Corrigendum: Thermal dynamics in the flux-coordinate independent turbulence code GRILLIX (Contributions to Plasma Physics, (2020), 60, 5-6, (e201900131), 10.1002/ctpp.201900131)

We have discovered that one of the original articles [1] findings, that the actual choice of the dimensionless parameter χ_∥i0 for the ion heat conductivity*χ_∥i0 is obtained by normalizing the Braginskii ion parallel heat conductivity to (Formula presented.), with (Formula presented.). seemed to play no role for the simulation results, was not physical. Instead, due to a mistake in the handling of input parameters, χ_∥i0 was actually not used in the code - the dimensionless electron heat conductivity χ_∥e0 was used instead. Hence, the results in chapter 4 and the conclusions are correct only if χ_∥i0 = χ_∥e0. For the reference case, this means χ_∥i0 = χ_∥e0 = 26.6 was used,^†We have for deuterium χ_∥i0/χ_∥e0 = 23 ≠ 35 because the electron collision frequency was calculated with Z_eff = 1.5. instead of what we thought was χ_∥i0 = 1.15 and χ_∥e0 = 26.6. The rest of the code and model is correct. We have fixed the error, verified the code and rerun all the simulations. The main conclusion is that the dimensionless ion heat conductivity χ_∥i0 plays as much of a role for the equilibrium ion temperature profile T_i as the electron heat conductivity χ_∥e0 for the electron profile T_e. Further, with the correct heat conductivity χ_∥i0 = 1.15, T_i saturates faster - after (Formula presented.) ms - while it was still not saturated at 1.5 ms with the wrong χ_∥i0 = χ_∥e0 = 26.6. The saturation time for the plasma density n and electron temperature T_e remain the same - (Formula presented.) ms. Figure 1, left, shows the saturated radial profiles for the reference simulation. We find that in comparison to the mistakenly used χ_∥i0 = 26.6, the proper, lower ion heat conductivity χ_∥i0 = 1.15 increases the stationary ion temperature gradient ∂_rT_i in the confined region, leading to T_i < T_e at the separatrix. The T_i profile and fluctuation level are now similar to those of the plasma density n. The T_e and n profiles remain unaffected. The stationary profile of the electrostatic potential ϕ flattens in the confined region due to the lower T_i, while it remains the same in the SOL following T_e. In the far SOL, T_i > T_e is found due to electron sheath heat transmission - unlike in the case without this boundary condition (γ_e = 0). We note that the previously observed result, T_i > T_e also at the separatrix, is recovered again at higher temperature, see double temperature case in Figure 1, right. 1 FIGURE (Figure presented.) Mean radial profiles (T_i, T_e, n, −ϕ/Λ) at the outboard mid-plane in saturated state. Dotted lines indicate the ±σ_f fluctuation level. The negative potential −ϕ and its fluctuation level are divided by Λ = 2.69. LCFS and source region are marked. Left: reference case with T_e = T_i = 90 eV at the core boundary, with additionally the T_e profile from the simulation with no sheath heat conduction (case 1 from chapter 4.1, γ_e = 0). Right: simulation with double the temperature 2 FIGURE (Figure presented.) Frequency spectrum of poloidally and toroidally averaged electrostatic potential fluctuations Other results of the original article [1] hold true, at least qualitatively. The GAM frequency spectrum, shown in Figure 2, is somewhat different quantitatively. With the lower ion heat conductivity χ_∥i0, the ion temperature fluctuates more, but overall the turbulence is nonetheless enhanced with increasing density and suppressed with increasing temperature, see Figure 3. In cases 2 and 3 from chapter 4.1, we already had χ_∥i0 = χ_∥e0 (and case 4 was actually nearly the same as the reference scenario), so the result holds that reducing χ_∥i0 and χ_∥e0 below 0.1 has no impact on outboard midplane profiles. 3 FIGURE (Figure presented.) Outboard mid-plane ion temperature snapshot at 1.44 ms in: double density, reference, double temperature (left to right). Horizontal axis is (R − R₀)/R₀. LCFS marked by blue dashed line We additionally remark that the Bohm sheath boundary conditions (7) for parallel velocity should contain T_i, (Formula presented.). Also, there is a mistake in the indexes in Equation (9): instead of ∇_⊥p^{i + j}, it should read (Formula presented.). Acknowledgments This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.