Poloidal Beta Research Articles

Plasma shape control for the JET tokamak: an optimal output regulation approach

The eXtreme Shape Controller, designed and implemented on the JET tokamak, was described. The controller regulates the plasma shape as specified in terms of plasma-wall distances and maintains this plasma shape in the presence of significant variations of critical plasma parameters, namely the poloidal beta, the internal inductance, and the plasma current. The design procedure is based on the SVD of the plant output matrix. This procedure accounts for specifications on the accuracy of the controller variables as well as the maximum allowable control effort. The new controller has been fully commissioned on the JET tokamak, is in regular operation, and is delivering the expected performance.

The stability of the ideal internal kink mode in realistic tokamak geometry

The ideal stability of the internal kink mode is analysed for realistic tokamak geometry. Accurate numerical results demonstrate convergence with Bussac's toroidal solution (Bussac M N, Pellat R, Edery D and Soulé J L 1975 Phys. Rev. Lett. 35 1638) for inverse aspect ratio ϵ1 ∼ 0.01 at the q = 1 rational surface. For realistic inverse aspect ratio (e.g. ϵ1 ∼ 0.1) the growth rate is found to scale linearly with the poloidal beta and to be smaller than the analytical prediction of the toroidal growth rate. The effect of the shaping of the plasma cross-section is also analysed. Analytical results are found to disagree with numerical results at realistic inverse aspect ratio primarily because of the toroidal nature of the Mercier mode shaping terms. Furthermore, in addition to the Mercier shaping terms, there are quasicylindrical contributions to the kink mode which are quadratic and stabilizing in both triangularity and ellipticity. To verify this empirically and to further demonstrate the importance of the ideal internal kink stability boundary, discharges in the tokamak à configuration variable are shown to display longer sawteeth for both very positive and negative triangularity. Finally, a parameter scan in the triangularity, elongation, aspect ratio and poloidal beta has been undertaken using the code KINX. Versatile predictions of the ideal internal kink stability in future tokamaks should be assisted by the functional fitting presented here of the parameter scans.

Design, implementation and test of the XSC extreme shape controller in JET

A new model-based plasma current and shape controller has been set up and tested on the JET Tokamak with the existing active circuits and control. The installation has been carried out without causing any interference to the plasma operation and without requiring a long commissioning time. Eventually, the new controller was used on really extremely shaped internal transport barrier experiments at high poloidal beta and in the presence of quite large variations of the plasma current density profile (variation range Δβpol up to 1.5 and Δli up to 0.5). The extreme shape controller (XSC) controller architecture and philosophy also offer new interesting opportunities, e.g., the separatrix sweeping on the divertor plates without significantly affecting the overall plasma shape, and the possibility of improving the overall tokamak performance via combined control of plasma shape, current and profile. The adopted methodology constitutes also an important test bed for feedback control strategies of ITER relevance.

Capabilities of the ITER Upper Launcher for ELMy-H mode plasmas at low magnetic fields

The capabilities of the ITER ECRH upper port launcher to drive a well localized current (co-ECCD) either at the q = 1.5 or at the q = 2 surface by injecting EC waves as first harmonic O-mode at the nominal frequency f = 170 GHz have been already explored for a number of ITER scenarios relevant for neoclassical tearing modes (NTM) stabilization. The analysis, made by including the hybrid scenario 3 and a low q scenario (scenario 5) as well as equilibrium and poloidal beta variations in addition to the Q = 10 reference scenario 2, explored a wide range of relevant surfaces with different kinetic data for each scenario. "Optimal" toroidal and poloidal injection angles for application of co-ECCD on the relevant flux surfaces have been identified for the two rows of mirrors, and performance evaluations by taking into account several beam parameters have been carried out. However, the analysis so far has been done only for one specific value of the vacuum toroidal magnetic field (B0 ∼5.3 T at R0 = 6.2 m). In this work the capabilities to drive efficient and well localized co-current for a range of relevant surfaces in ELMy-H mode ITER plasmas at lower magnetic fields are explored by an updated version of the Milano beam tracing code. On the beam trajectories fully relativistic EC absorption and CD are calculated at both first and second harmonic. The changes of the "optimal" launch angles as a consequence of the shift of the resonance to lower values of major radius are shown. The range of magnetic fields for which power deposition and current drive at relevant surfaces becomes impossible for EC waves injected from upper launcher as first harmonic O-mode is pointed out. Further, the effectiveness of the upper launcher for stabilization of (3,2) and (2,1) NTM is investigated in the range of magnetic fields where EC waves at f = 170 GHz should be injected as second harmonic X-mode.

