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flux_average now in magsurf_data works anal/num , new subr fluxval, some routines moved into equilibrium, minor bugs fixed

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This commit is contained in:
Daniela Farina 2015-11-05 18:24:21 +00:00
parent f77624d5ba
commit 198feb7a1f
5 changed files with 1556 additions and 1057 deletions
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6
Makefile
View File

@ -44,8 +44,10 @@ dispersion.o: const_and_precisions.o eierf.o math.o quadpack.o
eccd.o: const_and_precisions.o conical.o magsurf_data.o dierckx.o numint.o
eierf.o: const_and_precisions.o
gray_params.o: const_and_precisions.o utils.o
equilibrium.o: const_and_precisions.o dierckx.o minpack.o simplespline.o utils.o
magsurf_data.o: const_and_precisions.o
equilibrium.o: const_and_precisions.o dierckx.o minpack.o simplespline.o \
utils.o gray_params.o
magsurf_data.o: const_and_precisions.o gray_params.o equilibrium.o dierckx.o \
simplespline.o utils.o
math.o: const_and_precisions.o
minpack.o: const_and_precisions.o
numint.o: const_and_precisions.o

308
src/equilibrium.f90
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@ -2,32 +2,35 @@ module equilibrium
use const_and_precisions, only : wp_
implicit none
REAL(wp_), SAVE :: btaxis,rmaxis,zmaxis,sgnbphi
REAL(wp_), SAVE :: btrcen ! used only for Jcd_ASTRA def.
REAL(wp_), SAVE :: rcen ! computed as fpol(a)/btrcen
REAL(wp_), SAVE :: rmnm,rmxm,zmnm,zmxm
REAL(wp_), SAVE :: zbinf,zbsup
! REAL(wp_), SAVE :: rup,zup,rlw,zlw
real(wp_), save :: btaxis,rmaxis,zmaxis,sgnbphi
real(wp_), save :: btrcen ! used only for jcd_astra def.
real(wp_), save :: rcen ! computed as fpol(a)/btrcen
real(wp_), save :: rmnm,rmxm,zmnm,zmxm
real(wp_), save :: zbinf,zbsup
! real(wp_), save :: rup,zup,rlw,zlw
INTEGER, PARAMETER :: kspl=3,ksplp=kspl+1
! === 2D spline psi(R,z), normalization and derivatives ==========
INTEGER, SAVE :: nsr, nsz
REAL(wp_), SAVE :: psia, psiant, psinop
REAL(wp_), DIMENSION(:), ALLOCATABLE, SAVE :: tr,tz
REAL(wp_), DIMENSION(:), ALLOCATABLE, SAVE :: cceq, cceq01, cceq10, &
integer, parameter :: kspl=3,ksplp=kspl+1
! === 2d spline psi(r,z), normalization and derivatives ==========
integer, save :: nsr, nsz
real(wp_), save :: psia, psiant, psinop
real(wp_), dimension(:), allocatable, save :: tr,tz
real(wp_), dimension(:), allocatable, save :: cceq, cceq01, cceq10, &
cceq20, cceq02, cceq11
! === 1D spline Fpol(psi) ========================================
! INTEGER, SAVE :: npsiest
INTEGER, SAVE :: nsf
REAL(wp_), DIMENSION(:), ALLOCATABLE, SAVE :: tfp, cfp
REAL(wp_), SAVE :: fpolas
! === 1D spline rhot(rhop), rhop(rhot), q(psi) ===================
! computed on psinr,rhopnr [,rhotnr] arrays
INTEGER, SAVE :: nq,nrho
REAL(wp_), DIMENSION(:), ALLOCATABLE, SAVE :: psinr,rhopr,rhotr
REAL(wp_), DIMENSION(:,:), ALLOCATABLE, SAVE :: cq,crhop,crhot
REAL(wp_), SAVE :: phitedge,aminor
REAL(wp_), SAVE :: q0,qa,alq
! === 1d spline fpol(psi) ========================================
! integer, save :: npsiest
integer, save :: nsf
real(wp_), dimension(:), allocatable, save :: tfp, cfp
real(wp_), save :: fpolas
! === 1d spline rhot(rhop), rhop(rhot), q(psi) ===================
! computed on psinr,rhopnr [,rhotnr] arrays
integer, save :: nq,nrho
real(wp_), dimension(:), allocatable, save :: psinr,rhopr,rhotr
real(wp_), dimension(:,:), allocatable, save :: cq,crhop,crhot
real(wp_), save :: phitedge,aminor
real(wp_), save :: q0,qa,alq
contains
@ -146,15 +149,14 @@ contains
if(in==0) psin=(psin-psiaxis)/psia
end subroutine read_eqdsk
subroutine read_equil_an(filenm,rv,zv,fpol,q,unit)
use utils, only : get_free_unit
implicit none
! arguments
character(len=*), intent(in) :: filenm
integer, optional, intent(in) :: unit
! integer, intent(in) :: isgnbphi
! real(wp_), intent(in) :: factb
! real(wp_), intent(out) :: rvac,rax,zax
real(wp_), dimension(:), allocatable, intent(out) :: rv,zv,fpol,q
! local variables
integer :: u
@ -199,7 +201,6 @@ contains
real(wp_), intent(inout) :: psia
real(wp_), dimension(:), intent(inout) :: fpol,q
integer, intent(in) :: cocosin, cocosout
! real(wp_), intent(out) :: isign,bsign
integer, intent(out), optional :: ierr
! local variables
real(wp_) :: isign,bsign
@ -209,7 +210,7 @@ contains
call decode_cocos(cocosin,exp2pi,phiccw,psiincr,qpos)
call decode_cocos(cocosout,exp2piout,phiccwout,psiincrout,qposout)
! check sign consistency
! check sign consistency
isign=sign(one,psia)
if (.not.psiincr) isign=-isign
bsign=sign(one,fpol(size(fpol)))
@ -222,17 +223,14 @@ contains
end if
! convert cocosin to cocosout
if (phiccw.neqv.phiccwout) then
! opposite direction of toroidal angle phi in cocosin and cocosout
! bsign=-bsign
! isign=-isign
fpol=-fpol
end if
! q has opposite sign for given sign of Bphi*Ip
! opposite direction of toroidal angle phi in cocosin and cocosout
if (phiccw.neqv.phiccwout) fpol=-fpol
! q has opposite sign for given sign of Bphi*Ip
if (qpos .neqv. qposout) q=-q
! psi and Ip signs don't change accordingly
! psi and Ip signs don't change accordingly
if ((phiccw.eqv.phiccwout) .neqv. (psiincr.eqv.psiincrout)) psia=-psia
! convert Wb to Wb/rad or viceversa
! convert Wb to Wb/rad or viceversa
psia=psia*(2.0_wp_*pi)**(exp2piout-exp2pi)
end subroutine change_cocos
@ -301,8 +299,8 @@ contains
real(wp_), dimension(:), allocatable :: fvpsi,wf,wrk
integer, dimension(:), allocatable :: iwrk
integer :: ier,ixploc,info
!
