Ideal Wall Limit Research Articles

Simultaneous stabilization and control of the n = 1 and n = 2 resistive wall mode

DIII-D experiments demonstrate simultaneous stability measurements and control of resistive wall modes (RWMs) with toroidal mode numbers n = 1 and n = 2. RWMs with n > 1 are sometimes observed on DIII-D following the successful feedback stabilization of the n = 1 mode, motivating the development of multi-n control. A new model-based multi-mode feedback algorithm based on the VALEN physics code has been implemented on the DIII-D tokamak using a real-time GPU installed directly into the DIII-D plasma control system. In addition to stabilizing RWMs, the feedback seeks to control the stable plasma error field response, enabling compensation of the typically unaddressed DIII-D n = 2 error field component. Experiments recently demonstrated this algorithm’s ability to simultaneously control n = 1 and n = 2 perturbed fields for the first time in a tokamak, using reactor relevant external coils. Control was maintained for hundreds of wall-times above the n = 1 no-wall pressure limit and approaching the n = 1 and n = 2 ideal-wall limits. Furthermore, a rotating non-zero target was set for the feedback, allowing stability to be assessed by monitoring the rotating plasma response (PR) while maintaining control. This novel technique can be viewed as a closed-loop extension of active MHD spectroscopy, which has been used to validate stability models through comparisons of the PR to applied, open-loop perturbations. The closed-loop response measurements are consistent with open-loop MHD spectroscopy data over a wide range of β N approaching the n = 1 ideal-wall limit. These PR measurements were then fit to produce both VALEN and single-mode stability models. These models allowed for important plasma stability information to be determined and have been shown to agree with experimentally observed RWM growth rates.

Bifurcation-driven vertical plasma displacement

This paper considers vertical plasma motion resulting from plasma current decay during the disruption event. The presented filament-based model describes the motion in the ideal wall limit as an adiabatically slow evolution of the plasma equilibrium. The equilibrium exhibits a pitchfork bifurcation when the decaying plasma current passes a critical value determined by the external magnetic field. This bifurcation affects the disruption-induced mechanical loads on the first wall.

Resistive wall modes and related sideways forces in tokamak

This paper presents the results of analytical and numerical calculations of the sideways force acting on the resistive wall due to eddy currents induced by n=1 kink instability. The inertia-less ideal MHD model for resistive wall mode is explicitly shown to be compatible with the condition of vanishing sideways force in the ideal wall limit. In the frame of standard high aspect ratio approximation, assuming that tokamak plasma is separated from the coaxial resistive wall by a vacuum layer, we calculate analytically the sideways force as a function of the growth rate γ taking into account the known relation between γ and the value of the safety factor q. It is noted that this dependence is determined by the single mode m/n=1/1 instability in the range of q-values q<1 giving the maximal force at γτw≥2, where τw is the resistive wall time. The numerically estimated magnitude of the sideways force for ITER relevant cases with q>1 is smaller because the sideways force is generated by toroidally coupled satellite harmonic m/n=1/1. The forces due to resistive wall mode with conformal and one-sided wall proximity to the plasma boundary are compared.

Stability of DIII-D high-performance, negative central shear discharges

Tokamak plasma experiments on the DIII-D device (Luxon et al 2005 Fusion Sci. Tech. 48 807) demonstrate high-performance, negative central shear (NCS) equilibria with enhanced stability when the minimum safety factor exceeds 2, qualitatively confirming theoretical predictions of favorable stability in the NCS regime. The discharges exhibit good confinement with an L-mode enhancement factor H89 = 2.5, and are ultimately limited by the ideal-wall external kink stability boundary as predicted by ideal MHD theory, as long as tearing mode (TM) locking events, resistive wall modes (RWMs), and internal kink modes are properly avoided or controlled. Although the discharges exhibit rotating TMs, locking events are avoided as long as a threshold minimum safety factor value is maintained. Fast timescale magnetic feedback control ameliorates RWM activity, expanding the stable operating space and allowing access to values approaching the ideal-wall limit. Quickly growing and rotating instabilities consistent with internal kink mode dynamics are encountered when the ideal-wall limit is reached. The RWM events largely occur between the no- and ideal-wall pressure limits predicted by ideal MHD. However, evaluating kinetic contributions to the RWM dispersion relation results in a prediction of passive stability in this regime due to high plasma rotation. In addition, the ideal MHD stability analysis predicts that the ideal-wall limit can be further increased to by broadening the current profile. This path toward improved stability has the potential advantage of being compatible with the bootstrap-dominated equilibria envisioned for advanced tokamak (AT) fusion reactors.

