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The need for a model able to provide the dynamic evolution of the intrinsic magnetic error fields amplitude in tokamaks is of a significant importance in order to develop strategies to correct its destabilizing effect. The present paper specifically aims to deliver this kind of model and adjacent code. A previously built direct perturbations interpretative model (Miron (JET Contributors) 2021 Nucl. Fusion 61 106016) is used to calculate the plasma instabilities amplitude and frequency aiming to match the same quantities provided by the device diagnostics data analysis specific code for various discharges at JET. The mentioned good match ensures our model validity against the experimental results. Based on its proven structural validity, our model considering the error field quantities is inverted. This time the initial direct model output results, namely the plasma perturbations amplitude and frequency, become input data for our inverse model aiming to solve the corresponding error field modes system of equations searched as unknowns. The error fields basically satisfy the same outer plasma perturbed equations as the plasma perturbations do (vacuum/wall/plasma column external structures). Obviously they do not satisfy the perturbed plasma equations. A clear and explicit dynamic error field solution is finally provided. It has been demonstrated that whenever the error fields are responsible for the mode locking effect and plasma rotation damping, the calculated error fields shows its expected disruptive resonant behavior during various discharges at JET. [ABSTRACT FROM AUTHOR]

The spectrum effects on toroidal rotation braking, induced by n = 1 resonant magnetic perturbations (RMPs) in the discharges with q 95 = 4.1 and q 95 = 5.1 , are studied in the EAST tokamak. Here n is the toroidal mode number, RMP spectrum is varied by scanning δ ϕ U L , the phase difference between the upper and lower rows of RMP coils. The toroidal rotation changes periodically with the periodic δ ϕ U L scanning and such an effect is stronger in the discharge with lower q 95 = 4.1. The spectrum dependence of the neoclassical toroidal viscosity (NTV) torque, modeled by NTVTOK based on the magnetic perturbation obtained from MARS-F calculation, agrees well with that of the experimentally observed braking torques in both discharges. The modeled NTV torque is stronger in the discharge with lower q 95, which also agrees with the observations. The comparisons between the spectrum dependence of the NTV and magnetic perturbations show that the resonant mode of magnetic perturbations near the plasma edge mainly contribute the NTV torque. These agreements between modeling and experiments highlight the capability of NTV theory in explaining the experimental observation in the EAST tokamak. [ABSTRACT FROM AUTHOR]

The effect of externally applied resonant magnetic perturbations (RMPs) on the local equilibrium plasma current density profile is studied numerically based on two-fluid equations in simplified cylindrical geometry. It is found that a moderate RMP below its penetration threshold, via non-linear mode coupling, induces a parallel electric field around its rational surface that can significantly change the local flux-surface-averaged current density gradient. At a given RMP amplitude, the modification of the current density profile increases with increasing electron temperature, and it significantly depends on the bi-normal electron fluid velocity at the resonant surface. The effect of this modification on the magnetic island growth is demonstrated by the example of small m/n = 2/1 islands (m/n being the poloidal/toroidal mode numbers), driven by an unfavorable plasma current density profile and bootstrap current perturbation. The 2/1 mode growth is stabilized by moderate static 4/2 or 6/3 RMPs if the local electron fluid velocity is in the ion drift direction or sufficiently large in the electron drift direction. These results reveal that a weakly three-dimensional equilibrium, containing a moderate 4/2 RMP and the associated shielding current, can be more stable against the 2/1 mode, which often causes tokamak plasma major disruptions. [ABSTRACT FROM AUTHOR]

Lower hybrid (LH) and magneto-sonic (MS) waves are well known modes of magnetized plasma. These modes play important roles in many phenomena. The LH wave is often employed in magnetic confinement fusion experiments for current drive and heating purposes. Both LH and MS waves are observed in various astrophysical and space plasma observations. These waves involve ion motion and have not therefore been considered in high power pulsed laser experiments. This paper shows, with the help of particle-in-cell simulations, a simple mechanism for excitation of LH and magnetosonic excitations in the context of laser plasma interaction. A detailed study characterising the formation and propagation of these modes have been provided. The scheme for generating these perturbations relies on the application of a strong magnetic field in the plasma to constrain the motion of lighter electron species in the laser electric field. The magnetic field strength is chosen so as to leave the heavier ions un-magnetized at the laser frequency. This helps in the excitation of the LH waves. At the slower time scale associated with the laser pulse duration, even the ions show a magnetized response and magnetosonic excitations are observed to get excited. [ABSTRACT FROM AUTHOR]

