Runaway electron plateau current profile reconstruction from synchrotron imaging and Ar-II line polarization angle measurements in DIII-D

Current profile reconstructions are obtained for high current ( Ip≃550 kA) post-disruption runaway electron (RE) plateau plasmas in DIII-D. Two novel methods of measuring the RE current profile in high-current RE plateaus are introduced and compared: localization of the q = 2 rational surface using visible synchrotron emission (SE) imaging and the measurement of the polarization angle of line-integrated Ar-II line emission. The two methods are found to be consistent with each other within the data uncertainties. Different simulations of the RE current profile are compared with the measurements: the toroidal fluid RE model is found to best fit the data, within the measurement uncertainties. In addition to introducing two novel methods to measure the RE current profile and validating present simulation capabilities, this work demonstrates that instabilities can grow at q = 2 and q = 1 surfaces without necessarily causing a RE final loss instability. Numerical simulations are also presented to elucidate the role of these instabilities on synchrotron emission.


Introduction
Disruptions are global discharge-terminating instabilities which can occur in tokamak plasmas after control system failures or when passing stability boundaries [1].Minimizing potential disruption wall damage is a critical challenge for future magnetic fusion energy reactors based on the tokamak geometry [2].Of the different types of potential damage, one of the most dangerous is localized damage from high toroidal current runaway electron (RE) wall strikes [3].In the presence of in-plasma impurities on closed field lines during disruptions, super-thermal electron 'seeds' can be formed; given sufficiently good confinement, these can amplify by the knock-on avalanche mechanism to take over most of the initial plasma toroidal current, forming a RE 'plateau' or current beam [4].This RE plateau typically limits against the tokamak center post and is also vertically unstable, moving upward or downward into the upper or lower divertor region.After contracting against the vessel wall, the RE beam becomes kink unstable and is lost rapidly (typically on a ≃ ms timescale) to the vessel wall, potentially causing localized wall damage [5].
To predict and minimize wall damage, the radial and vertical stability of the RE beam, as well as its scrape off, contraction, and final loss instability must be understood.These are all affected by the RE beam current profile; for example, force balance in the major radius direction depends on the current profile [6], as does stability of the RE beam to global kink modes [7].Measurement of the RE current profile is challenging, both in equilibrium and transiently (such as when the RE plateau is scraping off against the vacuum vessel).
The reconstruction of aspects of the equilibrium RE plateau current profile (such as the internal inductance l i ) has been attempted using magnetic reconstructions [5,8].However, to date, these have not been constrained with internal magnetic measurements and therefore cannot accurately reconstruct the internal current profile, especially since RE plateau plasmas tend to be circular, with low elongation.This contrasts with standard tokamak discharges, where magnetic reconstructions such as EFIT can be constrained with internal magnetic pitch angle measurements such as motional Stark effect (MSE) [9].Estimates of the RE plateau current profile have been attempted using line-integrated hard x-ray (HXR) measurements [10]; however, these are very indirect, require inversion of line-integrated data, and are only applicable in low impurity RE plateaus, where HXR pulse pileup does not occur.
Transiently, during the final loss instability, the RE current profile is even more challenging to reconstruct than in steady-state and has also not been measured experimentally.It is expected that magnetic reconstructions based on external magnetic signals, such as EFIT [11] or JFIT [12], can give a reasonable estimate of the edge safety factor q a , and these tend to give values in the vicinity of q a ≃ 2 during the final loss instability, supporting the hypothesis that a (2/1) kink instability is responsible for the RE final loss instability [5].Final loss instabilities at higher edge q ≃ 4-6 have been observed in JET; here, it was hypothesized that the current profile was hollow and that a double tearing mode was responsible for the final loss instability [13].
Theoretically, calculating the RE plateau current profile is challenging because the current is not carried by a normal thermal plasma but by relativistic electrons with an anisotropic velocity distribution [6].Normal Ohmic (Spitzer) plasma resistivity is therefore not applicable; instead RE current increases and decreases with the applied toroidal electric field in a complicated manner depending on avalanche gain and pitch angle scattering; which both depend on the background impurity level [4].Normal Grad-Shafranov equilibrium is not completely valid for REs since the pressure is in general anisotropic and higher energy REs have orbits which can deviate significantly from their nominal flux surfaces [6,14].Efforts have been made to calculate RE current profiles considering the anisotropic RE pressure, showing that RE equilibria can be strongly shifted outward in major radius (>10 cm) if the current carrying REs have sufficiently high kinetic energy (⩾10 MeV) [15].Fokker-Planck simulations of the RE current profile have been performed in both cylindrical and toroidal geometry; significant differences between the two can be seen in some conditions due to the variation in RE pitch angle along the orbit in toroidal geometry [16].
In this work, two novel methods of constraining the RE plateau current profile are introduced.First, a bright band seen in visible synchrotron emission (SE) imaging is identified as the q = 2 surface; knowing the internal location of the q = 2 surface then provides a strong constraint on the current profile.Second, the line-integrated polarization angle of Ar-II line emission is measured.Since the Ar-II emission dominantly comes from inside the RE plateau plasma, this angle provides a constraint on the RE current profile.The two methods are compared in steady state (on time scales long compared with the final loss instability) and agree within the measurement uncertainties.The RE current profile is found to be centrally peaked (not hollow).It is found that the q = 2 surface can exist locked and stable well within the plasma for extended periods of time, demonstrating that a locked (2/1) mode in the plasma is not a sufficient condition for final loss instability onset.Three different models, run to steady-state, are compared to the data: a cylindrical RE test particle model, a cylindrical fluid RE model, and a toroidal fluid RE model.Of these three, the toroidal fluid RE model appears to give the best match to the measured current profile.