High internal inductance for steady-state operation in ITER and a reactor

Increased confinement and ideal stability limits at relatively high values of the internal inductance () have enabled an attractive scenario for steady-state tokamak operation to be demonstrated in DIII-D. Normalized plasma pressure in the range appropriate for a reactor has been achieved in high elongation and triangularity double-null divertor discharges with at , near the ideal kink stability limit calculated without the effect of a stabilizing vacuum vessel wall, with the ideal-wall limit still higher at . Confinement is above the H-mode level with . At , the current is overdriven, with bootstrap current fraction , noninductive current fraction and negative surface voltage. For ITER (which has a single-null divertor shape), operation at is a promising option with and the remaining current driven externally near the axis where the electron cyclotron current drive efficiency is high. This scenario has been tested in the ITER shape in DIII-D at , so far reaching and at with performance appropriate for the ITER Q=5 mission, . Modeling studies explored how increased current drive power for DIII-D could be applied to maintain a stationary, fully noninductive high discharge. Stable solutions in the double-null shape are found without the vacuum vessel wall at , and , and at with the vacuum vessel wall.

Tokamak halo currents

A halo current flows for part of its path through the plasma edge and for part through the chamber walls and can be as large as tenths of the plasma current. The primary interest in halo currents is the large force that they can exert on machine components. Two discordant constraints are central to the theory: (1) Halo currents must produce the magnetic field distribution required to maintain plasma force balance—a distribution that depends on the two angular coordinates of a torus. (2) Halo currents must flow along the magnetic field lines in the plasma, which implies a dependence on a linear combination of the two angular coordinates—only one angular coordinate is free. The physics basis of these two constraints is explained as is their application to the calculation of the properties of halo currents, such as their broad toroidal spectrum. Existing codes could be used to (1) provide detailed comparisons with experiments to validate that the critical elements of physics are adequately included, (2) allow more complete predictions for future machines such as ITER, and (3) design shunts and resistive elements to ensure halo currents follow paths that are the least damaging to the machine. The physics of halo currents implies that it may be possible to feedback stabilize resistive wall modes beyond the ideal-wall limit.

Control of magnetohydrodynamic modes in reversed field pinches with normal and tangential magnetic field sensing and two resistive walls

Numerical results are presented on control of magnetohydrodynamic (MHD) modes in reversed field pinches (RFPs) for a geometry with two resistive walls. We use measurements of the normal component of the magnetic field and introduce the use of both tangential components. In Richardson et al (2010 Phys. Plasmas 17 112511), RFP control studies were performed sensing the radial (normal) component of the magnetic field and a single tangential component just inside the wall, showing that it is possible to stabilize the MHD modes in an RFP for current up to the ideal plasma–ideal wall limit in that configuration. Here, we extend our modeling by including two resistive walls, in a configuration relevant to experiments such as RFX-mod, and measuring all three magnetic field components, i.e. including a second tangential component, as an exploratory effort. We present our study incrementally, starting with a single resistive wall, and conclude that with the first tangential sensor located inside the wall, the plasma can be stabilized up to the ideal plasma–ideal wall limit, as in Richardson et al. With the first tangential sensor outside the wall, stabilization is possible only up to the ideal wall–resistive plasma (tearing) limit. We then show that for experimentally relevant parameters the thin-wall approximation is indeed valid for the MHD modes of interest but invalid for the high-frequency magnetosonic mode (Richardson et al) driven by the (first) tangential component feedback. In fact, when a thick-wall formulation with realistic parameters is considered, the high-frequency magnetosonic mode is found to be destabilized only for a very high gain parameter, and we conclude that this mode can be ignored for an experimentally relevant analysis. Consequently, the plasma can be stabilized in a much larger region of feedback gain parameter space than found in Richardson et al. In the presence of two walls, with the first tangential component measured just outside the inner wall and with RFX-mod relevant time constants, we show that feedback control can stabilize the plasma at currents much larger than the ideal wall–resistive plasma limit. The current limit is still less, however, than the ideal plasma–ideal wall limit. Use of the second tangential component appears in all cases to lead to significantly different but not necessarily improved feedback stabilization. These results may lead to better understanding and improved stability properties in current-day RFP experiments through robust access to quasi-single-helicity states.