! compute array sizes and prepare working space arrays
! compute array sizes and prepare working space arrays
nr=size(rv)
nz=size(zv)
nrz=nr*nz
@ -310,34 +308,34 @@ contains
nzest=nz+ksplp
lwrk=4+nrest*nz+(nrest+nzest)*(2*kspl+5)+(nr+nz)*ksplp+max(nz,nrest)
liwrk=nz+nr+nrest+nzest+kspl
!
npsi=size(psinr)
npsest=npsi+ksplp
lwrkf=npsi*ksplp+npsest*(7+3*kspl)
!
allocate(wrk(max(lwrk,lwrkf)),iwrk(max(liwrk,npsest)))
!
! spline fitting/interpolation of psin(i,j) and derivatives
!
! length in m !!!
!
! spline fitting/interpolation of psin(i,j) and derivatives
! length in m !!!
rmnm=rv(1)
rmxm=rv(nr)
zmnm=zv(1)
zmxm=zv(nz)
! allocate knots and spline coefficients arrays
! allocate knots and spline coefficients arrays
if (allocated(tr)) deallocate(tr)
if (allocated(tz)) deallocate(tz)
allocate(tr(nrest),tz(nzest),cceq(nrz))
! allocate work arrays
! reshape 2D psi array to 1D (transposed) array and compute spline coeffs
! allocate work arrays
! reshape 2D psi array to 1D (transposed) array and compute spline coeffs
allocate(fvpsi(nrz))
fvpsi=reshape(transpose(psin),(/nrz/))
sspln=sspl
call regrid(iopt,nr,rv,nz,zv,fvpsi,rmnm,rmxm,zmnm,zmxm, &
kspl,kspl,sspln,nrest,nzest,nsr,tr,nsz,tz,cceq,fp, &
wrk(1:lwrk),lwrk,iwrk(1:liwrk),liwrk,ier)
! if ier=-1 data are re-fitted using sspl=0
! if ier=-1 data are re-fitted using sspl=0
if(ier==-1) then
sspln=0.0_wp_
call regrid(iopt,nr,rv,nz,zv,fvpsi,rmnm,rmxm,zmnm,zmxm, &
@ -345,7 +343,7 @@ contains
wrk(1:lwrk),lwrk,iwrk(1:liwrk),liwrk,ier)
end if
deallocate(fvpsi)
! compute spline coefficients for psi partial derivatives
! compute spline coefficients for psi partial derivatives
lw10 = nr*(ksplp-1) + nz*ksplp + nrz
lw01 = nr*ksplp + nz*(ksplp-1) + nrz
lw20 = nr*(ksplp-2) + nz*ksplp + nrz
@ -362,10 +360,10 @@ contains
call coeff_parder(tr,nsr,tz,nsz,cceq,kspl,kspl,2,0,cceq20,lw20,ier)
call coeff_parder(tr,nsr,tz,nsz,cceq,kspl,kspl,0,2,cceq02,lw02,ier)
call coeff_parder(tr,nsr,tz,nsz,cceq,kspl,kspl,1,1,cceq11,lw11,ier)
!
! spline interpolation of fpol(i)
!
! allocate knots and spline coefficients arrays
! spline interpolation of fpol(i)
! allocate knots and spline coefficients arrays
if (allocated(tfp)) deallocate(tfp)
if (allocated(cfp)) deallocate(cfp)
allocate(tfp(npsest),cfp(npsest))
@ -375,22 +373,22 @@ contains
call curfit(iopt,npsi,psinr,fpol,wf,zero,one,kspl,ssfp,npsest,nsf, &
tfp,cfp,fp,wrk(1:lwrkf),lwrkf,iwrk(1:npsest),ier)
call splev(tfp,nsf,cfp,kspl,psinr(npsi:npsi),fpoli,1,ier)
! set vacuum value used outside 0<=psin<=1 range
! set vacuum value used outside 0<=psin<=1 range
fpolas=fpoli(1)
sgnbphi=sign(one,fpolas)
! free temporary arrays
! free temporary arrays
deallocate(wrk,iwrk,wf)
!
! re-normalize psi after spline computation
!
! start with un-corrected psi
!
! re-normalize psi after spline computation
! start with un-corrected psi
psia=psiwbrad
psinop=0.0_wp_
psiant=1.0_wp_
!
! use provided boundary to set an initial guess for the search of O/X points
!
! use provided boundary to set an initial guess for the search of O/X points
nbnd=0
if(present(rbnd).and.present(zbnd)) then
nbnd=min(size(rbnd),size(zbnd))
@ -408,9 +406,9 @@ contains
rbmin=rv(2)
rbmax=rv(nr-1)
end if
!
! search for exact location of the magnetic axis
!
! search for exact location of the magnetic axis
if(present(rax)) then
rax0=rax
else
@ -423,9 +421,9 @@ contains
end if
call points_ox(rax0,zax0,rmaxis,zmaxis,psinoptmp,info)
print'(a,2f8.4,es12.5)','O-point',rmaxis,zmaxis,psinoptmp
!