Experimental setup
In this section, we present the hardware setup section 2.1 and the typical discharge time evolution section 2.2 for the shots used in this work.

Hardware setup
The experiments described here were performed on the DIII-D tokamak [17].The line of sight (LOS) of the main diagnostics used in this work are shown in figure 1, together with the material injectors used here and the DIII-D vessel outline.
The two visible cameras used here both view tangentially as shown in 1(a) and are located at toroidal angles ϕ = 90 and 225 • [18]; this toroidal separation helps identify toroidal variations in the RE synchrotron emission.For these experiments, these cameras were set up to measure visible RE SE at a wavelength of 790 nm, with a passband of 10 nm.The two camera fields of view (FOV) are geometrically similar.A high spectral resolution multi-chord visible spectrometer [19] was used to measure Ar-II line emission at 480 nm.The line was viewed in 2nd order of diffraction of the grating to improve spectral resolution, while usually the 1st order of diffraction is employed to maximize the signal intensity.Three view chords of the visible spectrometer were used: a midplane view chord, shown in figure 1(a), and two vertical view chords, shown in figure 1(b).At each view chord, vertically and horizontally polarized light is split and analyzed separately to allow determination of the Ar-II line emission polarization angle.Line-integrated cold (thermal) electron density is measured by an interferometer at ϕ = 225 • [20].Hard x-ray (HXR) signal is measured with a toroidal array of bismuth germanate (BGO) scintillators [21] (not shown in figure 1).Thermal electron density and temperature profiles are measured with Thomson scattering (TS) [22], also not shown here.The material injectors used in these experiments are shown in figure 1(a) and are used for Ar pellet injection (ArPI) at ϕ = 135 • and a massive gas injection (MGI) at ϕ = 15 • .The injection trajectories of both MGI and ArPI in the poloidal plane are shown in figure 1(b), in addition to an EFIT magnetic reconstruction of a RE plateau flux surfaces, showing approximate plasma location.

Discharge evolution
The basic shot sequence for the discharges used in this work is shown in figure 2. The shot starts as an inner wall limited, ECH-heated L-mode Deuterium discharge.A RE plateauforming disruption is triggered by 14 Torr-L ArPI at time t = 1200 ms (see figure 2

Synchrotron emission imaging to estimate current profile
In these experiments, SE is observed to have poloidal structure which varies toroidally; this variation is interpreted as being caused dominantly by the presence of a locked (2/1) island.To show this, we proceed with steps of increasing complexity: (1) firstly we characterize the features of a simulated SE image in an axisymmetric case, setting the expectation for SE measurements in a MHD free scenario, featuring intensity peaking at the LCFS and SE toroidally symmetric, (2) then we show measured SE images, featuring a poloidal phase shift at different toroidal positions and intensity peaking well inside the LCFS, and (3) finally we show that hops in the SE poloidal phase are due to a (1/1) mode.

