Real-time Equilibrium Research Articles

Prospects for stabilization of neoclassical tearing modes by electron cyclotron current drive in ITER

The system planned for electron cyclotron current drive (ECCD) in ITER can mitigate the deleterious effects of neoclassical tearing modes (NTMs) provided that either adequate alignment of the ECCD to the rational surface is maintained or too large a misalignment is corrected on a time scale shorter than the deleterious plasma response to ‘large’ islands. Resistive neoclassical tearing modes will be the principal limit on stability and performance in the ITER standard scenario as the drag from rotating island induced eddy current in the resistive wall (particularly from the m/n = 2/1 mode) can slow the plasma rotation, produce locking to the wall and cause loss of high-confinement H-mode and disruption. Continuous wave (cw) ECCD at the island rational surface is successful in stabilization and/or prevention of NTMs in ASDEX Upgrade, DIII-D and JT-60U. Modulating the ECCD so that it is absorbed only on the rotating island O-point is proving successful in recovering effectiveness in ASDEX Upgrade when the ECCD is configured for wider deposition as expected in ITER. The models for the effect of misalignment on ECCD effectiveness are applied to ITER. Tolerances for misalignment are presented to establish criteria for both the alignment (by moving mirrors in ITER) in the presence of an island, and for the accuracy of real-time ITER MHD equilibrium reconstruction in the absence of an island, i.e. alignment to the mode or to the rational surface in the absence of the mode. The narrower ECCD with front steering makes precise alignment more necessary for the most effective stabilization even though the ECCD is still relatively broad, with current density deposition (full width half maximum) almost twice the marginal island width. This places strict requirements on ECCD alignment with the expected ECCD effectiveness dropping to zero for misalignments as small as 1.7 cm. The system response time for growing islands and slowing rotation without and with ECCD (at different misalignments) are provided for the plasma system controller to be developed. An alignment resolution error of no more than 1 cm and a realignment rate of at least 1 cm s−1 are required for a moderate cw ECCD power so as to avoid locking. Finally, a case study in ITER of prompt dynamic alignment and suppression is presented.

Real-time plasma equilibrium reconstruction in a Tokamak

The problem of equilibrium of a plasma in a Tokamak is a free boundary problem described by the Grad-Shafranov equation in axisymmetric configurations. The right hand side of this equation is a non linear source, which represents the toroidal component of the plasma current density. This paper deals with the real time identification of this non linear source from experimental measurements. The proposed method is based on a fixed point algorithm, a finite element resolution, a reduced basis method and a least-square optimization formulation.

Progress towards steady state at low aspect ratio on the National Spherical Torus Experiment (NSTX)

Modifications to the plasma control capabilities and poloidal field coils of the National Spherical Torus Experiment (NSTX) have enabled a significant enhancement in shaping capability which has led to the transient achievement of a record shape factor (S ≡ q95 (Ip/a Bt)) of ∼41 (MA m−1 T−1) simultaneous with a record plasma elongation of κ ≡ b/a ∼ 3. This result was obtained using isoflux control and real-time equilibrium reconstruction. Achieving high shape factor together with tolerable divertor loading is an important result for future ST burning plasma experiments as exemplified by studies for future ST reactor concepts, as well as neutron producing devices, which rely on achieving high shape factors in order to achieve steady state operation while maintaining MHD stability. Statistical evidence is presented which demonstrates the expected correlation between increased shaping and improved plasma performance. Plasmas with high shape factor have been sustained for pulse lengths which correspond to τpulse = 1.6s ∼ 50 τE ∼ 5 τCR, where τCR is the current relaxation time and τE is the energy confinement time. Plasmas with higher βt ∼ 20% have been sustained for τpulse = 1.2s ∼ 25 τE ∼ 3 τCR with non-inductive current fractions fNI ∼ 50%, with ∼40% pressure driven current and ∼10% neutral beam driven current. An interesting feature of these discharges is the observation that the central value of the safety factor q(0) remains elevated and constant for several current diffusion times without sawteeth, similar to the ‘hybrid mode’. Calculations of the profiles of inductive and non-inductive current are compared with measurements of the total current profile and are shown to be in quantitative agreement. Results are shown from experiments which investigate the applicability of high harmonic fast waves (HHFWs) and electron Bernstein waves (EBWs) as current drive and heating sources, and the possibility of LHCD for future ST devices is raised. A calculated scenario which provides 100% non-inductive current drive is described. NSTX operates with peak divertor heat fluxes which are in the same range as those expected for the ITER device, i.e. with . High triangularity, high elongation plasmas on NSTX have been demonstrated to have reduced peak heat flux to the divertor plates to <3 MW m−2.

