate goal of simultaneously regulating more than one plasma property. Some of these integrated-control solutions should have the capability of arbitrating the authority of the individual plasma-control algorithms over the available actuators within the tokamak. Such decision-making process must run in real time since its outcome depends on the plasma state. Therefore, control architectures including supervisory and/or exception-handling algorithms will play an essential role in future fusion reactors like ITER. However, most plasma-control experiments in present devices have focused so far on demonstrating control solutions for isolated objectives. In this work, initial experimental results are reported for simultaneous current-profile control, normalized-beta control, and Neoclassical Tearing Mode (NTM) suppression in DIII-D. Neutral beam injection (NBI), electron-cyclotron (EC) heating & current drive (H&CD), and plasma current modulation are the actuation methods. The NBI power and plasma current are always modulated by the Profile Control category within the DIII-D Plasma Control System (PCS) in order to control both the current profile and the normalized beta. EC H&CD is utilized by either the Profile Control or the Gyrotron categories within the DIII-D PCS as dictated by the Off-Normal and Fault Response (ONFR) system, which monitors the occurrence of an NTM and regulates the authority over the gyrotrons. The total EC power and poloidal mirror angles are the gyrotron-related actuation variables. When no NTM suppression is required, the gyrotrons are used by the Profile Control category, but when NTM suppression is required, the ONFR transfers the authority over the gyrotrons to the NTM stabilization algorithm located in the Gyrotron category. Initial experimental results show that simultaneous control of different aspects of the plasma dynamics may improve the overall control and plasma performances. Also, the potential of the ONFR system to successfully integrate competing control algorithms is demonstrated.

TRANSP-based closed-loop simulations of current profile optimal regulation in NSTX-Upgrade

Active control of the toroidal current density profile is critical for the upgraded National Spherical Torus eXperiment device (NSTX-U) to maintain operation at the desired high-performance, MHD-stable, plasma regime. Initial efforts towards current density profile control have led to the development of a control-oriented, physics-based, plasma-response model, which combines the magnetic diffusion equation with empirical correlations for the kinetic profiles and the non-inductive current sources. The developed control-oriented model has been successfully tailored to the NSTX-U geometry and actuators. Moreover, a series of efforts have been made towards the design of model-based controllers, including a linear-quadratic-integral optimal control strategy that can regulate the current density profile around a prescribed target profile while rejecting disturbances. In this work, the tracking performance of the proposed current-profile optimal controller is tested in numerical simulations based on the physics-oriented code TRANSP. These high-fidelity closed-loop simulations, which are a critical step before experimental implementation and testing, are enabled by a flexible framework recently developed to perform feedback control design and simulation in TRANSP.

Robust control of the current profile and plasma energy in EAST

Integrated control of the toroidal current density profile, or alternatively the q-profile, and plasma stored energy is essential to achieve advanced plasma scenarios characterized by high plasma confinement, magnetohydrodynamics stability, and noninductively driven plasma current. The q-profile evolution is closely related to the evolution of the poloidal magnetic flux profile, whose dynamics is modeled by a nonlinear partial differential equation (PDE) referred to as the magnetic-flux diffusion equation (MDE). The MDE prediction depends heavily on the chosen models for the electron temperature, plasma resistivity, and non-inductive current drives. To aid control synthesis, control-oriented models for these plasma quantities are necessary to make the problem tractable. However, a relatively large deviation between the predictions by these control-oriented models and experimental data is not uncommon. For this reason, the electron temperature, plasma resistivity, and non-inductive current drives are modeled for control synthesis in this work as the product of an “uncertain” reference profile and a nonlinear function of the different auxiliary heating and current-drive (H&CD) source powers and the total plasma current. The uncertainties are quantified in such a way that the family of models arising from the modeling process is able to capture the q-profile and plasma stored energy dynamics from a typical EAST shot. A control-oriented nonlinear PDE model is developed by combining the MDE with the “uncertain” models for the electron temperature, plasma resistivity, and non-inductive current drives. This model is then rewritten into a control framework to design a controller that is robust against the modeled uncertainties. The resulting controller utilizes EAST's H&CD powers and total plasma current to regulate the q profile and plasma stored energy even when mismatches between modeled and actual dynamics are present. The effectiveness of the controller is demonstrated through nonlinear simulations.

