src/equilibrium.f90: use enums
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Michele Guerini Rocco
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@ -8,6 +8,8 @@
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module equilibrium
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use const_and_precisions, only : wp_
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use splines, only : spline_simple, spline_1d, spline_2d, linear_1d
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use gray_params, only : EQ_VACUUM, EQ_ANALYTICAL, &
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EQ_EQDSK_FULL, EQ_EQDSK_PARTIAL
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implicit none
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@ -360,36 +362,34 @@ contains
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! 3. q = 1/2π ∂Φ/∂ψ ~ ∂Φ/∂r⋅∂r/∂ψ < 0.
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! 4. In general, sgn(q) = -sgn(I_p)⋅sgn(B_φ).
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if (iequil < 2) then
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! Analytical model
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select case(iequil)
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case (EQ_ANALYTICAL) ! Analytical model
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! Apply signs
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if (params%sgni /= 0) then
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model%q0 = sign(model%q0, -params%sgni*one)
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model%q1 = sign(model%q1, -params%sgni*one)
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end if
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if (params%sgnb /= 0) then
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model%B0 = sign(model%B0, +params%sgnb*one)
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end if
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! Rescale
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model%B0 = model%B0 * params%factb
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! Apply signs
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if (params%sgni /= 0) then
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model%q0 = sign(model%q0, -params%sgni*one)
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model%q1 = sign(model%q1, -params%sgni*one)
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end if
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if (params%sgnb /= 0) then
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model%B0 = sign(model%B0, +params%sgnb*one)
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end if
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! Rescale
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model%B0 = model%B0 * params%factb
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else
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! Numeric data
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case (EQ_EQDSK_FULL, EQ_EQDSK_PARTIAL) ! Numeric data
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! Apply signs
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if (params%sgni /= 0) &
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data%psia = sign(data%psia, -params%sgni*one)
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if (params%sgnb /= 0) &
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data%fpol = sign(data%fpol, +params%sgnb*one)
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! Rescale
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data%psia = data%psia * params%factb
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data%fpol = data%fpol * params%factb
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! Apply signs
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if (params%sgni /= 0) &
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data%psia = sign(data%psia, -params%sgni*one)
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if (params%sgnb /= 0) &
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data%fpol = sign(data%fpol, +params%sgnb*one)
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! Rescale
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data%psia = data%psia * params%factb
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data%fpol = data%fpol * params%factb
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! Compute the signs to be shown in the outputs header when cocos≠0,10.
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! Note: In these cases the values sgni,sgnb from gray.ini are unused.
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params%sgni = int(sign(one, -data%psia))
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params%sgnb = int(sign(one, +data%fpol(size(data%fpol))))
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end if
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! Compute the signs to be shown in the outputs header when cocos≠0,10.
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! Note: In these cases the values sgni,sgnb from gray.ini are unused.
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params%sgni = int(sign(one, -data%psia))
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params%sgnb = int(sign(one, +data%fpol(size(data%fpol))))
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end select
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end subroutine scale_equil
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@ -398,7 +398,7 @@ contains
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! in their respective global variables, see the top of this file.
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use const_and_precisions, only : zero, one
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use gray_params, only : equilibrium_parameters, equilibrium_data
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use gray_params, only : iequil
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use gray_params, only : iequil, X_AT_TOP, X_AT_BOTTOM, X_IS_MISSING
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use utils, only : vmaxmin, vmaxmini, inside
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use logger, only : log_info
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@ -434,77 +434,80 @@ contains
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! Spline interpolation of ψ(R, z)
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if (iequil>2) then
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! data valid only inside boundary (data%psin=0 outside), e.g. source==ESCO
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! presence of boundary anticipated here to filter invalid data
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nbnd = min(size(data%rbnd), size(data%zbnd))
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select case (iequil)
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! allocate knots and spline coefficients arrays
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if (allocated(psi_spline%knots_x)) deallocate(psi_spline%knots_x)
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if (allocated(psi_spline%knots_y)) deallocate(psi_spline%knots_y)
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if (allocated(psi_spline%coeffs)) deallocate(psi_spline%coeffs)
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allocate(psi_spline%knots_x(nrest), psi_spline%knots_y(nzest))
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allocate(psi_spline%coeffs(nrz))
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case (EQ_EQDSK_PARTIAL)
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! Data valid only inside boundary (data%psin=0 outside),
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! presence of boundary anticipated here to filter invalid data
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nbnd = min(size(data%rbnd), size(data%zbnd))
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! determine number of valid grid points
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nrz=0
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do j=1,nz
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do i=1,nr
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if (nbnd.gt.0) then
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if(.not.inside(data%rbnd,data%zbnd,data%rv(i),data%zv(j))) cycle
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else
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if(data%psin(i,j).le.0.0d0) cycle
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end if
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nrz=nrz+1
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! allocate knots and spline coefficients arrays
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if (allocated(psi_spline%knots_x)) deallocate(psi_spline%knots_x)
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if (allocated(psi_spline%knots_y)) deallocate(psi_spline%knots_y)
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if (allocated(psi_spline%coeffs)) deallocate(psi_spline%coeffs)
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allocate(psi_spline%knots_x(nrest), psi_spline%knots_y(nzest))
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allocate(psi_spline%coeffs(nrz))
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! determine number of valid grid points
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nrz=0
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do j=1,nz
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do i=1,nr
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if (nbnd.gt.0) then
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if(.not.inside(data%rbnd,data%zbnd,data%rv(i),data%zv(j))) cycle
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else
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if(data%psin(i,j).le.0.0d0) cycle
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end if
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nrz=nrz+1
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end do
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end do
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end do
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! store valid data
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allocate(rv1d(nrz),zv1d(nrz),fvpsi(nrz),wf(nrz))
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ij=0
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do j=1,nz
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do i=1,nr
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if (nbnd.gt.0) then
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if(.not.inside(data%rbnd,data%zbnd,data%rv(i),data%zv(j))) cycle
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else
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if(data%psin(i,j).le.0.0d0) cycle
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end if
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ij=ij+1
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rv1d(ij)=data%rv(i)
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zv1d(ij)=data%zv(j)
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fvpsi(ij)=data%psin(i,j)
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wf(ij)=1.0d0
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! store valid data
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allocate(rv1d(nrz),zv1d(nrz),fvpsi(nrz),wf(nrz))
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ij=0
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do j=1,nz
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do i=1,nr
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if (nbnd.gt.0) then
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if(.not.inside(data%rbnd,data%zbnd,data%rv(i),data%zv(j))) cycle
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else
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if(data%psin(i,j).le.0.0d0) cycle
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end if
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ij=ij+1
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rv1d(ij)=data%rv(i)
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zv1d(ij)=data%zv(j)
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fvpsi(ij)=data%psin(i,j)
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wf(ij)=1.0d0
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end do
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end do
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end do
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! Fit as a scattered set of points
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! use reduced number of knots to limit memory comsumption ?
