Z_eff / Fusion power discrepancies

[matt-pharr]

When reproducing the POPCON from the MANTA paper, OpenPOPCON estimates Z_eff to be twice the Z_eff in the paper for the same impurity content. Additionally, fusion power is higher in OpenPOPCON than it is in the paper. Is there a factor of 2 floating around somewhere, or does P_fusion in the paper not refer to alpha + neutron power?

[nelsonand]

Hi @matt-pharr, how are you seeing the Z_eff in OpenPOPCON?

I guess a first trial here should be to compare to CFSPOPCON, see if we can recover the same result with the same inputs.

[matt-pharr]

@nelsonand in OpenPOPCON, I am specifying Z_eff via #5. For the example, resources/examples/MANTA/POPCON_input_example.yaml, we assume 2% Helium ash; this yields Krypton concentration of 0.123115 % when requesting Z_eff = 2.26. However, the MANTA paper reports a Krypton concentration of 0.315%.

Here is the POPCON in the MANTA paper:

And here is the output of OpenPOPCON 2.0, using 0.123115 % Krypton:

[matt-pharr]

inputs.zip Here is a zip file with the Jupyter notebook, plot settings, and input file used to generate the above plot

[nelsonand]

Hi @matt-pharr, when I try this I get an error: KeyError: "Key 'B_0' not found in ./resources/MANTA_zeff_example/POPCON_input_example.yaml"

I see in the .yaml that B_0 and B_coil are supposed to be interchangable:

# B_0 and B_coil can be calculated from each other. Pick one to specify:
# B_0: 11.0 # on-axis magnetic field in Tesla
# or
B_coil: 24.0 # magnetic field at the coil in Tesla

Is there something additional I need to do to complete this switch?

(The same thing happens with I_p and qstar)

[nelsonand]

I see - you already updated the code for https://github.com/hansec/OpenPOPCON/issues/5! Nice!

[matt-pharr]

Hi @nelsonand, are you using the newest version of the main branch? I merged the ability to do adjustments around when I posted this plot.

Edit: I think you sniped me there, let me know if you still have issues.

[nelsonand]

These lines should be commented (at least to identify what element is what): https://github.com/hansec/OpenPOPCON/blob/71b467aebec507d70655a663e2961710924c778d/src/lib/phys_lib.py#L54C1-L287

(They look right to me, upon initial inspection.)

[nelsonand]

A manual calculation of Zeff after running POPCON looks ok:

Zeff plotting code

```python # Let's calculate Zeff from the outputs to check i_params = -1 n_G_frac = 0.7 Ti_av = 13 n_G = pc.params[i_params].n_GR rho = pc.params[i_params].sqrtpsin n_average = pc.params[i_params].volume_integral(rho, pc.params[i_params].get_extprof(rho, 2))/pc.params[i_params].V n20 = n_G_frac*n_G/n_average Ti_average = pc.params[i_params].volume_integral(rho, pc.params[i_params].get_extprof(rho, 3))/pc.params[i_params].V Ti = Ti_av/Ti_average ni_prof = n20 * pc.params[i_params].extprof_ni ne = n20*pc.params[i_params].get_extprof(rho, 1)/pc.params[i_params].get_plasma_dilution(Ti/pc.params[i_params].tipeak_over_tepeak) ne_prof = n20 * pc.params[i_params].extprof_ne impfracs = pc.params[i_params].impurityfractions from src.lib import phys_lib as phys Te0 = Ti/pc.params[i_params].tipeak_over_tepeak Te_prof = Te0 * pc.params[i_params].extprof_Te Z_eff_prof = np.zeros(len(Te_prof)) for i, Te in enumerate(Te_prof): Zeffs = phys.get_Zeffs(Te) nis = impfracs*ne_prof[i] Z_eff_prof[i] = (ni_prof[i] + np.sum(nis * Zeffs**2)) / ne_prof[i] plt.plot(rho, Z_eff_prof) plt.ylabel('Z_eff') plt.xlabel('rho') ```

[nelsonand]

@matt-pharr I don't see any obvious errors in the Zeff coding... the MANTA plot you pasted above is quite different than what your file gets, but note also that it is conducted with fairly different assumptions... I believe they use constant H89=1.44, have different profiles (both shape and magnitude (eg. Te_core=20 instead of 40) so I'm not surprised that they are different...

[matt-pharr]

I see... I used the most recent profiles I could find on the slack, maybe I did the temperature averaging wrong? I will take a look. I will also see what we get with H89.

[matt-pharr]

@nelsonand I figured out this issue and put a solution in #17. The issue arose from my misunderstanding of the function of radiation: from my current understanding after reading N. A. Uckan and ITER Physics Group, ITER Physics Design Guidelines: 1989 is:

• Impurities should be considered a way to take conduction or turbulent transport/etc losses that are part of W/tau_E and turn it into light radiation that does not have to hit the diverter, thus lowering the heat flux through the separatrix
• Bremsstrahlung radiation needs to be subtracted from the power degradation term in scaling laws, as otherwise we get a runaway cycle of increasing bremsstrahlung losses and increasing P_aux at high densities.

Implementing this pair of changes made the MANTA example match the CFSPOPCON result almost perfectly, at least compared to the previous result!

vs

[matt-pharr]

The radiative ARC POPCON is also recovered: