Evolution Of Neoclassical Tearing Modes Research Articles

Effects of plasma radiation on the nonlinear evolution of neo-classical tearing modes in tokamak plasmas with reversed magnetic shear

Effects of plasma radiation on the nonlinear evolution of neo-classical double tearing modes (NDTMs) in tokamak plasmas with reversed magnetic shear are numerically investigated based on a set of reduced magnetohydrodynamics (MHD) equations. Cases with different separations Δ rs = |r s2–r s1| between the two same rational surfaces are considered. In the small Δ rs cases, the plasma radiation destabilizes the NDTMs and makes the kinetic energy still grow gradually in the late nonlinear phase. Moreover, the NDTM harmonics with high mode numbers reach a high level in the presence of plasma radiation, forming a broad spectrum of MHD perturbations that induces a radially broadened region of MHD turbulence. As a result, the profiles of safety factors also enter a nonlinear oscillation phase. In the intermediate Δ rs case, the plasma radiation can advance the explosive burst of kinetic energy that results from the fast driven reconnection between the two rational surfaces, because it can further promote the destabilizing effects of bootstrap current perturbation on the magnetic island near the outer rational surfaces. In the large Δ rs case, through destabilizing the outer islands significantly, the plasma radiation can even induce the explosive burst in the reversed magnetic shear configuration where the burst cannot be induced in the absence of plasma radiation.

Effects of plasma radiation on the nonlinear evolution of neo-classical tearing modes in tokamak plasmas

The effects of plasma radiation on the nonlinear evolution of neo-classical tearing modes are investigated based on a set of reduced magnetohydrodynamic equations. It is found that the radiation can reduce the pressure near the rational surface. During the nonlinear evolution, the magnitude of perturbed bootstrap current is drastically enhanced in the presence of the radiation. Besides, the radiation can increase the growth rate of the magnetic islands by diminishing the pressure, such that the magnetic islands do not saturate compared with that without radiation. On the other hand, with the increase of the ratio of parallel to perpendicular transport coefficient the reduction of pressure can further increase the growth rate of magnetic islands in the presence of plasma radiation. Finally, the mechanisms of the destabilizing effects driven by the radiation are discussed in detail as well.

On the effect of electron cyclotron waves on the evolution of neoclassical tearing modes in tokamak plasmas

In this paper we study the generation of current in a tokamak plasma in the presence of a magnetic island, using electron cyclotron (EC) waves in a process known as electron cyclotron current drive. We study some features related to the efficiency of the method, adopting a simplified model for a tokamak which incorporates the existence of a magnetic island associated with the occurrence of a neoclassical tearing mode instability. The study utilizes a self-consistent treatment of the interaction of EC waves with the plasma in the tokamak and the consequent current generation, taking into account the existence of the tokamak loop voltage and the occurrence of radial transport of particles, and also the existence of induced effects. The formalism also includes an approximate self-consistent description of the evolution of the width of the magnetic islands, which depends on the plasma current through the so-called modified Rutherford equation. The evolution of the islands depends on classical effects, which are driven mainly by the equilibrium current gradient, on neoclassical effects related to the perturbed bootstrap current and on the current generated by the radio waves. The results obtained in our numerical analyses confirm that the width of the islands can be substantially reduced by the use of EC waves, and lead to an estimate of the minimum amount of EC power required to be effective in reducing the width of magnetic islands. The results also show that, although the density of current generated by EC waves in the island region decreases along late time evolution, the total amount of plasma current is increased compared with the case in which the width of the island is assumed to remain constant.

Finite ion orbit width effect on the neoclassical tearing mode threshold in a tokamak plasma

A new drift kinetic theory for the response of ions to small magnetic islands in toroidal plasma is presented. Islands whose width w is comparable to the ion poloidal Larmor radius are considered, expanding the ion response solution in terms of , where r is the minor radius. In this limit, the ion distribution can be represented as a function of toroidal canonical momentum, . With effects of grad-B and curvature drifts taken into account, the ion distribution function is a constant on a ‘drift island’ structure, which is identical to the magnetic island but radially shifted by . The distribution is then flattened across the drift island, rather than the magnetic island. For small islands , the pressure gradient is maintained across the magnetic island, suppressing the bootstrap current drive for the neoclassical tearing mode (NTM) growth. As , the ions are largely unperturbed. However, the electrons respond to the electrostatic potential required for quasi-neutrality and this provides a stabilizing contribution to the NTM evolution. This gives a new physical understanding of the NTM threshold mechanism, with implications for the design of NTM control systems for future tokamaks such as ITER.