Enhancements of residual Reynolds stresses and symmetry breaking with resonant magnetic perturbations (RMPs) are presented. These experiments were performed using a Langmuir probe array in the edge plasmas of the J-TEXT tokamak. This study aims to explain the mechanisms for generating residual stresses and intrinsic rotations. It is observed that with RMPs, peaked residual stresses, steeper pressure gradients and stronger shear layers all appear around the resonant surface. The toroidal rotation is accelerated in the direction of the plasma current and shows a correlation with turbulence and the measured residual stresses near the resonant surfaces of RMPs. Symmetry breaking induced by magnetic islands is proposed as a new mechanism, which qualitatively explains the enhanced residual stresses and the acceleration of the toroidal rotation. The changes to the residual stresses and symmetry breaking with RMPs near the last closed surface are also discussed. [ABSTRACT FROM AUTHOR]

Toroidal Alfvén eigenmodes (TAE) and ellipticity induced Alfvén eigenmodes (EAE) driven by fast electrons are observed for the first time in steady-state EAST plasmas heated by lower hybrid wave (LHW). For the analyzed discharge four modes appear after the injection of LHW. Comparing experimental observations with simulation, high frequency modes are located near and low frequency mode is near . The two positions are very close to where most of the heating power is deposited and population inversion occurs. Analysis of resonance condition between particles and waves indicates that barely-passing, deeply trapped and barely-trapped electrons can drive the mode. [ABSTRACT FROM AUTHOR]

Magnetic triggering of edge localized modes (ELMs) in Ohmic H-mode plasmas was first reported in the TCV tokamak (Degeling et al 2003 Plasma Phys. Control. Fusion45 1637). This method, showing reliable locking of the ELM frequency to an imposed axisymmetric vertical plasma oscillation, was also demonstrated in the ITER-relevant type-I ELM regime in ASDEX Upgrade (Lang et al 2004 Plasma Phys. Control. Fusion46 L31) and JET (de la Luna et al 2015 Nucl. Fusion56 026001). However, the mechanisms of the ELM triggering due to a vertical motion has not been studied extensively. The non-linear reduced MHD code JOREK-STARWALL has been extended for 3D free-boundary computations (Hölzl et al 2012 J. Phys.: Conf. Ser. 401 012010), which has allowed us to simulate for the first time realistic vertical oscillations together with ELM simulations in a single consistent scheme. Our simulations demonstrate that stable plasmas can be destabilized by the application of a vertical oscillation for ITER. During the vertical motion, a toroidal current is induced in the pedestal. The origin of this current is analysed in detail with the use of simulations and a simple analytical model, revealing that it arises from the compression of the plasma cross section due to its motion through an inhomogeneous magnetic field. Lower pedestal currents between ELMs require bigger vertical displacements to destabilize ELMs, which directly points towards the increased edge current as the ELM driving mechanism. Finally the ELM triggering shows a very weak dependence on the plasma velocity for ITER in agreement with experiments. [ABSTRACT FROM AUTHOR]

Axisymmetric geodesic acoustic mode (GAM) oscillations of the magnetic field, plasma potential and electron temperature have been identified on the COMPASS tokamak. This work brings an overview of their electromagnetic properties studied by multi-pin reciprocating probes and magnetic diagnostics. The n  =  0 fluctuations form a continuous spectrum in limited plasmas but change to a single dominant peak in diverted configuration. At the edge of diverted plasmas the mode exhibits a non-local structure with a constant frequency over a radial extent of at least several centimeters. Nevertheless, the frequency still reacts on temporal changes of plasma temperature caused by an auxiliary NBI heating as well as those induced by periodic sawtooth crashes. Radial wavelength of the mode is found to be about 1–4 cm, with values larger for the plasma potential than for the electron temperature. The mode propagates radially outward and its radial structure induces oscillations of a poloidal E  ×  B velocity, that can locally reach the level of the mean poloidal flow. Bicoherence analysis confirms a non-linear interaction of GAM with a broadband ambient turbulence. The mode exhibits strong axisymmetric magnetic oscillations that are studied both in the poloidal and radial components of the magnetic field. Their poloidal standing-wave structure was confirmed and described for the first time in diverted plasmas. In limited plasmas their amplitude scales with safety factor. Strong suppression of the magnetic GAM component, and possibly of GAM itself, is observed during co-current but not counter-current NBI. [ABSTRACT FROM AUTHOR]

