## We compare growth rates between stella and GENE for a linear ITG instability. In the stella calculation, we notice excitation of spurious modes at small scales (kyρ > 8.5), as shown in the figure below (negative growth rates excluded):

## We focus on the wavenumbers kyρ=4.7 (left) associated to the maximum growth rate and ky ρ=9.7 (right) corresponding to the maximum spurious growth rate, and plot the evolution of the growth rate with respect to the stella iterations:

## It is clearly seen that the spurious mode fails to converge and fluctuates around 0. The strongest mode, on the other hand, quickly converges to the resulting growth rate.

To remedy the spurious mode, we increase nstep by doubling it from 3e4 to 6e4. However, as the following figure suggests, this method does not resolve the issue:

# Testing memory consumption with HAS_ISO_C_BINDING ?= on and lu_option="local"

# Using cobra cluster (RZG), using 80 GB/node. Green combinations are successful. Red combinations crash.

## nx ny nz

97 190 128

130 190 128

175 190 128

205 190 128

223 190 128

## nx ny nz

205 190 128

205 232 128

205 253 128

205 274 128

205 301 128

205 322 128

# Geometry: We are using the reference equilibrium 001, which corresponds to the vacuum "standard" W7-X configuration. The selected flux surface for the simulations is s=0.5. The selected flux tube for the simulations is α=0.

# Benchmark vs. GENE

# Linear Simulations: We simulate ITG with adiabatic electrons. The normalized ion temperature gradient is and the density gradient is . The comparison for the growth rates and frequencies is shown below:

# Next, we show ITG with kinetic electrons, the gradients remain as before, and in addition we set and

The comparison for the growth rates and frequencies is shown below:

# Zonal flow response: We use . The comparison for the squared zonal potential is shown below:

# Nonlinear Simulations: We simulate ITG with adiabatic electrons. The normalized ion temperature gradient is and the density gradient is . The comparison for the ion heat fluxes rates is shown below:

# Next, we show ITG with kinetic electrons, the gradients remain as before, and in addition we set and

The comparison for ion and electron heat fluxes is shown below:

# In addition, we show the comparison for the particle flux:

# Testing the parallel b.c. We present the comparison for ITG turbulence simulations for stella, using either the twist and shift boundary condition or the periodic boundary condition.

# Relating ITG heat flux with max-J. In the following stella simulations we apply plus a density gradient. We use the vacuum W7-X configurations: ref_128 (mr=8%) and ref_404 (mr=-4%), also a tokamak as reference case. The surface for the simulations is r/a=0.75.

# Formally, only W7-X mr=8% is max-J. However, we may characterize the configurations according to a degree of max-J. For instance, mr=8% has a higher degree than mr=-4%, which in turn has a higher degree than TOK. We should then expect that the ITG ion heat fluxes respond to the density gradient according to that degree: for TOK, the ion heat flux is enhanced by the density gradient, for mr=-4% the heat flux is almost unchanged, and for mr=8% the ion heat flux is reduced.

# mr=+8%

# mr=-4%

# TOK