# Published Data

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### Publication Figures

Publication Date:

0000-00-00

First Author:

Yueqiang Liu

Title:

Toroidal modelling of RMP response in ASDEX Upgrade: coil phase scan, q95 dependence, and toroidal torques

Paper Identifier:

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Figure Reference | Title | Description | Number of Figure Data Items | Identifier | Download Figure Details | ||
---|---|---|---|---|---|---|---|

Fig. 1 | AUG_NF15_fig01 | The plasma boundary shape reconstructed for discharge 31131 at 6400ms, and the locations of the RMP coils on the $(R,Z)$-plane. | 0 | CF/15/370 | Download | ||

Fig. 2 | AUG_NF15_fig02 | Comparison of the amplitude of the pitch-aligned components of the vacuum field, computed by MARS-F and ERGOS, respectively, for the discharge 28061 at 1615ms, with the $n=2$ coil configuration at even parity. | 0 | CF/15/371 | Download | ||

Fig. 3 | AUG_NF15_fig03 | Plasma response field (solid) compared with the vacuum field (dashed), for (a-b) the $m/n=2/2$ and (c-d) the $m/n=3/2$ harmonics, based on discharge 30835 at 3200ms. Both (a,c) real and (b,d) imaginary parts of the Fourier components are shown. The field from the upper coils alone (blue) is compared with that from the lower coils alone (red), with zero toroidal phase for the coil current in both cases. Vertical dashed lines indicate the radial location of rational surfaces. | 0 | CF/15/372 | Download | ||

Fig. 4 | AUG_NF15_fig04 | The (a) real, and (b) imaginary, parts of the MARS-F computed plasma surface displacement along the geometric poloidal angle, for discharge 30835 at 3200ms with the $n=2$ RMP field configuration. Compared are two cases where the upper coils alone (blue) and lower coils alone (red) are powered, with zero toroidal phasing for the coil current in both cases. | 0 | CF/15/373 | Download | ||

Fig. 5 | AUG_NF15_fig05 | Comparison of (a) the real, and (b) the imaginary, parts of the the $m/n=2/1$ harmonics of the plasma response field, and (c) the real, (d) the imaginary, parts of the plasma surface displacement, based on discharge 30835 at 3200ms with the $n=1$ RMP configuration. The results from the upper coils alone (blue) is compared with that from the lower coils alone (red), with zero toroidal phasing for the coil current in both cases. Vertical dashed lines in (a) and (b) indicate the radial location of rational surfaces. | 0 | CF/15/374 | Download | ||

Fig. 6 | AUG_NF15_fig06 | Poloidal spectrum of the computed plasma response radial field with weak (top panel) and strong (bottom panel) sound wave damping model, for the toroidal phasing of the coil currents $DeltaPhi=0^{rm o}$ (a,d), $DeltaPhi=90^{rm o}$ (b,e), and $DeltaPhi=180^{rm o}$ (c,f), respectively. Modelling is based on an equilibrium from the low $q_{95}$ discharge 31128 at 3500ms, with the $n=2$ coil configuration.} | 0 | CF/15/375 | Download | ||

Fig. 7 | AUG_NF15_fig07 | Poloidal Fourier harmonics of the computed radial displacement of the plasma, with weak (upper panel) and strong (lower panel) sound wave damping model, for the toroidal phasing of the coil currents $DeltaPhi=0^{rm o}$ (a,d), $DeltaPhi=90^{rm o}$ (b,e), and $DeltaPhi=180^{rm o}$ (c,f), respectively. Modelling is based on an equilibrium from the low $q_{95}$ discharge 31128 at 3500ms, with the $n=2$ coil configuration. Shown in blue are the harmonics $m=1-4$, and in red all harmonics with $m>10$. Vertical dashed lines indicate the radial location of rational surfaces.} | 0 | CF/15/376 | Download | ||

