Current Ramp-up Phase Research Articles

Optimizing the current ramp-up phase for the hybrid ITER scenario

The current ramp-up phase for the ITER hybrid scenario is analysed with the CRONOS integrated modelling suite. The simulations presented in this paper show that the heating systems available at ITER allow, within the operational limits, the attainment of a hybrid q profile at the end of the current ramp-up. A reference ramp-up scenario is reached by a combination of NBI, ECCD (UPL) and LHCD. A heating scheme with only NBI and ECCD can also reach the target q profile; however, LHCD can play a crucial role in reducing the flux consumption during the ramp-up phase. The optimum heating scheme depends on the chosen transport model, and on assumptions of parameters like ne peaking, edge Te,i and Zeff. The sensitivity of the current diffusion on parameters that are not easily controlled, shows that development of real-time control is important to reach the target q profile. A first step in that direction has been indicated in this paper. Minimizing resistive flux consumption and optimizing the q profile turn out to be conflicting requirements. A trade-off between these two requirements has to be made. In this paper it is shown that fast current ramp with L-mode current overshoot is at the one extreme, i.e. the optimum q profile at the cost of increased resistive flux consumption, whereas early H-mode transition is at the other extreme.

NBI-driven Alfvénic modes at ASDEX Upgrade

A large variety of electromagnetic modes excited by NBI-generated energetic ions are observed in the early phase of many discharges at ASDEX Upgrade. In addition to the well-known reversed shear Alfvén eigenmodes (RSAE) and the toroidal Alfvén eigenmodes (TAE), a set of modes around 70 kHz is observed as recently described in []. The modes were identified to be beta-induced Alfvén eigenmodes (BAE) connected with the appearance of the q = 2 and the q = 1.5 surface during the current ramp-up phase. In the view of ITER, these BAEs may occur in scenarios with q ≈ 2 (scenario 4) and therefore add significantly to the transport of energetic ions due to RSAEs and TAEs.Experimentally, the combination of ECE, soft-x-ray and magnetic measurements allows for a very reliable mode position and mode structure determination. The measurements are compared with linear gyrokinetic calculations employing the LIGKA code that uses a fully kinetic model to describe fast-particle-driven modes in general tokamak geometry.

Characterization of Alfvén eigenmodes using NBI during current ramp-up in the ASDEX Upgrade tokamak

Alfvén cascades (ACs) and beta-induced Alfvén eigenmodes (BAEs) have been studied in the ASDEX Upgrade tokamak during the current ramp-up phase of neutral beam heated (NBI) discharges using principally reflectometry, but also soft x-ray (SXR) and electron cyclotron emission imaging (ECEI). ACs have been observed on the tokamak high-field side and low-field side in reflectometer signals even in the absence of a cutoff. Under this condition it is shown that the response is not due to an interferometry effect but due to backscatter. The radial structure of BAEs and ACs has been obtained by cross-correlating the reflectometer with SXR, ECEI and magnetic signals. The reflectometer signals reveal a variety of Alfvén eigenmodes with different characteristics depending on the plasma heating scheme. Here, discharges with similar plasma parameters but varying NBI sources and/or additional electron cyclotron resonance heating were performed. It is shown that the bursting behaviour of ACs for qmin < 2 depends on the NBI beam geometry. Also, a discrepancy in the n = 2 AC minimum frequency of a Grand Cascade is explained by the linear gyro-kinetic code LIGKA simulations which include energetic particle effects.

Progress in characterization and modelling of the current ramp-up phase of ASDEX Upgrade discharges

Measurements of plasma core impurity ion temperature and toroidal rotation are obtained during the current ramp-up phases of plasma discharges in the ASDEX Upgrade tokamak, by means of charge exchange recombination spectroscopy utilizing short neutral beam injected blips. The phenomenology of these profiles as the current is varied is presented. The observations are reported for both ohmically heated and electron cyclotron heating assisted ramps, with auxiliary heating applied both on-axis and off-axis. The evolution of global parameters is also reported. A comparison between ion and electron kinetic profiles evolution is made. Power balance analysis is performed to establish the local confinement properties and their evolution during the current ramp. Transport modelling of several cases with a theory-based model is carried out and a recipe, which involves edge-relevant parameters, is proposed to account for the transport in the outer plasma region. Finally, linear gyrokinetic calculations of dominant microinstabilities allow us to correlate the observed transport with the background turbulence regime.

