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A new fluid model for runaway electron simulation based on fluid description is introduced and implemented in the magnetohydrodynamics code M3D-C1, which includes self-consistent interactions between plasma and runaway electrons. The model utilizes the method of characteristics to solve the continuity equation for the runaway electron density with large convection speed, and uses a modified Boris algorithm for pseudo particle pushing. The model was employed to simulate magnetohydrodynamics instabilities happening in a runaway electron final loss event in the DIII-D tokamak. Nonlinear simulation reveals that a large fraction of runaway electrons get lost to the wall when kink instabilities are excited and form stochastic field lines in the outer region of the plasma. Plasma current converts from runaway electron current to Ohmic current, and get pinched at the magnetic axis. Given the good agreement with experiment, the simulation model provides a reliable tool to study macroscopic plasma instabilities in existence of runaway electron current, and can be used to support future studies of runaway electron mitigation strategies in ITER., Comment: 26 pages, 16 figures

Plasma response to resonant magnetic perturbations (RMPs) near the pedestal top is crucial for accessing edge localized modes (ELMs) suppression in tokamaks. Since radial location of rotation zero-crossing plays a key role in determining the threshold for field penetration of RMP, plasma response may be different in low input torque plasmas. In this work, the linear MHD code MARS-F is applied to reveal the dependence of plasma response to RMP on rotation zero-crossing by a scan of rotation profiles based on an EAST equilibrium. It is shown that the plasma response is enhanced when zero-crossing occurs near rational surfaces. The dependence of plasma response on the location of rotation zero-crossing is well fitted by a double Gaussian, indicating two effects in this enhancement. One is induced by rotation screening effect shown as a wide base (with a width around 10-20 krad/s), and the other is related to resistive singular layer effect characterized by a localized peak (with a width around 3-4 krad/s). The width of the peak scales with the resistive singular layer width. The plasma displacement suggests the response is tearing like when zero-crossing is within the singular layer, while it is kink like when zero-crossing is far from the layer. The enhancement of magnetic islands width at the peak is only around a factor of two, when the absolute value of local rotation is not larger than 10-20 krad/s. It is further confirmed in a modeling of plasma response in an EAST ELM suppression discharge. Though there is a zero-crossing in $E\times B$ rotation but not in electron perpendicular rotation, no significant difference in plasma response is obtained using these two rotation profiles. This suggests that the rotation near pedestal top should not be far away from zero but may not be necessary to have zero-crossing for accessing ELM suppression., Comment: 9 pages, 9 figures, submitted to Physics of Plasmas

Using the orbit-following code ASCOT, we model alpha particle transport in ITER under the influence of ELM control coils (ECCs), toroidal field ripple, and test blanket modules, with emphasis on how the plasma response (PR) modifies the transport mechanisms and fast ion loads on the divertor. We found that while PR shields the plasma by healing broken flux surfaces, it also opens a new loss channel for marginally trapped particles: PR causes strong toroidal variation of the poloidal field near the X-point which leads to de-localisation of banana tips and collisionless transport. The reduction in passing particle losses and the increase in marginally trapped particle losses shift divertor loads from targets to the dome and under-the-dome structures. The plasma response was calculated by both MARS-F and JOREK codes. The new transport mechanism was stronger for PR calculated by JOREK which, unlike MARS-F, explicitly includes the X-point.

Resonant magnetic perturbations (RMP) have extensively been demonstrated as a plausible technique for mitigating or suppressing large edge localized modes (ELMs). Associated with this is a substantial amount of theory and modelling efforts during recent years. Various models describing the plasma response to the RMP fields have been proposed in the literature, and are briefly reviewed in this work. Despite their simplicity, linear response models can provide alternative criteria, than the vacuum field based criteria, for guiding the choice of the coil configurations to achieve the best control of ELMs. The role of the edge peeling response to the RMP fields is illustrated as a key indicator for the ELM mitigation in low collisionality plasmas, in various tokamak devices., Comment: 32 pages, 10 figures. This is an author-created, un-copyedited version of an article submitted for publication in Plasma Physics and Controlled Fusion. IoP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