Advanced tokamak research in DIII-D

Advanced tokamak (AT) research in DIII-D seeks to provide a scientific basis for steady-state high performance operation in future devices. These regimes require high toroidal beta to maximize fusion output and high poloidal beta to maximize the self-driven bootstrap current. Achieving these conditions requires integrated, simultaneous control of the current and pressure profiles and active magnetohydrodynamic stability control. The building blocks for AT operation are in hand. Resistive wall mode stabilization by plasma rotation and active feedback with non-axisymmetric coils allows routine operation above the no-wall beta limit. Neoclassical tearing modes are stabilized by active feedback control of localized electron cyclotron current drive (ECCD). Plasma shaping and profile control provide further improvements. Under these conditions, bootstrap supplies most of the current. Steady-state operation requires replacing the remaining inductively driven current, mostly located near the half radius, with non-inductive external sources. In DIII-D this current is provided by ECCD, and nearly stationary AT discharges have been sustained with little remaining inductive current. Fast wave current drive is being developed to control the central magnetic shear. Density control, with divertor cryopumps, of AT discharges with ELMing H-mode edges facilitates high current drive efficiency at reactor relevant collisionalities. An advanced plasma control system allows integrated control of these elements. Close coupling between modelling and experiment is key to understanding the separate elements, their complex nonlinear interactions, and their integration into self-consistent high performance scenarios. This approach has resulted in fully non-inductively driven plasmas with βN ≤ 3.5 and βT ≤ 3.6% sustained for up to 1 s, which is approximately equal to one current relaxation time. Progress in this area, and its implications for next-step devices, will be illustrated by results of these and other recent experiment and simulation efforts.

Design and Stress Analysis of Support Structure of Toroidal Field Coil for the JT-60SC

The modification of JT-60 to a full superconducting tokamak (JT-60SC) is being planned. The support structures of the TF coils are designed to withstand the large electromagnetic force on the basis of the stress analyses. Shear panels are inserted between the neighboring TF coils against the overturning force and settled after the installation of the peripheral components like NBI ports. The maximum displacement and the Tresca stress of the TF coil have been evaluated in the case of the plasma disruption at the end of plasma current flat-top. In order to analyze the profiles of stress and displacement in detail, the bolts tightening the shear panel are considered in the FEM model. The maximum displacement of a TF coil is evaluated to be about 8.8 mm that is within the design requirement to keep space between the coils and the peripheral ports. The peak Tresca stress of 611 MPa appears at a bolt on the shear panel at the lower midplane. This value is within the allowable stress of SS316LN at 4 K, 667 MPa. In addition, the analyses for the various plasma operations, especially for the high poloidal beta (/spl sim/2) plasma operation, were carried out and the validity of the support structure was confirmed.

Soft x-ray tangential imaging of the NSTX core plasma by means of an MPGD pinhole camera

A fast x-ray system based on a micro pattern gas detector has been used for the first time, to investigate emission from the plasma core of the National Spherical Tokamak eXperiment (NSTX), at the Princeton Plasma Physics Laboratory. The results presented in this work demonstrate the capability of such a device to measure with a time resolution of the order of 1 ms, the curvature and the elongation of the x-ray iso-emissivity contours, under various plasma conditions. Also, comparisons with the magnetic surface structure calculated by the EFIT code show good agreement between reconstructed flux surface and the soft x-ray (SXR) emissions for poloidal beta values up to 0.6. For greater values of beta, x-ray iso-emissivity contours become circular, while magnetic flux surface reconstructions yield elongation 1.5 < k < 2.2.The x-ray images have been acquired with a (statistical) signal to noise ratio (SNR) per pixel of about 30. Thanks to the direct and efficient x-ray conversion and its operation in a photon counting mode, this new diagnostic tool allows the routine investigation of the plasma core with a sampling rate of 1 kHz and extremely high SNR under all experimental conditions in NSTX.

