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.