Non-linear model-based optimization of actuator trajectories for tokamak plasma profile control

A computational method is presented to determine the tokamak actuator time evolution (trajectories) required to optimally reach a given point in the tokamak operating space while satisfying a set of constraints. Usually, trajectories of plasma auxiliary heating, current drive and plasma current required during the transient phases of a tokamak shot to reach a desired shape of the plasma temperature and safety factor (q) profiles are determined by trial-and-error by physics operators. In this paper, these trajectories are calculated by solving a non-linear, constrained, finite-time optimal control problem.The optimization problem contains a physics model of the non-linear plasma profile dynamics, a cost function to be minimized, and a set of constraints on the actuators and plasma quantities. The method is tested by optimizing the trajectories of Ip, heating and current drive power to obtain a typical hybrid plasma q profile at the end of the current ramp-up phase, while minimizing both the Ohmic flux swing and the distance from a stationary condition, and requiring q > 1 and edge Vloop > 0 at all times. The optimized trajectories feature an Ip overshoot similar to that used in existing experiments, and are shown to perform significantly better than a set of non-optimized trajectories, allowing stationary profiles to be obtained at the beginning of the flat-top phase. Additional information is obtained, including the parameter sensitivity of the optimal solution, a linear model describing the linearized dynamics of the profiles around the optimal trajectory, as well as a classification of the actuator trajectories based on the critical constraint which limits their value at a given time. This provides a solid basis for subsequent closed-loop feedback controller design. The tools presented in this paper could be useful to improve existing tokamak operational scenarios, to prepare operation of future machines and optimize their design.

Statistical Analysis of the Convective Intermittent Transport at the Edge Region of QUEST

Ambient fluctuations and the generation of coherent convective structures are investigated as a function of vertical to toroidal magnetic field ratio (Bz/Bt) in the spherical tokamak QUEST [K. Hanada et al., Plasma Fusion Research 5, S1007]. Fluctuation signals are obtained at a high spatial and temporal resolution using the fast visible camera. The coherent structures (blobs) were seen to be apparent only beyond a critical Bz/Bt ratio (~ 10). This clearly indicates a shift from the drift to the interchange mode with the increase in vertical magnetic field. The blobs are propagated radially at a high speed ~ 10 m/s which is ~ 1/10 of the ion acoustic speed in QUEST. Lifetime of the blobs is about 700 μs. Second part of the study comprises of the investigation of the finer structures in the current ramp-up phase which is characterized by lower levels of fluctuations. Singular value decomposition (SVD) and principal component analysis (PCA) techniques are applied on the fast camera images to reveal the structures which are otherwise embedded in the overall intensity image. Electron banana orbits were seen to form from the slab annular plasma and grow wider to eventually shape the plasma current front.

Optimizing the Current Ramp-Up Phase for Hybrid ITER Scenario

This paper reports on a systematic effort to optimize the current ramp-up phase for the ITER hybrid scenario, and to assess the sensitivity of the results to the assumptions made.

Investigation of fast particle driven instabilities by 2D electron cyclotron emission imaging on ASDEX Upgrade

Detailed measurements of the 2D mode structure of Alfvén instabilities in the current ramp-up phase of neutral beam heated discharges were performed on ASDEX Upgrade, using the electron cyclotron emission imaging (ECEI) diagnostic. This paper focuses on the observation of reversed shear Alfvén eigenmodes (RSAEs) and bursting modes that, with the use of the information from ECEI, have been identified as beta-induced Alfvén eigenmodes (BAEs). Both RSAEs with first and second radial harmonic mode structures were observed. Calculations with the linear gyro-kinetic code LIGKA revealed that the ratio of the damping rates and the frequency difference between the first and second harmonic modes strongly depended on the shape of the q-profile. The bursting character of the BAE type modes, which were radially localized to rational q surfaces, was observed to sensitively depend on the plasma parameters, ranging from strongly bursting to almost steady state.

Current ramps in tokamaks: from present experiments to ITER scenarios

In order to prepare adequate current ramp-up and ramp-down scenarios for ITER, present experiments from various tokamaks have been analysed by means of integrated modelling in view of determining relevant heat transport models for these operation phases. A set of empirical heat transport models for L-mode (namely, the Bohm–gyroBohm model and scaling based models with a specific fixed radial shape and energy confinement time factors of H96−L = 0.6 or HIPB98 = 0.4) has been validated on a multi-machine experimental dataset for predicting the li dynamics within ±0.15 accuracy during current ramp-up and ramp-down phases. Simulations using the Coppi–Tang or GLF23 models (applied up to the LCFS) overestimate or underestimate the internal inductance beyond this accuracy (more than ±0.2 discrepancy in some cases). The most accurate heat transport models are then applied to projections to ITER current ramp-up, focusing on the baseline inductive scenario (main heating plateau current of Ip = 15 MA). These projections include a sensitivity study to various assumptions of the simulation. While the heat transport model is at the heart of such simulations (because of the intrinsic dependence of the plasma resistivity on electron temperature, among other parameters), more comprehensive simulations are required to test all operational aspects of the current ramp-up and ramp-down phases of ITER scenarios. Recent examples of such simulations, involving coupled core transport codes, free-boundary equilibrium solvers and a poloidal field (PF) systems controller are also described, focusing on ITER current ramp-down.