Plasma perturbations from the core and/or boundary regions of tokamaks can provide seed islands for the excitation of neo-classical tearing modes (NTMs) with negative , where is the linear instability parameter of the classical tearing mode. In this work, by means of reduced magnetohydrodynamic simulations, we numerically investigate the nonlinear evolution of multi-helicity NTMs in rotating tokamak plasmas with these two types of plasma perturbations with different boundary conditions. In the first case of initial plasma perturbations from the core region with a zero boundary condition, the meta-stable property of seed-island triggered NTM with negative is verified in the single helicity simulation. Nevertheless in the multiple helicity simulation, this seed-island triggered NTM with negative can be suppressed by a spontaneous NTM with positive through the competitive interaction between NTMs with different helicities. If a fixed poloidal rotation is taken into account in the first case, two different helicity NTMs could coexist in the saturation stage, which is different qualitatively from the process without plasma rotation. In the second case of initial plasma perturbations from the boundary region with a nonzero boundary condition, as the amplitude of plasma perturbations on the boundary increases, the mode with negative gradually changes from the driven-reconnection state to the NTM state, accompanied by an enhancement of magnetic island width in the single helicity simulation. Nevertheless in the multi-helicity simulation, the spontaneous NTM with positive can make the driven-reconnection triggered NTM with negative transfer from the NTM state back to the driven-reconnection state again. The underlying mechanism behind these transitions is analyzed step by step. Effects of fixed and unfixed poloidal rotations on the nonlinear interaction processes are also investigated in detail. In addition, the appearance and disappearance of the magnetic stochasticity resulting from the nonlinear coupling among the multi-helicity NTMs are discussed in the second case. [ABSTRACT FROM AUTHOR]

To understand the connection between the dynamics of microscopic turbulence and the macroscale power scaling in the L–I–H transition in magnetically confined plasmas, a new time-dependent, one-dimensional (in radius) model has been developed. The model investigates the radial force balance equation at the edge region of the plasma and applies the quenching effect of turbulence via the E × B flow shear rate exceeding the shear suppression threshold. By slightly ramping up the heating power, the spatio-temporal evolution of turbulence intensity, density and pressure profiles, poloidal flow and E × B flow self-consistently displays the L–H transition with an intermediate phase (I-phase) characterized by limit-cycle oscillations. Since the poloidal flow is partially damped to the neoclassical flow in the edge region, the numerical results reveal two different oscillation relationships between the E × B flow and the turbulence intensity depending on which oscillation of the diamagnetic flow or poloidal flow is dominant. Specifically, by including the effects of boundary conditions of density and temperature, the model results in a linear dependence of the H-mode access power on the density and magnetic field. These results imply that the microscopic turbulence dynamics and the macroscale power scaling for the L–H transition are strongly connected. [ABSTRACT FROM AUTHOR]

The influence of externally applied magnetic perturbations (MPs) on neoclassical tearing modes (NTM) and the plasma rotation in general is investigated at the ASDEX Upgrade tokamak (AUG). The low n resonant components of the applied field exert local torques and influence the stability of NTMs. The non-resonant components of the error field do not influence MHD modes directly but slow down the plasma rotation globally due to a neoclassical toroidal viscous torque (NTV). Both components slow down the plasma rotation, which in consequence increases the probability for the appearance of locked modes. To investigate the impact of externally applied MPs on already existing modes and the influence on the rotation profile, experimental observations are compared to modelling results. The model used here solves a coupled equation system that includes the Rutherford equation and the equation of motion, taking into account the resonant effects and the resistive wall. It is shown that the NTV torque can be neglected in this modelling. To match the experimental frequency evolution of the mode the MP field strength at the resonant surface has to be increased compared to the vacuum approximation. This leads to an overestimation of the stabilizing effect on the NTMs. The reconstruction of the entire rotation profile via the equation of motion including radial dependencies, confirms that the NTV is negligibly small and that small resonant torques at different resonant surfaces have the same effect as one large one. This modelling suggests that in the experiment resonant torques at different surfaces are acting and slowing down the plasma rotation requiring a smaller torque at the specific resonant surface of the NTM. This additionally removes the overestimated influence on the island stability, whereas the braking of the island's rotation is caused by the sum of all torques. Consequently, to describe the effect of MPs on the evolution of one island, all other islands and the corresponding torques must also be taken into account. [ABSTRACT FROM AUTHOR]