A mechanism of neoclassical tearing modes onset by drift wave turbulence

The evolution of neoclassical tearing modes (NTMs) in the presence of electrostatic drift wave turbulence is investigated. In contrast with anomalous transport effect induced by turbulence on NTMs, a new mechanism that turbulence-driven current can affect the onset threshold of NTMs significantly is suggested. Turbulence acts as a source or sink to exchange energy with NTMs. The turbulence-driven current can change the parallel current in magnetic islands and affect the evolution of NTMs, depending on the direction of turbulence intensity gradient. When the turbulence intensity gradient is negative, the turbulence-driven current enhances the onset threshold of NTMs. When the turbulence intensity gradient is positive, it can reduce or even overcome the stabilizing effect of neoclassical polarization current, leading to a small onset threshold of NTMs. This implies that NTMs can appear without noticeable magnetohydrodynamics (MHD) events.

Effect of electron cyclotron beam width to neoclassical tearing mode stabilization by minimum seeking control in ITER

We report the effect of the electron cyclotron (EC) beam width on the full suppression time of neoclassical tearing mode (NTM) using the finite difference method (FDM) based minimum seeking controller in ITER. An integrated numerical system is setup for time-dependent simulations of the NTM evolution in ITER by solving the modified Rutherford equation together with the plasma equilibrium, transport, and EC heating and current drive. The calculated magnetic island width and growth rate is converted to the Mirnov diagnostic signal as an input to the controller to mimic the real experiment. In addition, 10% of the noise is enforced to this diagnostic signal to evaluate the robustness of the controller. To test the dependency of the NTM stabilization time on the EC beam width, the EC beam width scan is performed for a perfectly aligned case first, then for cases with the feedback control using the minimum seeking controller. When the EC beam is perfectly aligned, the narrower the EC beam width, the smaller the NTM stabilization time is observed. As the beam width increases, the required EC power increases exponentially. On the other hand, when the minimum seeking controller is applied, NTM stabilization sometimes fails as the EC beam width decreases. This is consistently observed in the simulation with various representations of the noise as well as without the noise in the Mirnov signal. The higher relative misalignment, misalignment divided by the beam width, is found to be the reason for the failure with the narrower beam widths. The EC stabilization effect can be lower for the narrower beam widths than the broader ones even at the same misalignment due to the smaller ECCD at the island O-point. On the other hand, if the EC beam is too wide, the NTM stabilization time takes too long. Accordingly, the optimal EC beam width range is revealed to exist in the feedback stabilization of NTM.

Multi-field/-scale interactions of turbulence with neoclassical tearing mode magnetic islands in the DIII-D tokamak

We present the first localized measurements of long and intermediate wavelength turbulent density fluctuations (ñ) and long wavelength turbulent electron temperature fluctuations (T̃e) modified by m/n=2/1 Neoclassical Tearing Mode (NTM) islands (m and n are the poloidal and toroidal mode numbers, respectively). These long and intermediate wavelengths correspond to the expected Ion Temperature Gradient and Trapped Electron Mode scales, respectively. Two regimes have been observed when tracking ñ during NTM evolution: (1) small islands are characterized by a steep Te radial profile and turbulence levels comparable to those of the background; (2) large islands have a flat Te profile and reduced turbulence level at the O-point. Radially outside the large island, the Te profile is steeper and the turbulence level increased compared to the no or small island case. Reduced turbulence at the O-point compared to the X-point leads to a 15% modulation of ñ2 across the island that is nearly in phase with the Te modulation. Qualitative comparisons to the GENE non-linear gyrokinetic code are promising with GENE replicating the observed scaling of turbulence modification with island size. These results are significant as they allow the validation of gyrokinetic simulations modeling the interaction of these multi-scale phenomena.