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psi_spline%nknots_x=nr/4+4
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psi_spline%nknots_y=nz/4+4
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tension = params%ssplps
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call scatterspl(rv1d, zv1d, fvpsi, wf, nrz, kspl, tension, &
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rmnm, rmxm, zmnm, zmxm, &
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psi_spline%knots_x, psi_spline%nknots_x, &
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psi_spline%knots_y, psi_spline%nknots_y, &
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psi_spline%coeffs, err)
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! if failed, re-fit with an interpolating spline (zero tension)
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if(err == -1) then
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err = 0
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tension = 0
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! Fit as a scattered set of points
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! use reduced number of knots to limit memory comsumption ?
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psi_spline%nknots_x=nr/4+4
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psi_spline%nknots_y=nz/4+4
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tension = params%ssplps
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call scatterspl(rv1d, zv1d, fvpsi, wf, nrz, kspl, tension, &
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rmnm, rmxm, zmnm, zmxm, &
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psi_spline%knots_x, psi_spline%nknots_x, &
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psi_spline%knots_y, psi_spline%nknots_y, &
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psi_spline%coeffs, err)
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end if
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deallocate(rv1d, zv1d, wf, fvpsi)
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! reset nrz to the total number of grid points for next allocations
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nrz = nr*nz
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else
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! iequil==2: data are valid on the full R,z grid
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! if failed, re-fit with an interpolating spline (zero tension)
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if(err == -1) then
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err = 0
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tension = 0
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psi_spline%nknots_x=nr/4+4
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psi_spline%nknots_y=nz/4+4
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call scatterspl(rv1d, zv1d, fvpsi, wf, nrz, kspl, tension, &
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rmnm, rmxm, zmnm, zmxm, &
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psi_spline%knots_x, psi_spline%nknots_x, &
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psi_spline%knots_y, psi_spline%nknots_y, &
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psi_spline%coeffs, err)
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end if
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deallocate(rv1d, zv1d, wf, fvpsi)
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! reset nrz to the total number of grid points for next allocations
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nrz = nr*nz
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case (EQ_EQDSK_FULL)
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! Data are valid on the full R,z grid
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! reshape 2D ψ array to 1D (transposed)
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allocate(fvpsi(nrz))
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@ -523,7 +526,7 @@ contains
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err = 0
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end if
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deallocate(fvpsi)
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end if
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end select
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if (err /= 0) then
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err = 2
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@ -592,11 +595,11 @@ contains
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'r', rmaxis, 'z', zmaxis, 'ψ', psinoptmp
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call log_info(msg, mod='equilibrium', proc='set_equil_spline')
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! search for X-point if params%ixp /= 0
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! Search for X-point
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ixploc = params%ixp
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if(ixploc/=0) then
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if(ixploc<0) then
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select case (ixploc)
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case (X_AT_BOTTOM)
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call points_ox(rbinf,zbinf,r1,z1,psinxptmp,info)
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if(psinxptmp/=-1.0_wp_) then
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write (msg, '("X-point found:", 3(x,a,"=",g0.3))') &
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@ -611,7 +614,8 @@ contains
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else
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ixploc=0
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end if
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else
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case (X_AT_TOP)
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call points_ox(rbsup,zbsup,r1,z1,psinxptmp,info)
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if(psinxptmp.ne.-1.0_wp_) then
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write (msg, '("X-point found:", 3(x,a,"=",g0.3))') &
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@ -626,26 +630,22 @@ contains
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else
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ixploc=0
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end if
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end if
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end if
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if (ixploc==0) then
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psinop=psinoptmp
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psiant=one-psinop
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! Find upper horizontal tangent point
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call points_tgo(rmaxis,0.5_wp_*(zmaxis+zbsup),r1,z1,one,info)
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zbsup=z1
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rbsup=r1
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! Find lower horizontal tangent point
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call points_tgo(rmaxis,0.5_wp_*(zmaxis+zbinf),r1,z1,one,info)
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zbinf=z1
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rbinf=r1
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write (msg, '("X-point not found in", 2(x,a,"∈[",g0.3,",",g0.3,"]"))') &
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'r', rbinf, rbsup, 'z', zbinf, zbsup
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call log_info(msg, mod='equilibrium', proc='set_equil_spline')
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end if
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case (X_IS_MISSING)
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psinop=psinoptmp
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psiant=one-psinop
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! Find upper horizontal tangent point
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call points_tgo(rmaxis,0.5_wp_*(zmaxis+zbsup),r1,z1,one,info)
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zbsup=z1
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rbsup=r1
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! Find lower horizontal tangent point
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call points_tgo(rmaxis,0.5_wp_*(zmaxis+zbinf),r1,z1,one,info)
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zbinf=z1
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rbinf=r1
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write (msg, '("X-point not found in", 2(x,a,"∈[",g0.3,",",g0.3,"]"))') &
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'r', rbinf, rbsup, 'z', zbinf, zbsup
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call log_info(msg, mod='equilibrium', proc='set_equil_spline')
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end select
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! Adjust all the B-spline coefficients
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! Note: since ψ_n(R,z) = Σ_ij c_ij B_i(R)B_j(z), to correct ψ_n
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@ -908,128 +908,131 @@ contains
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real(wp_) :: dqdr, dqdz ! ∇q
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real(wp_) :: dphidr2, ddphidr2dr2 ! dΦ_n/d(r²), d²Φ_n/d(r²)²
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if (iequil < 2) then
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! Analytical model
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!