Tests of advanced RF off-axis current drive techniques on DIII-D

The establishment of reactor-relevant radiofrequency heating and current drive techniques is a focus of work on DIII-D in the next five-year period. This paper gives an overview of the planned experimental work in the areas of (1) nearly vertically launched ECCD, (2) ‘helicon’ (whistlers or fast waves in the lower hybrid range of frequencies) current drive, and (3) high-field-side-launch (HFS) lower hybrid (slow wave) current drive. Each of these techniques addresses the need for efficient off-axis current drive for a steady-state tokamak reactor to supplement the bootstrap current and to provide current profile control, and each will be experimentally assessed at a coupled power level of ~1 MW on DIII-D in the next few years.

Review of recent experimental and modeling advances in the understanding of lower hybrid current drive in ITER-relevant regimes

Progress in understanding lower hybrid current drive (LHCD) at high density has been made through experiments and modeling, which is encouraging given the need for an efficient off-axis current profile control technique in burning plasma. By reducing the wall recycling of neutrals, the edge temperature is increased and the effect of parametric instability (PI) and collisional absorption (CA) is reduced, which is beneficial for increasing the current drive efficiency. Strong single pass absorption is preferred to prevent CA and high LH operating frequency is essential for wave propagation to the core region at high density, presumably to mitigate the effect of PI. The dimensionless parameter that characterizes LH wave accessibility and wave refraction for the experiments in this joint study is shown to bracket the region in parameter space where ITER LHCD experiments will operate in the steady state scenario phase. Further joint experiments and cross modeling are necessary to understand the LHCD physics in weak damping regimes which would increase confidence in predictions for ITER where the absorption is expected to be strong.

Observation of trapped-electron-mode microturbulence in reversed field pinch plasmas

Density fluctuations in the large-density-gradient region of improved confinement Madison Symmetric Torus reversed field pinch (RFP) plasmas exhibit multiple features that are characteristic of the trapped-electron mode (TEM). Core transport in conventional RFP plasmas is governed by magnetic stochasticity stemming from multiple long-wavelength tearing modes. Using inductive current profile control, these tearing modes are reduced, and global confinement is increased to that expected for comparable tokamak plasmas. Under these conditions, new short-wavelength fluctuations distinct from global tearing modes appear in the spectrum at a frequency of f ∼ 50 kHz, which have normalized perpendicular wavenumbers k⊥ρs≲0.2 and propagate in the electron diamagnetic drift direction. They exhibit a critical-gradient threshold, and the fluctuation amplitude increases with the local electron density gradient. These characteristics are consistent with predictions from gyrokinetic analysis using the Gene code, including increased TEM turbulence and transport from the interaction of remnant tearing magnetic fluctuations and zonal flow.

Computational studies on scattering of radio frequency waves by density filaments in fusion plasmas

In modern magnetic fusion devices, such as tokamaks and stellarators, radio frequency (RF) waves are commonly used for plasma heating and current profile control, as well as for certain diagnostics. The frequencies of the RF waves range from ion cyclotron frequency to the electron cyclotron frequency. The RF waves are launched from structures, like waveguides and current straps, placed near the wall in a very low density, tenuous plasma region of a fusion device. The RF electromagnetic fields have to propagate through this scrape-off layer before coupling power to the core of the plasma. The scrape-off layer is characterized by turbulent plasmas fluctuations and by blobs and filaments. The variations in the edge density due to these fluctuations and filaments can affect the propagation characteristics of the RF waves—changes in density leading to regions with differing plasma permittivity. Analytical full-wave theories have shown that scattering by blobs and filaments can alter the RF power flow into the core of the plasma in a variety of ways, such as through reflection, refraction, diffraction, and shadowing [see, for example, Ram and Hizanidis, Phys. Plasmas 23, 022504 (2016), and references therein]. There are changes in the wave vectors and the distribution of power–scattering leading to coupling of the incident RF wave to other plasma waves, side-scattering, surface waves, and fragmentation of the Poynting flux in the direction towards the core. However, these theoretical models are somewhat idealized. In particular, it is assumed that there is step-function discontinuity in the density between the plasma inside the filament and the background plasma. In this paper, results from numerical simulations of RF scattering by filaments using a commercial full-wave code are described. The filaments are taken to be cylindrical with the axis of the cylinder aligned along the direction of the ambient magnetic field. The plasma inside and outside the filament is assumed to be cold. There are three primary objectives of these studies. The first objective is to validate the numerical simulations by comparing with the analytical results for the same plasma description—a step-function discontinuity in density. A detailed comparison of the Poynting flux shows that numerical simulations lead to the same results as those from the theoretical model. The second objective is to extend the simulations to take into account a smooth transition in density from the background plasma to the interior of the filament. The ensuing comparison shows that the deviations from the results of the theoretical model are quite small. The third objective is to consider the scattering process for situations well beyond a reasonable theoretical analysis. This includes scattering off multiple filaments with different densities and sizes. Simulations for these complex arrangements of filaments show that, in spite of the obvious limitations, the essential physics of RF scattering is captured by the analytical theory for a single filament.