Reduction of neoclassical polarization current contribution to NTM evolution

The neoclassical polarization current, which can be generated by a time-dependent electric field resulting from magnetic island rotation, is believed to play an important role in the initial stage of the neoclassical tearing mode (NTM) evolution in tokamak plasmas. In the previous analytical description of the neoclassical polarization current contribution to the evolution of NTMs in the limit of low collision frequency (νii≪εω, νii is ion collision frequency, ε is the inverse aspect ratio, and ω is the island propagation frequency in the plasma rest frame), the width of magnetic islands has been assumed to be much larger than the finite-banana-width (FBW) of the trapped ions in order to solve the drift-kinetic equation of ions by using the perturbation method. In this paper, we introduce a new analytical approach to investigate the neoclassical polarization current contribution to the NTM evolution without the assumption of the large island width by solving the drift-kinetic equation in a so-called ion-banana-center coordinate system. The results show that, when the island width is comparable to the FBW of the thermal ion, the neoclassical polarization current term in the equation of the NTM evolution is much smaller than the previous analytical expression but matches well with the empirical anticipation commonly adopted in experiments.

Influence of ion orbit width on onset threshold of neoclassical tearing modes

The onset threshold of neoclassical tearing modes with finite ion orbit width is studied. The evolution of neoclassical tearing modes including the effect of ion orbit is derived analytically. When ion orbit width is comparable to island width, the effect of ion orbit is significant. It would increase the island width needed to flatten pressure in the island, and reduce the amplitude of ion perturbed bootstrap current. It is found that ion orbit effect tends to increase the onset threshold βθonset for a given seed island. It also would increase the lowest threshold βθ,min and the corresponding marginal island width. It has important implications for the onset of neoclassical tearing modes with comparable ion orbit width and island width in International Thermonuclear Experimental Reactor.

Nonlinear evolution of neo-classical tearing modes in reversed magnetic shear tokamak plasmas

Linear and nonlinear neo-classical double tearing modes (NDTMs) in the reversed magnetic shear configuration with different separations Δrs between two same rational surfaces are numerically studied by means of reduced magnetohydrodynamic simulations, taking into account different bootstrap current fractions fb. It is found that in the case of large Δrs, an explosive burst of fast reconnection, which was previously observed only in the intermediate Δrs case with fb = 0 (Ishii Y. et al 2002 Phys. Rev. Lett. 89 205002), can also be induced if the fraction of bootstrap current fb is sufficiently high. In the case of intermediate Δrs, such explosive bursts can effectively be brought forward, since the bootstrap current significantly destabilizes the tearing mode on the outer rational surface. In the case of small Δrs, higher order harmonics of the NDTMs become dominantly unstable in the linear phase, if fb continues increasing. In its nonlinear phase, the local modification of bootstrap current near the magnetic islands makes the islands move inwards, while the recovery of the Ohm current tends to make them move outwards. The different dynamics of complicated motions of magnetic islands (or rational surfaces) determined by these two effects are analysed in detail in the cases of different fb values.

Effect of Finite-Ion-Banana-Width on the Polarization Contribution to the Neoclassical Tearing Modes Evolution

In the previous analytical description of the neoclassical polarization current effect on the neoclassical tearing modes (NTMs), it is usually assumed that the magnetic island is much larger than the finite-ion-banana-width (FBW). This assumption is questionable when the experimentally observed seed island width of the NTMs is comparable to the FBW. We introduce a simple and direct theoretical method to investigate the FBW effect on the neoclassical polarization contribution to the NTM evolution in collisional plasmas. The results show that, the FBW effect can strongly modify the neoclassical polarization current profile near the island separatrix, and thus weaken its probably stabilizing effect on the NTMs.

Electron-cyclotron wave propagation, absorption and current drive in the presence of neoclassical tearing modes

We analyze the propagation of electron-cyclotron waves, their absorption and current drive when neoclassical tearing modes (NTMs), in the form of magnetic islands, are present in a tokamak plasma. So far, the analysis of the wave propagation and power deposition in the presence of NTMs has been performed mainly in the frame of an axisymmetric magnetic field, ignoring any effects from the island topology. Our analysis starts from an axisymmetric magnetic equilibrium, which is perturbed such as to exhibit magnetic islands. In this geometry, we compute the wave evolution with a ray-tracing code, focusing on the effect of the island topology on the efficiency of the absorption and current drive. To increase the precision in the calculation of the power deposition, the standard analytical flux-surface labeling for the island region has been adjusted from the usual cylindrical to toroidal geometry. The propagation up to the O-point is found to be little affected by the island topology, whereas the power absorbed and the driven current are significantly enhanced, because the resonant particles are bound to the small volumes in between the flux surfaces of the island. The consequences of these effects on the NTM evolution are investigated in terms of the modified Rutherford equation.