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! The normalised poloidal flux ψ_n(R, z) is computed as follows:
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! 1. ψ_n = ρ_p²
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! 2. ρ_p = ρ_p(ρ_t), using `frhopol`, which in turns uses q(ψ)
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! 3. ρ_t = √Φ_n
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! 4. Φ_n = Φ(r)/Φ(a), where Φ(r) is the flux of B_φ=B₀R₀/R
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! through a circular surface
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! 5. r = √[(R-R₀)²+(z-z₀)²] is the geometric minor radius
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r_g = hypot(R - model%R0, z - model%z0)
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! Values for vacuum/outside the domain
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if (present(psi_n)) psi_n = -1
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if (present(dpsidr)) dpsidr = 0
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if (present(dpsidz)) dpsidz = 0
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if (present(ddpsidrr)) ddpsidrr = 0
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if (present(ddpsidzz)) ddpsidzz = 0
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if (present(ddpsidrz)) ddpsidrz = 0
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! The exact flux of the toroidal field B_φ = B₀R₀/R is:
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!
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! Φ(r) = B₀πr² 2γ/(γ + 1) where γ=1/√(1 - r²/R₀²).
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!
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! Notes:
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! 1. the function Φ(r) is defined for r≤R₀ only.
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! 2. as r → 0, γ → 1, so Φ ~ B₀πr².
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! 3. as r → 1⁻, Φ → 2B₀πr² but dΦ/dr → -∞.
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! 4. |B_R|, |B_z| → +-∞.
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!
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if (r_g > model%R0) then
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if (present(psi_n)) psi_n = -1
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if (present(dpsidr)) dpsidr = 0
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if (present(dpsidz)) dpsidz = 0
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if (present(ddpsidrr)) ddpsidrr = 0
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if (present(ddpsidzz)) ddpsidzz = 0
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if (present(ddpsidrz)) ddpsidrz = 0
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return
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end if
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select case (iequil)
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case (EQ_ANALYTICAL)
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! Analytical model
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!
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! The normalised poloidal flux ψ_n(R, z) is computed as follows:
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! 1. ψ_n = ρ_p²
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! 2. ρ_p = ρ_p(ρ_t), using `frhopol`, which in turns uses q(ψ)
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! 3. ρ_t = √Φ_n
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! 4. Φ_n = Φ(r)/Φ(a), where Φ(r) is the flux of B_φ=B₀R₀/R
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! through a circular surface
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! 5. r = √[(R-R₀)²+(z-z₀)²] is the geometric minor radius
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r_g = hypot(R - model%R0, z - model%z0)
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gamma = 1 / sqrt(1 - (r_g/model%R0)**2)
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phi_n = model%B0 * pi*r_g**2 * 2*gamma/(gamma + 1) / phitedge
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rho_t = sqrt(phi_n)
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rho_p = frhopol(rho_t)
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! The exact flux of the toroidal field B_φ = B₀R₀/R is:
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!
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! Φ(r) = B₀πr² 2γ/(γ + 1) where γ=1/√(1 - r²/R₀²).
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!
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! Notes:
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! 1. the function Φ(r) is defined for r≤R₀ only.
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! 2. as r → 0, γ → 1, so Φ ~ B₀πr².
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! 3. as r → 1⁻, Φ → 2B₀πr² but dΦ/dr → -∞.
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! 4. |B_R|, |B_z| → +-∞.
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!
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if (r_g > model%R0) then
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if (present(psi_n)) psi_n = -1
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if (present(dpsidr)) dpsidr = 0
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if (present(dpsidz)) dpsidz = 0
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if (present(ddpsidrr)) ddpsidrr = 0
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if (present(ddpsidzz)) ddpsidzz = 0
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if (present(ddpsidrz)) ddpsidrz = 0
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return
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end if
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! For ∇Φ_n and ∇∇Φ_n we also need:
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!
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! ∂Φ∂(r²) = B₀π γ(r)
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! ∂²Φ∂(r²)² = B₀π γ³(r) / (2 R₀²)
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!
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dphidr2 = model%B0 * pi * gamma / phitedge
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ddphidr2dr2 = model%B0 * pi * gamma**3/(2 * model%R0**2) / phitedge
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gamma = 1 / sqrt(1 - (r_g/model%R0)**2)
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phi_n = model%B0 * pi*r_g**2 * 2*gamma/(gamma + 1) / phitedge
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rho_t = sqrt(phi_n)
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||||
rho_p = frhopol(rho_t)
|
||||
|
||||
! ∇Φ_n = ∂Φ_n/∂(r²) ∇(r²)
|
||||
! where ∇(r²) = 2[(R-R₀), (z-z₀)]
|
||||
dphidr = dphidr2 * 2*(R - model%R0)
|
||||
dphidz = dphidr2 * 2*(z - model%z0)
|
||||
! For ∇Φ_n and ∇∇Φ_n we also need:
|
||||
!
|
||||
! ∂Φ∂(r²) = B₀π γ(r)
|
||||
! ∂²Φ∂(r²)² = B₀π γ³(r) / (2 R₀²)
|
||||
!