! search for X-point if ixp not = 0
!
! search for X-point if ixp not = 0
if(present(ixp)) then
ixploc=ixp
else
@ -462,21 +460,21 @@ contains
if (ixploc==0) then
psinop=psinoptmp
psiant=one-psinop
! find upper horizontal tangent point
! find upper horizontal tangent point
call points_tgo(rmaxis,0.5_wp_*(zmaxis+zbsup),r1,z1,one,info)
zbsup=z1
rbsup=r1
! find lower horizontal tangent point
! find lower horizontal tangent point
call points_tgo(rmaxis,0.5_wp_*(zmaxis+zbinf),r1,z1,one,info)
zbinf=z1
rbinf=r1
print'(a,4f8.4)','no X-point ',rbinf,zbinf,rbsup,zbsup
end if
print*,' '
!
! save Bt value on axis (required in flux_average and used in Jcd def)
! and vacuum value B0 at ref. radius R0 (used in Jcd_astra def)
!
! save Bt value on axis (required in flux_average and used in Jcd def)
! and vacuum value B0 at ref. radius R0 (used in Jcd_astra def)
call equinum_fpol(0.0_wp_,btaxis)
btaxis=btaxis/rmaxis
if(present(r0)) then
@ -522,9 +520,9 @@ contains
integer, dimension(liwrk) :: iwrk
real(wp_), dimension(1) :: rrs,zzs,ffspl
real(wp_), dimension(lwrk) :: wrk
!
! here lengths are measured in meters
!
! here lengths are measured in meters
if (rpsim.le.rmxm .and. rpsim.ge.rmnm .and. &
zpsim.le.zmxm .and. zpsim.ge.zmnm) then
@ -608,6 +606,7 @@ contains
end subroutine equinum_fpol
subroutine bfield(rpsim,zpsim,bphi,br,bz)
use gray_params, only : iequil
implicit none
! arguments
real(wp_), intent(in) :: rpsim,zpsim
@ -615,11 +614,16 @@ contains
! local variables
real(wp_) :: psin,fpol
call equinum_psi(rpsim,zpsim,psinv=bphi,dpsidr=bz,dpsidz=br)
if (present(bphi)) then
psin=bphi
call equinum_fpol(psin,fpol)
bphi=fpol/rpsim
if (iequil < 2) then
call equian(rpsim,zpsim,fpolv=bphi,dpsidr=bz,dpsidz=br)
if (present(bphi)) bphi=bphi/rpsim
else
call equinum_psi(rpsim,zpsim,psinv=bphi,dpsidr=bz,dpsidz=br)
if (present(bphi)) then
psin=bphi
call equinum_fpol(psin,fpol)
bphi=fpol/rpsim
end if
end if
if (present(br)) br=-br/rpsim
if (present(bz)) bz= bz/rpsim
@ -629,11 +633,11 @@ contains
use const_and_precisions, only : pi
use simplespline, only : difcs
implicit none
! arguments
! arguments
real(wp_), dimension(:), intent(in) :: psinq,q
real(wp_), intent(in) :: psia
real(wp_), dimension(:), intent(out), optional :: rhotn
! local variables
! local variables
real(wp_), dimension(size(q)) :: phit
real(wp_) :: dx
integer, parameter :: iopt=0
@ -646,9 +650,8 @@ contains
psinr=psinq
call difcs(psinr,q,nq,iopt,cq,ier)
!
! Toroidal flux phi = 2*pi*Integral q dpsi
!
! Toroidal flux phi = 2*pi*Integral q dpsi
phit(1)=0.0_wp_
do k=1,nq-1
dx=psinr(k+1)-psinr(k)
@ -729,10 +732,10 @@ contains
use utils, only : locate
use simplespline, only : spli
implicit none
! arguments
! arguments
real(wp_), intent(in) :: rhot
real(wp_) :: frhopol
! local variables
! local variables
integer :: i
real(wp_) :: dr
@ -746,10 +749,10 @@ contains
use utils, only : locate
use simplespline, only : spli
implicit none
! arguments
! arguments
real(wp_), dimension(:), intent(in) :: rhot
real(wp_), dimension(size(rhot)) :: frhopolv
! local variables
! local variables
integer :: i,i0,j
real(wp_) :: dr
@ -767,10 +770,10 @@ contains
use utils, only : locate
use simplespline, only : spli
implicit none
! arguments
! arguments
real(wp_), intent(in) :: rhop
real(wp_) :: frhotor
! local variables
! local variables
integer :: i
real(wp_) :: dr
@ -818,7 +821,7 @@ contains
real(wp_), dimension(ldfjac,n), intent(inout) :: fjac
! local variables
real(wp_) :: dpsidr,dpsidz,ddpsidrr,ddpsidzz,ddpsidrz
!