KSTAR equilibrium operating space and projected stabilization at high normalized beta

Along with an expanded evaluation of the equilibrium operating space of the Korea Superconducting Tokamak Advanced Research, KSTAR, experimental equilibria of the most recent plasma discharges were reconstructed using the EFIT code. In near-circular plasmas created in 2009, equilibria reached a stored energy of 54 kJ with a maximum plasma current of 0.34 MA. Highly shaped plasmas with near double-null configuration in 2010 achieved H-mode with clear edge localized mode (ELM) activity, and transiently reached a stored energy of up to 257 kJ, elongation of 1.96 and normalized beta of 1.3. The plasma current reached 0.7 MA. Projecting active and passive stabilization of global MHD instabilities for operation above the ideal no-wall beta limit using the designed control hardware was also considered. Kinetic modification of the ideal MHD n = 1 stability criterion was computed by the MISK code on KSTAR theoretical equilibria with a plasma current of 2 MA, internal inductance of 0.7 and normalized beta of 4.0 with simple density, temperature and rotation profiles. The steep edge pressure gradient of this equilibrium resulted in the need for significant plasma toroidal rotation to allow thermal particle kinetic resonances to stabilize the resistive wall mode (RWM). The impact of various materials and electrical connections of the passive stabilizing plates on RWM growth rates was analysed, and copper plates reduced the RWM passive growth rate by a factor of 15 compared with stainless steel plates at a normalized beta of 4.4. Computations of active RWM control using the VALEN code showed that the n = 1 mode can be stabilized at normalized beta near the ideal wall limit via control fields produced by the midplane in-vessel control coils (IVCCs) with as low as 0.83 kW control power using ideal control system assumptions. The ELM mitigation potential of the IVCC, examined by evaluating the vacuum island overlap created by resonant magnetic perturbations, was analysed using the TRIP3D code. Using a combination of all IVCCs with dominant n = 2 field and upper/lower coils in an even parity configuration, a Chirikov parameter near unity at normalized poloidal flux 0.83, an empirically determined condition for ELM mitigation in DIII-D, was generated in theoretical high-beta equilibria. Chirikov profile optimization was addressed in terms of coil parity and safety factor profile.

Equilibrium and global MHD stability study of KSTAR high beta plasmas under passive and active mode control

The Korea Superconducting Tokamak Advanced Research, KSTAR, is designed to operate a steady-state, high beta plasma while retaining global magnetohydrodynamic (MHD) stability to establish the scientific and technological basis of an economically attractive fusion reactor. An equilibrium model is established for stability analysis of KSTAR. Reconstructions were performed for the experimental start-up scenario and experimental first plasma operation using the EFIT code. The VALEN code was used to determine the vacuum vessel current distribution. Theoretical high beta equilibria spanning the expected operational range are computed for various profiles including generic L-mode and DIII-D experimental H-mode pressure profiles. Ideal MHD stability calculations of toroidal mode number of unity using the DCON code shows a factor of 2 improvement in the wall-stabilized plasma beta limit at moderate to low plasma internal inductance. The planned stabilization system in KSTAR comprises passive stabilizing plates and actively cooled in-vessel control coils (IVCCs) designed for non-axisymmetric field error correction and stabilization of slow timescale MHD modes including resistive wall modes (RWMs). VALEN analysis using standard proportional gain shows that active stabilization near the ideal wall limit can be reached with feedback using the midplane segment of the IVCC. The RMS power required for control using both white noise and noise taken from NSTX active stabilization experiments is computed for beta near the ideal wall limit. Advanced state-space control algorithms yield a factor of 2 power reduction assuming white noise while remaining robust with respect to variations in plasma beta.