Suppression of Alfvén Modes on the National Spherical Torus Experiment Upgrade with Outboard Beam Injection.

In this Letter we present data from experiments on the National Spherical Torus Experiment Upgrade, where it is shown for the first time that small amounts of high pitch-angle beam ions can strongly suppress the counterpropagating global Alfvén eigenmodes (GAE). GAE have been implicated in the redistribution of fast ions and modification of the electron power balance in previous experiments on NSTX. The ability to predict the stability of Alfvén modes, and developing methods to control them, is important for fusion reactors like the International Tokamak Experimental Reactor, which are heated by a large population of nonthermal, super-Alfvénic ions consisting of fusion generated α's and beam ions injected for current profile control. We present a qualitative interpretation of these observations using an analytic model of the Doppler-shifted ion-cyclotron resonance drive responsible for GAE instability which has an important dependence on k_{⊥}ρ_{L}. A quantitative analysis of this data with the hym stability code predicts both the frequencies and instability of the GAE prior to, and suppression of the GAE after the injection of high pitch-angle beam ions.

Role of the lower hybrid spectrum in the current drive modeling for DEMO scenarios

The active control of the radial current density profile is one of the major issues of thermonuclear fusion energy research based on magnetic confinement. The lower hybrid current drive could in principle be used as an efficient tool. However, previous understanding considered the electron temperature envisaged in a reactor at the plasma periphery too large to allow penetration of the coupled radio frequency (RF) power due to strong Landau damping. In this work, we present new numerical results based on quasilinear theory, showing that the injection of power spectra with different widths of the main lobe produce an RF-driven current density profile spanning most of the outer radial half of the plasma ( is the refractive index in a parallel direction to the confinement magnetic field). Plasma kinetic profiles envisaged for the DEMO reactor are used as references. We demonstrate the robustness of the modeling results concerning the key role of the spectral width in determining the lower hybrid-driven current density profile. Scans of plasma parameters are extensively carried out with the aim of excluding the possibility that any artefact of the utilised numerical modeling would produce any novelty. We neglect here the parasitic effect of spectral broadening produced by linear scattering due to plasma density fluctuations, which mainly occurs for low magnetic field devices. This effect will be analyzed in other work that completes the report on the present breakthrough.

Physics-based control-oriented modeling of the current density profile evolution in NSTX-Upgrade

Active control of the toroidal current density profile is among those plasma control milestones that the National Spherical Torus eXperiment-Upgrade (NSTX-U) program must achieve to realize its next-step operational goals. Motivated by the coupled, nonlinear, multivariable, distributed-parameter plasma dynamics, the first step towards control design is the development of a physics-based, control-oriented model for the current profile evolution in response to non-inductive current drives and heating systems. The evolution of the toroidal current density profile is closely related to the evolution of the poloidal magnetic flux profile, whose dynamics is modeled by a nonlinear partial differential equation (PDE) referred to as the magnetic-flux diffusion equation (MDE). The proposed control-oriented model predicts the spatial-temporal evolution of the current density profile by combining the nonlinear MDE with physics-based correlations obtained at NSTX-U for the electron density, electron temperature, and non-inductive current drives (neutral beams). The resulting first-principles-driven, control-oriented model is tailored for NSTX-U based on predictions by the time-dependent transport code TRANSP. Main objectives and possible challenges associated with the use of the developed model for the design of both feedforward and feedback controllers are also discussed.