|
||||
dphidr2 = model%B0 * pi * gamma / phitedge
|
||||
ddphidr2dr2 = model%B0 * pi * gamma**3/(2 * model%R0**2) / phitedge
|
||||
|
||||
! ∇∇Φ_n = ∇[∂Φ_n/∂(r²)] ∇(r²) + ∂Φ_n/∂(r²) ∇∇(r²)
|
||||
! = ∂²Φ_n/∂(r²)² ∇(r²)∇(r²) + ∂Φ_n/∂(r²) ∇∇(r²)
|
||||
! where ∇∇(r²) = 2I
|
||||
ddphidrdr = ddphidr2dr2 * 4*(R - model%R0)*(R - model%R0) + dphidr2*2
|
||||
ddphidzdz = ddphidr2dr2 * 4*(z - model%z0)*(z - model%z0) + dphidr2*2
|
||||
ddphidrdz = ddphidr2dr2 * 4*(R - model%R0)*(z - model%z0)
|
||||
! ∇Φ_n = ∂Φ_n/∂(r²) ∇(r²)
|
||||
! where ∇(r²) = 2[(R-R₀), (z-z₀)]
|
||||
dphidr = dphidr2 * 2*(R - model%R0)
|
||||
dphidz = dphidr2 * 2*(z - model%z0)
|
||||
|
||||
! ψ_n = ρ_p(ρ_t)²
|
||||
if (present(psi_n)) psi_n = rho_p**2
|
||||
! ∇∇Φ_n = ∇[∂Φ_n/∂(r²)] ∇(r²) + ∂Φ_n/∂(r²) ∇∇(r²)
|
||||
! = ∂²Φ_n/∂(r²)² ∇(r²)∇(r²) + ∂Φ_n/∂(r²) ∇∇(r²)
|
||||
! where ∇∇(r²) = 2I
|
||||
ddphidrdr = ddphidr2dr2 * 4*(R - model%R0)*(R - model%R0) + dphidr2*2
|
||||
ddphidzdz = ddphidr2dr2 * 4*(z - model%z0)*(z - model%z0) + dphidr2*2
|
||||
ddphidrdz = ddphidr2dr2 * 4*(R - model%R0)*(z - model%z0)
|
||||
|
||||
! Using the definitions in `frhotor`:
|
||||
!
|
||||
! ∇ψ_n = ∂ψ_n/∂Φ_n ∇Φ_n
|
||||
!
|
||||
! ∂ψ_n/∂Φ_n = Φ_a/ψ_a ∂ψ/∂Φ
|
||||
! = Φ_a/ψ_a 1/2πq
|
||||
!
|
||||
! Using ψ_a = 1/2π Φ_a / (q₀ + Δq), then:
|
||||
!
|
||||
! ∂ψ_n/∂Φ_n = (q₀ + Δq)/q
|
||||
!
|
||||
q = model%q0 + (model%q1 - model%q0) * rho_p**model%alpha
|
||||
dq = (model%q1 - model%q0) / (model%alpha/2 + 1)
|
||||
dpsidphi = (model%q0 + dq) / q
|
||||
! ψ_n = ρ_p(ρ_t)²
|
||||
if (present(psi_n)) psi_n = rho_p**2
|
||||
|
||||
! Using the above, ∇ψ_n = ∂ψ_n/∂Φ_n ∇Φ_n
|
||||
if (present(dpsidr)) dpsidr = dpsidphi * dphidr
|
||||
if (present(dpsidz)) dpsidz = dpsidphi * dphidz
|
||||
! Using the definitions in `frhotor`:
|
||||
!
|
||||
! ∇ψ_n = ∂ψ_n/∂Φ_n ∇Φ_n
|
||||
!
|
||||
! ∂ψ_n/∂Φ_n = Φ_a/ψ_a ∂ψ/∂Φ
|
||||
! = Φ_a/ψ_a 1/2πq
|
||||
!
|
||||
! Using ψ_a = 1/2π Φ_a / (q₀ + Δq), then:
|
||||
!
|
||||
! ∂ψ_n/∂Φ_n = (q₀ + Δq)/q
|
||||
!
|
||||
q = model%q0 + (model%q1 - model%q0) * rho_p**model%alpha
|
||||
dq = (model%q1 - model%q0) / (model%alpha/2 + 1)
|
||||
dpsidphi = (model%q0 + dq) / q
|
||||
|
||||
! For the second derivatives:
|
||||
!
|
||||
! ∇∇ψ_n = ∇(∂ψ_n/∂Φ_n) ∇Φ_n + (∂ψ_n/∂Φ_n) ∇∇Φ_n
|
||||
!
|
||||
! ∇(∂ψ_n/∂Φ_n) = - (∂ψ_n/∂Φ_n) ∇q/q
|
||||
!
|
||||
! From q(ψ) = q₀ + (q₁-q₀) ψ_n^α/2, we have:
|
||||
!
|
||||
! ∇q = α/2 (q-q₀) ∇ψ_n/ψ_n
|
||||
! = α/2 (q-q₀)/ψ_n (∂ψ_n/∂Φ_n) ∇Φ_n.
|
||||
!
|
||||
dqdr = model%alpha/2 * (model%q1 - model%q0)*rho_p**(model%alpha-2) * dpsidphi * dphidr
|
||||
dqdz = model%alpha/2 * (model%q1 - model%q0)*rho_p**(model%alpha-2) * dpsidphi * dphidz
|
||||
ddpsidphidr = - dpsidphi * dqdr/q
|
||||
ddpsidphidz = - dpsidphi * dqdz/q
|
||||
! Using the above, ∇ψ_n = ∂ψ_n/∂Φ_n ∇Φ_n
|
||||
if (present(dpsidr)) dpsidr = dpsidphi * dphidr
|
||||
if (present(dpsidz)) dpsidz = dpsidphi * dphidz
|
||||
|
||||
! Combining all of the above:
|
||||
!
|
||||
! ∇∇ψ_n = ∇(∂ψ_n/∂Φ_n) ∇Φ_n + (∂ψ_n/∂Φ_n) ∇∇Φ_n
|
||||
!
