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3D Gyrokinetic Plasma Turbulence Simulations

Flux surface simulations with stella and GENE codes

Flux-surface simulations

Task: We compare ITG growth rates between stella and GENE for a W7-X (high-mirror) vacuum configuration.

Input: s=0.25, a/LTi=3, a/Ln=0, Te=Ti, adiabatic electrons, ρ=0.00441968
Note that ρ for GENE is defined as ρ/a (a= VMEC minor radius) and ρ=cs/Ωi Here, cs does not contain .

Equilibrium:

(please remove .txt extension)

W7-X

HSX

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):

Spurious modes

parameters GENE

frequencies GENE

VMEC wout stella

parameters stella

frequencies stella

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:

Memory testing

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

Benchmark linear

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:

Benchmark NL

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

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