High performance advanced tokamak regimes in DIII-D for next-step experiments

Advanced Tokamak (AT) research in DIII-D [K. H. Burrell for the DIII-D Team, in Proceedings of the 19th Fusion Energy Conference, Lyon, France, 2002 (International Atomic Energy Agency, Vienna, 2002) published on CD-ROM] seeks to provide a scientific basis for steady-state high performance operation in future devices. These regimes require high toroidal beta to maximize fusion output and poloidal beta to maximize the self-driven bootstrap current. Achieving these conditions requires integrated, simultaneous control of the current and pressure profiles, and active magnetohydrodynamic stability control. The building blocks for AT operation are in hand. Resistive wall mode stabilization via plasma rotation and active feedback with nonaxisymmetric coils allows routine operation above the no-wall beta limit. Neoclassical tearing modes are stabilized by active feedback control of localized electron cyclotron current drive (ECCD). Plasma shaping and profile control provide further improvements. Under these conditions, bootstrap supplies most of the current. Steady-state operation requires replacing the remaining Ohmic current, mostly located near the half radius, with noninductive external sources. In DIII-D this current is provided by ECCD, and nearly stationary AT discharges have been sustained with little remaining Ohmic current. Fast wave current drive is being developed to control the central magnetic shear. Density control, with divertor cryopumps, of AT discharges with edge localized moding H-mode edges facilitates high current drive efficiency at reactor relevant collisionalities. A sophisticated plasma control system allows integrated control of these elements. Close coupling between modeling and experiment is key to understanding the separate elements, their complex nonlinear interactions, and their integration into self-consistent high performance scenarios. Progress on this development, and its implications for next-step devices, will be illustrated by results of recent experiment and simulation efforts.

Aspect ratio dependence of the ideal internal kink mode stability in a toroidal plasma with circular cross section

The theory by Bussac et al. [Phys. Rev. Lett. 35, 1638 (1975)] on the stability of the ideal, internal kink mode in a toroidal plasma with circular cross section is extended to finite values of the inverse aspect ratio εa. The aspect ratio dependence comes from the term following the Bussac term in a large aspect ratio expansion of the potential energy δW of the mode. Although formally of higher order in the inverse aspect ratio, this term is of the same order of magnitude as the Bussac term when the safety factor q is close to (but below) unity at the plasma center and εa is finite. The new term is always stabilizing, but affects δW only marginally when the poloidal beta value βp is small and/or εa is small. For values of εa relevant for most tokamaks and βp larger than 0.3–0.5, however, the new term strongly modifies δW and leads to a second stability regime of the ideal, internal kink mode, in agreement with earlier numerical calculations.

Development of plasma stored energy feedback control and its application to high performance discharges on JT-60U

The real-time feedback control of the plasma stored energy has been developed for control of the plasma MHD stability in the JT-60U tokamak. The plasma stored energy can be detected with high accuracy in real-time by a function parameterization method for various plasmas available in JT-60U, such as Ohmic plasmas, the L-mode, the H-mode, the high poloidal beta mode and the reversed shear mode over a wide range of the plasma parameters. By manipulating the neutral beam injection power, the plasma stored energy has been successfully controlled along the preprogrammed reference waveform. Especially in the reversed shear mode, this feedback control scheme has improved the reproducibility of the formation of the internal transport barrier, and MHD activities could be suppressed keeping the normalized beta in a stable region. A DT equivalent fusion amplification gain of 0.5 was sustained for 0.8 s in a reversed shear plasma by employing this feedback control scheme.

