Investigation of energy transport in DIII-D High-βP EAST-demonstration discharges with the TGLF turbulent and NEO neoclassical transport models

Energy transport analyses of the DIII-D high-βP EAST-demonstration discharges have been performed using the TGYRO transport package with the TGLF turbulent and NEO neoclassical transport models under the OMFIT integrated modeling framework. Ion energy transport is shown to be dominated by neoclassical transport and ion temperature profiles predicted by TGYRO agree closely with the experimental measured profiles for these high-βP discharges. Ion energy transport is largely insensitive to reductions in the E×B flow shear stabilization. The Shafranov shift is shown to play a role in the suppression of the ion turbulent energy transport below the neoclassical level. Electron turbulent energy transport is under-predicted by TGLF and a significant shortfall in the electron energy transport over the whole core plasma is found with TGLF predictions for these high-βP discharges. TGYRO can successfully predict the experimental ion and electron temperature profiles by artificially increasing the saturated turbulence level for ETG driven modes used in TGLF.


Introduction
A high fraction of bootstrap current, f BS , the self-generated current due to the plasma density and temperature gradients [1][2][3][4], is desirable for steady-state tokamak operation, especially for future fusion reactor operation. It will minimize the need for external current drive. High poloidal beta β P and high normalized toroidal beta β N are the characteristics of the DIII-D high-β P and high bootstrap current fraction discharges [5].
A TA 2 0 is the dimensionless plasma pressure, and B TA is the toroidal magnetic field at the plasma geometry center, B PA is the averaged poloidal magnetic field for normalization, p A is the volume average plasma pressure; and /( / ) β β = I aB N T P T with I P is the total plasma current and a is the plasma minor radius. Recently the high-β P experiments with EAST-similar operational conditions have been realized on the DIII-D tokamak by the joint DIII-D and EAST teams [6][7][8][9][10]. This research is to develop and test a possible scenario for the steady-state operation on the EAST tokamak. The superconducting EAST tokamak aims at the demonstration of long-pulse high performance plasma operation [11]. The DIII-D/EAST joint experiments (Some figures may appear in colour only in the online journal)

International Atomic Energy Agency
Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. aim to develop on DIII-D a fully non-inductive operating scenario compatible with the EAST hardware constraints. The good confinement observed in these high-β P discharges is investigated in this paper.
As is well known, the cross-field energy transport in the tokamak plasmas generally exceeds the neoclassical predictions. Understanding the underlying processes can increase our confidence in the extrapolation of present tokamak behaviors towards reactor regimes. It is commonly accepted that most of the transport in the tokamak plasmas is driven by plasma turbulence. The turbulent transport is mainly produced by micro-instabilities including, but not limited to, ion temper ature gradient (ITG) driven modes, trapped electron modes (TEMs), and electron temperature gradient (ETG) driven modes.
Solving the fundamental gyrokinetic equations for the turbulent transport is computationally expensive to predict the profiles on a transport time scale. Reduced transport models of the turbulent transport, such as TGLF [12][13][14][15], have been developed and implemented in analysis and predictive codes. TGLF, which is calibrated to GYRO [16] non-linear simulation results and is widely used to analyze and predict the turbulent transport in the tokamak plasmas [17][18][19][20][21][22][23], is a quasilinear transport model that uses a reduced gyro-fluid system of moments of the linear gyrokinetic equation to compute the spectrum of linear eigenmode instabilities. The linear eigenmodes and a model of the saturated turbulence fluctuation amplitude are combined to compute the fluxes of energy, particle and momentum.
The first-principle code NEO [24][25][26], provides an accurate numerical solution of the drift-kinetic equation and computes the neoclassical and classical collisional transport fluxes. NEO can calculate more accurate edge bootstrap current, which is important for the kinetic equilibrium reconstructions in the high-β P and high collisionality tokamak plasmas [27].
TGLF + NEO has proven to be an accurate predictive theory-based transport model for the core of L-mode, H-mode inductive discharges, and DIII-D hybrid regimes [17][18][19]28]. The high-β P discharges push into plasma conditions that are quite different from the discharges where TGLF + NEO have been successful at predicting transport. It is important to test and validate the prediction ability of TGLF + NEO in the high-β P experiments.
TGYRO [29,30], which can utilize GYRO or TGLF for turbulent transport and NEO for neoclassical transport, is a transport manager that has been integrated into the OMFIT (one modeling framework for integrated tasks) framework [31,32]. The TGLF turbulent and NEO neoclassical transport models will be used in the present analyses. TGYRO calculates the steady-state temperature profiles, which yield the total energy flux equal to the target flux given by the volume integrals of relevant energy source and sink terms.
The remaining part of this paper is organized as follows. In section 2, the overview of the high-β P discharges to be analyzed will be presented. In section 3, the ion and electron energy transport will be analyzed in details. In section 4, the conclusions and discussions will be presented.