|
||||
if (present(ddpsidrr)) ddpsidrr = ddpsidphidr * dphidr + dpsidphi * ddphidrdr
|
||||
if (present(ddpsidzz)) ddpsidzz = ddpsidphidz * dphidz + dpsidphi * ddphidzdz
|
||||
if (present(ddpsidrz)) ddpsidrz = ddpsidphidr * dphidz + dpsidphi * ddphidrdz
|
||||
else
|
||||
! Numerical data
|
||||
if (inside(psi_domain%R, psi_domain%z, R, z)) then
|
||||
! Within the interpolation range
|
||||
if (present(psi_n)) psi_n = psi_spline%eval(R, z)
|
||||
if (present(dpsidr)) dpsidr = psi_spline%deriv(R, z, 1, 0)
|
||||
if (present(dpsidz)) dpsidz = psi_spline%deriv(R, z, 0, 1)
|
||||
if (present(ddpsidrr)) ddpsidrr = psi_spline%deriv(R, z, 2, 0)
|
||||
if (present(ddpsidzz)) ddpsidzz = psi_spline%deriv(R, z, 0, 2)
|
||||
if (present(ddpsidrz)) ddpsidrz = psi_spline%deriv(R, z, 1, 1)
|
||||
else
|
||||
! Outside
|
||||
if (present(psi_n)) psi_n = -1
|
||||
if (present(dpsidr)) dpsidr = 0
|
||||
if (present(dpsidz)) dpsidz = 0
|
||||
if (present(ddpsidrr)) ddpsidrr = 0
|
||||
if (present(ddpsidzz)) ddpsidzz = 0
|
||||
if (present(ddpsidrz)) ddpsidrz = 0
|
||||
end if
|
||||
end if
|
||||
! For the second derivatives:
|
||||
!
|
||||
! ∇∇ψ_n = ∇(∂ψ_n/∂Φ_n) ∇Φ_n + (∂ψ_n/∂Φ_n) ∇∇Φ_n
|
||||
!
|
||||
! ∇(∂ψ_n/∂Φ_n) = - (∂ψ_n/∂Φ_n) ∇q/q
|
||||
!
|
||||
! From q(ψ) = q₀ + (q₁-q₀) ψ_n^α/2, we have:
|
||||
!
|
||||
! ∇q = α/2 (q-q₀) ∇ψ_n/ψ_n
|
||||
! = α/2 (q-q₀)/ψ_n (∂ψ_n/∂Φ_n) ∇Φ_n.
|
||||
!
|
||||
dqdr = model%alpha/2 * (model%q1 - model%q0)*rho_p**(model%alpha-2) * dpsidphi * dphidr
|
||||
dqdz = model%alpha/2 * (model%q1 - model%q0)*rho_p**(model%alpha-2) * dpsidphi * dphidz
|
||||
ddpsidphidr = - dpsidphi * dqdr/q
|
||||
ddpsidphidz = - dpsidphi * dqdz/q
|
||||
|
||||
! Combining all of the above:
|
||||
!
|
||||
! ∇∇ψ_n = ∇(∂ψ_n/∂Φ_n) ∇Φ_n + (∂ψ_n/∂Φ_n) ∇∇Φ_n
|
||||
!
|
||||
if (present(ddpsidrr)) ddpsidrr = ddpsidphidr * dphidr + dpsidphi * ddphidrdr
|
||||
if (present(ddpsidzz)) ddpsidzz = ddpsidphidz * dphidz + dpsidphi * ddphidzdz
|
||||
if (present(ddpsidrz)) ddpsidrz = ddpsidphidr * dphidz + dpsidphi * ddphidrdz
|
||||
|
||||
case (EQ_EQDSK_FULL, EQ_EQDSK_PARTIAL)
|
||||
! Numerical data
|
||||
if (inside(psi_domain%R, psi_domain%z, R, z)) then
|
||||
! Within the interpolation range
|
||||
if (present(psi_n)) psi_n = psi_spline%eval(R, z)
|
||||
if (present(dpsidr)) dpsidr = psi_spline%deriv(R, z, 1, 0)
|
||||
if (present(dpsidz)) dpsidz = psi_spline%deriv(R, z, 0, 1)
|
||||
if (present(ddpsidrr)) ddpsidrr = psi_spline%deriv(R, z, 2, 0)
|
||||
if (present(ddpsidzz)) ddpsidzz = psi_spline%deriv(R, z, 0, 2)
|
||||
if (present(ddpsidrz)) ddpsidrz = psi_spline%deriv(R, z, 1, 1)
|
||||
end if
|
||||
|
||||
end select
|
||||
end subroutine pol_flux
|
||||
|
||||
|
||||
@ -1043,21 +1046,28 @@ contains
|
||||
real(wp_), intent(out) :: fpol ! poloidal current
|
||||
real(wp_), intent(out), optional :: dfpol ! derivative
|
||||
|
||||
if (iequil < 2) then
|
||||
! Analytical model
|
||||
! F(ψ) = B₀⋅R₀, a constant
|
||||
fpol = model%B0 * model%R0
|
||||
if (present(dfpol)) dfpol = 0
|
||||
else
|
||||
! Numerical data
|
||||
if(psi_n <= 1 .and. psi_n >= 0) then
|
||||
fpol = fpol_spline%eval(psi_n)
|
||||
if (present(dfpol)) dfpol = fpol_spline%deriv(psi_n)
|
||||
else
|
||||
fpol = fpolas
|
||||
select case (iequil)
|
||||
case (EQ_VACUUM)
|
||||
! Vacuum, no plasma
|
||||
fpol = 0
|
||||
if (present(dfpol)) dfpol = 0
|
||||
end if
|
||||
end if
|
||||
|
||||
case (EQ_ANALYTICAL)
|
||||
! Analytical model
|
||||
! F(ψ) = B₀⋅R₀, a constant
|
||||
fpol = model%B0 * model%R0
|
||||
if (present(dfpol)) dfpol = 0
|
||||
|
||||
case (EQ_EQDSK_FULL, EQ_EQDSK_PARTIAL)
|
||||
! Numerical data
|
||||
if(psi_n <= 1 .and. psi_n >= 0) then
|
||||
fpol = fpol_spline%eval(psi_n)
|
||||
if (present(dfpol)) dfpol = fpol_spline%deriv(psi_n)
|
||||
else
|
||||
fpol = fpolas
|
||||
if (present(dfpol)) dfpol = 0
|
||||
end if
|
||||
end select
|
||||
end subroutine pol_curr
|
||||
|
||||
|
||||
@ -1069,30 +1079,34 @@ contains
|
||||
real(wp_), intent(in) :: rho_p
|
||||
real(wp_) :: frhotor
|
||||
|
||||
if (iequil < 2) then
|
||||
! Analytical model
|
||||
block
|
||||
! The change of variable is obtained by integrating
|
||||
!