Fig. 7 | AUG_NF15_fig08 | Comparison of various computed quantities versus the toroidal phasing $DeltaPhi$ of the coil currents, for (a) the amplitude of the last pitch resonant radial field component between the vacuum field (dashed) and the total field including the plasma response (solid), (b) the amplitude of the plasma surface displacement at the low field side mid-plane (dashed) and near the X-point (solid), (c) the internal plasma radial displacement amplitude of the core kink (dashed) versus the edge peeling-tearing (solid) components, and (d) the ratio of the peeling-tearing/kink response amplitude (dashed) versus that of the X-point/mid-plane plasma surface displacement (solid). A {it weak} parallel sound wave damping model is used, for an equilibrium from the low $q_{95}$ discharge 31128 at 3500ms, with the $n=2$ coil configuration. | 0 | CF/15/377 | Download | ||

Fig. 9 | AUG_NF15_fig09 | Comparison of various computed quantities versus the toroidal phasing $DeltaPhi$ of the coil currents, for (a) the amplitude of the last pitch resonant radial field component between the vacuum field (dashed) and the total field including the plasma response (solid), (b) the amplitude of the plasma surface displacement at the low field side mid-plane (dashed) and near the X-point (solid), (c) the internal plasma radial displacement amplitude of the core kink (dashed) versus the edge peeling-tearing (solid) components, and (d) the ratio of the peeling-tearing/kink response amplitude (dashed) versus that of the X-point/mid-plane plasma surface displacement (solid). A {it strong} parallel sound wave damping model is used, for an equilibrium from the low $q_{95}$ discharge 31128 at 3500ms, with the $n=2$ coil configuration. | 0 | CF/15/378 | Download | ||

Fig. 10 | AUG_NF15_fig10 | Comparison of the amplitude of the last pitch resonant radial field component between the vacuum field (dashed) and the total field including the plasma response (solid), for the low $q_{95}$ plasmas from discharge 31128 at 3500ms (thick lines) and from discharge 30835 at 3200ms (thin lines), with the $n=2$ coil configuration. A strong parallel sound wave damping model is assumed for both plasmas. | 0 | CF/15/379 | Download | ||

Fig. 11 | AUG_NF15_fig11 | Comparison of various computed quantities versus the toroidal phasing $DeltaPhi$ of the coil currents, for (a) the amplitude of the last pitch resonant radial field component between the vacuum field (dashed) and the total field including the plasma response (solid), (b) the amplitude of the plasma surface displacement at the low field side mid-plane (dashed) and near the X-point (solid), (c) the internal plasma radial displacement amplitude of the core kink (dashed) versus the edge peeling-tearing (solid) components, and (d) the ratio of the peeling-tearing/kink response amplitude (dashed) versus that of the X-point/mid-plane plasma surface displacement (solid). A strong parallel sound wave damping model is used, for an equilibrium from the high $q_{95}$ high $B_T$ discharge 30684 at 4005ms, with the $n=2$ coil configuration. | 0 | CF/15/380 | Download | ||

Fig. 12 | AUG_NF15_fig12 | Comparison of various computed quantities versus the toroidal phasing $DeltaPhi$ of the coil currents, for (a) the amplitude of the last pitch resonant radial field component between the vacuum field (dashed) and the total field including the plasma response (solid), (b) the amplitude of the plasma surface displacement at the low field side mid-plane (dashed) and near the X-point (solid), (c) the internal plasma radial displacement amplitude of the core kink (dashed) versus the edge peeling-tearing (solid) components, and (d) the ratio of the peeling-tearing/kink response amplitude (dashed) versus that of the X-point/mid-plane plasma surface displacement (solid). A strong parallel sound wave damping model is used, for an equilibrium from the high $q_{95}$ low $B_T$ discharge 31131 at 6400ms, with the $n=2$ coil configuration. | 0 | CF/15/381 | Download | ||

Fig. 13 | AUG_NF15_fig13 | Correlation between (a) a large $m/n=11/2$ radial field response, and (b) the local flattening of the safety factor near the $q=11/2$ rational surface, for the high $q_{95}$ plasma from discharge 30684 at 4005ms, with the $n=2$ coil configuration. Vertical dashed lines indicate the radial location of rational surfaces. | 0 | CF/15/382 | Download | ||