select case(iflag)
case(1)
call equinum_psi(x(1),x(2),dpsidr=dpsidr,dpsidz=dpsidz)
@ -826,7 +829,7 @@ contains
fvec(2) = dpsidz/psia
case(2)
call equinum_psi(x(1),x(2),ddpsidrr=ddpsidrr,ddpsidzz=ddpsidzz, &
ddpsidrz=ddpsidrz)
ddpsidrz=ddpsidrz)
fjac(1,1) = ddpsidrr/psia
fjac(1,2) = ddpsidrz/psia
fjac(2,1) = ddpsidrz/psia
@ -851,7 +854,6 @@ contains
real(wp_), dimension(n) :: xvec,fvec,f0
real(wp_), dimension(lwa) :: wa
real(wp_), dimension(ldfjac,n) :: fjac
! common/external functions/variables
xvec(1)=rz
xvec(2)=zz
@ -860,8 +862,8 @@ contains
tol = sqrt(comp_eps)
call hybrj1mv(fcntgo,n,xvec,f0,fvec,fjac,ldfjac,tol,info,wa,lwa)
if(info.gt.1) then
print'(a,i2,a,2f8.4)',' info subr points_tgo =',info, &
' R,z coord.',xvec
print'(a,i2,a,5f8.4)',' info subr points_tgo =',info, &
' R,z coord.',xvec,rz,zz,psin0
end if
rf=xvec(1)
zf=xvec(2)
@ -885,7 +887,7 @@ contains
fvec(2) = dpsidr/psia-f0(2)
case(2)
call equinum_psi(x(1),x(2),dpsidr=dpsidr,dpsidz=dpsidz, &
ddpsidrr=ddpsidrr,ddpsidrz=ddpsidrz)
ddpsidrr=ddpsidrr,ddpsidrz=ddpsidrz)
fjac(1,1) = dpsidr/psia
fjac(1,2) = dpsidz/psia
fjac(2,1) = ddpsidrr/psia
@ -927,12 +929,13 @@ contains
end if
if (allocated(psinr)) deallocate(psinr)
allocate(psinr(nq),rhotn(nq),rhopn(nq))
dr=one/(nq-1)
rhotn(1)=zero
psinr(1)=zero
res=zero
fq0=zero
do i=2,n
do i=2,nq
rn=(i-1)*dr
qq=q0+(q1-q0)*rn**qexp
fq1=rn/qq
@ -941,11 +944,13 @@ contains
rhotn(i)=rn
psinr(i)=res
end do
phitedge=btaxis*aminor**2 ! temporary
psia=res*phitedge
phitedge=pi*phitedge ! final
psinr=psinr/res
rhopn=sqrt(psinr)
call set_rhospl(rhopn,rhotn)
end subroutine set_equian
@ -958,11 +963,10 @@ contains
real(wp_), intent(out), optional :: psinv,fpolv,dfpv,dpsidr,dpsidz, &
ddpsidrr,ddpsidzz,ddpsidrz
! local variables
real(wp_) :: cst,dpsidrp,d2psidrp,dqq,qq,rn,rpm,snt,rhop,rhot
! real(wp_) :: frhopol
real(wp_) :: cst,dpsidrp,d2psidrp,dqq,qq,rn,rpm,snt,rhop,rhot,btaxqq
! simple model for equilibrium: large aspect ratio
! outside plasma: analytical continuation, not solution Maxwell eqs
! simple model for equilibrium: large aspect ratio
! outside plasma: analytical continuation, not solution Maxwell eqs
rpm=sqrt((rrm-rmaxis)**2+(zzm-zmaxis)**2) !!! rpm==rho_tor[m], rn=rho_tor_norm
rn=rpm/aminor
@ -987,12 +991,14 @@ contains
if(rn <= 1.0_wp_) then
qq=q0+(qa-q0)*rn**alq
dpsidrp=btaxis*aminor*rn/qq
btaxqq=btaxis/qq
dpsidrp=btaxqq*rpm
dqq=alq*(qa-q0)*rn**(alq-1.0_wp_)
d2psidrp=btaxis/qq*(1.0_wp_-rn*dqq/qq)
d2psidrp=btaxqq*(1.0_wp_-rn*dqq/qq)
else
dpsidrp=btaxis*rpm/qa
d2psidrp=btaxis/qa
btaxqq=btaxis/qa
dpsidrp=btaxqq*rpm
d2psidrp=btaxqq
end if
if(present(fpolv)) fpolv=btaxis*rmaxis
@ -1000,10 +1006,80 @@ contains
if(present(dpsidr)) dpsidr=dpsidrp*cst
if(present(dpsidz)) dpsidz=dpsidrp*snt
if(present(ddpsidrr)) ddpsidrr=dpsidrp*snt**2/rpm+cst**2*d2psidrp
if(present(ddpsidrz)) ddpsidrz=cst*snt*(d2psidrp-dpsidrp/rpm)
if(present(ddpsidzz)) ddpsidzz=dpsidrp*cst**2/rpm+snt**2*d2psidrp
if(present(ddpsidrr)) ddpsidrr=btaxqq*snt**2+cst**2*d2psidrp
if(present(ddpsidrz)) ddpsidrz=cst*snt*(d2psidrp-btaxqq)
if(present(ddpsidzz)) ddpsidzz=btaxqq*cst**2+snt**2*d2psidrp
end subroutine equian
subroutine tor_curr(rpsim,zpsim,ajphi)
use const_and_precisions, only : wp_,ccj=>mu0inv
use gray_params, only : iequil
implicit none
! arguments
real(wp_) :: rpsim,zpsim,ajphi
! local variables
real(wp_) :: bzz,dbvcdc13,dbvcdc31
real(wp_) :: dpsidr,ddpsidrr,ddpsidzz
if(iequil < 2) then
call equian(rpsim,zpsim,dpsidr=dpsidr, &
ddpsidrr=ddpsidrr,ddpsidzz=ddpsidzz)
else
call equinum_psi(rpsim,zpsim,dpsidr=dpsidr, &
ddpsidrr=ddpsidrr,ddpsidzz=ddpsidzz)
end if
bzz= dpsidr/rpsim
dbvcdc13=-ddpsidzz/rpsim
dbvcdc31= ddpsidrr/rpsim-bzz/rpsim