Sustained ELM mitigation has been achieved on MAST and AUG using RMPs with a range of toroidal mode numbers over a wide region of low to medium collisionality discharges. The ELM energy loss and peak heat loads at the divertor targets have been reduced. The ELM mitigation phase is typically associated with a drop in plasma density and overall stored energy. In one particular scenario on MAST, by carefully adjusting the fuelling it has been possible to counteract the drop in density and to produce plasmas with mitigated ELMs, reduced peak divertor heat flux and with minimal degradation in pedestal height and confined energy. While the applied resonant magnetic perturbation field can be a good indicator for the onset of ELM mitigation on MAST and AUG there are some cases where this is not the case and which clearly emphasise the need to take into account the plasma response to the applied perturbations. The plasma response calculations show that the increase in ELM frequency is correlated with the size of the edge peeling-tearing like response of the plasma and the distortions of the plasma boundary in the X-point region., Comment: 31 pages, 28 figures. This is an author-created, un-copyedited version of an article submitted for publication in Nuclear Fusion. IoP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

The misalignment of field coils in tokamaks can lead to toroidal asymmetries in the magnetic field, which are known as intrinsic error fields. These error fields often lead to the formation of locked modes in the plasma, which limit the lowest density that is achievable. The intrinsic error fields on MAST have been determined by the direct measurement of the toroidal asymmetry of the fields from these coils and have been parameterised in terms of distortions to the coils. The error fields are corrected using error field correction coils, where the optimum correction is found by determining the current required to ensure that the discharge is furthest from the onset of a locked mode. These empirically derived corrections have been compared with the known coil distortions. In the vacuum approximation there is a factor of ~ 3 difference between the predicted and empirically determined correction. When the plasma response is included better agreement is obtained, but there are still some cases where the agreement is not good, which suggests that other effects such as the non-linear coupling of the error field to the plasma are important., Comment: 42 pages, 19 figures

Edge localised modes (ELMs) are a concern for future devices, such as ITER, due to the large transient heat loads they generate on the divertor surfaces which could limit the operational time of the device. This paper discusses the application of resonant magnetic perturbations (RMPs) as a mechanism for ELM control on MAST. Experiments have been performed using an n=3 toroidal mode number perturbation and measurements of the strike point splitting performed. The measurements have been made using both infrared and visible imaging to measure the heat and particle flux to the divertor. The measured profiles have shown clear splitting in L-mode which compares well with the predication of the splitting location from modelling including the effect of screening. The splitting of the strike point has also been studied as a function of time during the ELM. The splitting varies during the ELM, being the strongest at the time of the peak heat flux and becoming more filamentary at the end of the ELM (200 microseconds after the peak midplane D(alpha) emission). Variation in the splitting profiles has also been seen, with some ELMs showing clear splitting and others no splitting. A possible explanation of this effect is proposed, and supported by modelling, which concerns the relative phase between the RMP field and the ELM filament location., Comment: 26 pages, 26 figures. Presented at the Stochasticity in Fusion Plasmas Workshop, Aachen, March 2013

Lobe structures due to the application of resonant magnetic perturbations (RMPs) have been observed using wide-angle imaging of light from He1+ ions in the vicinity of the lower X-point in MAST. The data presented are from lower single-null discharges where RMPs of toroidal mode number, n, of 4 and 6 were applied. It has been found that, above a threshold value, the lobe structures extend radially, linearly with the coil current, both in L-mode and H-mode. It is observed that after the application of the RMP, as the toroidal rotation in the confined plasma decreases, the lobes extend radially, suggesting the plasma is less effectively screening the RMP field. Comparing the imaging data with results from vacuum modelling shows that this technique can accurately predict the number and poloidal location of the lobes, but over-estimates their radial extent. More accurate estimates of the extent of the lobes can be made by accounting for plasma screening of the RMP field. Qualitative agreement between simulation and experiment is found if it is assumed that the RMP penetrates 2% in normalised radius from the last closed flux surface., Comment: 32 pages, 20 figures

Sustained ELM mitigation has been achieved using RMPs with a toroidal mode number of n=4 and n=6 in lower single null and with n=3 in connected double null plasmas on MAST. The ELM frequency increases by up to a factor of eight with a similar reduction in ELM energy loss. A threshold current for ELM mitigation is observed above which the ELM frequency increases approximately linearly with current in the coils. A comparison of the filament structures observed during the ELMs in the natural and mitigated stages shows that the mitigated ELMs have the characteristics of type I ELMs even though their frequency is higher, their energy loss is reduced and the pedestal pressure gradient is decreased. During the ELM mitigated stage clear lobe structures are observed in visible-light imaging of the X-point region. The size of these lobes is correlated with the increase in ELM frequency observed. The RMPs produce a clear 3D distortion to the plasma and it is likely that these distortions explain why ELMs are destabilised and hence why ELM mitigation occurs., Comment: 41 pages, 19 figures. arXiv admin note: text overlap with arXiv:1305.3061