Optimal current profile control for enhanced repeatability of L-mode and H-mode discharges in DIII-D

In this work, model-based control techniques are used to obtain target current profiles in low-confinement-mode (L-mode) as well as high-confinement-mode (H-mode) DIII-D discharges. The control problem is formulated as a trajectory optimization problem to search for a feasible path from the expected initial condition to the desired target. The result comprises a sequence of feedforward (open-loop) control requests and a corresponding state evolution from the initial condition to the desired target. On top of this optimal feedforward control sequence a feedback (closed-loop) controller based on a linearized model and optimal control design techniques is added to track the desired state evolution. The effectiveness of the control approach is demonstrated with experiments.

Data-driven robust control of the plasma rotational transform profile and normalized beta dynamics for advanced tokamak scenarios in DIII-D

A control-oriented, two-timescale, linear, dynamic, response model of the rotational transform ι profile and the normalized beta βN is proposed based on experimental data from the DIII-D tokamak. Dedicated system-identification experiments without feedback control have been carried out to generate data for the development of this model. The data-driven dynamic model, which is both device-specific and scenario-specific, represents the response of the ι profile and βN to the electric field due to induction as well as to the heating and current drive (H&CD) systems during the flat-top phase of an H-mode discharge in DIII-D. The control goal is to use both induction and the H&CD systems to locally regulate the plasma ι profile and βN around particular target values close to the reference state used for system identification. A singular value decomposition (SVD) of the plasma model at steady state is carried out to decouple the system and identify the most relevant control channels. A mixed-sensitivity robust control design problem is formulated based on the dynamic model to synthesize a stabilizing feedback controller without input constraints that minimizes the reference tracking error and rejects external disturbances with minimal control energy. The feedback controller is then augmented with an anti-windup compensator, which keeps the given controller well-behaved in the presence of magnitude constraints in the actuators and leaves the nominal closed-loop system unmodified when no saturation is present. The proposed controller represents one of the first feedback profile controllers integrating magnetic and kinetic variables ever implemented and experimentally tested in DIII-D. The preliminary experimental results presented in this work, although limited in number and constrained by actuator problems and design limitations, as it will be reported, show good progress towards routine current profile control in DIII-D and leave valuable lessons for further advancements in the field.

High Field Side Lower Hybrid Current Drive Simulations for Off- axis Current Drive in DIII-D

Efficient off-axis current drive scalable to reactors is a key enabling technology for developing economical, steady state tokamak. Previous studies have focussed on high field side (HFS) launch of lower hybrid current drive (LHCD) in double null configurations in reactor grade plasmas and found improved wave penetration and high current drive efficiency with driven current profile peaked near a normalized radius, ρ, of 0.6-0.8, consistent with advanced tokamak scenarios. Further, HFS launch potentially mitigates plasma material interaction and coupling issues. For this work, we sought credible HFS LHCD scenario for DIII-D advanced tokamak discharges through utilizing advanced ray tracing and Fokker Planck simulation tools (GENRAY+CQL3D) constrained by experimental considerations. For a model and existing discharge, HFS LHCD scenarios with excellent wave penetration and current drive were identified. The LHCD is peaked off axis, ρ∼0.6-0.8, with FWHM Δρ=0.2 and driven current up to 0.37 MA/MW coupled. For HFS near mid plane launch, wave penetration is excellent and have access to single pass absorption scenarios for variety of plasmas for n|| =2.6-3.4. These DIII-D discharge simulations indicate that HFS LHCD has potential to demonstrate efficient off axis current drive and current profile control in DIII-D existing and model discharge.

Update on the DIII-D ECH system: experiments, gyrotrons, advanced diagnostics, and controls

The ECH system on DIII-D is continuing to be upgraded, while simultaneously being operated nearly daily for plasma experiments. The latest major hardware addition is a new 117.5 GHz gyrotron, which generated 1.7 MW for short pulses during factory testing. A new gyrotron control system based on Field Programmable Gate Array (FPGA) technology with very high speed system data acquisition has significantly increased the flexibility and reliability of individual gyrotron operation. We have improved the performance of the fast mirror scanning, both by increasing the scan speeds and by adding new algorithms for controlling the aiming using commands generated by the Plasma Control System (PCS). The system is used for transport studies, ELM control, current profile control, non-inductive current generation, suppression of MHD modes, startup assist, plasma density control, and other applications. A program of protective measures, which has been in place for more than two years, has eliminated damage to hardware and diagnostics caused by overdense operation. Other activities not directly related to fusion research have used the ECH system to test components, study methods for improving production of semiconductor junctions and materials, and test the feasibility of using ground based microwave systems to power satellites into orbit.