ajphi=ccj*(dbvcdc13-dbvcdc31)
end subroutine tor_curr
subroutine psi_raxis(psin,r1,r2)
use const_and_precisions, only : wp_
use gray_params, only : iequil
use dierckx, only : profil,sproota
implicit none
! local constants
integer, parameter :: mest=4
! arguments
real(wp_) :: psin,r1,r2
! local variables
integer :: iopt,ier,m
real(wp_) :: zc,val
real(wp_), dimension(mest) :: zeroc
real(wp_), dimension(nsr) :: czc
if (iequil < 2) then
val=frhotor(sqrt(psin))
r1=rmaxis-val*aminor
r2=rmaxis+val*aminor
else
iopt=1
zc=zmaxis
call profil(iopt,tr,nsr,tz,nsz,cceq,kspl,kspl,zc,nsr,czc,ier)
if(ier.gt.0) print*,' profil =',ier
val=psin*psiant+psinop
call sproota(val,tr,nsr,czc,zeroc,mest,m,ier)
r1=zeroc(1)
r2=zeroc(2)
end if
end subroutine psi_raxis
subroutine tor_curr_psi(psin,ajphi)
use const_and_precisions, only : wp_
implicit none
! arguments
real(wp_) :: psin,ajphi
! local variables
real(wp_) :: r1,r2
call psi_raxis(psin,r1,r2)
call tor_curr(r2,zmaxis,ajphi)
end subroutine tor_curr_psi
end module equilibrium

1874
src/gray-externals.f
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File diff suppressed because it is too large Load Diff

16
src/graycore.f90
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@ -13,6 +13,7 @@ subroutine gray(rv,zv,psin,psia,psinr,fpol,qpsi,rvac,rax,zax,rbnd,zbnd,eqp, &
rtrparam_type, hcdparam_type, set_codepar, igrad, iequil, iprof
use beams, only : read_beam0, read_beam1, launchangles2n, xgygcoeff
use equilibrium, only : set_equian, set_eqspl, setqphi_num, set_rhospl
use magsurf_data, only : flux_average
use beamdata, only : init_rtr, dealloc_beam, nstep, dst
use reflections, only : set_lim
implicit none
@ -49,7 +50,7 @@ subroutine gray(rv,zv,psin,psia,psinr,fpol,qpsi,rvac,rax,zax,rbnd,zbnd,eqp, &
if(iequil<2) then
call set_equian(rv(1),zv(1),rv(2), fpol(1)/rv(1), qpsi(1),qpsi(2),qpsi(3))
call flux_average_an
call flux_average
else
call set_eqspl(rv,zv,psin, psia, psinr,fpol, eqp%ssplps,eqp%ssplf, rvac, &
rax,zax, rbnd,zbnd, eqp%ixp)
@ -97,6 +98,7 @@ subroutine gray(rv,zv,psin,psia,psinr,fpol,qpsi,rvac,rax,zax,rbnd,zbnd,eqp, &
call prfile
call paraminit
call vectinit
if(igrad==0) then
call ic_rt(x0,y0,z0,anx0,any0,anz0,ak0,xgcn,bres, &
w1,w2,ri1,ri2,phiw,phir,sox,psipol0,chipol0)
@ -104,20 +106,22 @@ subroutine gray(rv,zv,psin,psia,psinr,fpol,qpsi,rvac,rax,zax,rbnd,zbnd,eqp, &
call ic_gb(x0,y0,z0,anx0,any0,anz0,ak0,xgcn,bres, &
w1,w2,ri1,ri2,phiw,phir,sox,psipol0,chipol0)
end if
! if(ierr==0) return
! beam/ray propagation
! beam/ray propagation
! st0=0.0_wp_
! if(index_rt.gt.1) st0=strfl11
do i=1,nstep
istep=i
st=i*dst !+st0
! advance one step
! advance one step
call rkint4(sox,xgcn,bres)
! calculations after one step:
! calculations after one step:
call after_onestep(p0,sox,ak0,xgcn,bres,i,istop,ierr)
if(istop.eq.1) exit
end do
! postprocessing
! postprocessing
call after_gray_integration(pec,icd,dpdv,jcd)
! ======= main loop END ======

403
src/magsurf_data.f90
View File

@ -2,23 +2,23 @@ module magsurf_data
use const_and_precisions, only : wp_
implicit none
INTEGER, SAVE :: npsi, npoints !# sup mag, # punti per sup
INTEGER, SAVE :: njpt, nlmt
integer, save :: npsi, npoints !# sup mag, # punti per sup
integer, save :: njpt, nlmt
REAL(wp_), SAVE :: rarea
real(wp_), save :: rarea
REAL(wp_), DIMENSION(:), ALLOCATABLE, SAVE :: psicon,pstab,rhot_eq, &
real(wp_), dimension(:), allocatable, save :: psicon,pstab,rhot_eq, &
rhotqv,bav,varea,vcurrp,vajphiav,qqv,ffc,vratja,vratjb
REAL(wp_), DIMENSION(:), ALLOCATABLE, SAVE :: rpstab
REAL(wp_), DIMENSION(:), ALLOCATABLE, SAVE :: vvol,rri,rbav,bmxpsi,bmnpsi
REAL(wp_), DIMENSION(:), ALLOCATABLE, SAVE :: tjp,tlm,ch,ch01