Stabilization and prevention of the 2/1 neoclassical tearing mode for improved performance in DIII-D

The m = 2/n = 1 neoclassical tearing mode (NTM) has been observed to strongly degrade confinement and frequently lead to a disruption in high β discharges in DIII-D if allowed to grow to a large size. Stabilization of grown NTMs by the application of a highly localized electron cyclotron current drive (ECCD) at the island location has led to operation at an increased plasma pressure, up to the no-wall kink limit. After the NTM is stabilized by the ECCD, the correct location for the current drive is maintained using information from real-time equilibrium reconstructions which include measurements from the motional Stark effect diagnostic. This same process is used alternatively to prevent the mode from ever growing, leading to performance at the pressure limit in high performance hybrid discharges with β above 4%. Modelling using the modified Rutherford equation shows that the required power is in close agreement with the experimental threshold for the prevention of the 2/1 NTM.

Real-Time Time-Varying Equilibrium Interest Rates: Evidence on the Czech Republic

This paper examines (real-time) equilibrium interest rates in the Czech Republic in 2001:1-2005:12 estimating various specifications of simple Taylor-type monetary policy rules. First, we estimate it using GMM. Second, we apply structural time-varying coefficient model with endogenous regressors to evaluate fluctuations of equilibrium interest rate over time. The results suggest that there is substantial interest rate smoothing and central bank primarily responds to inflation (forecast) developments. The estimated parameters seem to sustain the equilibrium determinacy. We find that the equilibrium interest rates gradually decreased over sample period to the levels comparable to those of in the euro area reflecting capital accumulation, smaller risk premium and successful disinflation in the Czech economy.

Status of the control system on the National Spherical Torus Experiment (NSTX)

In 2003, the National Spherical Torus Experiment (NSTX) plasma control system was used for plasma shape control using real-time equilibrium reconstruction (using the rtEFIT code). rtEFIT is now in routine use for plasma boundary control. More recently, the system has been upgraded to support feedback control of the resistive wall mode (RWM). This paper describes the hardware and software improvements that were made in support of these physics requirements. The control computer is an eight processor embedded system. The real-time data acquisition system now acquires 352 channels of data at 5 kHz for each NSTX plasma discharge. The latency for the data acquisition, which uses the Front Panel Data Port (FPDP) protocol, is measured to be ∼8 μs. A Stand-Alone Digitizer (SAD), designed at PPPL, along with an FPDP Input Multiplexing Module (FIMM) allows for simple modular upgrades. An interface module was built to interface between the FPDP output of the NSTX control system and the legacy Power Conversion Link (PCLink) used for communicating with the PPPL power supplies (first used for TFTR). Additionally a module has been built for communicating with the switching power amplifiers (SPA) recently installed on NSTX. In addition to the hardware developments, the control software on the NSTX control system has been upgraded. The device driver software for the hardware described above will be discussed, as well as the new control algorithms that have been developed to control the switching power supplies for RWM control. A reliable mode detection algorithm for RWM feedback is currently under development.

Neoclassical tearing modes and their control

A principal pressure limit in tokamaks is set by the onset of neoclassical tearing modes (NTMs), which are destabilized and maintained by helical perturbations to the pressure-gradient driven “bootstrap” current. The resulting magnetic islands break up the magnetic surfaces that confine the plasma. The NTM is linearly stable but nonlinearly unstable, and generally requires a “seed” to destabilize a metastable state. In the past decade, NTM physics has been studied and its effects identified as performance degrading in many tokamaks. The validation of NTM physics, suppressing the NTMs, and/or avoiding them altogether are areas of active study and considerable progress. Recent joint experiments give new insight into the underlying physics, seeding, and threshold scaling of NTMs. The physics scales toward increased NTM susceptibility in ITER, underlying the importance of both further study and development of control strategies. These strategies include regulation of “sawteeth” to reduce seeding, using static “bumpy” magnetic fields to interfere with the perturbed bootstrap current, and/or applying precisely located microwave power current drive at an island to stabilize (or avoid destabilization of) the NTM. Sustained stable operation without the highly deleterious m=2, n=1 island has been achieved at a pressure consistent with the no-wall n=1 ideal kink limit, by using electron cyclotron current drive at the q=2 rational surface, which is found by real-time accurate equilibrium reconstruction. This improved understanding of NTM physics and stabilization strategies will allow design of NTM control methods for future burning-plasma experiments like ITER.