|
||||
! q(ψ) = 1/2π ∂Φ/∂ψ
|
||||
!
|
||||
! and defining ψ = ψ_a ρ_p², Φ = Φ_a ρ_t².
|
||||
! The result is:
|
||||
!
|
||||
! - ψ_a = 1/2π Φ_a / [q₀ + Δq]
|
||||
!
|
||||
! - ρ_t = ρ_p √[(q₀ + Δq ρ_p^α)/(q₀ + Δq)]
|
||||
!
|
||||
! where Δq = (q₁ - q₀)/(α/2 + 1)
|
||||
real(wp_) :: dq
|
||||
dq = (model%q1 - model%q0) / (model%alpha/2 + 1)
|
||||
frhotor = rho_p * sqrt((model%q0 + dq*rho_p**model%alpha) &
|
||||
/ (model%q0 + dq))
|
||||
end block
|
||||
else
|
||||
! Numerical data
|
||||
frhotor = rhot_spline%eval(rho_p)
|
||||
end if
|
||||
select case (iequil)
|
||||
|
||||
case (EQ_ANALYTICAL)
|
||||
! Analytical model
|
||||
block
|
||||
! The change of variable is obtained by integrating
|
||||
!
|
||||
! q(ψ) = 1/2π ∂Φ/∂ψ
|
||||
!
|
||||
! and defining ψ = ψ_a ρ_p², Φ = Φ_a ρ_t².
|
||||
! The result is:
|
||||
!
|
||||
! - ψ_a = 1/2π Φ_a / [q₀ + Δq]
|
||||
!
|
||||
! - ρ_t = ρ_p √[(q₀ + Δq ρ_p^α)/(q₀ + Δq)]
|
||||
!
|
||||
! where Δq = (q₁ - q₀)/(α/2 + 1)
|
||||
real(wp_) :: dq
|
||||
dq = (model%q1 - model%q0) / (model%alpha/2 + 1)
|
||||
frhotor = rho_p * sqrt((model%q0 + dq*rho_p**model%alpha) &
|
||||
/ (model%q0 + dq))
|
||||
end block
|
||||
|
||||
case (EQ_EQDSK_FULL, EQ_EQDSK_PARTIAL)
|
||||
! Numerical data
|
||||
frhotor = rhot_spline%eval(rho_p)
|
||||
|
||||
end select
|
||||
end function frhotor
|
||||
|
||||
|
||||
@ -1105,26 +1119,32 @@ contains
|
||||
real(wp_), intent(in) :: rho_t
|
||||
real(wp_) :: frhopol
|
||||
|
||||
if (iequil < 2) then
|
||||
! Analytical model
|
||||
block
|
||||
! In general there is no closed form for ρ_p(ρ_t) in the
|
||||
! analytical model, we thus solve numerically the equation
|
||||
! ρ_t(ρ_p) = ρ_t₀ for ρ_p.
|
||||
use minpack, only : hybrj1
|
||||
select case (iequil)
|
||||
case (EQ_VACUUM)
|
||||
! Vacuum, no plasma
|
||||
frhopol = 0
|
||||
|
||||
real(wp_) :: rho_p(1), fvec(1), fjac(1,1), wa(7)
|
||||
integer :: info
|
||||
case (EQ_ANALYTICAL)
|
||||
! Analytical model
|
||||
block
|
||||
! In general there is no closed form for ρ_p(ρ_t) in the
|
||||
! analytical model, we thus solve numerically the equation
|
||||
! ρ_t(ρ_p) = ρ_t₀ for ρ_p.
|
||||
use minpack, only : hybrj1
|
||||
|
||||
rho_p = [rho_t] ! first guess, ρ_p ≈ ρ_t
|
||||
call hybrj1(equation, n=1, x=rho_p, fvec=fvec, fjac=fjac, &
|
||||
ldfjac=1, tol=comp_eps, info=info, wa=wa, lwa=7)
|
||||
frhopol = rho_p(1)
|
||||
end block
|
||||
else
|
||||
! Numerical data
|
||||
frhopol = rhop_spline%eval(rho_t)
|
||||
end if
|
||||
real(wp_) :: rho_p(1), fvec(1), fjac(1,1), wa(7)
|
||||
integer :: info
|
||||
|
||||
rho_p = [rho_t] ! first guess, ρ_p ≈ ρ_t
|
||||
call hybrj1(equation, n=1, x=rho_p, fvec=fvec, fjac=fjac, &
|
||||
ldfjac=1, tol=comp_eps, info=info, wa=wa, lwa=7)
|
||||
frhopol = rho_p(1)
|
||||
end block
|
||||
|
||||
case (EQ_EQDSK_FULL, EQ_EQDSK_PARTIAL)
|
||||
! Numerical data
|
||||
frhopol = rhop_spline%eval(rho_t)
|
||||
end select
|
||||
|
||||
contains
|
||||
|
||||
@ -1162,19 +1182,25 @@ contains
|
||||
real(wp_), intent(in) :: psin
|
||||
real(wp_) :: fq
|
||||
|
||||
if (iequil < 2) then
|
||||
! Analytical model
|
||||
! The safety factor is a power law in ρ_p:
|
||||
! q(ρ_p) = q₀ + (q₁-q₀) ρ_p^α
|
||||
block
|
||||
real(wp_) :: rho_p
|
||||
rho_p = sqrt(psin)
|
||||
fq = abs(model%q0 + (model%q1 - model%q0) * rho_p**model%alpha)
|
||||
end block
|
||||
else
|
||||
! Numerical data
|
||||
fq = q_spline%eval(psin)
|
||||
end if
|
||||
select case(iequil)
|
||||
case (EQ_VACUUM)
|
||||
! Vacuum, q is undefined
|
||||
fq = 0
|
||||
|
||||
case (EQ_ANALYTICAL)
|
||||
! Analytical model
|
||||
! The safety factor is a power law in ρ_p:
|
||||
! q(ρ_p) = q₀ + (q₁-q₀) ρ_p^α
|
||||
block
|
||||
real(wp_) :: rho_p
|
||||
rho_p = sqrt(psin)
|
||||
fq = abs(model%q0 + (model%q1 - model%q0) * rho_p**model%alpha)
|
||||
end block
|
||||
|
||||
case (EQ_EQDSK_FULL, EQ_EQDSK_PARTIAL)
|
||||
! Numerical data
|
||||
fq = q_spline%eval(psin)
|
||||
end select
|
||||
end function fq
|
||||
|
||||
|
||||
@ -1183,6 +1209,7 @@ contains
|
||||
! (R, z) in cylindrical coordinates
|
||||
!