EAST-demonstration high-β P discharges on DIII-D
Plasma production using a slow plasma current ramp-up rate consistent with the constraints of the superconducting coils on EAST was demonstrated on the DIII-D tokamak. The joint experiments on DIII-D exhibit excellent confinement, H~1.5 y 98 2 , with β~3 N and β~3 P [6][7][8][9][10]. High-β P enables fully non-inductive discharges with the excellent confinement quality, desirable for the steady-state demonstration on the EAST tokamak. One of the important features of these highβ P discharges is that a large radius ITB (internal transport barrier) is sustained.
Energy transport analyses have been performed for several discharges from the DIII-D high-β P experiments and the results are similar. This paper will focus the discussions on the analysis of discharges 154372 and 154406 that exhibit excellent confinement with the lower NBI torque expected on EAST. An overview of these discharges is shown in figure 1. These discharges have good confinement, and with a large radius ITB. The energy transport analyses will be performed for discharge 154372 at =  current calculated by NEO as a constraint. The plasma kinetic profiles for these time slices are shown in figure 2. There are high q 95 (>10) and high bootstrap current fraction (>70%) as shown in figures 3 and 4 for these high-β P discharges. The energy transport analysis results will be presented in the following section.

Energy transport analyses by TGYRO with TGLF + NEO
In this paper, we focus on the ion and electron energy transport and the steady-state ion and electron temperature profiles will be predicted by TGYRO with TGLF + NEO. The total calculated energy flux is composed of the turbulent energy flux calculated by the TGLF model and the neoclassical energy flux calculated by the NEO model. The predicted ion and electron temperature profiles are obtained by matching the total calculated energy flux with the target energy flux that is calculated with the experimental energy sources and sinks from the ONETWO transport code [33]. The energy sources and sinks include the auxiliary heating, the radiation loss and the energy exchange between the ions and the electrons which is computed self-consistently in TGYRO.

Ion neoclassical energy transport
Firstly, the ion energy transport is analyzed. The electron temper ature profile and the other profiles (ion and electron density, toroidal rotation) are kept fixed and only the ion temperature profile is predicted by TGYRO with TGLF + NEO to distinguish the ion and electron channel energy transport. The boundary condition is imposed at ρ = 0.8. Figures 5(a)-(c) show the ion temperature profiles from the experimental data fit (blue lines) and the TGYRO predictions (red lines) for discharge 154372 at = t 3.0 s, 4.0 s and discharge 154406 Table 1. Key parameters for discharge 154372 at = t 3.0 s, 4.0 s and discharge 154406 at = t 5.17 s: the plasma current I P , the vacuum toroidal magnetic field at the center of the vacuum vessel B t0 , the line-averaged electron density n e , the safety factor on axis q 0 , and q 95 . It is clear that the ion energy transport is dominated by the neoclassical energy transport. The ion turbulent energy transport is small and negligible inside ρ~0.63. The ion energy transport is on the neoclassical level inside ρ = 0.8. The ion neoclassical transport is strongly related to the ion banana orbit width, which is proportional to the safety factor and the poloidal gyro-radius. The ion banana orbit is large due to the high safety factor q and high β P in these high-β P discharges. The large ion neoclassical energy transport will reduce the ion temperature gradient and it may play a role in the formation of ion-ITB by keeping the ion temperature gradient below the ITG threshold.

DIII-D plasma
It is well known that × E B flow shear [34,35] has a stabilizing effect on the low-k micro-instabilities, such as ITG and TEM modes. There are experiments with strong flow shear such that the ion energy transport is reduced to the neoclassical level [36]. This is the conventional definition of an ITB. It has been validated that the ITG is suppressed by the × E B flow shear within the ITB for these cases. To study the effect of × E B flow shear on the ion energy transport in the DIII-D high-β P discharges, the predictions of the ion energy transport by TGYRO with the × E B turned off artificially are performed as shown in figure 6. The ion temperature profiles predicted by TGYRO without ×  figure 6( f ). The experimental ion temperature profiles for these high-β P discharges can be well predicted with only the NEO neoclassical transport model as shown in figure 7. The ion energy transport in the DIII-D high-β P discharge 154366    also has this characteristic [8]. These TGLF + NEO simulation results are consistent with the experimental measurements that there is no significant change in measured fluctuations in these high-β P discharges with lower and higher plasma rotation and with the gyrokinetic simulations [37]. The Shafranov shift, which increases with the pressure gradient and β P or β N increased, also has a stabilizing effect on the transport in the tokamak plasmas [38]. The Shafranov shift cannot be neglected in the high-β P discharges. To investigate whether the Shafranov shift plays a role in the suppression of the ion turbulent energy transport in the high-β P discharges, the ion turbulent energy fluxes will be calculated by TGLF for a sequence of model equilibria, which are generated by scaling down the pressure profile used in the EFIT   [39] equilibrium calculation while holding the plasma gradients and the q profile nearly fixed. Then the β N scanning for the ion turbulent energy fluxes is done with the plasma profiles fixed, which are taken from the DIII-D high-β P discharge 154372 at = t 4.0 s. The impact of the Shafranov shift or β N on the ion turbulent energy transport could be studied through this method. The ion turbulent energy fluxes calculated by TGLF at ρ = 0.63, which is in the ion-ITB region, decrease with β N increased as shown in figure 8. Hence, the Shafranov shift has a stabilizing effect on the ion turbulent energy transport in this region. The ion neoclassical energy fluxes calculated by NEO are also shown in figure 8, which are not sensitive to β N . The ion energy transport is dominated by the neoclassical energy transport with the larger β N . The ion turbulent energy flux is comparable with or even larger than the ion neoclassical energy flux with β N decreased to ~1. 25. This indicates that the Shafranov shift could play a role in the formation of ion-ITB due to the suppression of the ion turbulent transport below the neoclassical level. In the ion-ITB foot, at ρ = 0.71, the ion turbulent energy fluxes calculated by TGLF increase with β N increased as shown clearly in figure 9. These calculations are consistent with the shape of the experimental ion temperature profile as shown in figure 2(b). The destabilization effect of the Shafranov shift in the ion-ITB foot makes the ion temperature profile flatter there, while the steeper ion temperature profile in the ion-ITB region is due to the stabilization effect of the Shafranov shift.