Simulated SE.
Observation of islands using SE is complicated by the fact that SE is not expected to be poloidally symmetric even for an axisymmetric plasma.In this section the result of a 'simple' synthetic diagnostic code are presented, showing the theoretically expected SE features for an axisimmetric case.This is illustrated in figure 3(a) for SE in the visible region, with a wavelength range of 10 nm around the central wavelength of 790 nm.This simulation, performed with a code we developed, uses a smooth 'toy' tanh kinetic energy K runaway distribution f K shown in figure 3(b), with knee at K 0 = 15 MeV and scale K scale = 5 MeV.The pitch variable λ has a more complicated distribution, that depends on energy; the total RE distribution function f RE is: where the dλ distribution, shown in figure 3(c), has a knee K 0,λ = 8 MeV, a scale factor K scale,λ = 3 MeV and a minimum value λ min = 0.1.These parameters were chosen considering previous studies in DIII-D [23].The RE density is assumed to have a Gaussian radial profile with width R p = 0.2 m.The REs are assumed to be collisionless with standard collisionless pitch variable λ = sin 2 θ p /b conserved on flux surfaces, where θ p is the RE pitch angle relative to the magnetic field B and b = B/B max is the normalized magnetic field strength [24].Relativistic orbit shifts are ignored.To calculate the received SE, the Schwinger equation for gyro-averaged radiation received from a relativistic electron performing helical motion in a homogeneous magnetic field is used [25,26].This 'simple' code, as compared with more sophisticated codes, like KORC or SOFT, retains enough physics to produce realistic images, letting us scan the RE beam parameters in a reasonable amount of time.From figure 3(a), it is apparent that the SE image from a collisionless axisymmetric RE beam is strongly shifted to the high field side (HFS).This results from a pile-up of RE density on the HFS due to two factors: (a) the conservation of magnetic moment increases pitch angle and slows toroidal RE velocity on the HFS compared with the low field side (LFS) and (b) the higher toroidal magnetic field on the HFS results in a lower field line pitch on the HFS compared with the LFS.There is an off-midplane rotation of the peak HFS SE θ peak which is due to the plasma current forming helical field lines.In the simulations, the SE spot rotation angle θ peak is observed to decrease linearly with increasing plasma current, consistently with what reported in [27], and to have a constant negative offset if the viewing camera is moved vertically away from the RE beam axis (Z cam ̸ = 0).In addition, θ peak depends only very weakly on the shape of the RE energy and pitch distributions (see figure 3(d)).

Measured SE and rational surface identification.
Actual SE images measured in these experiments are shown in figures 4(a) and (b).The SE is not observed to peak at the LCFS (red curve from EFIT) but rather well inside the LCFS.Additionally, the SE shows toroidal variation in structure, seen comparing figures 4(a) and (b).Our hypothesis is that this enhanced ring structure of SE is due to a locked (2/1) island inside the RE plateau.This hypothesis is supported by the fit θ peak as a function of time during a shot with a plasma current ramp, shown in figure 4(c) for both 90 and 225 degree camera views and for the plasma 'edge' (outer edge of measurable SE) and 'q = 2' (band of brightest SE) minor radii.The HFS peak SE angle θ peak is not found experimentally to decrease monotonically with increasing plasma current.Additionally, it is different at different toroidal viewing locations.Finally, there is a sudden 'hop' in θ peak at all locations following internal (1/1) sawtooth-like instabilities.This suggests that the (1/1) mode causes a current profile perturbation which causes a shift in the locked (2/1) mode phase, causing a sudden change in θ peak .
Because they cause a sudden (≃ ms time scale) phase jump in the (2/1) island phase which is fast compared with typical evolution timescales of the RE plateau current profile (>10 ms), the (1/1) modes allow difference imaging to be applied, to enhance contrast and allow better imaging of the (2/1) mode structure.This is illustrated in figures 5(c) and (d), where difference (before minus after the mode) SE images are shown for (1/1) modes occurring at two different times: (c) t = 1472 ms, and (d) t = 1879 ms.The corresponding SE radiance before the mode onset is shown in figures 5(a) and (b) for completeness.Several minor radii of interest are tentatively identified by curves added to the difference images.The red curve labeled 'edge' denotes the outermost boundary where strong SE is observed.This serves as a marker for the edge of the RE current channel.The magenta circle labeled 'q = 2' refers to the band of strongest SE (see figures 5(a) and (b)), as was previously shown in figures 4(a) and (b).A completely different mode phase (positive vs negative) can be observed when comparing this region in figures 5(c) and (d).This strongly support our hypothesis of the (2/1) mode modulating the RE SE and shifting its phase as a consequence of a (1/1) mode.The blue circle refers to the outermost region where no change in SE is observed; this is labeled 'q = 1', while half way between 'q = 1' and 'q = 2' is labeled 'q = 3/2'.

(1/1) mode identification.
The identification of the internal modes seen in figures 4 and 5 as (1/1) modes is performed using external magnetic sensors.This is shown in figure 6 for the mode we identified in figure 4(c), but the same A poloidal profile at time t = 1473.35ms, at the mode peak, is shown in figure 6(h).The mode clearly has a poloidal m = 1 structure, consistent with a (1/1) mode, which supports the hypothesis that a q = 1 surface exists in these plasmas.

Discussion on rational surface identification.
Although the q surface identifications of figure 5 are somewhat speculative, the localization of the q = 2 surface, is at least supported by further evidence including: (1) the SE q = 2 surface approaches the plasma edge in a manner consistent with EFIT and JFIT (in RE plateau discharges), (2) the SE q = 2 surface localization gives a current profile consistent with Ar-II line polarization angle (in RE plateau discharges), and (3) enhanced SE emission clearly observed at the q = 2 surface in a QRE shot where MSE is available to confirm the location of q = 2 (this is, however, not a RE plateau discharge).More details on point 3 above (see figure 13) will be discussed in section 6.The next section 3.2 describes the constraint of the RE plateau current profile using Ar-II line polarization angle.