Effect of plasma shaping on performance in the National Spherical Torus Experiment

The National Spherical Torus Experiment (NSTX) has explored the effects of shaping on plasma performance as determined by many diverse topics including the stability of global magnetohydrodynamic (MHD) modes (e.g., ideal external kinks and resistive wall modes), edge localized modes (ELMs), bootstrap current drive, divertor flux expansion, and heat transport. Improved shaping capability has been crucial to achieving βt∼40%. Precise plasma shape control has been achieved on NSTX using real-time equilibrium reconstruction. NSTX has simultaneously achieved elongation κ∼2.8 and triangularity δ∼0.8. Ideal MHD theory predicts increased stability at high values of shaping factor S≡q95Ip∕(aBt), which has been observed at large values of the S∼37[MA∕(m∙T)] on NSTX. The behavior of ELMs is observed to depend on plasma shape. A description of the ELM regimes attained as shape is varied will be presented. Increased shaping is predicted to increase the bootstrap fraction at fixed Ip. The achievement of strong shaping has enabled operation with 1s pulses with Ip=1MA, and for 1.6s for Ip=700kA. Analysis of the noninductive current fraction as well as empirical analysis of the achievable plasma pulse length as elongation is varied will be presented. Data are presented showing a reduction in peak divertor heat load due to increasing in flux expansion.

Plasma shape control on the National Spherical Torus Experiment (NSTX) using real-time equilibrium reconstruction

Plasma shape control using real-time equilibrium reconstruction has been implemented on the National Spherical Torus Experiment (NSTX). The rtEFIT code originally developed for use on DIII-D was adapted for use on NSTX. The real-time equilibria provide calculations of the flux at points on the plasma boundary, which are used as input to a shape control algorithm known as isoflux control. The flux at the desired boundary location is compared with a reference flux value, and this flux error is used as the basic feedback quantity for the poloidal field coils on NSTX. The hardware that comprises the control system is described, as well as the software infrastructure. Examples of precise boundary control are also presented.

Real-time motional Stark effect in jet

The increasing importance of real-time measurements and control systems in JET experiments, regarding e.g. Internal Transport Barrier (ITB) and q-profile control, has motivated the development of a real-time motional Stark effect (MSE) system. The MSE diagnostic allows the measurement of local magnetic fields in different locations along the neutral beam path providing, therefore, local measurement of the current and q-profiles. Recently in JET, an upgrade of the MSE diagnostic has been implemented, incorporating a totally new system which allows the use of this diagnostic as a real-time control tool as well as an extended data source for off-line analysis. This paper will briefly describe the technical features of the real-time diagnostic with main focus on the system architecture, which consists of a VME crate hosting three PowerPC processor boards and a fast ADC, all connected via Front Panel Data Port (FPDP). The DSP algorithm implements a lockin-amplifier required to demodulate the JET MSE signals. Some applications for the system will be covered such as: feeding the real-time equilibrium reconstruction code (EQUINOX) and allowing the full coverage analysis of the Neutral Beam time window. A brief comparison between the real-time MSE analysis and the off-line analysis will also be presented.

Poloidal Field Control for the HT-7U Superconducting Tokamak

Controlling the poloidal field (PF) in the HT-7U superconducting tokamak is critical to the realization of the mission of advanced tokamak research. Plasma start-up, plasma position, shape, current control and plasma shape reconstruction have been performed as a part of its design process. The PF coils have been designed to produce a wide range of plasmas. Plasma start-up can be achieved for multiple conditions. Fast controlling coils for plasma position inside the vacuum vessel are used for controlling the plasma vertical position on a short timescale. The PF coils control the plasma current and shape on a slower timescale. VXI (VME bus extensions for Instrumentation) Bus system and DSP (Digital Signal Processor is a basic unit of the feedback control system), the response time of which is about (2-4) ms. The basic unit of this system, the shape-controlling algorithms of a few critical points on plasma boundary and real-time equilibrium fitting (RTEFIT) will be described in this paper.

Effective theory forω≪k≪gTcolor dynamics in hot non-Abelian plasmas

A proper sequence of effective theories, corresponding to larger and larger distance scales, is crucial for analyzing real-time equilibrium physics in hot non-Abelian plasmas. For the study of color dynamics (by which I mean physics involving long wavelength gauge fluctuations), an important stepping stone in the sequence of effective theories is to have a good effective theory for dynamics with wave number k well below the Debye screening mass. I review how such dynamics is associated with inverse time scales $\ensuremath{\omega}\ensuremath{\ll}k.$ I then give a compact way to package, in the $\ensuremath{\omega}\ensuremath{\ll}k$ limit, B\"odeker's description of $k\ensuremath{\ll}m$ physics, which was in terms of Vlasov equations with collision terms. Finally, I show how the resulting effective theory can be reformulated as a path integral.