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Time-dependent integrated simulations through codes such as TRANSP are becoming an indispensable tool for the interpretation of existing experiments and predictions of optimized scenarios. For many practical cases, quantitative simulations need to include the effect of plasma instabilities on the evolution of a tokamak discharge. An example is the degradation in energetic particle (EP) confinement induced by instabilities, which in turn affects important source terms for heating, non-inductive current, and momentum in a simulation. The reduced-physics kick model provides phase-space resolved transport probability matrices to TRANSP that are used to account for enhanced EP transport by instabilities in addition to neoclassical transport. The model has recovered the measured Alfvén eigenmode (AE) spectrum on NSTX, NSTX-U and DIII-D, and has reproduced details of phase-space resolved fast ion diagnostic data measured on DIII-D for EP-driven modes and tearing modes. In general, the kick model has proven the potential of phase-space resolved EP simulations to unravel details of EP transport for detailed theory/experiment comparison and for scenario planning based on optimization of neutral beam injection parameters. In this work, the extension of the kick model to low-frequency instabilities such as tearing modes and fishbones, in addition to AEs, is assessed. The goal is to enable TRANSP simulations that retain the main effects of multiple types of instabilities through a common framework. Results from the NSTX/NSTX-U and DIII-D tokamaks show that the extension to multi-mode scenarios can expand the range of applicability of the model for more reliable, quantitative integrated simulations. [ABSTRACT FROM AUTHOR]

This work is an extension of the previous semi-analytical work (Teng et al 2016 Nucl. Fusion56 106001), explaining the density limit with a thermo-resistive tearing mode model. The thermo-resistive island growth is calculated with a 3D MHD code M3D-C1 (Jardin et al 2012 Comput. Sci. Discovery5 014002). It is shown with nonlinear 3D MHD simulations that impurity radiation stimulates large magnetic islands at the density limit. The impact of thermal perturbations inside and outside of the island is explored. Inside the island, net cooling enhances the island growth and net heating suppresses its growth. Outside the island, thermal perturbations have a much smaller impact on the island growth. When the plasma density is increased towards the density limit, the island changes from being heated to being cooled and grows to a much larger island width. The convergence test of the simulations over the temporal and spatial grid is performed. The numerical model and the semi-analytical model are compared by calculating the terms, which are defined in the modified Rutherford equation, and good agreement is observed. [ABSTRACT FROM AUTHOR]

We use the guiding center code ORBIT to study the broadening of resonances and the parametric dependence of the resonance frequency broadening width on the nonlinear particle trapping frequency of wave-particle interaction with specific examples using realistic equilibrium DIII-D shot 159243 (Collins et al 2016 Phys. Rev. Lett. 116 095001). When the mode amplitude is small, the pendulum approximation for energetic particle dynamics near the resonance is found to be applicable and the ratio of the resonance frequency width to the deeply trapped bounce frequency equals 4, as predicted by theory. It is found that as the mode amplitude increases, the coefficient becomes increasingly smaller because of the breaking down of the nonlinear pendulum approximation for the wave-particle interaction. [ABSTRACT FROM AUTHOR]

The magnetic topology of the stochastic edge of a helical reversed-field pinch, with helicity , shows to be deeply influenced by higher harmonics , with the same n, due to toroidal coupling. As a consequence, by measuring kinetic quantities in a particular location, one can incur in substantial errors or mis-interpretations of the kinetic plasma response: only a full 3D coverage of angles can reveal the real topology of the plasma. This can be a caveat for MP application in tokamaks, because it shows that toroidal and poloidal sidebands, though smaller than the base mode by a factor  ∼, can have a sizable effect on the kinetic response of the edge plasma, and thus on related issues (for example, ELM stabilization and suppression). [ABSTRACT FROM AUTHOR]

Experiments in the DIII-D tokamak show that many overlapping small-amplitude Alfvén eigenmodes (AEs) cause fast-ion transport to sharply increase above a critical threshold in beam power, leading to fast-ion density profile resilience and reduced fusion performance. The threshold is above the AE linear stability limit and varies between diagnostics that are sensitive to different parts of fast-ion phase-space. Comparison with theoretical analysis using the nova and orbit codes shows that, for the neutral particle diagnostic, the threshold corresponds to the onset of stochastic particle orbits due to wave-particle resonances with AEs in the measured region of phase space. The bulk fast-ion distribution and instability behavior was manipulated through variations in beam deposition geometry, and no significant differences in the onset threshold outside of measurement uncertainties were found, in agreement with the theoretical stochastic threshold analysis. Simulations using the ‘kick model’ produce beam ion density gradients consistent with the empirically measured radial critical gradient and highlight the importance of including the energy and pitch dependence of the fast-ion distribution function in critical gradient models. The addition of electron cyclotron heating changes the types of AEs present in the experiment, comparatively increasing the measured fast-ion density and radial gradient. These studies provide the basis for understanding how to avoid AE transport that can undesirably redistribute current and cause fast-ion losses, and the measurements are being used to validate AE-induced transport models that use the critical gradient paradigm, giving greater confidence when applied to ITER. [ABSTRACT FROM AUTHOR]

Thanks to its advanced system for the control of magnetohydrodynamic modes, the RFX-mod device run as a tokamak is particularly suited to the study of the possible impact on runaway electron (RE) de-confinement in response to applied magnetic perturbations. This paper shows that during the flat-top phase in RFX-mod discharges, with a plasma current of kA and a low density ( m−3), the amount of REs scales with the m  =  2,n  =  1 perturbation both in q(a)  <  2 and q(a)  >  2 plasmas. Similar results have also been obtained in post-disruption phases, but still with limited statistics. The mechanisms generating REs and the effect of magnetic perturbation (MP) on their confinement are interpreted by numerical simulations with the relativistic guiding center code ORBIT. The role played by different magnetic equilibria on the energy of REs and on their loss rates is investigated. ORBIT simulations indicate that RE-enhanced losses are associated with a raised level of stochasticity, the effect being more pronounced when the MP amplitude is higher and internally resonant. [ABSTRACT FROM AUTHOR]