Ar-II line polarization angle measurement for constraint of RE current profile
Line polarization angle is routinely used to constrain tokamak plasma current profiles via MSE measurement of D α [9].However, this diagnostic has to-date not been successfully applied to RE plateau plasmas due to huge background D α signals, motivating a search for alternative methods to constrain RE current profile.In these RE plateaus, Ar-II line emission is a good candidate for line polarization measurements because Ar + is found inside the RE plateau and emits strongly throughout much of the visible region.Here, we use measurements of the Ar-II 480.6 nm line obtained with a spectrometer set to 2nd order diffraction.An example of an unpolarized line spectrum is shown in figure 7(a), while the line seen on the same (radial) view chord at the same time, after passing through a vertical polarizer, showing strong reduction in the relative strength of the π component, is shown in figure 7(b).The spectra (black curves) are fit (red curves) including the spectral response of the spectrometer and varying as free parameters the total area under the spectra (total brightness), the central major radius R of the Ar-II emission region along the LOS, the Gaussian width of the emission region in R, and the mean polarization angle (with 0 being horizontal).Figure 7(c) shows the Ar-II brightness as a function of minimum tangency radius a Tan .Triangles correspond to vertical view chords, shown in figure 1(b), and circles correspond to the radial view chord, shown in figure 1(a).The multiple points are taken from a vertical downward scan of the RE plateau, allowing multiple tangency radii to be measured with one view chord.Lineintegrated mean Ar-II polarization angles as a function of tangency radius a Tan are shown in figure 7(d).The fit uncertainties are fairly small near the center of the plasma, but become quite large past the edge of the plasma, around minor radius a min ≃ 0.4 m.Predicted polarization angle for a flat current profile is shown by the dashed magenta curve in figure 7(d).Depolarizing reflections off graphite wall tiles are expected to cause a small (≃ 0.02 radian) shift in the measured polarization angle, as shown by the solid magenta line in figure 7(d).This effect is corrected for in the remainder of this paper using a double-bounce ray tracing model and reflection depolarization data taken at the wavelength of interest measured on an actual plasma-exposed graphite wall tile from DIII-D.
To convert a given current profile to a predicted lineintegrated Ar-II polarization angle, it is necessary to know the Ar-II emissivity profile ϵ(x, y) across the poloidal plane.For this purpose, we use a hybrid inversion of the spectrometer data, which combines a Zeeman inversion, that uses measurement of the Ar-II σ component broadening vs tangency radius, with a brightness inversion, that uses the total Ar-II brightness vs tangency radius.The resulting Ar-II emissivity prediction is shown in figure 8(a).A comparison study of different inversion techniques was performed and is shown in figures 8(b)-(d), albeit not for the target plasma studied here (I p = 550 kA) but for a lower current (I p = 275 kA) target plasma.Figure 8(b) shows a camera inversion, where a line-integrated tangential Ar-II image was taken and is then inverted assuming toroidal symmetry of the Ar-II emissivity.Figure 8(c) shows a Zeeman inversion, using just the broadening of the Ar-II σ component as a function of tangency radius, and figure 8(d) shows a brightness inversion, using the Ar-II brightness measured with the spectrometer as a function of tangency radius.Overall, the three methods are found to be in reasonable agreement, lending credibility to the hybrid approach of combining Zeeman and brightness inversion techniques to obtain the best possible Ar-II emissivity profile with the available data.There is no Ar-II camera imaging data available in the I p = 550 kA target shots studied here, as both cameras were set on SE imaging.
The q = 2 surface identification of figure 5 from SE imaging appears to be consistent with the Ar-II polarization angles and with the edge q estimated from magnetic reconstructions.This is shown in figure 9 where time traces from a CP compression shot are shown.Figure 9(a) shows the major radius R 0 of the RE beam as a function of time from JFIT, EFIT, Ar-II spectroscopy, and from SE, showing reasonable agreement between different methods of measuring the RE beam radial position.Figure 9(b) shows the RE beam minor radius (distance from R 0 to the center post and LCFS) a min from EFIT and JFIT.The edge, q = 1, and q = 2 radii estimated from SE (as shown in figure 5) are shown as well.Interestingly, the SE rational surfaces appear unaffected by the motion to the CP, indicating that the RE beam current channel is initially detached from the wall.This is distinct from normal tokamak plasmas, where the current channel fills the available flux surfaces up to the LCFS. Figure 9(c) shows the central safety factor q 0 estimated from EFIT, JFIT, SE, and Ar-II spectroscopy.The EFIT estimate simply uses a standard EFIT run without any internal constraints on current profile, giving initially a very low q 0 ≃ 0.25.The JFIT estimate uses the magnetic axis and minor radius calculated by JFIT and then varies the width of a Gaussian current profile to match radial force balance (including time-dependent wall currents and assuming zero plasma pressure).This estimate is higher than EFIT, giving an initial q 0 ≃ 0.5.The SE estimate uses the q = 1, 3/2, and 2 surfaces as shown in figure 5.The current profile j(r) is assumed to be smooth and monotonically decreasing.From this current profile we can calculate q 0 .This method arrives at a central q just below 1, in the range q 0 ≃ 0.8-1.The Ar-II estimate also assumes a Gaussian current profile, and varies the Gaussian width to best match the line-integrated Ar-II polarization angle and then calculates q 0 .This method also arrives at q 0 just below 1, again in the range q 0 ≃ 0.8-1 for most of the RE plateau duration, consistent with the SE estimate.Figure 9(d) shows the edge safety factor q a (at the minor radius a min ) estimated from EFIT and JFIT.This is initially quite large q a ≃ 4-6, but then drops to q a ≃ 2.5-3 at later times, as the RE plateau is pushed against the CP.This is consistent with the SE estimate of the q = 2 surface radius, figure 9(b), which indicates that the q = 2 surface lies just inside a min at later times.