Electron energy transport under-predicted with TGLF
In these series of simulations, both the ion and electron temperature profiles are predicted by TGYRO with the boundary condition at ρ = 0.8 for the DIII-D high-β P discharge 154372 at = t 3.0 s, 4.0 s and discharge 154406 at = t 5.17 s as shown in figure 10(a)-( f ). The electron turbulent energy flux is calculated by TGLF with the default ETG turbulence saturation level. Both the predicted ion and electron temperature as shown by the red lines are much higher than the experimental measured values as shown by the blue lines. The higher predicted ion temperature, which is not as shown in figures 5(a)-(c), is due to the dynamic ion-electron energy exchange. The main reason for the increased ion temper ature is that the electron energy transport is dramatically under-predicted by TGLF. There is a significant shortfall in the electron energy transport over the whole core plasma with the TGLF predictions. The electron particle transport in these high-β P discharges is also under-predicted by TGLF when only the electron density profiles are predicted with TGYRO as shown in figures 11(a)-(c). The near edge transport shortfall has been found in DIII-D L-mode plasmas [40][41][42][43][44][45] and Alcator C-Mod L-mode plasmas [46] but such a large shortfall over most of the core is unprecedented.
An increase in the ion-scale turbulent transport is ruled out by the lack of measurable ion-scale turbulence in these highβ P discharges. Recent multi-scale simulations have shown that there is strong coupling between the ion and electron scales in the streamer regime characterized by the high electron-scale turbulence; the contribution of the electron-scale (high-k) turbulence increases when the drive for the ion-scale turbulence is weak [47][48][49][50]. The TGLF saturation model for the high-k ETG modes is based on a single multi-scale GYRO simulation that included both ion and electron scales [51]. There is a /k 1 y C 3 (k y is the normalized poloidal wave number) factor within the saturation rule for the nonlinear intensity of the turbulence due to each high-k ETG mode ( > k 1 y ). By default = C 1.25 3 is used which yields the GYRO simulation predicted a ratio of / χ χ k l k high-e, ow-of approximately 12% for the GA standard case [17,18]. The transport level for the ETG modes turbulence increases with the factor /k 1 y C 3 increased. To investigate the possibility that ETG instabilities could cause the electron energy transport in these high-β P discharges, the saturated turbulence level for the high-k ETG modes used in TGLF is increased artificially. By increasing the saturated turbulence level for the ETG modes, the predicted ion and electron temper ature profiles can well match the experimental measured ion and electron temperature profiles as shown in figures 12(a)-( f ). TGLF can predict the experimental electron temperature profiles with the ETG turbulence saturated amplitude multiplied by a factor k y 2.25 compared to the standard setting as shown by the olive lines. The enhanced ETG turbulence transport due to the strong coupling of the high-k modes to the low-k modes could play an important role for the electron energy transport in these high-β P discharges [47][48][49][50]. Multiscale non-linear simulations need to be done for these high-β P discharges in order to validate this conjecture.

Summary and conclusions
The energy transport analyses of the DIII-D high-β P EASTdemonstration discharges have been performed using TGYRO transport package with the TGLF turbulent and NEO neoclassical transport models. The results show that in these high-β P discharges the ion energy transport is very much neoclassical and the ion temperature profiles predicted by TGYRO agree closely with the experimental measured profiles. The ion energy transport is largely insensitive to reductions in the × E B flow shear. The ion energy transport is still dominated by the neoclassical contribution even without the × E B flow shear stabilization effect. The Shafranov shift plays a role in the suppression of the ion turbulent energy transport and the formation of ion-ITB. A significant shortfall in the electron energy transport over the whole core plasma is found with TGLF predictions for these high-β P discharges. TGYRO can successfully predict the experimental ion and electron temperature profiles by artificially increasing the saturated turbulence level for ETG driven modes computed in TGLF. This indicates a possible resolution to the shortfall in the predicted transport.