|
||||
! Note: all output arguments are optional.
|
||||
use gray_params, only : iequil
|
||||
|
||||
! subroutine arguments
|
||||
real(wp_), intent(in) :: R, z
|
||||
@ -1191,6 +1218,14 @@ contains
|
||||
! local variables
|
||||
real(wp_) :: psi_n, fpol, dpsidr, dpsidz
|
||||
|
||||
if (iequil == EQ_VACUUM) then
|
||||
! Vacuum, no plasma nor field
|
||||
if (present(B_R)) B_R = 0
|
||||
if (present(B_z)) B_z = 0
|
||||
if (present(B_phi)) B_phi = 0
|
||||
return
|
||||
end if
|
||||
|
||||
call pol_flux(R, z, psi_n, dpsidr, dpsidz)
|
||||
call pol_curr(psi_n, fpol)
|
||||
|
||||
|
||||
@ -12,7 +12,7 @@ contains
|
||||
use coreprofiles, only : temp, fzeff
|
||||
use dispersion, only : expinit
|
||||
use gray_params, only : gray_parameters, gray_data, gray_results, &
|
||||
print_parameters
|
||||
print_parameters, EQ_VACUUM
|
||||
use beams, only : xgygcoeff, launchangles2n
|
||||
use beamdata, only : pweight, rayi2jk
|
||||
use gray_errors, only : is_critical, print_err_raytracing, print_err_ecrh_cd
|
||||
@ -100,12 +100,14 @@ contains
|
||||
! Initialise the dispersion module
|
||||
if(params%ecrh_cd%iwarm > 1) call expinit
|
||||
|
||||
! Initialise the magsurf_data module
|
||||
call flux_average ! requires frhotor for dadrhot,dvdrhot
|
||||
if (params%equilibrium%iequil /= EQ_VACUUM) then
|
||||
! Initialise the magsurf_data module
|
||||
call flux_average ! requires frhotor for dadrhot,dvdrhot
|
||||
|
||||
! Initialise the output profiles
|
||||
call pec_init(params%output%ipec, rhout)
|
||||
nnd = size(rhop_tab) ! number of radial profile points
|
||||
! Initialise the output profiles
|
||||
call pec_init(params%output%ipec, rhout)
|
||||
nnd = size(rhop_tab) ! number of radial profile points
|
||||
end if
|
||||
|
||||
call alloc_multipass(nnd, iwait, iroff, iop, iow, yynext, yypnext, yw0, ypw0, stnext, &
|
||||
stv, p0ray, taus, tau1, etau1, cpls, cpl1, lgcpl1, jphi_beam, &
|
||||
@ -138,11 +140,13 @@ contains
|
||||
|
||||
! print Btot=Bres
|
||||
! print ne, Te, q, Jphi versus psi, rhop, rhot
|
||||
call print_bres(bres)
|
||||
call print_prof(params%profiles)
|
||||
call print_maps(bres, xgcn, &
|
||||
norm2(params%antenna%pos(1:2)) * 0.01_wp_, &
|
||||
sin(params%antenna%beta*degree))
|
||||
if (params%equilibrium%iequil /= EQ_VACUUM) then
|
||||
call print_bres(bres)
|
||||
call print_prof(params%profiles)
|
||||
call print_maps(bres, xgcn, &
|
||||
norm2(params%antenna%pos(1:2)) * 0.01_wp_, &
|
||||
sin(params%antenna%beta*degree))
|
||||
end if
|
||||
! ========= pre-proc prints END =========
|
||||
|
||||
! =========== main loop BEGIN ===========
|
||||
@ -518,9 +522,11 @@ contains
|
||||
icd_beam = sum(ccci(:,i))
|
||||
call vmaxmin(tau0,params%raytracing%nray,taumn,taumx) ! taumn,taumx for print
|
||||
|
||||
! compute power and current density profiles for all rays
|
||||
call spec(psjki,ppabs,ccci,iiv,pabs_beam,icd_beam,dpdv_beam,jphi_beam,jcd_beam, &
|
||||
pins_beam,currins_beam)
|
||||
if (params%equilibrium%iequil /= EQ_VACUUM) then
|
||||
! compute power and current density profiles for all rays
|
||||
call spec(psjki,ppabs,ccci,iiv,pabs_beam,icd_beam,dpdv_beam, &
|
||||
jphi_beam,jcd_beam,pins_beam,currins_beam)
|
||||
end if
|
||||
|
||||
pabs_pass(iox) = pabs_pass(iox) + pabs_beam ! 0D results for current pass, sum on O/X mode beams
|
||||
icd_pass(iox) = icd_pass(iox) + icd_beam
|
||||
@ -563,17 +569,20 @@ contains
|
||||
end if
|
||||
end if
|
||||
|
||||
call print_pec(rhop_tab,rhot_tab,jphi_beam,jcd_beam,dpdv_beam,currins_beam, &
|
||||
pins_beam,ip) ! *print power and current density profiles for current beam
|
||||
if (params%equilibrium%iequil /= EQ_VACUUM) then
|
||||