Simulation of current profile
This section describes attempts at modeling the current profile of the I p = 550 kA RE plateaus studied here.Any accurate modeling of the RE current profile must begin with the impurity profile, since the impurity profile sets the drag and pitch angle scattering on the REs which carry the current.Here, a 1D cylindrical diffusion model is used to estimate the radial profile of different impurities.As part of the 1D cylindrical diffusion model, a 1D cylindrical RE test particle model is run, providing an initial estimate of the RE current profile.Refined single step (non-iterative) RE current profiles are then estimated by feeding the impurity profile from the 1D diffusion model into fluid RE models, which encompasses a cylindrical model and a toroidal model.

1D diffusion model of impurity profile
The 1D impurity diffusion model used here has been described extensively in a previous work [28].An infinitely long cylinder is assumed where cold thermal ions diffuse radially with an anomalous radial diffusion coefficient D i = 2 m 2 s −1 as determined from pulsed impurity deposition experiments [29].For neutrals, standard neutral collisional diffusion is used, but with a scale factor D N = 5 used to account for large scale convective cells [30].To approximate the toroidal (noncylindrical) vacuum chamber, where the RE current channel leans against the CP but a significant volume of the vacuum chamber remains free of REs for neutrals to populate, the REs are assumed to limit at a minor radius r/a min = 1, but the thermal plasma and neutrals are assumed to recycle at a larger radius, halfway between a min and the radius required to give the correct vacuum chamber volume.This model is found to give best agreement with recycled neutral line brightnesses [31]; which corresponds to r/a min = 1.5 here.Plasma chemistry (including thermal and RE ionization, thermal recombination, charge exchange, and dissociation) is included between all dominant ion species.The model is run until it reaches a steady-state.The electric field diffusion problem is not solved: the loop voltage is assumed flat across the profile and this loop voltage is adjusted until the desired total plasma current is reached.The ion diffusion and RE test particle model (described in the next section 4.2) are iterated together consistently.Radial profiles predicted by the 1D diffusion model for the I p = 550 kA RE plateaus studied here are shown in figure 10. Figure 10(a) shows radial profiles of different neutrals: as expected, neutral profiles are hollow and He is the dominant neutral species.

Test particle RE model
Heating of the background thermal plasma in the 1D diffusion model comes from RE collisions.A rough radial and energy distribution of the background REs is therefore required.For this purpose, a simple RE test particle model [32] is run self-consistently with the 1D diffusion model.A mono-energy/mono-pitch distribution function is assumed, where REs at a specific kinetic energy have a single pitch angle.REs are moved up and down in energy according to the test particle force balance and assigned a weight which can change in time as REs are depleted or re-formed.The model includes synchrotron drag and the avalanche source term but ignores bremsstrahlung energy loss and cannot accurately model toroidal effects like trapped particles and variation of pitch angle during the RE orbit.The RE test particle model typically matches the experimental loop voltage, i.e. the loop voltage in the model is adjusted till the current matches the experimental I p , within a factor of 2 or better.In this case a loop voltage of 1.4 V is predicted, while 3.2 V is measured.