Kinetic analysis of the resistive wall modes in the ITER advanced tokamak scenario

It is found that n = 1 resistive wall modes in the ITER advanced scenario can be fully stabilized by modestly low rotation with a rotation frequency (normalized to the Alfvén frequency at the magnetic axis) of about Ω = 0.0075. The existence of this stabilization scheme is proved with the AEGIS-K (Adaptive EiGenfunction Independent Solution-Kinetic) code, which provides a fully kinetic (non-hybrid) and self-consistent (non-perturbative) description of the system. Wave-particle resonances, shear Alfvén continuum damping, trapped particle effect and the parallel electric effects are all taken into account. The rotation frequency for full stabilization is much larger than the diamagnetic drift frequency; therefore, finite Larmor radius effects are negligible. We also find that the rotation stabilization window opens first near the ideal wall limit.

Feedback suppression of rotating external kink instabilities in the presence of noise

The authors report on the first experimental demonstration of active feedback suppression of rotating external kink modes near the ideal wall limit in a tokamak using Kalman filtering to discriminate the n=1 kink mode from background noise. The Kalman filter contains an internal model that captures the dynamics of a rotating, growing n=1 mode. Suppression of the external kink mode is demonstrated over a broad range of phase angles between the sensed mode and applied control field, and performance is robust at noise levels that render proportional gain feedback ineffective. Suppression of the kink mode is accomplished without excitation of higher frequencies as was observed in previous experiments using lead-lag loop compensation [A. J. Klein et al., Phys Plasmas 12, 040703 (2005)].

Design optimization for plasma performance and assessment of operation regimes in JT-60SA

The design of the modification of JT-60U, JT-60SA has been optimized from the viewpoint of plasma performance, and operation regimes have been evaluated with the latest design. Upper and lower divertors with different geometries will be prepared for flexibility of the plasma shape, which will enable both low aspect ratio (A ∼ 2.65) and ITER shape (A = 3.1) configurations. The beam lines of negative-ion neutral beam injection will be shifted downwards by ∼0.6 m for the off-axis current drive (CD), in order to obtain a weak/reversed shear plasma, as well as having the capability of heating the central region. The feedback control coils along the openings in the stabilizing plate are found effective in suppressing the resistive wall mode and sustaining high βN close to the ideal wall limit. Sustainment of plasma current of 3–3.5 MA for 100 s will be possible in ELMy H-mode plasmas with moderate heating power, βN, and density within an available flux swing. It is also expected that higher βN, high-density ELMy H-mode plasmas will be maintained for 100 s with higher heating power. The expected regime of full CD operation has been extended with upgraded heating and CD power. Full CD operation for 100 s with reactor-relevant high values of normalized beta and bootstrap current fraction (Ip = 2.4 MA, βN = 4.3, fBS = 0.69, , HH98y2 = 1.3) is expected in a highly-shaped low-aspect-ratio configuration (A = 2.65).

Overview of JT-60U results for the development of a steady-state advanced tokamak scenario

Recent JT-60U experimental results towards the development of a steady-state advanced tokamak scenario are presented. The JT-60U experiments within the past two years emphasize the extension of the operation regimes and the development of active control for high bootstrap current fraction plasmas with a strong linkage between pressure and current profiles. Reduction of a toroidal magnetic field ripple by installing ferritic steel tiles decreases the fast ion loss and consequently enables one to access the new regimes due to an increase in net heating power. The decrease in the fast ion loss also contributes to access to the new regimes through confinement improvement attributed to the reduction of counter toroidal rotation. High βN (∼4.2) exceeding the no-wall ideal limit is achieved at li = 0.8–1 in the high βp ELMy H-mode plasmas with a weak positive shear at the large volume configuration close to the wall. The large volume configuration had so far suffered from the large toroidal field ripple. The value of βN reaches the ideal wall limit, where RWM is suppressed by the plasma rotation. Small critical rotation velocity about 0.3% of Alfvén velocity is found for suppressing RWM. High βN · HH98(y,2) of 2.2 with βN ∼ 2.3 and HH98(y,2) ∼ 1 is sustained for 23.1 s, significantly longer than the current diffusion time (∼12τR) in the high βp ELMy H-mode plasmas. This duration is extended to a time scale for enhancement of recycling owing to a decrease in the wall-pumping rate. Successful recycling and density control is demonstrated for ∼30 s in the enhanced recycling regime even with outgas from the wall by maximizing the divertor pumping rate in the high-density ELMy H-mode plasmas. With small effects of the toroidal field ripple reduction, the controllability is investigated in the reversed shear (RS) plasmas with a high bootstrap current fraction (fBS) of ∼0.7–1. It is difficult to sustain these plasmas using a feedback control scheme for global parameter such as stored energy and the duration is determined by the ideal limit or slow ITB degradation in the linkage of current and pressure profiles. Real time qmin control is demonstrated with MSE diagnostic and LHCD at fBS = 0.46 with the strong pressure and current profile linkage. Physics studies also progress towards burning plasma control. Semi-global change of the ITB structure is observed in both high βp mode and RS plasmas. Complete NTM suppression is demonstrated with misalignment of ECCD position less than about half of the island width. Fast ELM propagation to the main chamber wall is observed, and significant hydrogen retention in the main chamber wall is found. In the plasma-shadowed area underneath the divertor region, the averaged carbon deposition rate is significantly low, however the (H + D)/C retention rate is high (∼0.8).