Real-time calculation of plasma parameters for feedback control in JET

Plasma parameters, like the internal inductance, li, and the diamagnetic poloidal beta, βDIA, are of particular relevance for a reliable real-time control system of next step tokamaks. These and other quantities have been obtained at Joint European Torus (JET) with a method that uses the Shafranov integrals S1, S2 and S3. Indeed they allow the direct calculation of the Shafranov parameter Λ = βMHD + li/2 and of βDIA. Moreover, in discharges with a sufficiently high elongation (k > 1.3 typically), the internal inductance can be separated from the MHD poloidal beta, βMHD, and calculated independently, through the Shafranov integrals, with a precision that is more than satisfactory for real-time applications. It is worth mentioning that, since S1, S2 and S3 are integrals defined on the plasma boundary, a specific algorithm, depending on the fast code XLOC, has been expressively developed to determine this quantity.The method to determine the plasma parameters has been verified off-line, benchmarking its outputs with the estimates of the most sophisticated equilibrium codes available. The results of this systematic comparison have been very encouraging both in the limiter and x-point phases of the discharges and on all the investigated plasma configurations. The computational time, necessary to determine the plasma boundary and about 50 signals is only about 1.5 ms on a PC equipped with a 400 MHz Pentium II, well below the 10 ms constraint of JET real-time applications. The code has therefore been implemented on-line, and its outputs have already been exploited to achieve the feedback control of some plasma parameters.

Formation of advanced tokamak plasmas without the use of an ohmic-heating solenoid.

A new operational scenario of advanced tokamak formation was demonstrated in the JT-60U tokamak. This was accomplished by electron cyclotron and lower hybrid waves, neutral beam injection, and the loop voltage supplied by the vertical field and shaping coils. The Ohmic heating (OH) solenoid was not used but a small inboard coil (part of the shaping coil), providing less than 20% of total poloidal flux, was used. The plasma thus obtained had both internal and edge transport barriers, with an energy confinement time of 1.6 times H-mode scaling, a poloidal beta of 3.6, and a normalized beta of 1.6, and a large bootstrap current fraction (>90%). This result opens up a possibility to reduce, and eventually eliminate, the OH solenoid from a tokamak reactor, which will greatly improve its economic competitiveness.

Characteristics of global confinement properties in TPE-series reversed-field pinch devices

A confinement database of the reversed-field pinch (RFP) devices of the toroidal pinch experiment (TPE) series has been established. The TPE database contains global confinement properties under various experimental conditions for four different devices and seven different cases, which cover two decades of experiments. Characteristics of the TPE database have been extracted under consistent experimental conditions of conventional RFP discharges, and scaling laws of the poloidal beta, βp and energy confinement time, τ E, are given against independent parameters that include the size of the plasma and the pinch parameter Θ. Scaling laws of and are obtained for a set of scans, where a is the plasma minor radius, Ip the plasma current and N the column density. The scaling of τ E on a, Ip, and I/N is similar to that dominated by the transport under tearing instability. Another scaling shows that τ E is inversely proportional to the Joule input power. The scaling for the apparent effective charge shows a positive correlation both with Ip and I/N.

Comparison of confinement in resistive-shell reversed-field pinch devices with two different magnetic shell penetration times

A loop voltage is required to sustain the reversed-field pinch (RFP) equilibrium. The configuration is characterized by redistribution of magnetic helicity but with the condition that the total helicity is maintained constant. The magnetic field shell penetration time, τs, has a critical role in the stability and performance of the RFP. Confinement in the EXTRAP device has been studied with two values of τs, first (EXTRAP-T2) with τs of the order of the typical relaxation cycle timescale and then (EXTRAP-T2R) with τs much longer than the relaxation cycle timescale, but still much shorter than the pulse length. Plasma parameters show significant improvements in confinement in EXTRAP-T2R. The typical loop voltage required to sustain comparable electron poloidal beta values is a factor of 3 lower in the EXTRAP-T2R device. The improvement is attributed to reduced magnetic turbulence.