A field programmable gate array unit for the diagnosis and control of neoclassical tearing modes on MAST

A real-time system has been developed to trigger both the MAST Thomson scattering (TS) system and the plasma control system on the phase and amplitude of neoclassical tearing modes (NTMs), extending the capabilities of the original system. This triggering system determines the phase and amplitude of a given NTM using magnetic coils at different toroidal locations. Real-time processing of the raw magnetic data occurs on a low cost field programmable gate array (FPGA) based unit which permits triggering of the TS lasers on specific amplitudes and phases of NTM evolution. The MAST plasma control system can receive a separate trigger from the FPGA unit that initiates a vertical shift of the MAST magnetic axis. Such shifts have fully removed m∕n = 2∕1 NTMs instabilities on a number of MAST discharges.

The influence of finite radial transport on the structure and evolution of m/n = 2/1 neoclassical tearing modes on MAST

Finite radial transport around magnetic islands is believed to play an important role in the threshold, spatial structure and temporal evolution of neoclassical tearing modes (NTMs). We report on novel measurements of NTMs with mode structure m/n = 2/1 on the MAST spherical tokamak (ST), which have allowed a direct evaluation of the effect of transport on island behaviour for the first time on an ST. Temperature profiles obtained with the upgraded Thomson scattering (TS) system on MAST have been used to constrain the solutions of a heat transport equation for the NTM magnetic island (Fitzpatrick 1995 Phys. Plasmas 2 825), allowing the determination of the critical width for temperature flattening across an island wc, an important parameter in the modified Rutherford equation (MRE) for NTM evolution. The measured value of wc = 0.7 ± 0.2 cm obtained for an ensemble of high βN MAST discharges has been used in an analysis of the MRE for 2/1 NTM growth and saturation on MAST. Using a probabilistic method for parameter and error estimation, which takes account of the experimental uncertainty on measured equilibrium parameters, it is found that the temporal evolution of island size is well described by marginally, classically unstable NTMs with strongly destabilizing bootstrap current and stabilizing curvature terms. Finally, further analysis of a β ramp-down discharge is presented, in which the measured wc value explains the observed threshold width well.

The role of asymmetries in the growth and suppression of neoclassical tearing modes

The evolution of neoclassical tearing modes (NTMs) is usually described by the generalized Rutherford equation for a symmetric magnetic island. Despite the success of this representation, various experiments have found the evidence of asymmetries in the island geometry. A generalization of the model suggests that a number of effects, such as a quasi-linear correction of the constant-ψ approximation, a shear flow or a temperature gradient across the island, might be responsible for the deformation of the island geometry. In addition, it is noted that the symmetry is broken in the radial direction also by a finite third order derivative in the equilibrium helical flux function. This paper addresses the role of these asymmetries in the growth and suppression of NTMs in a slab geometry, with particular attention to the implications for the local current drive (ECCD) and resonant heating (ECRH) terms. The stabilizing contributions provided by electron cyclotron waves to NTMs are found to be largely unaffected by these perturbations. These results correct and extend some of the conclusions presented in Lazzaro and Nowak (2009 Plasma Phys. Control. Fusion 51 035005).

Temporal evolution of neoclassical tearing modes in the frequently interrupted regime

A phenomenological method for description of temporal evolution of neoclassical tearing modes in the frequently interrupted regime (FIR) is proposed. The method makes it possible to predict the beginning and the end of the FIR regime as well as the frequency of the FIR drops. A few experimental parameters which are used in the model are commonly measured quantities. Several specific ASDEX Upgrade (http://en.wikipedia.org/wiki/ASDEX_Upgrade) FIR discharges with different heating and different FIR behavior are analyzed in detail.

ETG turbulence effects on the evolution of an NTM

We study the effect of a background of microturbulence generated by unstable short scale length electron temperature gradient (ETG) modes on the excitation and nonlinear evolution of neoclassical tearing modes (NTMs) in a tokamak. A self-consistent model calculation is carried out in which low frequency stresses generated by the ETG modes act on the NTM and which in turn acts back on the ETG evolution by modulating the turbulence profile. The principal physical consequences of the ETG turbulence are to create an anomalous current diffusivity and an anomalous resistivity contribution. These turbulent transport contributions are incorporated in the evolution equations of a single helicity NTM to obtain a generalized Rutherford equation, and their impact on the instability threshold and growth rate is discussed.