real(wp_), dimension(:), allocatable, save :: rpstab
real(wp_), dimension(:), allocatable, save :: vvol,rri,rbav,bmxpsi,bmnpsi
real(wp_), dimension(:), allocatable, save :: tjp,tlm,ch,ch01
REAL(wp_), DIMENSION(:,:), ALLOCATABLE, SAVE :: rcon,zcon
REAL(wp_), DIMENSION(:,:), ALLOCATABLE, SAVE :: cdadrhot,cdvdrhot
real(wp_), dimension(:,:), allocatable, save :: rcon,zcon
real(wp_), dimension(:,:), allocatable, save :: cdadrhot,cdvdrhot
REAL(wp_), DIMENSION(:,:), ALLOCATABLE, SAVE :: cvol,crri,crbav,cbmx,cbmn,carea,cfc
REAL(wp_), DIMENSION(:,:), ALLOCATABLE, SAVE :: crhotq
REAL(wp_), DIMENSION(:,:), ALLOCATABLE, SAVE :: cratja,cratjb,cratjpl
real(wp_), dimension(:,:), allocatable, save :: cvol,crri,crbav,cbmx,cbmn,carea,cfc
real(wp_), dimension(:,:), allocatable, save :: crhotq
real(wp_), dimension(:,:), allocatable, save :: cratja,cratjb,cratjpl
contains
@ -103,4 +103,383 @@ contains
if(allocated(cratjb)) deallocate(cratjb)
end subroutine dealloc_surfvec
subroutine flux_average
use const_and_precisions, only : wp_,zero,one,pi,ccj=>mu0inv
use gray_params, only : iequil
use equilibrium, only : btrcen,btaxis,rmaxis,zmaxis,phitedge,zbsup,zbinf, &
equian,equinum_psi,bfield,frhotor,fq,tor_curr
use simplespline, only : difcs
use dierckx, only : regrid,coeff_parder
use utils, only : get_free_unit
implicit none
! local constants
integer, parameter :: nnintp=101,ncnt=100,nlam=101,ksp=3, &
njest=nnintp+ksp+1,nlest=nlam+ksp+1, &
lwrk=4*(nnintp+nlam)+11*(njest+nlest)+njest*nnintp+nlest+54, &
kwrk=nnintp+nlam+njest+nlest+3,lw01=nnintp*4+nlam*3+nnintp*nlam
! local variables
integer :: ier,ierr,l,jp,ipr,jpr,inc,inc1,iopt,njp,nlm,ninpr,u56,unit
integer, dimension(kwrk) :: iwrk
real(wp_) :: lam,dlam,anorm,b2av,dvdpsi,dadpsi,ratio_cdator, &
ratio_cdbtor,ratio_pltor,fc,height,height2,r2iav,currp, &
area,volume,ajphiav,bbav,bmmx,bmmn,btot0,bpoloid0,rpsim0,dla,dlb, &
dlp,drc,ph,area2,rzp,rz,rpsim,zpsim,btot,bpoloid,dlph,ajphi0, &
shlam,srl,rl2,rl0,rl,dhlam,dhlam0,ccfh,s,ajphi, &
bphi,brr,bzz,riav,fp,psinjp,rhopjp,rhotjp,qq,rup,rlw,zup,zlw
real(wp_), dimension(nnintp) :: dadrhotv,dvdrhotv,vratjpl
real(wp_), dimension(2*ncnt) :: dlpv
real(wp_), dimension(2*ncnt+1) :: bv,bpv
real(wp_), dimension(nlam) :: alam,weights
real(wp_), dimension(nnintp,nlam) :: fhlam
real(wp_), dimension(nnintp*nlam) :: ffhlam,dffhlam
real(wp_), dimension(lwrk) :: wrk
real(wp_), dimension(:), allocatable :: rctemp,zctemp
! common/external functions/variables
real(wp_) :: fpolv,ddpsidrr,ddpsidzz
u56=get_free_unit()
open(file='f56.txt',unit=u56)
npsi=nnintp
ninpr=(npsi-1)/10
npoints = 2*ncnt+1
call alloc_surfvec(ierr)
if(allocated(tjp)) deallocate(tjp)
if(allocated(tlm)) deallocate(tlm)
if(allocated(ch)) deallocate(ch)
allocate(tjp(njest),tlm(nlest),ch((njest-4)*(nlest-4)), &
rctemp(npoints),zctemp(npoints),stat=ierr)
if (ierr.ne.0) return
! computation of flux surface averaged quantities
write(71,*)' #i psin R z'
dlam=1.0_wp_/dble(nlam-1)
do l=1,nlam-1
alam(l)=dble(l-1)*dlam
fhlam(1,l)=sqrt(1.0_wp_-alam(l))
ffhlam(l)=fhlam(1,l)
dffhlam(l)=-0.5_wp_/sqrt(1.0_wp_-alam(l))
weights(l)=1.0_wp_
end do
weights(1)=0.5_wp_
weights(nlam)=0.5_wp_
alam(nlam)=1.0_wp_
fhlam(1,nlam)=0.0_wp_
ffhlam(nlam)=0.0_wp_
dffhlam(nlam)=-99999.0_wp_
jp=1
anorm=2.0_wp_*pi*rmaxis/abs(btaxis)
dvdpsi=2.0_wp_*pi*anorm
dadpsi=2.0_wp_*pi/abs(btaxis)
b2av=btaxis**2
ratio_cdator=abs(btaxis/btrcen)
ratio_cdbtor=1.0_wp_
ratio_pltor=1.0_wp_
fc=1.0_wp_
if(iequil < 2) then
call equian(rmaxis,zmaxis,ddpsidrr=ddpsidrr,ddpsidzz=ddpsidzz)
else
call equinum_psi(rmaxis,zmaxis,ddpsidrr=ddpsidrr,ddpsidzz=ddpsidzz)
end if
qq=btaxis/sqrt(ddpsidrr*ddpsidzz)
ajphiav=-ccj*(ddpsidrr+ddpsidzz)/rmaxis
psicon(1)=0.0_wp_