Tokamak plasmas can feature a large population of energetic particles (EP) from neutral beam injection or fusion reactions. In turn, energetic particles can drive instabilities, which affect the driving EP population leading to a distortion of the original EP distribution function and of quantities that depend on it. The latter include, for example, neutral beam (NB) current drive and plasma heating through EP thermalization. Those effects must be taken into account to enable reliable and quantitative simulations of discharges for present devices as well as predictions for future burning plasmas. Reduced models for EP transport are emerging as an effective tool for long time-scale integrated simulations of tokamak plasmas, possibly including the effects of instabilities on EP dynamics. Available models differ in how EP distribution properties are modified by instabilities, e.g. in terms of gradients in real or phase space. It is therefore crucial to assess to what extent different assumptions in the transport models affect predicted quantities such as EP profile, energy distribution, NB driven current and energy/momentum transfer to the thermal populations. A newly developed kick model, which includes modifications of the EP distribution by instabilities in both real and velocity space, is used in this work to investigate these issues. Coupled to TRANSP simulations, the kick model is used to analyze NB-heated NSTX and DIII-D discharges featuring unstable Alfvén eigenmodes (AEs). Results show that instabilities can strongly affect the EP distribution function, and modifications propagate to macroscopic quantities such as NB-driven current profile and NB power transferred to the thermal plasma species. Those important aspects are only qualitatively captured by simpler fast ion transport models that are based on radial diffusion of energetic ions only. [ABSTRACT FROM AUTHOR]

The redistribution and potential loss of energetic particles due to MHD modes can limit the performance of fusion plasmas by reducing the plasma heating rate. In this work, we present validation studies of the 1.5D critical gradient model (CGM) for Alfvén eigenmode (AE) induced EP transport in NSTX and DIII-D neutral beam heated plasmas. In previous comparisons with a single DIII-D L-mode case, the CGM model was found to be responsible for 75% of measured AE induced neutron deficit [1]. A fully kinetic HINST is used to compute mode stability for the non-perturbative version of CGM (or nCGM). We have found that AEs show strong local instability drive up to violating assumptions of perturbative approaches used in NOVA-K code. We demonstrate that both models agree with each other and both underestimate the neutron deficit measured in DIII-D shot by approximately a factor of 2. On the other hand in NSTX the application of CGM shows good agreement for the measured flux deficit predictions. We attempt to understand these results with the help of the so-called kick model which is based on the guiding center code ORBIT. The kick model comparison gives important insight into the underlying velocity space dependence of the AE induced EP transport as well as it allows the estimate of the neutron deficit in the presence of the low frequency Alfvénic modes. Within the limitations of used models we infer that there are missing modes in the analysis which could improve the agreement with the experiments. [ABSTRACT FROM AUTHOR]

The Greenwald density limit, found in all tokamak experiments, is reproduced for the first time using a phenomenologically correct model with parameters in the range of experiments. A simple model of equilibrium evolution and local power balance inside the island has been implemented to calculate the radiation-driven thermo-resistive tearing mode growth and explain the density limit. Strong destabilization of the tearing mode due to an imbalance of local Ohmic heating and radiative cooling in the island predicts the density limit within a few percent. The density limit is found to be a local edge limit and weakly dependent on impurity densities. Results are robust to a substantial variation in model parameters within the range of experiments. [ABSTRACT FROM AUTHOR]

A new wave particle resonance mechanism is found explaining the first-orbit prompt neutral beam-ion losses induced by shear Alfvén Eigenmodes (AEs) in the DIII-D tokamak. Because of the large banana width, a typical trapped beam ion can only interact locally with a core localised Alfvén Eigenmode for a fraction of its orbit, i.e. part of its inner leg of the banana orbit. These trapped beam ions can experience substantial radial kick within one bounce as long as the phases of the wave seen by the particles are nearly constant during this local interaction. A wave particle resonant condition is found based on the locally averaged particle orbit frequencies over the interaction part of the particle orbit. It is further found that the frequency width of the local resonance is quite large because the interaction time is short. This implies that particles over a considerable region of phase space can interact effectively with the localised AEs and experience large radial kicks within one bounce orbit. The radial kick size is found numerically and analytically to scale linearly in AE amplitude and is about 5 cm for typical experimental parameters. These results are consistent with experimental measurement. [ABSTRACT FROM AUTHOR]

Neutral beam injection (NBI) is one of the primary tools foreseen for heating, current drive (CD) and q-profile control in future fusion reactors such as ITER and a Fusion Nuclear Science Facility. However, fast ions from NBI may also provide the drive for energetic particle-driven instabilities (e.g. Alfvénic modes (AEs)), which in turn redistribute fast ions in both space and energy, thus hampering the control capabilities and overall efficiency of NB-driven current. Based on experiments on the NSTX tokamak (M. Ono et al 2000 Nucl. Fusion40 557), the effects of AEs and other low-frequency magneto-hydrodynamic instabilities on NB-CD efficiency are investigated. A new fast ion transport model, which accounts for particle transport in phase space as required for resonant AE perturbations, is utilized to obtain consistent simulations of NB-CD through the tokamak transport code TRANSP. It is found that instabilities do indeed reduce the NB-driven current density over most of the plasma radius by up to ∼50%. Moreover, the details of the current profile evolution are sensitive to the specific model used to mimic the interaction between NB ions and instabilities. Implications for fast ion transport modeling in integrated tokamak simulations are briefly discussed. [ABSTRACT FROM AUTHOR]