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):

gamma.png
 

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:

gamma_trace_ky4,7.png
gamma_trace_ky9,7.png

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:

gamma_kylarge.png
 

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:

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_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
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