Updates on the equilibrium reconstruction
Minwoo has tested the equilibrium reconstruction procedure described in this post. He has noticed that the q-profile changes significantly when the direct solution is reconstructed from the inverse solution by the TEQ code. I can reproduce the Minwoo observations and confirm that the whole q-profile shifts by about 10% when the direct equilibrium is generated from the inverse equilibrium. It might be useful if the TEQ developers can address this problem. Meantime, I have modified the equilibrium reconstruction procedure to avoid the problem with the q-profile. In the modified procedure, we postpone the generation of the direct equilibrium until very last step:
caltrans 007328_4400.sav -probname ss-test kstar.bas
thetac=1e-3; epsrk=5.e-9; nht=5000; start_inv psave=... teq_inv(0,1); teq_inv(0,1)
saveq("s13-t00-01.sav")
thetac=1e-3; epsrk=5.e-9; nht=5000; start_inv
qsave=... teq_inv(0,1); teq_inv(0,1)
saveq("s13-t00-02.sav")
jparsave(81:101)=jparsave(80)
real ndens=psibar; ndens=2.6e19 real prbs=psave/10./2. real tebs=prbs/ndens/1.602e-19 real zeffbs=psave; zeffbs=1. real pbeambs=psibar; pbeambs=0. read jbootstrap.bas
real jbs1 = jbootstrap(prbs,ndens,tebs,tebs,zeffbs, pbeambs, 1., 1., 0.) real jbs0 = jbs1(:,1) real foo1=tanh((1.01-psibar)/0.05) real foo2=(1+tanh((psibar-0.7)/0.05))/2. jparsave=jparsave*foo1+jbs0/bsqrf*foo2
thetac=1e-3; residj=1e-9; nht=5000; start_inv
jparsave=jparsave*foo1+jbs0/bsqrf*foo2
nf; plot [jparsrf,jparsave], asrf+rsrf
teq_inv(3,0); teq_inv(0,1); teq_inv(0,1)
inv_eq=0; inv_k=0; run
saveq("s13-t00-03.sav")
gridup; run; saveq("s13-t00-04.sav")
gridup; run; saveq("s13-t00-05.sav")
weqdsk
In the plasma core region, the q-profile is not affected now. In the plasma edge region, the q-profile is modified. However, these changes are consistent with the bootstrap current model. It looks that the bootstrap current fractions computed in TEQ and TOQ does not agree well. In order to reproduce the TOQ bootstrap current, a scaling factor for the parallel current density is needed.
. The 
and 
toroidal mode numbers that are close to the experimentally observed modes are marked on the diagram. Note, the transition from 
to 
will be associated with very small changes in the normalized plasma density and with relatively large changes in the parallel current density. The pedestal plasma density for both equilibria was 
, the pedestal temperatures were 
and 
for the cases of 
. However, the constant resistivity profile is used in these simulations. There are several conclusions from these and other NIMROD/BOUT++ comparison simulations:
. Based on this information and typical KSTAR temperature profiles found in the KSTAR experiments, an unique solution for the equilibrium does not exist. Additional assumptions are needed. Stability analysis of equilibrium solutions might help to reduce the uncertainty. Here, I compare two sets of equilibria that are generated by Minwoo and myself. Minwoo used the Corsica code to generate the equilibrium. In order to match the midpoint of the H-mode pedestal with the experimental observations, he shifted the H-
and the electron and ion temperatures are set to 500 eV. The pedestal temperature in two other XGC0 cases is varied slightly above the experimental error bars. The temperatures in the second case (xks1304) are set to 800 eV and temperatures in the third case (xks1305) are set to 300 eV. The density in these two cases are changes to keep the total plasma
in the case xks1304 and to 
in the case xks1305. The plasma collisionality for the case xks1304 is 4.38 times smaller than the plasma collisionality in the case xks1303 and the plasma collisionality in the case xks1305 is 4.63 times larger than the plasma collisionality in the case xks1303. The plasma collisionalities for the cases xks1305 and xks1304 differ by a factor of 20. Comparing the XGC0 results for the normalized plasma pressure that are given below, one can notice that the pedestal width is reducing for the low conditionality case.