On the merits of heating and current drive for tearing mode stabilization

Neoclassical tearing modes (NTMs) are magnetohydrodynamic modes that can limit the performance of high β discharges in a tokamak, leading eventually to a plasma disruption. A NTM is sustained by the perturbation of the ‘bootstrap’ current, which is a consequence of the pressure flattening across a magnetic island. Control and suppression of this mode can be achieved by means of electron cyclotron waves (ECWs) which allow the deposition of highly localized power at the island location. The ECW power replenishes the missing bootstrap current by generating a current perturbation either inductively, through a temperature perturbation (electron cyclotron resonance heating), or non-inductively by direct current drive (electron cyclotron current drive). Although both methods have been applied successfully to experiments showing a predominance of ECRH for medium-sized limiter tokamaks (TEXTOR, T-10) and of ECCD for mid-to-large-sized divertor tokamaks (AUG, DIII-D, JT-60), conditions determining their relative importance are still unclear. We address this problem with a numerical study focused on the contributions of heating and current drive to the temporal evolution of NTMs as described by the modified Rutherford equation. For the effects of both heating as well as current drive, simple analytical expressions have been found in terms of an efficiency fore-factor times a ‘geometrical’ term depending on the power deposition width wdep, location and modulation. When the magnetic island width w equals the width of the deposition profile, w ≈ wdep, both geometric terms are practically identical. Whereas for current drive the geometric term approaches a constant for small island widths and is inversely proportional to (w/wdep)2 for large island widths, the heating term approaches a constant for large island widths and is proportional to (w/wdep) for small island widths. For medium-sized tokamaks (TEXTOR, AUG) the heating and current drive efficiencies are of the same order of magnitude, whereas in a future, large reactor like ITER the current drive efficiency is expected to be significantly larger.

Suppression of NTM Towards Stationary High-Beta Plasmas in JT-60U

Results from stabilization of neoclassical tearing modes (NTMs) in JT-60U are described. NTM stabilization and confinement improvement have been demonstrated by employing a real-time NTM stabilization system, where the identification of the location of an NTM and the optimization of the injection angle of the electron cyclotron wave are performed in real time. Also, a high-beta plasma with the normalized beta of 3 has been sustained by suppressing NTM by applying the electron cyclotron current drive (ECCD) before the onset (`preemptive ECCD'). In addition, a simulation code for analysis of the NTM evolution has been developed by combining the modified Rutherford equation with the transport code TOPICS. It is found that the simulation well reproduces the NTM behavior in JT-60U. The simulation also shows that the ECCD width is also important for NTM stabilization, and that the EC wave power for complete stabilization can be reduced by narrowing the ECCD profile.

Role of anomalous transport in onset and evolution of neoclassical tearing modes

A key role in the evolution of the neoclassical tearing modes (NTMs) belongs to the radial profiles of the perturbed plasma flow, temperature and density which are determined by the conjunction of the longitudinal and cross-field transport arising from thermal conduction, particle diffusion and viscosity. In a tokamak, the perpendicular transport of particles, heat and momentum is typically anomalous. In this paper the results of theoretical studies on the influence of anomalous perpendicular heat transport and anomalous ion perpendicular viscosity on early stages of NTM evolution are presented. Several parallel transport mechanisms competitive with anomalous cross-island heat transport in the formation of the perturbed electron and ion temperature profiles within the island are considered. The perturbed electron temperature profile is established in competition between anomalous perpendicular electron heat conductivity and parallel electron heat convection. The formation of the ion perturbed temperature profile was found to be dependent on the island rotation frequency. The perpendicular ion heat conductivity is balanced by the parallel transport associated with the ion inertia for an island rotating with subsonic frequency or with island rotation with respect to the plasma for supersonic islands. The partial contributions from the plasma electron and ion temperature perturbations in the bootstrap drive of the mode and magnetic curvature effect were taken into account in construction of a generalized transport threshold model of NTMs. This model gives more favourable predictions for NTM stability and qualitatively modifies the scaling law for βonset. The anomalous perpendicular ion viscosity is shown to modify the collisionality dependence of the polarization current effect, reducing it to the low collisionality limit. In its turn a viscous contribution to the bootstrap drive of NTMs is found to be of the same order as a conventional bootstrap drive for the islands of width close to the characteristic one of the transport threshold model. A viscous contribution to the perturbed bootstrap current is destabilizing for the island rotating in the ion diamagnetic drift direction. In this case, an alternative threshold mechanism should be considered.