A toroidal, quasi-linear model is proposed to study the penetration dynamics of the resonant magnetic perturbation (RMP) field into the plasma. The model couples the linear, fluid plasma response to a toroidal momentum balance equation, which includes torques induced by both fluid electromagnetic force and by (kinetic) neoclassical toroidal viscous force. The numerical results for a test toroidal equilibrium quantify the effects of various physical parameters on the field penetration and on the plasma rotation braking. The neoclassical toroidal viscous torque plays a dominant role in certain region of the plasma, for the RMP penetration problem considered in this work., Comment: 20 pages, 14 figures. Copyright 2013 United Kingdom Atomic Energy Authority. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics

The non-linear interplay between the resistive wall mode (RWM) and the toroidal plasma flow is numerically investigated in a full toroidal geometry, by simultaneously solving the initial value problems for the n=1 RWM and the n=0 toroidal force balance equation. Here n is the toroidal mode number. The neoclassical toroidal viscous torque is identified as the major momentum sink that brakes the toroidal plasma flow during the non-linear evolution of the RWM. This holds for a mode that is initially either unstable or stable. For an initially stable RWM, the braking of the flow, and hence the eventual growth of the mode, depends critically on the initial perturbation amplitude., Comment: 26 pages, 16 figures. copyright 2013 United Kingdom Atomic Energy Authority. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics

The application of resonant magnetic perturbations (RMPs) with a toroidal mode number of n=4 or n=6 to lower single null plasmas in the MAST tokamak produces up to a factor of 5 increase in Edge Localized Mode (ELM) frequency and reduction in plasma energy loss associated with type-I ELMs. A threshold current for ELM mitigation is observed above which the ELM frequency increases approximately linearly with current in the coils. Despite a large scan of parameters, complete ELM suppression has not been achieved. The results have been compared to modelling performed using either the vacuum approximation or including the plasma response. During the ELM mitigated stage clear lobe structures are observed in visible-light imaging of the X-point region. The size of these lobes is correlated with the increase in ELM frequency observed. The characteristics of the mitigated ELMs are similar to those of the natural ELMs suggesting that they are type I ELMs which are triggered at a lower pressure gradient. The application of the RMPs in the n=4 and n=6 configurations before the L-H transition has little effect on the power required to achieve H-mode while still allowing the first ELM to be mitigated., Comment: 48 pages, 23 figures. This is an author-created, un-copyedited version of an article accepted for publication in Plasma Phys. Control. Fusion. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

The application of resonant magnetic perturbations (RMPs) with a toroidal mode number of n=3 to connected double null plasmas in the MAST tokamak produces up to a factor of 9 increase in Edge Localized Mode (ELM) frequency and reduction in plasma energy loss associated with type-I ELMs. A threshold current for ELM mitigation is observed above which the ELM frequency increases approximately linearly with current in the coils. The effect of the RMPs is found to be scenario dependent. In one scenario the mitigation is only due to a large density pump out event and if the density is recovered by gas puffing a return to type I ELMs is observed. In another scenario sustained ELM mitigation can be achieved irrespective of the amount of fuelling. Despite a large scan of parameters complete ELM suppression has not been achieved. The results have been compared to modelling performed using either the vacuum approximation or including the plasma response. The requirement for a resonant condition, that is an optimum alignment of the perturbation with the plasma, has been confirmed by performing a scan in the pitch angle of the applied field., Comment: 39 pages,19 figures

The application of non-axisymmetric resonant magnetic perturbations (RMPs) with a toroidal mode number n=6 in the MAST tokamak produces a significant reduction in plasma energy loss associated with type-I Edge Localized Modes (ELMs), the first such observation with n>3. During the ELM mitigated stage clear lobe structures are observed in visible-light imaging of the X-point region. These lobes or manifold structures, that were predicted previously, have been observed for the first time in a range of discharges and their appearance is correlated with the effect of RMPs on the plasma i.e. they only appear above a threshold when a density pump out is observed or when the ELM frequency is increased. They appear to be correlated with the RMPs penetrating the plasma and may be important in explaining why the ELM frequency increases. The number and location of the structures observed can be well described using vacuum modelling. Differences in radial extent and poloidal width from vacuum modelling are likely to be due to a combination of transport effects and plasma screening., Comment: 15 pages, 5 figures