Current profile modification experiments in EXTRAP T2R

Pulsed poloidal current drive (PPCD) experiments have been conducted in the resistive shell EXTRAP T2R reversed-field pinch experiment. During the current profile modification phase, the fluctuation level of the m = 1 internally resonant tearing modes decreases, and the velocity of these modes increases. The m = 0 modes are not affected during PPCD, although termination occurs with a burst in the m = 0 amplitude. The PPCD phase is characterized by an increase in the central electron temperature (up to 380 eV) and in the soft x-ray signal. Spectroscopic observations confirm an increase in the central electron temperature. During PPCD, the plasma poloidal beta increases to 14%, and the estimated energy confinement time doubles, reaching 380 µs. The reduction in the fluctuation level and the corresponding increase in the energy confinement time are qualitatively consistent with a reduction in parallel transport along stochastic magnetic field lines.

Turbulence trigger for neoclassical tearing modes in tokamaks

A stochastic trigger by micro-turbulence for neoclassical tearing modes (NTMs) is studied. NTMs induce topological change of magnetic structure and have a subcritical nature. It is found that the NTM can be excited regardless of the presence of seed islands. The transition rate of the NTM, its probability density function and its statistically averaged amplitude are obtained. The boundary in the phase diagram is determined as the statistical long time average of the transition conditions. The NTM can be excited by crossing this boundary even in the absence of other global instabilities. The boundary is expressed in terms of the poloidal beta value. Its dependence on the ratio between the ion banana width and radius of the rational surface, ρb/rs, is found to vary in the range ρb/rs–(ρb/rs)2, depending on the linear stability of the tearing mode.

Real-time determination of confinement parameters in JET

The main confinement parameters, like the internal inductance l i and the diamagnetic poloidal beta β DIA , are of particular relevance for a reliable real-time control system of next step tokamaks. These quantities have been obtained at Joint European Torus (JET), with a precision more than satisfactory for real-time applications, through a method, known as BETALI, that uses the Shafranov integrals S 1, S 2 and S 3. Since S 1, S 2 and S 3 are defined on the plasma boundary, a technique, that exploits the real-time boundary code XLOC, has been expressively developed to determine the last closed flux surface (LCFS). BETALI has been verified on several experimental plasma configurations, giving very encouraging results both in the limiter and x-point phase of the discharges. The compatibility with the time restrictions has also been tested successfully. This application has, therefore, been implemented and it has already been used during last JET campaigns.

Upgrade of the present JET shape and vertical stability controller

The development of linear model of the present JET (Joint European Torus) electromagnetic system has allowed the design of an optimized Plasma Shape Controller. Quite extreme plasma boundaries (elongation k=1.9 and triangularity 〈 δ〉=0.6) are shown to be controllable also in the presence of large variations of the values of poloidal beta (0.1< β p<0.6) and/or internal magnetic inductance (0.8< l i<1.4). The developed model gives also an excellent simulation of the growth rate of the experimental vertical disruptions.

On the poloidal beta evolution of fixed-q heating in tokamaks

For typical tokamak safety factor, q, profiles and aspect ratio, A, fixed-q heating leads to a limit for equilibrium code convergence near a poloidal beta value of 1+A. Also presented is a simple tanh functional fit that saturates just above the 1+A limit. This poloidal beta limit does not depend on the q-profile, but the total beta achieved at this critical poloidal beta does depend strongly on q. In this paper we confirm very early computations of the flux-conserving tokamak that routinely achieved a poloidal beta &amp;gt;A.

A class of high εβp equilibria in strongly shaped finite aspect ratio tokamak plasmas

A class of very high poloidal beta (βp) equilibria is exhibited in which εβp (ε is the inverse aspect ratio) exceeds analytic equilibrium limits previously anticipated from simplified large aspect ratio models, as well as previous experimental equilibrium limits. The extension in these limits is shown to be due to a combination of finite aspect ratio effects and strong cross section shaping. In a conventional aspect ratio configuration, equilibria with εβp=3 exist, which is 50% higher than both the previously observed record and the analytically predicted limit. For very low aspect ratio with ε−1=1.4, typical of spherical tori, values of εβp=5 are possible.