rcon(1,:)=rmaxis
zcon(1,:)=zmaxis
pstab(1)=0.0_wp_
rpstab(1)=0.0_wp_
vcurrp(1)=0.0_wp_
vajphiav(1)=ajphiav
bmxpsi(1)=abs(btaxis)
bmnpsi(1)=abs(btaxis)
bav(1)=abs(btaxis)
rbav(1)=1.0_wp_
rri(1)=rmaxis
varea(1)=0.0_wp_
vvol(1)=0.0_wp_
vratjpl(1)=ratio_pltor
vratja(1)=ratio_cdator
vratjb(1)=ratio_cdbtor
ffc(1)=fc
qqv(1)=qq
dadrhotv(1)=0.0_wp_
dvdrhotv(1)=0.0_wp_
rup=rmaxis
rlw=rmaxis
zup=zmaxis+(zbsup-zmaxis)/10.0_wp_
zlw=zmaxis-(zmaxis-zbinf)/10.0_wp_
do jp=2,npsi
height=dble(jp-1)/dble(npsi-1)
if(jp.eq.npsi) height=0.9999_wp_
ipr=0
jpr=mod(jp,ninpr)
if(jpr.eq.1) ipr=1
rhopjp=height
psinjp=height*height
rhotjp=frhotor(rhopjp)
psicon(jp)=height
if(iequil<2) then
call contours_psi_an(psinjp,rctemp,zctemp,ipr)
else
call contours_psi(psinjp,rup,zup,rlw,zlw,rctemp,zctemp,ipr)
end if
rcon(jp,:) = rctemp
zcon(jp,:) = zctemp
r2iav=0.0_wp_
anorm=0.0_wp_
dadpsi=0.0_wp_
currp=0.0_wp_
b2av=0.0_wp_
area=0.0_wp_
volume=0.0_wp_
ajphiav=0.0_wp_
bbav=0.0_wp_
bmmx=-1.0e+30_wp_
bmmn=1.0e+30_wp_
call tor_curr(rctemp(1),zctemp(1),ajphi0)
call bfield(rctemp(1),zctemp(1),bphi,br=brr,bz=bzz)
fpolv=bphi*rctemp(1)
btot0=sqrt(bphi**2+brr**2+bzz**2)
bpoloid0=sqrt(brr**2+bzz**2)
bv(1)=btot0
bpv(1)=bpoloid0
rpsim0=rctemp(1)
do inc=1,npoints-1
inc1=inc+1
dla=sqrt((rctemp(inc)-rmaxis)**2+(zctemp(inc)-zmaxis)**2)
dlb=sqrt((rctemp(inc1)-rmaxis)**2+(zctemp(inc1)-zmaxis)**2)
dlp=sqrt((rctemp(inc1)-rctemp(inc))**2+(zctemp(inc1)-zctemp(inc))**2)
drc=(rctemp(inc1)-rctemp(inc))
! compute length, area and volume defined by psi=psinjp=height^2
ph=0.5_wp_*(dla+dlb+dlp)
area2=ph*(ph-dla)*(ph-dlb)*(ph-dlp)
area=area+sqrt(area2)
rzp=rctemp(inc1)*zctemp(inc1)
rz=rctemp(inc)*zctemp(inc)
volume=pi*(rzp+rz)*drc+volume
! compute line integrals on the contour psi=psinjp=height^2
rpsim=rctemp(inc1)
zpsim=zctemp(inc1)
call bfield(rpsim,zpsim,br=brr,bz=bzz)
call tor_curr(rpsim,zpsim,ajphi)
bphi=fpolv/rpsim
btot=sqrt(bphi**2+brr**2+bzz**2)
bpoloid=sqrt(brr**2+bzz**2)
dlpv(inc)=dlp
bv(inc1)=btot
bpv(inc1)=bpoloid
dlph=0.5_wp_*dlp
anorm=anorm+dlph*(1.0_wp_/bpoloid+1.0_wp_/bpoloid0)
dadpsi=dadpsi+dlph*(1.0_wp_/(bpoloid*rpsim)+1.0_wp_/(bpoloid0*rpsim0))
currp=currp+dlph*(bpoloid+bpoloid0)
b2av=b2av+dlph*(btot0**2/bpoloid0+btot**2/bpoloid)
bbav=bbav+dlph*(btot/bpoloid+btot0/bpoloid0)
r2iav=r2iav+dlph*(1.0_wp_/(bpoloid*rpsim**2)+1.0_wp_/(bpoloid0*rpsim0**2))
ajphiav=ajphiav+dlph*(ajphi0/(bpoloid0*rpsim0)+ajphi/(bpoloid*rpsim))
ajphi0=ajphi
rpsim0=rpsim
bpoloid0=bpoloid
btot0=btot
! computation maximum/minimum B values on given flux surface
if(btot.le.bmmn) bmmn=btot
if(btot.ge.bmmx) bmmx=btot
end do
! bav=<B> [T] , b2av=<B^2> [T^2] , rbav=<B>/b_min
! anorm = int d l_p/B_p = dV/dpsi/(2pi)
! r2iav=<1/R^2> [m^-2] ,
! riav=<1/R> [m^-1] = dA/dpsi/(dV/dpsi/(2pi)),
! rri = <B>/(|R B_tor|<1/R^2>) , used to compute I_tor [m^-1]
! currp = plasma current within psi=const
bbav=bbav/anorm
r2iav=r2iav/anorm
dvdpsi=2.0_wp_*pi*anorm
riav=dadpsi/anorm
b2av=b2av/anorm
vcurrp(jp)=ccj*currp
vajphiav(jp)=ajphiav/dadpsi
! area == varea, volume == vvol
! flux surface minor radius == (area/pi)^1/2
! ratio_cdator = Jcd_astra/J_phi Jcd_astra = <Jcd.B>/B0
! ratio_cdbtor = Jcd_jintrac/J_phi Jcd_jintrac = <Jcd.B>/<B>
! ratio_pltor = Jcd_||/J_phi Jcd_|| = <Jcd.b>
pstab(jp)=psinjp
rpstab(jp)=rhopjp
vvol(jp)=abs(volume)
varea(jp)=area
bav(jp)=bbav
rbav(jp)=bbav/bmmn
bmxpsi(jp)=bmmx
bmnpsi(jp)=bmmn
rri(jp)=bav(jp)/abs(fpolv*r2iav)
ratio_cdator=abs(b2av*riav/(fpolv*r2iav*btrcen))
ratio_cdbtor=abs(b2av*riav/(fpolv*r2iav*bbav))
ratio_pltor=abs(bbav*riav/(fpolv*r2iav))
vratjpl(jp)=ratio_pltor
vratja(jp)=ratio_cdator
vratjb(jp)=ratio_cdbtor
qq=abs(dvdpsi*fpolv*r2iav/(4.0_wp_*pi*pi))