call print_pec(rhop_tab,rhot_tab,jphi_beam,jcd_beam, &
|
||||
dpdv_beam,currins_beam,pins_beam,ip) ! *print power and current density profiles for current beam
|
||||
|
||||
call postproc_profiles(pabs_beam,icd_beam,rhot_tab,dpdv_beam,jphi_beam, &
|
||||
rhotpav,drhotpav,rhotjava,drhotjava,dpdvp,jphip,rhotp,drhotp,rhotj, &
|
||||
drhotj,dpdvmx,jphimx,ratjamx,ratjbmx) ! *compute profiles width for current beam
|
||||
call postproc_profiles(pabs_beam,icd_beam,rhot_tab,dpdv_beam, &
|
||||
jphi_beam, rhotpav,drhotpav,rhotjava,drhotjava,dpdvp,jphip, &
|
||||
rhotp,drhotp,rhotj,drhotj,dpdvmx,jphimx,ratjamx,ratjbmx) ! *compute profiles width for current beam
|
||||
|
||||
call print_finals(pabs_beam,icd_beam,dpdvp,jphip,rhotpav, &
|
||||
rhotjava,drhotpav,drhotjava,dpdvmx,jphimx,rhotp,rhotj, &
|
||||
drhotp,drhotj,ratjamx,ratjbmx,stv(1),psipv(index_rt), &
|
||||
chipv(index_rt),index_rt,sum(p0ray),cpl_beam1,cpl_beam2) ! *print 0D results for current beam
|
||||
end if
|
||||
|
||||
call print_finals(pabs_beam,icd_beam,dpdvp,jphip,rhotpav,rhotjava, &
|
||||
drhotpav,drhotjava,dpdvmx,jphimx,rhotp,rhotj,drhotp,drhotj,ratjamx, &
|
||||
ratjbmx,stv(1),psipv(index_rt),chipv(index_rt),index_rt,sum(p0ray), &
|
||||
cpl_beam1,cpl_beam2) ! *print 0D results for current beam
|
||||
! ============ post-proc END ============
|
||||
|
||||
end do beam_loop
|
||||
@ -1872,13 +1881,20 @@ contains
|
||||
bv(1)=br*csphi-bphi*snphi
|
||||
bv(2)=br*snphi+bphi*csphi
|
||||
bv(3)=bz
|
||||
call pol_limit(anv,bv,bres,sox,ext0(jk),eyt0(jk))
|
||||
|
||||
if (jk == 1) then
|
||||
call stokes_ce(ext0(jk),eyt0(jk),qq,uu,vv)
|
||||
call polellipse(qq,uu,vv,psipol0,chipol0)
|
||||
psipol0=psipol0/degree ! convert from rad to degree
|
||||
chipol0=chipol0/degree
|
||||
if (norm2(bv) > 0) then
|
||||
call pol_limit(anv,bv,bres,sox,ext0(jk),eyt0(jk))
|
||||
|
||||
if (jk == 1) then
|
||||
call stokes_ce(ext0(jk),eyt0(jk),qq,uu,vv)
|
||||
call polellipse(qq,uu,vv,psipol0,chipol0)
|
||||
psipol0=psipol0/degree ! convert from rad to degree
|
||||
chipol0=chipol0/degree
|
||||
end if
|
||||
else
|
||||
! X/O mode are undefined if B=0
|
||||
psipol0 = 0
|
||||
chipol0 = 0
|
||||
end if
|
||||
else
|
||||
call stokes_ell(chipol0*degree,psipol0*degree,qq,uu,vv)
|
||||
|
||||
10
src/main.f90
10
src/main.f90
@ -242,7 +242,7 @@ contains
|
||||
|
||||
! Set global variables
|
||||
select case (params%equilibrium%iequil)
|
||||
case (EQ_VACUUM, EQ_ANALYTICAL)
|
||||
case (EQ_ANALYTICAL)
|
||||
call set_equil_an
|
||||
|
||||
case (EQ_EQDSK_FULL, EQ_EQDSK_PARTIAL)
|
||||
@ -387,7 +387,7 @@ contains
|
||||
EQ_EQDSK_FULL, EQ_EQDSK_PARTIAL
|
||||
use utils, only : range2rect
|
||||
use limiter, only : limiter_set_globals=>set_globals
|
||||
use const_and_precisions, only : cm
|
||||
use const_and_precisions, only : cm, comp_huge
|
||||
|
||||
! subroutine arguments
|
||||
type(gray_parameters), intent(inout) :: params
|
||||
@ -415,7 +415,11 @@ contains
|
||||
|
||||
! Max radius, either due to the plasma extent or equilibrium grid
|
||||
select case (params%equilibrium%iequil)
|
||||
case (EQ_VACUUM, EQ_ANALYTICAL)
|
||||
case (EQ_VACUUM)
|
||||
! Use a very large R, ~ unbounded
|
||||
R_max = comp_huge
|
||||
|
||||
case (EQ_ANALYTICAL)
|
||||
! use R₀+a
|
||||
block
|
||||
use equilibrium, only : model
|
||||
|
||||
@ -1,4 +0,0 @@
|
||||
0.0 0.0 0.0 : rr0m,zr0m,rpam ! rhot[m] = min(sqrt((r-rr0m)**2+(z-zr0m)**2), rpam); tor flux phi = pi*b0*rhot**2
|
||||
0.0 : b0 ! Bphi[T] @ rr0m[m]
|
||||
1 3 2 : q0, qa, alq ! q = q0 + (qa-q0)*sqrt(psin)**alq
|
||||
0 : nlim ! number of points in first wall (rlim,zlim) polygon
|
||||
Loading…
Reference in New Issue
Block a user