Synthesis and simulation of a two-level magnetic control system for tokamak-reactor plasma

Synthesis and simulation of a hierarchical (two-level) magnetic system for controlling a tokamakreactor plasma throughout the entire divertor discharge stage, including the plasma current ramp-up phase, are carried out. The plasma vertical velocity is stabilized about zero by using a proportional controller in a scalar control loop. The gain of the controller—the coefficient that ensures the required stability margins—is found by using a second-order linear model constructed by solving the identification problem on the basis of numerical experiments carried out with the DINA plasmophysical computer code. The internal cascade (the lower level of the system) for tracking the scenario currents in the poloidal magnetic field coils is synthesized by using the complete dynamic channel decoupling method. The external cascade (the upper level of the system) for tracking the plasma current and shape is synthesized by using the method of pseudoseparation of the control channels and the multidimensional diagonal proportional-integral controller, with proportional, integrating, and double integrating units connected in parallel in each channel. In the hierarchical control system, the lower level (the internal cascade) is subordinated to the upper level (the external cascade). The external cascade acts on the internal one by the signals that set the required currents in the coils of the central solenoid and of the poloidal magnetic field in order to ensure the required plasma current and shape in accordance with the output signals from the plant, which are transmitted through the vector feedback channel. The lower level is aimed exclusively at tracking the reference inputs by tracking the currents in the control coils. An operating mode of the system under the conditions of current saturation in the control coils is proposed and implemented. Results are presented from numerical simulations of the two-level (cascade) control system for reference scenario no. 2 of the ITER database (www.iter.org) with the DINA nonlinear code.

Simserver simulation of a model-based current profile controller in the DIII-D Plasma Control System

Abstract Setting up a suitable current profile, characterized by a weakly reversed magnetic shear, has been demonstrated to be a key condition for one possible advanced tokamak operating scenario with improved confinement and possible steady-state operation. Experiments at DIII-D focus on creating the desired current profile during the plasma current ramp-up and early flat-top phases with the aim of maintaining this target profile throughout the subsequent phases of the discharge. The evolution in time of the current profile, or alternatively the safety factor q, is related to the evolution of the poloidal flux, which is modeled in normalized cylindrical coordinates using a partial differential equation referred to as the magnetic flux diffusion equation. A control-oriented model of the current profile evolution in DIII-D was recently developed for the plasma current ramp-up and early flat-top phases and used to synthesize both open-loop and closed-loop control schemes. In this work, we report on the implementation of an advanced model-based current profile controller in the DIII-D Plasma Control System (PCS) and on the assessment of this controller implementation in closed-loop Simserver (simulation server) simulations.

Confinement and transport properties during current ramps in the ASDEX Upgrade tokamak

A detailed analysis of experimental data from the ASDEX Upgrade tokamak is carried out to shed light on the properties of confinement and transport in the current ramp-up and ramp-down phases of the plasma discharge. The experimental database is used to identify the relevant ranges of parameters explored during the ramp-up and the ramp-down. The energy confinement time observed in the two ramps displays interesting evolution, in many cases attaining different values at the same current level between ramp-up and ramp-down. The possible reasons for this behaviour are investigated. Interpretative transport simulations are used as a tool to clarify the interplay between different parameters, which are coupled in a non-linear way. In addition, a theory-based transport model is used to understand the behaviour of confinement as observed in the experiment, evidencing the role of both turbulent and neoclassical transport. Linear gyrokinetic calculations are performed to identify the relevant turbulence regime, showing that a broad range of frequencies, in the trapped electron modes (TEMs) and in the ion temperature gradient modes (ITGs) regimes, is explored during both the ramp-up and ramp-down. In the same framework, a quasi-linear model is applied to calculate the value of the local logarithmic density gradient and compare it with the experimental value. Finally, first non-linear simulations of heat transport during the current ramps are presented.