Experiments and modelling of external kink mode control using modular internal feedback coils

We report on recent advances in modelling and experiments on resistive wall mode feedback control. The first experimental demonstration of feedback suppression of rotating external kink modes near the ideal wall limit in a tokamak is described [1]. This was achieved using an optimized control system employing a low latency digital controller and directly coupled modular feedback coils. The magnitude of plasma dissipation affecting kink mode behaviour has also been experimentally quantified for the first time using measurements of the radial eigenmode structure of the poloidal field fluctuations associated with the rotating kink mode. New capabilities of the VALEN code [2] are also reported. These include the ability to simulate multiple plasma modes and mode rotation in the model of the feedback control loop. Results from VALEN modelling of resistive wall mode feedback control in ITER are also presented, showing a significant improvement in performance with internal coils. Evidence for a lack of mode rigidity in HBT-EP is given, and plans to address this and other issues related to coil coverage and coil modularity are presented.

Enhanced ITER resistive wall mode feedback performance using optimal control techniques

In order to achieve the highest plasma pressure limits in ITER, resistive wall kink mode stabilization is required. A novel resistive wall mode linear observer and feedback controller designed using model reduction and optimal control theory and employing only proportional gain are described here that allow operation of ITER up to Cβ = 86% of the ideal wall limit using the present design external control coils. The full VALEN finite element ITER model containing ∼3000 modes was reduced to a minimum of 8 modes making real-time controller implementation possible. We find an order of magnitude reduction of the required control coil current and voltage in the presence of white noise from the no-wall limit to the optimal feedback system performance limit as compared with a traditional, classical controller.

Identification of a Low Plasma-Rotation Threshold for Stabilization of the Resistive-Wall Mode

The plasma rotation necessary for stabilization of resistive-wall modes (RWMs) is investigated by controlling the toroidal plasma rotation with external momentum input by injection of tangential neutral beams. The observed threshold is 0.3% of the Alfvén velocity and much smaller than the previous experimental results obtained with magnetic braking. This low critical rotation has a very weak beta dependence as the ideal wall limit is approached. These results indicate that for large plasmas such as in future fusion reactors with low rotation, the requirement of the additional feedback control system for stabilizing RWM is much reduced.

Control of magnetohydrodynamic modes with a resistive wall above the wall stabilization limit

Studies are shown of control of magnetohydrodynamic (MHD) modes in the presence of a resistive wall, below and above the regime for which stabilization is possible with a perfectly conducting wall, i.e., in and above the ideal wall limit. The results show that resistive plasma (tearing-like) modes can be feedback stabilized for current profiles which are unstable above the ideal wall limit, both for tokamak-like and reversed field pinch (RFP)-like profiles. However, above the limit for wall stabilization of ideal plasma modes, resonant or nonresonant, the feedback scheme cannot provide stabilization. The control scheme senses both normal and tangential components of the perturbed magnetic field, and the feedback is proportional to a linear combination of the two. Neither plasma rotation nor complex gain is included. A cylindrical reduced MHD model, in resistive or ideal form, is used, with tokamak-like profiles [increasing profile of q(r)] or RFP-like profiles [decreasing q(r)]. The possible relevance to RFPs and tokamaks is discussed.

