[en] The pressure profile and plasma shape, parameterized by elongation (κ), triangularity ((delta)), and squareness (ζ), strongly influence stability. In this study, ideal stability of single null and symmetric, double-null, advanced tokamak (AT) configurations is examined. All the various shapes are bounded by a common envelope and can be realized in the DIII-D tokamak. The calculated AT equilibria are characterized by P₀/(l_angle)P} ∼ 2.0-4.5, weak negative central shear, high q_min (>2.0), high bootstrap fraction, an H-mode pedestal, and varying shape parameters. The pressure profile is modeled by various polynomials together with a hyperbolic tangent pedestal, consistent with experimental observations. Stability is calculated with the DCON code and the resulting stability boundary is corroborated by GATO runs

[en] Nonlinear simulations of experimentally observed magnetohydrodynamic (MHD) bursts in DIII-D [J. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] L-mode negative central magnetic shear (NCS) discharges were performed with a full three-dimensional nonlinear MHD code. The effects of plasma rotation in the presence of resistivity and viscosity are included and an effectively implicit numerical scheme allows the transport profile to evolve self-consistently with the nonlinear MHD instabilities and externally applied sources and sinks. The simulations follow the MHD bursts and disruptions through the linear and nonlinear phases and identify the connections between the early MHD bursts and the ultimate disruption phase. Specific predictions of the growth and saturation of the modes are directly compared with experimental diagnostic measurements in DIII-D. The simulations show that the bursts observed in experiments are triggered by MHD instability of a resistive interchange mode and a resistive kink mode that are excited for critical plasma profiles. The critical profiles are determined by the balance between inductive and noninductive sources of current density

[en] Experimentally, during fast wave (FW) radio frequency (rf) heating in DIII-D L-mode discharges, strong acceleration of neutral beam (NB) deuterium beam ions has been observed. Significant effects on the n/m = 1/1 sawtooth stability are also seen. Simulations using the Monte-Carlo Hamiltonian code ORBIT-RF, coupled to the TORIC full wave code, predict beam ion tails up to a few hundred keV, in agreement with the experiment. The simulations and experiment both clearly show a much greater efficiency for 4th harmonic FW heating than for 8th harmonic heating. Simple analyses of the kinetic contribution to the ideal magnetohydrodynamic (MHD) potential energy from energetic beam ions generated by FW heating yields reasonable consistency with the observations. A more detailed analysis shows a more complicated picture, however. Other physics effects such as geometry, plasma rotation, and the presence of a free boundary, play a significant role

[en] Magnetohydrodynamic (MHD) n = 1 kink mode with n the toroidal mode number is studied and the operational beta limit, constrained by the mode, is calculated for the equilibrium of HL-2A by using the GATO code. Approximately the same beta limit is obtained for configurations with a value of the axial safety factor q₀ both larger and less than 1. Without the stabilization of the conducting wall, the beta limit is found to be 0.821% corresponding to a normalized beta value of β^c_N = 2.56 for a typical HL-2A discharge with a plasma current I_p = 0.245 MA, and the scaling of β^c_N ∼constant is confirmed. (magnetically confined plasma)

[en] The internal structure of the toroidicity-induced Alfven eigenmode (TAE) is studied by comparing soft x-ray profile and beam ion loss data taken during TAE activity in the DIII-D tokamak [W. W. Heidbrink , Nucl. Fusion 37, 1411 (1997)] with predictions from theories based on ideal magnetohydrodynamic (MHD), gyrofluid, and gyrokinetic models. The soft x-ray measurements indicate a centrally peaked eigenfunction, a feature which is closest to the gyrokinetic model's prediction. The beam ion losses are simulated using a guiding center code. In the simulations, the TAE eigenfunction calculated using the ideal MHD model acts as a perturbation to the equilibrium field. The predicted beam ion losses are an order of magnitude less than the observed ∼6%--8% losses at the peak experimental amplitude of {delta}B_r/B₀≅2--5 x 10^-4