A tomographic reconstruction technique is described for the inversion of a set of limited-angle high-resolution 2D visible light emission projections of global MHD eigenmodes in the H-1NF heliac. The technique is well suited to limited viewing access in toroidal devices and the strong shaping of optimized stellarator/heliotron configurations. Fluctuations are represented as a finite sum of Fourier modes characterized by toroidal and poloidal mode numbers having fixed amplitude and phase in a set of nested flux volumes in Boozer coordinates (Boozer 1980 Phys. Fluids23 904–8). Iterative tomographic inversion techniques and standard linear least-squares methods are used to solve for the complex amplitudes. The method is applied to synchronous camera images of singly charged carbon impurity ion emission at 514 nm obtained at three discrete poloidal viewing orientations (Haskey et al 2014 Rev. Sci. Instrum.85 033505). The 2D amplitude and phase projections provide high quality reconstructions of the radial structure of the fluctuations that are compact in Boozer space and allow clear determination of the poloidal mode number as well as some degree of toroidal mode number differentiation. [ABSTRACT FROM AUTHOR]

In order to understand the mechanism by which resonant magnetic perturbations (RMPs) mitigate or suppress edge-localized modes, it is necessary to understand the plasma response to the application of RMPs. TEXTOR's fast movable Mirnov probe can provide direct measurements of the plasma response to RMPs applied using the dynamic ergodic divertor. The effect of toroidal plasma rotation is investigated, and a change in the phase of the plasma response at certain values of rotation is found. Jumps in the phase of the magnetic field are found to occur on resonant surfaces, indicating the formation of screening currents on these surfaces. The first observations of screening currents on multiple surfaces are presented, and the transition from screening to field penetration with increasing strength of the applied RMP field is observed. [ABSTRACT FROM AUTHOR]

Plasma rotation effects on the trigger and the evolution of MHD activities in reversed shear profiles are studied by nonlinear MHD simulations. It is found that, in a rotating plasma, magnetic islands formed around the inner and outer magnetic resonant surfaces, which are stable for the tearing mode, by an external perturbation (driven magnetic island), evolve with different growth rates during an initial growth phase. After the initial growth phase, an outer magnetic island grows rapidly prior to the inner one and triggers a rapid growth of the inner magnetic island. At the final phase, enlarged magnetic islands flatten a q-profile in a wide radial region including the plasma centre. Though this final phase closely resembles a nonlinear destabilization of a spontaneous double tearing mode (Ishii et al 2002 Phys. Rev. Lett. 89 205002), this process can explain the time delay of a plasma edge oscillation in triggering an internal MHD event and disruption. [ABSTRACT FROM AUTHOR]

Time-dependent integrated predictive modelling is carried out using the PTRANSP code to predict fusion power and parameters such as alpha particle density and pressure in ITER H-mode plasmas. Auxiliary heating by negative ion neutral beam injection and ion-cyclotron heating of He3 minority ions are modelled, and the GLF23 transport model is used in the prediction of the evolution of plasma temperature profiles. Effects of beam steering, beam torque, plasma rotation, beam current drive, pedestal temperatures, sawtooth oscillations, magnetic diffusion and accumulation of He ash are treated self-consistently. Variations in assumptions associated with physics uncertainties for standard base-line DT H-mode plasmas (with Ip = 15 MA, BTF = 5.3 T and Greenwald fraction = 0.86) lead to a range of predictions for DT fusion power PDT and quasi-steady state fusion QDT ([?]PDT/Paux). Typical predictions assuming Paux = 50-53 MW yield PDT = 250-720 MW and QDT = 5-14. In some cases where Paux is ramped down or shut off after initial flat-top conditions, quasi-steady QDT can be considerably higher, even infinite. Adverse physics assumptions such as the existence of an inward pinch of the helium ash and an ash recycling coefficient approaching unity lead to very low values for PDT. Alternative scenarios with different heating and reduced performance regimes are also considered including plasmas with only H or D isotopes, DT plasmas with toroidal field reduced 10% or 20% and discharges with reduced beam voltage. In full-performance D-only discharges, tritium burn up is predicted to generate central tritium densities up to 1016 m[?]3 and DT neutron rates up to 5 × 1016 s[?]1, compared with the DD neutron rates of 6 × 1017 s[?]1. Predictions with the toroidal field reduced 10% or 20% below the planned 5.3 T and keeping the same q98, Greenwald fraction and bn indicate that the fusion yield PDT and QDT will be lower by about a factor of two (scaling as B3.5). [ABSTRACT FROM AUTHOR]