Influence of Collisionality

The collisional regime of the bulk ions represents an important parameter in neoclassical theory. Therefore, a collisionality (ν^∗) scan was performed to investigate the change in particle flux. TheD_W coefficient grows monotonously with the collisionality for the case of non-negative asymmetry as it is shown in Fig. 8.6a. However, a clearly different trend is present for a negative asymmetry. It is caused by a shift of the D_W minimum from valueδ_min/ε≈ −1 for W ions in the plateau regime to the valueδ_min/ε ≈ −2 for W ions in the Pfirsch-Schlüter regime (ν^∗1). Large changes can be observed also in theP_T coefficient (cf. Fig. 8.6b). When the bulk ions are deep in the banana regime (ν^∗ 0.03), P_T is about −1/3, independently of the asymmetry. The increase of the Pfirsch-Schlüter flow fraction towards higher collisionality enhances theT_i screening in the case without asymmetry, andP_T converges to−1/2 [68]. The presence of positive asymmetry reduces theT_i screening, and negative asymmetry can even reverse the flow direction. Then both, n_i andT_i gradients will drive inward impurity convection. Such conditions can occur at the edge of the plasma as it was discussed in [148].

30812 32566

= 0 = 0.25 = -0.25

30812 32566

a) b)

PnPT

P_T P_n

= 0 = 0.25 = -0.25

DW [m2 /s]

= 0 = 0.25

= -0.25

Figure 8.6.: The collisionality scan of the neoclassical transport coefficients calculated in presence of the poloidal asymmetries. a) The tungsten diffusion coefficient D_W evaluated without asymmetry (open markers), with positive asymmetry (half open markers), and negative asymmetry (full markers). b) Ion density (red) and temperature (green) peaking coefficient evaluated for various values of the asymmetry using identical marking as in a).

8.3.3. Comparison with the Experiment

The NEO code was applied to model the transport coefficients in the previously investigated discharge #32324. For the modeling we used time averaged kinetic

8.3. Neoclassical Transport Modeling

profiles and the asymmetry was varied in the range δ=−0.15 to 0.4. The missing core measurements ofn_e causes a substantial uncertainty in the coren_i gradient, resulting in a possible underestimation of the neoclassical pinch. Since we would like to analyze at least the trend ofv/Dversus the poloidal asymmetry, the core value of ∇lnn_iobtained from IDA was increased by 50 % to match our v/D measurements.

As shown in Fig. 8.7a, the neoclassical value ofD_W increases fromD_W =_{0.04 for} zero asymmetry to D_W = _{0.8 at} δ = 0.25. At low asymmetry, the measured D_W match well D_neo. However, during the Q3 phase with high asymmetry, the value of D_neo overestimates the measurements by factor 2–4. In other words, the timescale of the transport process should be 2–4 times faster. It could indicate limitations of our measurement method as was discussed in Sec. 8.2. The negative asymmetry region was not covered by this experiment, and further investigation should focus on the combination of ICRF and NBI to verify the neoclassical prediction also for δ <−ε. The neoclassical drift coefficient v/D depicted in Fig. 8.7b, depends only weakly on the asymmetry, mainly due to the variation of the Ti screening (cf. 8.5b). This trend is confirmed by experimental values, which stay unchanged within the uncertainty.

In conclusion, within the limitation of our method and the experimental uncertainty, the extended neoclassical theory has been validated.

SXR SXR

a) b)

Q4

Q3

Q3 Q4

Figure 8.7.:The neoclassical value of the transport coefficient (dashed lines) for the discharge

#32324 at ρtor =0.12 compared with the experimentally measured values (dots) in the Q3 phase (blue) and the Q4 phase (red) for the effective diffusion coefficientD_eff Eq. (8.3) a) and the drift coefficient v/Db).

8. Influence of Asymmetries on Radial Impurity Transport

8.4. Conclusions

This chapter was dedicated to the validation of the neoclassical theory extended for the poloidal variation of the impurities density. The investigated discharge #32324 was chosen for it’s two almost identical phases different only in the W asymmetry level, induced by a change in the NBI source. A low variation between these two phases is critical to minimize an influence of the other transport mechanisms unrelated to the poloidal asymmetry. Our investigation was focused on the most central region of plasma dominated by neoclassical transport, where the largest effects were expected.

Proper measurements of the core tungsten density and its asymmetry were achieved using high-resolution SXR tomography of the W emissivity. In order to disentangle the diffusive and the convective contribution to the impurity transport, perturbations in the core impurity flux caused by the sawtooth crashes were analyzed. The investigation was performed utilizing two independent techniques, i.e. the gradient flux method and the least squares method, to minimize the error introduced by our methodology. The measurements resolved the reduction of the diffusion coefficient D_W by a factor of five when the asymmetry was reduced from δ = 0.25 to zero. At the same time, no significant change in the drift coefficientv/D was observed.

The neoclassical modeling of tungsten transport was performed using the NEO code.

The influence of the poloidal asymmetry on the impurity density was illustrated by a scan over the Mach number. The minimum in the impurity flux occurs atδ_min/ε=−1, which is a factor of 2 weaker asymmetry then expected from the analytical theory.

Additionally, a significant reduction of the Ti screening was found for δ/ε <−1. The collisionality scan indicated a huge impact of the poloidal asymmetries on the T_i screening in the Pfirsch-Schlüter regime, while in the very low collisionality regime the screening was almost unaffected.

Finally, a comparison of the simulated D_W with the experimental values matches well with the low asymmetry case, while the measuredD_W in the high asymmetry case is underestimated by factor of 2–4. However, this might merely be a consequence of the limitations of the applied experimental technique.

These findings are expected to have a direct impact on optimization of AUG plasma scenarios. A proper combination of the perpendicular beams and the position of ICRF heating can keep the asymmetry between−1< δ/ε <0. In such a case, we can expect the reduction of the neoclassical flux by an order of magnitude, while theT_i screening is still significant. Also, a simple replacement of the parallel beams by more perpendicular ones should stabilize NBI-only discharges, which are prone to W accumulation. Finally, the proper choice of NBI beams can be an efficient method for avoiding tungsten accumulation in real-time, since less additional core electron heating will be required to suppress the neoclassical impurity influx.