[en] Multi-layer perceptron based neural networks (NNs) are trained to predict the Troyon no-wall beta limits due to the onset of low-n (n = 1–3, n is the toroidal mode number) ideal external kink instabilities in tokamak plasmas. It is found that a well trained NN can predict the n = 1 no-wall beta limit within 10% relative error. The NN performance is somewhat worse for the n = 2 and 3 no-wall beta limits, but still a relative error within 20% is achievable. The trained NNs well reproduce the known dependences of the no-wall beta limits on the plasma pressure (pressure peaking factor) and current (plasma internal inductance) profiles. Other scalings are also easily established with NNs, for parametric dependences such as on the aspect ratio, the elongation and triangularity of the plasma boundary shape. The results show that the semi-analytically generated training database can be used to train NNs for predicting the no-wall limit in realistic experiments. These NN-based Troyon beta limit predictors can be incorporated into integrated modeling platforms, or directly implemented as a real time stability estimator for the purpose of disruption avoidance or mitigation during experiments. (paper)

[en] The possibility of kinetic Alfven wave current drive at the center of tokamaks is proposed. The amount of driven current could be substantial and strongly affect the dynamics of the plasma central region. The relevance of this mechanism to present day and future tokamaks operating in the hybrid regime is discussed

[en] Experiments conducted at DIII-D investigate the role of drift kinetic damping and fast neutral beam injection (NBI)-ions in the approach to the no-wall β_N limit. Modelling results show that the drift kinetic effects are significant and necessary to reproduce the measured plasma response at the ideal no-wall limit. Fast neutral-beam ions and rotation play important roles and are crucial to quantitatively match the experiment. In this paper, we report on the model validation of a series of plasmas with increasing β_N, where the plasma stability is probed by active magnetohydrodynamic (MHD) spectroscopy. The response of the plasma to an externally applied field is used to probe the stable side of the resistive wall mode and obtain an indication of the proximity of the equilibrium to an instability limit. We describe the comparison between the measured plasma response and that calculated by means of the drift kinetic MARS-K code [Liu et al., Phys. Plasmas 15, 112503 (2008)], which includes the toroidal rotation, the electron and ion drift-kinetic resonances, and the presence of fast particles for the modelled plasmas. The inclusion of kinetic effects allows the code to reproduce the experimental results within ∼13% for both the amplitude and phase of the plasma response, which is a significant improvement with respect to the undamped MHD-only model. The presence of fast NBI-generated ions is necessary to obtain the low response at the highest β_N levels (∼90% of the ideal no-wall limit). The toroidal rotation has an impact on the results, and a sensitivity study shows that a large variation in the predicted response is caused by the details of the rotation profiles at high β_N

[en] The stability of resistive modes is examined using reconstructions of experimental equilibria in the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)], revealing the important physics in mode onset as discharges evolve to instability. Experimental attempts to access the highest β in tokamak discharges, including 'hybrid' discharges, are typically terminated by the growth of a large 2/1 tearing mode. Model equilibria, based on experimental reconstructions from one of these discharges with steady state axial q₀≅1, are generated varying q₀ and pressure. For each equilibrium, the PEST-III code [A. Pletzer, A. Bondeson, and R. L. Dewar, J. Comput. Phys. 115, 530 (1994)] is used to determine the ideal magnetohydrodynamic solution including both tearing and interchange parities. This outer region solution must be matched to the resistive inner layer solutions at the rational surface to determine resistive mode stability. From this analysis it is found that the approach to q=1 simultaneously causes the 2/1 mode to become unstable and the nonresonant 1/1 displacement to become large, as the ideal β limit rapidly decreases toward the experimental value. However, the 2/2 harmonic on axis, which is also large and is coupled to the saturated steady state 3/2 mode, is thought to contribute to the current drive sustaining q₀ above 1 in these hybrid discharges. Thus, the approach to the q=1 resonance is self-limiting in this context. This work suggests that sustaining q₀ slightly above 1 will avoid the 2/1 instability and will allow access to significantly higher β values in these discharges

[en] We evaluate the accuracy of the Porcelli sawtooth model using more realistic numerical models from the ORBIT-RF and GATO codes in DIII-D fast wave heating experiments. Simulation results confirm that the fast wave-induced energetic trapped particles may stabilize the sawtooth instability. The crucial kinetic stabilizing contribution strongly depends on both the experimentally reconstructed magnetic shear at the q = 1 surface and the calculated poloidal beta of energetic trapped particles inside the q = 1 surface