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### Description

**Introduction**

Turbulent particle transport is of vital importance for the performance of a future fusion power plant as it is interlinked with the density profiles. Studies have shown the NBI-source contribution to the density peaking to be around $20 \%$ in various tokamaks (1)-(3). Recent studies at JET shows a large importance of the NBI-source for certain discharges (4)-(5). The lower fraction of NBI heating at ITER makes this important to study.

ITER baseline scenario (strongly shaped configuration, $q_{95} \approx$ 3) demonstrating the possibility to achieve the confinement factor $H_{98,y}\approx 1$ at $\beta_N \approx 1.7$ have been performed at AUG and TCV. The AUG reference discharge analyzed here is 36143 and 64770 for TCV, global parameters are shown in Figure 1. The collsionality for the AUG discharge is $\nu^* \sim 10\nu^*_{\textit{ITER}}$ and for the TCV discharge $\nu^* \sim 100 \nu^*_{\textit{ITER}}$, at mid radius. The density peaking at AUG has recently been studied but in a different parameter regime than for our two discharges (6). The densitity preaking (PF), $\frac{a}{L_{\langle n_e \rangle}}$, quantifies the density peaking and it's obtained by setting $\frac{\partial {\langle n_e \rangle}}{\partial t}=0$ in the continuity equation.

$ \frac{a}{L_{\langle n_e \rangle }} = -\frac{a \langle | \vec{\nabla} \rho_t | \rangle}{\langle | \vec{\nabla} \rho_t|^2 \rangle} \frac{V_{\langle n_e \rangle }}{D_{\langle n_e \rangle }} + \frac{a \langle | \vec{\nabla} \rho_t | \rangle \int_0^{\rho_t} v' \langle S_n \rangle d \rho_t }{v' \langle | \vec{\nabla} \rho_t |^2 \rangle \langle n_e \rangle D_{\langle n_e \rangle}} $ (1)

$\rho_t$ is the square root of the normalized toroidal magnetic flux, $\langle | \vec{\nabla} \rho_t | \rangle$ is a metric component and $v'=\frac{\partial}{\partial \rho_t} \int_0^{\rho_t}dV$. The two terms on the RHS describes the two different physical mechanisms that contributes to the density peaking. The first term, here represented by the fraction of the inward pinch, $V_{\langle n_e \rangle}$, and the diffusion, $D_{\langle n_e \rangle}$, is the turbulent transports contribution. The second term describes the particle sources contribution. Certain important plasma parameters for the two discharges, at $\rho_t=0.5$, are presented in Figure 2. The data for the AUG discharge is at 3.5s and the TCV discharge at 1.4s. From the figure we can notice that the experimental normalized density gradient, $\frac{a}{L_{\langle n_e \rangle}}$, is much higher for 64770 than 36143.

**Method**

We have analyzed the two discharges with two different types of approaches and codes. Firstly, we have used the integrated modelling tool: European Transport Simulator (ETS) (7) –(8). By using ETS we can study both terms on the RHS in Equation (1). ETS is fully adapted to analyze AUG and TCV plasmas, it has a complete description of the machine specific heating schemes. Using ETS we have performed predictive simulations for one timeslice at t=3.5s for 36143 where the modelling tool is self-consistently evolving the temperature and density profiles until the plasma reaches a quasi steady-state. The neoclassical transport is calculated with NCLASS and the turbulent transport is computed with the Bohm-gyroBohm model. The particle and heat sources and the equilibrium are calculated at t=3.5s and kept constant throughout the simulation. Contribution from the ECRH is modelled with GRAY. For the ICRH, CYRANO calculates the wave deposition together with the Fokker-Plack solver STixReDist. For the NBI we use BBNBI for the wave deposition together with ASCOT. Finally, the equilibrium is calculated with CHEASE

Secondly, we have used the gyrokinetic code GENE (9) to study the turbulent transport. With GENE we have analyzed a specific radial position ($\rho_t=0.5$) with linear simulations. We have performed a scan in the binormal wavenumber $k_y \rho_s$ to study the growthrate for the two discharges. The results can be seen in Figure 3. Both discharges have an ITG-mode as the most unstable mode at ion scales, as the real frequencies (not presented) shows motion in the ion direction.

**Results**

Figure 4 illustrates the result of the predictive simulations for AUG discharge 36143. The electron density together with the electron and main ion temperature are simulated in ETS. The minority ion temperature is kept fixed throughout the simulation and the main and minority ion density profiles are calculated based on a quasi-neutrality condition. In Figure 4, the measured density and temperature profiles at 3.5s for each particle species are shown in blue and the predicted profiles when all three heating schemes are included are shown in green. With the Bohm-gyroBohm model we obtain good agreement for $n_e$ and $T_i$ while $T_e$ is overpredicted.

We have calculated the PF for the two discharges with GENE, which is achieved by determining when the particle flux in the linear regime (exponentially growing) changes sign during an $a/L_{ \langle n_e \rangle}$-scan. The results are shown in Figure 5. The calculated PF for the turbulent transport with GENE is much lower than the experimental measured one, for both discharges. This suggests that the density peaking comes mainly from the particle source.

We have also made three parameter scans for 36143 with GENE: collisionality, ion temperature gradient and electron temperature gradient. The results of these scans are shown in Figure 6. 36143 original values to the left, and the data points to the right are the PF when the parameters have changed. The vertical line shows the value for 64770. We can see from Figure 6 (left) that the PF is reduced for higher collisionality, which is supported by earlier observations (10). In (middle) we can see that the PF is reduced by a higher ion temperature gradient. In (right) we notice that a higher electron gradient yields a higher PF.

**Outlook**

Further investigations will be performed to confirm these preliminary results. Predictive simulations will be performed with ETS for both discharges using the turbulent transport model TGLF and the particle and power deposition profiles and equilibrium reconstruction will be calculated self-consistently. The effects of impurities and neutrals will be investigated. Nonlinear simulations with GENE will be performed, for both discharges, to confirm the low contribution of the turbulent transport to the density peaking under these experimental conditions.

**References**

(1) M. Valovič et al Nucl. Fusion 47, 196 (2007)

(2) C. Angioni et al Plasma Phys. Control. Fusion 51, 124017 (2009)

(3) M. Maslov et al Nucl. Fusion 49, 075037 (2009)

(4) T. Tala et al Nucl. Fusion 59, 126030 (2019)

(5) F. Eriksson et al Plasma Physics and Controlled Fusion 61, 102487 (2019)

(6) E. Fable et al Nucl. Fusion 59, 076042 (2019)

(7) D. Coster et al, IEEE Trans. Plasma Sci 38, 2085 (2010)

(8) Kaplan et al, Nucl. Fusion 53, 123007 (2013)

(9) F. Jenko and W. Dorland Plasma Phys. Contr. F. 43.12A (2001)

(10) C. Angioni et al Phys. Rev. Lett. 90, 205003 (2003)

Affiliation | Chalmers University of Technology |
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Country or International Organization | Sweden |