Optimal Tracking Control of Current Profile in Tokamaks

Setting up a suitable current spatial profile in tokamak plasmas has been demonstrated to be a key condition for one possible advanced scenario with improved confinement and possible steady-state operation. Experiments at the DIII-D tokamak focus on creating the desired current profile during the plasma current ramp-up and early flattop phases with the aim of maintaining this target profile during the subsequent phases of the discharge. The evolution in time of the current profile is related to the evolution of the poloidal magnetic flux, which is modeled in normalized cylindrical coordinates using a parabolic partial differential equation usually referred to as the magnetic diffusion equation. We propose a framework to solve a finite-time, optimal tracking control problem for the current profile evolution via diffusivity, interior, and boundary actuation during the ramp-up and early flattop phases of the discharge. The proposed approach is based on reduced order modeling via proper orthogonal decomposition and successive optimal control computation for a bilinear system. Simulation results illustrate the performance of the proposed controller.

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Modelling of the JET current ramp-up experiments and projection to ITER

The current ramp-up phase of ITER demonstration discharges, performed at JET, is analysed and the capability of the empirical L-mode Bohm–gyroBohm and Coppi–Tang transport models as well as the theory-based GLF23 model to predict the temperature evolution in these discharges is examined. The analysed database includes ohmic (OH) plasmas with various current ramp rates and plasma densities and the L-mode plasmas with the ion cyclotron radio frequency (ICRF) and neutral beam injection (NBI) heating performed at various ICRF resonance positions and NBI heating powers. The emphasis of this analysis is a data consistency test, which is particularly important here because some parameters, useful for the transport model validation, are not measured in OH and ICRF heated plasmas (e.g. ion temperature, effective charge). The sensitivity of the predictive accuracy of the transport models to the unmeasured data is estimated. It is found that the Bohm–gyroBohm model satisfactorily predicts the temperature evolution in discharges with central heating (the rms deviation between the simulated and measured temperature is within 15%), but underestimates the thermal electron transport in the OH and off-axis ICRF heated discharges. The Coppi–Tang model strongly underestimates the thermal transport in all discharges considered. A re-normalization of these empirical models for improving their predictive capability is proposed. The GLF23 model, strongly dependent on the ion temperature gradient and tested only for NBI heated discharges with measured ion temperatures, predicts accurately the temperature in the low power NBI heated discharge (rms < 10%) while the discrepancy with the data increases at high power. Based on the analysis of the JET discharges, the modelling of the current ramp-up phase for the H-mode ITER scenario is performed with particular emphasis on the sensitivity of the sawtooth-free duration of this phase to transport model.

Simulations of KSTAR high performance steady state operation scenarios

We report the results of predictive modelling of high performance steady state operation scenarios in KSTAR. Firstly, the capabilities of steady state operation are investigated with time-dependent simulations using a free-boundary plasma equilibrium evolution code coupled with transport calculations. Secondly, the reproducibility of high performance steady state operation scenarios developed in the DIII-D tokamak, of similar size to that of KSTAR, is investigated using the experimental data taken from DIII-D. Finally, the capability of ITER-relevant steady state operation is investigated in KSTAR. It is found that KSTAR is able to establish high performance steady state operation scenarios; βN above 3, H98(y, 2) up to 2.0, fBS up to 0.76 and fNI equals 1.0. In this work, a realistic density profile is newly introduced for predictive simulations by employing the scaling law of a density peaking factor. The influence of the current ramp-up scenario and the transport model is discussed with respect to the fusion performance and non-inductive current drive fraction in the transport simulations. As observed in the experiments, both the heating and the plasma current waveforms in the current ramp-up phase produce a strong effect on the q-profile, the fusion performance and also on the non-inductive current drive fraction in the current flattop phase. A criterion in terms of qmin is found to establish ITER-relevant steady state operation scenarios. This will provide a guideline for designing the current ramp-up phase in KSTAR. It is observed that the transport model also affects the predictive values of fusion performance as well as the non-inductive current drive fraction. The Weiland transport model predicts the highest fusion performance as well as non-inductive current drive fraction in KSTAR. In contrast, the GLF23 model exhibits the lowest ones. ITER-relevant advanced scenarios cannot be obtained with the GLF23 model in the conditions given in this work. Finally, ideal MHD stability is investigated for the ITER-relevant advanced scenarios in KSTAR. The methods and results presented in this paper are expected to contribute to improving the ITER and beyond ITER predictive simulations.