RE fluid model
To provide an improved estimate of the RE current profile over the RE test particle model described in the previous section 4.2, fluid RE simulations are performed using the DREAM code [16].DREAM is resolved radially (1D) using either cylindrical or toroidal geometry.It has the option to use fully kinetic or fluid REs.Benchmarks between the two modes of operation show that fully kinetic REs are desirable to accurately model the time dependence of RE seed formation, while the much less expensive fluid RE mode is sufficiently accurate for modeling steady-state current profiles.The electric field is allowed to evolve and diffuse in time through an Ampere-Faraday solver; the loop voltage profile is observed to flatten when steady-state is reached.This results in a flat electric field profile in cylindrical geometry, while a more realistic electric field profile is obtained in toroidal geometry.In this work DREAM is run in fluid mode using the impurity profiles generated with the 1D diffusion model.

Comparison between measured and simulated current profiles
Comparisons between measured and simulated RE plateau steady-state current profiles are shown in figure 11(a).The estimate from the SE imaging rational surface identifications is shown by a cyan curve.The calculated current profile from the test particle model, using a 1.4 V loop voltage to reach a steady-state current I p = 550 kA, is shown with an orange dashed curve.The cylindrical fluid RE model, when run with the experimentally measured loop voltage of 3.2 V, predicts a hollow current profile, represented by the magenta dashed curve.Turning up to a slightly higher loop voltage of 4.2 V, however, was found to give 550 kA current steady-state and centrally peaked current profile, green dashed curve.For a 3.2 V loop voltage, the toroidal fluid RE model does not give a steady-state solution, with the RE current damping down to zero.Increasing to 4.2 V loop voltage, however, gives a centrally peaked steady-state solution close to the SE prediction.Note that adjusting loop voltage to match experimental RE plateau current is typically required in simulations, with disagreements of order 2x between measured and modeled loop voltage being common.EFIT (see the solid magenta curve in figure 11(a)) predicts a very strongly peaked current profile, with a central current density twice as high as the SE prediction.
Figure 11(b) shows the different current profiles of figure 11(a) compared with the line-integrated Ar-II polarization angle measurements (shown already in figure 7(d)).In each case, the current profile prediction is combined with the 'hybrid' Ar-II emissivity inversion to give a predicted lineintegrated Ar-II polarization angle as a function of tangency minor radius a Tan .Within the uncertainty of the measurements, the SE measurement (cyan), test particle model (orange), and toroidal fluid RE model (red) are all in agreement with the Ar-II polarization angle.The EFIT current profile (magenta solid) and cylindrical fluid RE models (dashed magenta and green lines) fall outside the measurement uncertainty.We conclude that the actual current profile for these RE plateaus is best represented by the either the red, cyan, or orange curves of figure 11(a).

Synchrotron emission in the presence of a (2/1) mode and magnetic stochasticity
In the steady-state RE plateaus studied here, it appears that there is an annulus of enhanced SE at the q = 2 surface with some poloidal structure caused by a locked (2/1) mode.It is not clear from the data if the enhanced SE is coming from the island O-point or X-point, or how the mode structure is enhancing the SE.During CP compression of the RE plateau, dark regions appearing to be islands can be seen at rational surfaces, as shown in figure 12, where contrast is enhanced by normalizing the SE at each radial position separately, indicating that island O-points can be regions of reduced SE.This is consistent with observations in JET, where dark regions in SE imaging were identified as locked island O-points [33].A counterexample, where island O-points appear to cause enhanced SE, is shown in figure 13.The data of figure 13 was not taken from a post-disruption RE plateau, but from a 'QRE' discharge, where a low-density breakdown is used to create a non-thermal slide-away population at early times.A weak (low current) RE population is formed which slowly damps with time.An external rotating (I-coil) non-axisymmetric magnetic perturbation is intentionally applied to create a rotating (2/1) islands which can be seen to have enhanced SE in the O-point region, as shown in figure 13(a).In this shot, MSE-constrained EFIT is available, clearly identifying the q = 2 surface, also shown in figure 13(a).The enhanced O-point SE is observed to damp as a function of time, as seen in figure 13(b).The observed island O-point phase vs time is consistent with the island having poloidal mode number m = 2, as shown in figure 13(c).
Simulations indicate that changes in SE from magnetic islands are due to changes in RE transport, not from changes in pitch angle [34].This is demonstrated in figures 14 and 15, where SE in the vicinity of a 5 cm wide (2/1) island is simulated using the KORC full-orbit RE tracking code [14].In the simulation of figure 14, a pure (2/1) island is created with no island overlap or stochasticity, as shown in the Poincare plot figure 14(d).REs are released in an annulus at the (2/1) island minor radius and allowed to relax to a kinetic equilibrium, before SE is computed.In figure 14(a) a case with  no applied island is shown, while in figure 14(b) a case with an applied (2/1) island at 90 • phase (Φ O = 90 • ) is shown.Almost no difference in the SE poloidal structure, as well as in the radial profile at Z = 0 (figure 14(c)), is observed, demonstrating that a basic locked phase (2/1) island of 5 cm width does not create a poloidally-varying SE structure simply from its poloidally-varying perturbation to the RE orbit and pitch angle.Note that we would have reached the same conclusion for any other phase Φ O .The situation drastically changes when a region of stochastic magnetic field is created as shown in figure 15(e), by including at the edge of the simulation domain (q > 2) additional overlapping modes.In this simulation, the RE that are generated or diffuse in the stochastic region are rapidly lost, while the RE generated close to the island Opoint remain confined, as well as those located in the inner integrable magnetic field region.This results in a strong SE from the island O-point region, as shown in figures 15(a)-(c) for the island phase of Φ O = [0, 45, 90] degree respectively, together with a faint SE from the inner (integrable) zone.The relative emission intensity of the two zones can be compared in figure 15(d), that shows the normalized radial profile at Z = 0 for the three island phases.These simulations clearly show that an island surrounded by a stochastic region results in a strong poloidal RE SE structure.The simulation of figure 15 matches the QRE experimental case well (figure 13), showing the same enhanced SE from the (2/1) island O-point.For the post-disruption RE studied in this work, we identified a SE poloidal structure around a (2/1) locked mode, but we are unable to confirm the mode phase, and therefore if the enhanced emission is located at the O-point; we hypothesize that this is indeed the case and the simulations above suggest the presence of a stochastic edge region, generating the measured SE poloidal structure.

