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.

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:

1.png
aLn.png

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 i
s shown below: 

gamma_001aeLN.png
omega_001aeLN.png
aLTe.png
teti.png
gamma_001keLN.png
omega_001keLN.png

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

kx_edited.png
zf_001.png

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:

1.png
aLn.png
Qi_001keNL.png
Qe_001keNL.png

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

pflx_001keNL.png

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.

Qi_001aeNL_bc.png

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.

1.png
jinv.png

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.

Qi_128.png

mr=+8%

Qe_128.png
Qi_404.png

mr=-4%

Qe_404.png
Qi_TOK.png

TOK

Qe_TOK.png
Qi_001aeNL.png

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:

aLTe.png
teti.png