qqv(jp)=qq
dadrhotv(jp)=phitedge*frhotor(rhopjp)/fq(psinjp)*dadpsi/pi
dvdrhotv(jp)=phitedge*frhotor(rhopjp)/fq(psinjp)*dvdpsi/pi
! computation of fraction of circulating/trapped fraction fc, ft
! and of function H(lambda,rhop)
! ffhlam = Bmn/Bmx/fc integral_lambda^1 dlam/<sqrt(1-lam*B(rhop)/Bmx)>
fc=0.0_wp_
shlam=0.0_wp_
do l=nlam,1,-1
lam=alam(l)
srl=0.0_wp_
rl2=1.0_wp_-lam*bv(1)/bmmx
rl0=0.0_wp_
if(rl2.gt.0) rl0=sqrt(rl2)
do inc=1,npoints-1
rl2=1.0_wp_-lam*bv(inc+1)/bmmx
rl=0.0_wp_
if(rl2.gt.0) rl=sqrt(rl2)
srl=srl+0.5_wp_*dlpv(inc)*(rl/bpv(inc+1)+rl0/bpv(inc))
rl0=rl
end do
srl=srl/anorm
dhlam=0.5_wp_/srl
fc=fc+lam/srl*weights(l)
if(l.eq.nlam) then
fhlam(jp,l)=0.0_wp_
ffhlam(nlam*(jp-1)+l)=0.0_wp_
dffhlam(nlam*(jp-1)+l)=-dhlam
dhlam0=dhlam
else
shlam=shlam+0.5_wp_*(dhlam+dhlam0)*dlam
fhlam(jp,l)=shlam
dffhlam(nlam*(jp-1)+l)=-dhlam
dhlam0=dhlam
end if
end do
fc=0.75_wp_*b2av/bmmx**2*fc*dlam
ffc(jp)=fc
ccfh=bmmn/bmmx/fc
do l=1,nlam
ffhlam(nlam*(jp-1)+l)=ccfh*fhlam(jp,l)
dffhlam(nlam*(jp-1)+l)=ccfh*dffhlam(nlam*(jp-1)+l)
end do
end do
write(u56,*)' #rhop rhot |<B>| |Bmx| |Bmn| Area Vol |I_pl| <J_phi> fc ratJa ratJb'
do jp=1,npsi
if(jp.eq.npsi) then
rpstab(jp)=1.0_wp_
pstab(jp)=1.0_wp_
end if
rhotjp=frhotor(rpstab(jp))
write(u56,99) rpstab(jp),rhotjp,bav(jp),bmxpsi(jp),bmnpsi(jp), &
varea(jp),vvol(jp),vcurrp(jp),vajphiav(jp),ffc(jp), &
vratja(jp),vratjb(jp)
end do
close(u56)
! spline coefficients of area,vol,rbav,rri,bmxpsi,bmnpsi,fc,dadrhot,dvdrhot,ratioJs
! used for computations of dP/dV and J_cd
iopt=0
call difcs(rpstab,vvol,npsi,iopt,cvol,ier)
iopt=0
call difcs(rpstab,rbav,npsi,iopt,crbav,ier)
iopt=0
call difcs(rpstab,rri,npsi,iopt,crri,ier)
iopt=0
call difcs(rpstab,bmxpsi,npsi,iopt,cbmx,ier)
iopt=0
call difcs(rpstab,bmnpsi,npsi,iopt,cbmn,ier)
iopt=0
call difcs(rpstab,vratja,npsi,iopt,cratja,ier)
iopt=0
call difcs(rpstab,vratjb,npsi,iopt,cratjb,ier)
iopt=0
call difcs(rpstab,vratjpl,npsi,iopt,cratjpl,ier)
iopt=0
call difcs(rpstab,varea,npsi,iopt,carea,ier)
iopt=0
call difcs(rpstab,ffc,npsi,iopt,cfc,ier)
iopt=0
call difcs(rpstab,dadrhotv,npsi,iopt,cdadrhot,ier)
iopt=0
call difcs(rpstab,dvdrhotv,npsi,iopt,cdvdrhot,ier)
! iopt=0
! call difcs(rpstab,qqv,npsi,iopt,cqq,ier)
! spline interpolation of H(lambda,rhop) and dH/dlambda
iopt=0
s=0.0_wp_
call regrid(iopt,npsi,rpstab,nlam,alam,ffhlam,zero,one,zero,one, &
ksp,ksp,s,njest,nlest,njp,tjp,nlm,tlm,ch,fp, &
wrk,lwrk,iwrk,kwrk,ier)
njpt=njp
nlmt=nlm
99 format(20(1x,e12.5))
end subroutine flux_average
subroutine fluxval(rhop,area,vol,dervol,dadrhot,dvdrhot, &
rri,rbav,bmn,bmx,fc,ratja,ratjb,ratjpl)
use const_and_precisions, only : wp_
use utils, only : locate
use simplespline, only :spli,splid
implicit none
! arguments
real(wp_), intent(in) :: rhop
real(wp_), intent(out), optional :: vol,area,rri,rbav,dervol,bmn,bmx,fc, &
ratja,ratjb,ratjpl,dadrhot,dvdrhot
! local variables
integer :: ip
real(wp_) :: drh
call locate(rpstab,npsi,rhop,ip)
ip=min(max(1,ip),npsi-1)
drh=rhop-rpstab(ip)
if (present(area)) area=spli(carea,npsi,ip,drh)
if (present(vol)) vol=spli(cvol,npsi,ip,drh)
if (present(dervol)) dervol=splid(cvol,npsi,ip,drh)
if (present(dadrhot)) dadrhot=spli(cdadrhot,npsi,ip,drh)
if (present(dvdrhot)) dvdrhot=spli(cdvdrhot,npsi,ip,drh)
if (present(rri)) rri=spli(crri,npsi,ip,drh)
if (present(rbav)) rbav=spli(crbav,npsi,ip,drh)
if (present(bmn)) bmn=spli(cbmn,npsi,ip,drh)
if (present(bmx)) bmx=spli(cbmx,npsi,ip,drh)
if (present(fc)) fc=spli(cfc,npsi,ip,drh)
if (present(ratja)) ratja=spli(cratja,npsi,ip,drh)
if (present(ratjb)) ratjb=spli(cratjb,npsi,ip,drh)
if (present(ratjpl)) ratjpl=spli(cratjpl,npsi,ip,drh)
end subroutine fluxval
end module magsurf_data