Two Dimensional Density Fluctuation Measurements During the Non-Inductive Current Ramp-up Phase in the Compact Plasma Wall Interaction Experimental Device CPD

Two-dimensional structure of density fluctuations is examined during the current jump phase, indicating a change from the open magnetic fields to the closed ones. During the smooth current ramp-up phase the two-dimensional contour of the LiI intensity shows vertically alignment, consistent with the magnetic surfaces. At the inflection point in Ip ramp-up the LiI intensity contour becomes flat in the observation regime and then suddenly a steep gradient and higher intensity regime are formed in the vertical direction. This higher intensity corresponds to a burst of LiI waveform. According to these changes in the contour, it is found that, within ±1 ms around the burst of LiI, a low frequency coherent wave with a long wavelength rapidly grows. The relations with other signals (magnetic flux and microwave stray power) are discussed with respect to the topological change in the magnetic configuration and mode conversion of the incident electromagnetic waves.

Comparisons of predicted plasma performance in ITER H-mode plasmas with various mixes of external heating

Performance in H-mode DT plasmas in ITER with various choices of heating systems are predicted and compared. Combinations of external heating by negative ion neutral beam injection (NNBI), ion cyclotron range of frequencies and electron cyclotron heating are assumed. Scans with a range of physics assumptions about boundary temperatures in the edge pedestal, alpha ash transport and toroidal momentum transport are used to indicate effects of uncertainties. Time-dependent integrated modelling with the PTRANSP code is used to predict profiles of heating, beam torque and plasma profiles. The GLF23 model is used to predict temperature profiles. Either GLF23 or the assumption of a constant ratio for χϕ/χi is used to predict toroidal rotation profiles driven by the beam torques. Large differences for the core temperatures are predicted with different mixes of the external heating during the density and current ramp-up phase, but the profiles are similar during the flat-top phase. With χϕ/χi = 0.5, the predicted toroidal rotation is relatively slow and the flow shear implied by the pressure, toroidal rotation and neoclassical poloidal rotation are not sufficient to cause significant changes in the energy transport or steady state temperature profiles. The GLF23-predicted toroidal rotation is faster by a factor of six, and significant flow shear effects are predicted. Heating mixes with more NNBI power are predicted to have up to 20% higher fusion power during steady state phases. This advantage is decisive in some cases where the physics assumptions are close to marginal or critical values. L-mode plasmas are predicted having QDT ≃ 2–4.

Study of the fast ion confinement and current profile control on MAST

One of the main operational aims of the MAST experiment (Darke et al 1994 Proc. 18th Symp. on Fusion Technology (Karlsruhe, Germany, 1994) p 799) and the proposed MAST upgrade is to investigate possible mechanisms to control the q-profile and drive off-axis current. Experiments were carried out to determine the extent to which the q-profile may be modified using two different approaches, transient and steady-state. Transient effects during the plasma current ramp-up phase were investigated with the aim of developing a start-up regime that can later be used as a target plasma for non-inductive current drive or to access advanced modes of operation such as the hybrid or improved H-mode. The most significant effect in this case was observed when early neutral beam injection (NBI) was applied to the fast current ramp-rate start-up plasmas causing reversed magnetic shear and the plasma current to ‘pile-up’ off-axis.In steady-state experiments, in which off-axis NBI was studied, results indicate that broadening the fast ion deposition profile by off-axis neutral beam (NB) injection helps to avoid harmful plasma instabilities and significantly extends the operational window of MAST. Long pulse (>0.65 s) H-mode plasmas were achieved with plasma duration limited only by present machine and NBI engineering limits. In order to match the experimentally observed neutron rate and stored energy a low level of anomalous fast ion diffuse ion (Db ∼ 0.5 m2 s−1) is required. The introduction of the fast ion diffusion broadens the neutral beam current drive profile and degrades the relative contribution of NB driven current from ∼40% to ∼30%. To obtain direct measurements of the current profile, a multi-chord motional stark effect diagnostic has been commissioned on MAST and is currently delivering first results in order to confirm the off-axis location of the NB driven current.

Design and simulation of extremum-seeking open-loop optimal control of current profile in the DIII-D tokamak

In a magnetic fusion reactor, the achievement of a certain type of plasma current profiles, which are compatible with magnetohydrodynamic stability at high plasma pressure, is key to enable high fusion gain and non-inductive sustainment of the plasma current for steady-state operation. The approach taken toward establishing such plasma current profiles at the DIII-D tokamak is to create the desired profile during the plasma current ramp-up and early flattop phases. The evolution in time of the current profile is related to the evolution of the poloidal flux, which is modeled in normalized cylindrical coordinates using a partial differential equation usually referred to as the magnetic diffusion equation. The control problem is formulated as an open-loop, finite-time, optimal control problem for a nonlinear distributed parameter system, and is approached using extremum seeking. Simulation results, which demonstrate the accuracy of the considered model and the efficiency of the proposed controller, are presented.