Access to sustained high-beta with internal transport barrier and negative central magnetic shear in DIII-D

High values of normalized β (βN∼4) and safety factor (qmin∼2) have been sustained simultaneously for ∼2s in DIII-D [J.L. Luxon, Nucl. Fusion 42, 64 (2002)], suggesting a possible path to high fusion performance, steady-state tokamak scenarios with a large fraction of bootstrap current. The combination of internal transport barrier and negative central magnetic shear at high β results in high confinement (H89P>2.5) and large bootstrap current fraction (fBS>60%) with good alignment. Previously, stability limits in plasmas with core transport barriers have been observed at moderate values of βN (<3) because of the pressure peaking which normally develops from improved core confinement. In recent DIII-D experiments, the internal transport barrier is clearly observed in the electron density and in the ion temperature and rotation profiles at ρ∼0.5 but not in the electron temperature profile, which is very broad. The misalignment of Ti and Te gradients may help to avoid a large local pressure gradient. Furthermore, at low internal inductance ∼0.6, the current density gradients are close to the vessel and the ideal kink modes are strongly wall-coupled. Simultaneous feedback control of both external and internal sets of n=1 magnetic coils was used to maintain optimal error field correction and resistive wall mode stabilization, allowing operation above the free-boundary β limit. Large particle orbits at high safety factor in the core help to broaden both the pressure and the beam-driven current profiles, favorable for steady-state operation. At plasma current flat top and β∼5%, a noninductive current fraction of ∼100% has been observed. Stability modeling shows the possibility for operation up to the ideal-wall limit at β∼6%.

Control of the resistive wall mode with internal coils in the DIII–D tokamak

Internal coils, ‘I-Coils’, were installed inside the vacuum vessel of the DIII–D device to generate non-axisymmetric magnetic fields to act directly on the plasma. These fields are predicted to stabilize the resistive wall mode (RWM) branch of the long-wavelength external kink mode with plasma beta close to the ideal wall limit. Feedback using these I-Coils was found to be more effective as compared to using external coils located outside the vacuum vessel. Locating the coils inside the vessel allows for a faster response and the coil geometry also allows for better coupling to the helical mode structure. Initial results were reported previously (Strait E.J. et al 2004 Phys. Plasmas 11 2505). This paper reports on results from extended feedback stabilization operations, achieving plasma parameters up to the regime of Cβ ≈ 1.0 and open loop growth rates of γopenτw ≳ 25 where the RWM was predicted to be unstable with only the ‘rotational viscous stabilization mechanism’. Here Cβ ≈ (β − βno−wall.limit)/(βideal.wall.limit − βno−wall.limit) is a measure of the beta relative to the stability limits without a wall and with a perfectly conducting wall, and τw is the resistive flux penetration time of the wall. These feedback experimental results clarified the processes of dynamic error field correction and direct RWM stabilization, both of which took place simultaneously during RWM feedback stabilization operation. MARS-F modelling provides a critical rotation velocity in reasonable agreement with the experiment and predicts that the growth rate increases rapidly as rotation decreases below the critical. The MARS-F code also predicted that for successful RWM magnetic feedback, the characteristic time of the power supply should be limited to a fraction of the growth time of the targeted RWM. The possibility of further improvements in the presently achievable range of operation of feedback gain values is also discussed.

Measurement of resistive wall mode stability in rotating high-β DIII-D plasmas

Toroidal plasma rotation of the order of a few per cent of the Alfvén velocity can stabilize the resistive wall mode (RWM) and extend the operating regime of tokamaks from the conventional, ideal magnetohydrodynamic (MHD) no-wall limit up to the ideal MHD ideal-wall limit. The stabilizing effect has been measured in DIII-D passively by measuring the critical plasma rotation required for stability and actively by probing the plasma with externally applied resonant magnetic fields. The comparison of these measurements to predictions of rotational stabilization of the sound wave damping and of the kinetic damping model using the MARS-F code results in qualitative agreement, but also indicates the need for further refinement of the measurements and models.