Conclusion
In conclusion, this work has introduced two new methods of constraining the RE current profile in high-current (I p = 550 kA) RE plateaus in DIII-D: localization of the q = 2 surface from SE imaging, and Ar-II polarization angle measurements.The reconstructed current profiles are centrally peaked, not hollow, with central safety factor q 0 slightly below 1.This contrasts with previous work in JET which attributed hollow SE profiles to hollow current profiles [13].Periodic sawtooth-like internal (1/1) instabilities appear to cause current profile relaxation and are likely to play a role in keeping q 0 near 1.A locked (2/1) mode appears to form in these plasmas and this mode is seen to phase hop during the (1/1) instabilities.In a previous work, a (2/1) mode growth was hypothesized to cause the RE final loss instability; this work shows that the presence of a (2/1) mode by itself is insufficient to cause final loss instability onset.The RE plateaus appear to form a narrow current channel (radius ≃ 0.4 m) which does not fill the entire available volume up to the LCFS.Moving the RE beam toward the wall thus has almost no effect on the current profile until the RE magnetic axis moves closer than 0.4 m to the wall.This finding could have important implications in the efforts to control the RE plateau position in future large tokamaks.Various simulated current profiles are compared to the measurements: the simulation that closely matches the data in terms of current profile and loop voltage appears to be the toroidal fluid RE model.
The two new methods of constraining the RE current profile shown here are not universally applicable.The Ar-II polarization angle measurement requires a significant Ar + population throughout the RE plateau, which is not the case in all RE plateau experiments.In the case of the SE image analysis, the interpretation proves to be quite challenging.As shown in figures 3(a) and 14(a), the SE has a strong poloidal structure even in the absence of islands.Islands can then cause additional poloidal structure in the SE.Although the islands appear to affect SE brightness, it remains unclear in these experiments whether enhanced SE in equilibrium results from the island O-points or from the X-points.Simulations suggest that islands affect SE through changes in RE transport that affects RE density, not by changes in pitch angle.When the RE plateau is transiently pushed against the CP, island O-points appear to cause reduced SE.This suggests that the exact effect of magnetic islands on SE can vary from experiment to experiment, possibly depending on the degree of stochasticity created around the islands, as well as the time history and location of the RE source terms relative to the islands.

Figure 1 .
Figure 1.Hardware schematic showing (a) top view and (b) side view of the DIII-D tokamak.Showing most important diagnostics and material injectors used here.
(a)), followed by 200 Torr-L He MGI at t = 1250 ms.The He MGI forms a long-lived RE plateau with reasonably low dissipation but good diagnostic signals (such as Ar-II line emission).RE plateaus with fairly high plasma current I p = 550 kA are used here.The RE plateaus are held centered at constant I p until t = 1600 ms, at which point they are pushed by the plasma control system either into the lower divertor, figure 2(e) or the center post (CP), figure 2(f ).Last-closed flux surfaces (LCFS) predicted by JFIT for this 'push' phase are shown in figures 2(e) and (f ).

Figure 2 .
Figure 2. Time traces of experiment showing ArPI at 1200 ms and He MGI at 1250 ms.Subplots show (a) plasma current, (b) electron cyclotron heating, (c) hard x-ray signal, (d) single-pass electron line density.Subplot (e), (f ) show magnetic reconstructions from JFIT of the plasma last closed flux surface for (e) vertical loss case and (f ) center post loss case.