Fig. 14 | AUG_NF15_fig14 | Comparison of various computed quantities versus the toroidal phasing $DeltaPhi$ of the coil currents, for (a) the amplitude of the last pitch resonant radial field component between the vacuum field (dashed) and the total field including the plasma response (solid), (b) the amplitude of the plasma surface displacement at the low field side mid-plane (dashed) and near the X-point (solid), (c) the internal plasma radial displacement amplitude of the core kink (dashed) versus the edge peeling-tearing (solid) components, and (d) the ratio of the peeling-tearing/kink response amplitude (dashed) versus that of the X-point/mid-plane plasma surface displacement (solid). A strong parallel sound wave damping model is used, for an equilibrium from the low $q_{95}$ discharge 31128 at 3500ms, with the $n=4$ coil configuration. | 0 | CF/15/383 | Download | ||

Fig. 15 | AUG_NF15_fig15 | Comparison of the amplitude of the compute $n=4$ plasma surface displacement versus the geometric poloidal angle, between the odd (dashed) and even (solid) parity coil configurations, assuming (a) a weak, and (b) a strong parallel sound wave damping, based on the low $q_{95}$ discharge 31128 at 3500ms with the $n=4$ coil configuration. | 0 | CF/15/384 | Download | ||

Fig. 16 | AUG_NF15_fig16 | Comparison of various toroidal torque densities - the resonant electromagnetic torque (JXB), the neoclassical viscous torque (NTV), and the torque due to the Reynolds stress (REY) - computed from the linear plasma response, for the low $q_{95}$ discharge 31128 at 3500ms with the $n=2$ coil configuration. The decreasing thickness of the lines denotes $DeltaPhi=0^{rm o}, 90^{rm o}$, and $180^{rm o}$, respectively. | 0 | CF/15/385 | Download | ||

Fig. 17 | AUG_NF15_fig17 | Comparison of resonant (in the particle velocity phase space) versus non-resonant contributions to the NTV torque density, for the low $q_{95}$ discharge 31128 at 3500ms with the $n=2$ coil configuration at even parity ($DeltaPhi=0^{rm o}$). | 0 | CF/15/386 | Download | ||

Fig. 18 | AUG_NF15_fig18 | Comparison of various toroidal torque densities - the resonant electromagnetic torque (JXB), the neoclassical viscous torque (NTV), and the torque due to the Reynolds stress (REY) - computed from the linear plasma response for the low $q_{95}$ discharge 31128 at 3500ms with (a) the $n=2$, and (b) the $n=4$ coil configurations. Either odd (thin lines) or even (thick lines) parity of the coil current is assumed. | 0 | CF/15/387 | Download | ||

Fig. 19 | AUG_NF15_fig19 | Comparison of various toroidal torque densities - the resonant electromagnetic torque (JXB), the neoclassical viscous torque (NTV), and the torque due to the Reynolds stress (REY) - computed from the linear plasma response, for the low $q_{95}$ discharge 31128 at 3500ms with the $n=4$ coil configuration, assuming (a) 5 times reduced plasma flow speed compared with the experiment, and (b) the full flow speed and a full drift kinetic model for the NTV torque computation. Either odd (thin lines) or even (thick lines) parity of the coil current is assumed. | 0 | CF/15/388 | Download | ||

Table 1 | AUG_NF15_tab01 | Basic equilibrium parameters of the modelled plasmas. | 0 | CF/15/412 | Download | ||

Table 2 | AUG_NF15_tab02 | Toroidal phase DeltaPhi for peak amplitude of various quantities associated with the plasma response. kappa_parallel is the numerically assumed strength of the parallel sound wave damping. | 0 | CF/15/413 | Download | ||

Table 3 | AUG_NF15_tab03 | Net torques (Nm) integrated over psi_p in [0,0.99] ('full') and over psi_p in [0.9,0.99]. Strong parallel SWD assumed. | 0 | CF/15/414 | Download | ||

Table 4 | AUG_NF15_tab04 | Change of pedestal flow velocity Delta V_ped (km/s) measured in experiments versus total net torques (Nm) integrated over psi_p in [0.9,0.99] computed for reference discharges. Strong parallel SWD assumed. | 0 | CF/15/415 | Download | ||

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