Figure 3 .
Figure 3. (a) Simulated visible (790 nm) SE image for collisionless axisymmetric RE plasma using the tanh energy and pitch distributions shown in (b) and (c).Behavior of peak SE spot angle θ peak with plasma current for different kinetic energy K and pitch variable λ distributions and camera vertical position Zcam is shown in (d).The default case (a) uses K 0 = 10 MeV, K 0,λ = 8 MeV, λ min = 0.1, and Zcam = 0.

Figure 4 .
Figure 4. Measured visible SE images from toroidal angles (a) ϕ = 225 • and (b) ϕ = 90 • .The LCFS from EFIT is shown in red.(c) fit peak HFS SE angle θ peak at plasma edge and nominal q = 2 surface (region of brightest SE) as a function of Ip for a shot with ramped plasma current.

Figure 5 .
Figure 5. Measured RE-SE radiance before the onset of the (1/1) mode in shot #192200 at time (a) 1471 ms and (b) 1878 ms.Difference images formed by subtracting SE images immediately after from immediately before the (1/1) mode, for the modes at (c) 1472 ms and (d) 1879 ms.Circles tentatively identifying plasma edge and rational surfaces for q = 1, 3/2, and 2 are shown with colored lines.

Figure 6 .
Figure 6.Example of (1/1) mode data showing zoomed out time traces of (a) plasma current, (b) hard x-ray emission, and (c) Ar-II brightness; then (d)-(f ) zoomed in time traces of the same signals showing just a single (1/1) instability.(g) shows contours of external magnetic sensors measuring change in poloidal magnetic field, while (h) shows the poloidal mode structure at one time slice at the peak of the mode.

Figure 7 .
Figure 7. (a) unpolarized spectrum of Ar-II 480.6 nm, (b) same spectrum taken with vertical polarizer for the same view.(c) Ar-II brightness as a function of minimum tangency radius a Tan , and (d) LOS-integrated Ar-II line polarization angle (relative to horizontal) as a function of minimum tangency radius.The magenta lines show the depolarization effect for a flat test current profile: dashed line without and solid line with corrections.

Figure 8 .
Figure 8. Inversions of Ar-II 480.6 nm emissivity across the poloidal cross section.(a) Shows Ip = 550 kA case inverted with 'hybrid' system-combining both Zeeman inversion and brightness inversion methods.(b) Ip = 275 kA case, using camera image and inverting that assuming emission is toroidally symmetric.(c) Ip = 275 kA shot but using just Zeeman (line broadening) method.(d) Spectrometer line-integrated brightness inversion.EFIT and JFIT LCFS estimates are overplotted for comparison.EFIT and JFIT magnetic axis location is shown by '+' symbols in (a).

Figure 9 .
Figure 9.Time traces from a CP compression RE plateau showing (a) major radius R 0 estimated with different methods; (b) minorradius a min (distance to wall) estimated from JFIT and EFIT, as well as radii of edge, q = 2, and q = 1 estimated from SE; (c) central safety factor q 0 estimated with different methods; and (d) edge safety factor qa (at a min ) from EFIT and JFIT.
Figure 10(b) shows charged ion species radial profiles.He 2+ is the dominant ion at the center of the RE beam.Ar 2+ is the dominant Ar ion and it is also the ion which dominates RE drag and pitch angle scattering.Charge states of Ar higher than 4+ are expected to be present at a low level (approximately 10 −3 on the scale of figure 10(b)), and are not included in the model.D 2+ and D − are included in the model but are found to be at a scale ≃ 10 −3 or lower and are therefore not shown on figure 10(b).Radial profiles of neutrals

Figure 11 .
Figure 11.(a) Different measurements and models of the steady-state Ip = 550 kA RE plateau current profile and (b) resulting predictions for the line-integrated Ar-II polarization angle (relative to horizontal) for comparison with the measured values.

Figure 12 .
Figure 12.Islands with apparent reduced SE emission in O-point region seen at two different time steps (a) and (b) during center post compression of the RE plateau.Here contrast is enhanced by normalizing the SE at each radial position separately.

Figure 13 .
Figure 13.(a) Visible SE image of QRE shot with REs formed during startup and slowing damping in time during the shot.The q = 2 surface is identified using MSE-EFIT, as is the magnetic axis.The O-point of (2/1) island is marked with 'O'.The SE from this 'O', if held fixed, as a function of time is shown in (b), showing island rotation and RE population damping in time.The (2/1) island phase vs time is shown in (c).

Figure 14 .
Figure 14.KORC simulations of visible SE from 20 MeV REs in the presence and absence of an applied (2/1) island with 5 cm width showing: (a) no island, (b) phase = 90 • island, (c) radial profile at Z = 0 for both no-island and Φ O = 90 island case, (d) Poincare plot for phase Φ O = 90 • showing the (2/1) island surrounded by well defined flux surfaces.