combine equian and equinum_* subroutines
This change combines `equian` and `equinum_psi` into a new `pol_flux` subroutine that computes ψ(R,z) and derivatives for either numerical or analytical equilibria. Similarly, `equian` (the fpol and dfpol outputs) and `equinum_fpol` are combined intro `pol_curr` that computes F(ψ) and its derivative. Callers of these subroutines do not select a specific version based on the value of `iequil` anymore.
This commit is contained in:
Michele Guerini Rocco
parent
98dda6d6fa
commit
31a7b95fe1
GPG Key ID:
BFBAF4C975F76450
@ -451,7 +451,7 @@ contains
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! invalid as they are given assuming a vacuum (N=1)
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if (present(launch_pos)) then
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block
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use equilibrium, only : equinum_psi
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use equilibrium, only : pol_flux
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use const_and_precisions, only : cm
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real(wp_) :: R, Z, psi
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@ -461,7 +461,7 @@ contains
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! Get the poloidal flux at the launcher
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! Note: this returns -1 when the data is not available
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call equinum_psi(R, z, psi)
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call pol_flux(R, z, psi)
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if (psi > tail%start .and. psi < tail%end) then
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! Fall back to the midpoint of ψ₀ and the launcher ψ
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@ -52,9 +52,8 @@ module equilibrium
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private
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public read_eqdsk, read_equil_an ! Reading data files
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public scale_equil, change_cocos ! Transforming data
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public equian ! Analytical model
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public equinum_psi, equinum_fpol ! Interpolated data
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public fq, bfield, tor_curr, tor_curr_psi ! Accessing local quantities
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public pol_flux, pol_curr !
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public frhotor, frhopol ! Converting between poloidal/toroidal flux
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public set_equil_spline, set_equil_an ! Initialising internal state
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public unset_equil_spline ! Deinitialising internal state
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@ -661,7 +660,7 @@ contains
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! Save Bt value on axis (required in flux_average and used in Jcd def)
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! and vacuum value B0 at ref. radius data%rvac (used in Jcd_astra def)
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call equinum_fpol(zero, btaxis)
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call pol_curr(zero, btaxis)
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btaxis = btaxis/rmaxis
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btrcen = fpolas/data%rvac
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rcen = data%rvac
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@ -803,94 +802,94 @@ contains
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end subroutine set_rho_spline
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subroutine equinum_psi(R, z, psi, dpsidr, dpsidz, &
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ddpsidrr, ddpsidzz, ddpsidrz)
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! Computes the normalised poloidal flux ψ (and its derivatives)
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! as a function of (R, z) using the numerical equilibrium
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subroutine pol_flux(R, z, psi_n, dpsidr, dpsidz, &
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ddpsidrr, ddpsidzz, ddpsidrz)
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! Computes the normalised poloidal flux ψ_n and its
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! derivatives wrt (R, z) up to the second order.
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!
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! Note: all output arguments are optional.
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use gray_params, only : iequil
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implicit none
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! subroutine arguments
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real(wp_), intent(in) :: R, z
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real(wp_), intent(out), optional :: psi, dpsidr, dpsidz
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real(wp_), intent(out), optional :: ddpsidrr, ddpsidzz, ddpsidrz
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! Note: here lengths are measured in meters
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if (R <= rmxm .and. R >= rmnm .and. &
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z <= zmxm .and. z >= zmnm) then
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if (present(psi)) psi = psi_spline%eval(R, z)
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if (present(dpsidr)) dpsidr = psi_spline%deriv(R, z, 1, 0)
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if (present(dpsidz)) dpsidz = psi_spline%deriv(R, z, 0, 1)
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if (present(ddpsidrr)) ddpsidrr = psi_spline%deriv(R, z, 2, 0)
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if (present(ddpsidzz)) ddpsidzz = psi_spline%deriv(R, z, 0, 2)
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if (present(ddpsidrz)) ddpsidrz = psi_spline%deriv(R, z, 1, 1)
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else
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if (present(psi)) psi = -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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end if
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end subroutine equinum_psi
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subroutine equinum_fpol(psi, fpol, dfpol)
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! Computes the poloidal current function F(ψ)
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! (and its derivative) using the numerical equilibrium
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implicit none
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! subroutine arguments
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real(wp_), intent(in) :: psi
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real(wp_), intent(out) :: fpol
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real(wp_), intent(out), optional :: dfpol
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if(psi <= 1 .and. psi >= 0) then
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fpol = fpol_spline%eval(psi)
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if (present(dfpol)) dfpol = fpol_spline%deriv(psi) / psia
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else
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fpol = fpolas
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if (present(dfpol)) dfpol = 0
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end if
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end subroutine equinum_fpol
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subroutine equian(R, z, psin, fpolv, dfpv, dpsidr, dpsidz, &
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ddpsidrr, ddpsidzz, ddpsidrz)
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! Computes all MHD equilibrium parameters from a simple analytical model
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implicit none
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! subroutine arguments
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real(wp_), intent(in) :: R, z
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real(wp_), intent(out), optional :: psin, fpolv, dfpv, dpsidr, dpsidz, &
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real(wp_), intent(out), optional :: psi_n, dpsidr, dpsidz, &
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ddpsidrr, ddpsidzz, ddpsidrz
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! variables
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! local variables
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real(wp_) :: r_p ! poloidal radius
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real(wp_) :: rho_p ! poloidal radius normalised
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! ρ_p is just the geometrical poloidal radius divided by a
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r_p = hypot(R - model%R0, z - model%z0)
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rho_p = r_p / model%a
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if (iequil < 2) then
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! Analytical model
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! ρ_p is just the geometrical poloidal radius divided by a
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r_p = hypot(R - model%R0, z - model%z0)
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rho_p = r_p / model%a
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! ψ_n = ρ_p²(R,z) = [(R-R₀)² + (z-z₀)²]/a²
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if (present(psin)) psin = rho_p**2
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! ψ_n = ρ_p²(R,z) = [(R-R₀)² + (z-z₀)²]/a²
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if (present(psi_n)) psi_n = rho_p**2
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! ∂ψ/∂R, ∂ψ/∂z
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if (present(dpsidr)) dpsidr = 2*(R - model%R0)/model%a**2
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if (present(dpsidz)) dpsidz = 2*(z - model%z0)/model%a**2
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! ∂ψ_n/∂R, ∂ψ_n/∂z
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if (present(dpsidr)) dpsidr = 2*(R - model%R0)/model%a**2
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if (present(dpsidz)) dpsidz = 2*(z - model%z0)/model%a**2
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! ∂²ψ/∂R², ∂²ψ/∂z², ∂²ψ/∂R∂z
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if (present(ddpsidrr)) ddpsidrr = 2/model%a**2
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if (present(ddpsidzz)) ddpsidzz = 2/model%a**2
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if (present(ddpsidrz)) ddpsidrz = 0
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! ∂²ψ_n/∂R², ∂²ψ_n/∂z², ∂²ψ_n/∂R∂z
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if (present(ddpsidrr)) ddpsidrr = 2/model%a**2
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if (present(ddpsidzz)) ddpsidzz = 2/model%a**2
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if (present(ddpsidrz)) ddpsidrz = 0
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else
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! Numerical data
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if (R <= rmxm .and. R >= rmnm .and. &
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z <= zmxm .and. z >= zmnm) then
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! Within the interpolation range
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if (present(psi_n)) psi_n = psi_spline%eval(R, z)
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if (present(dpsidr)) dpsidr = psi_spline%deriv(R, z, 1, 0)
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if (present(dpsidz)) dpsidz = psi_spline%deriv(R, z, 0, 1)
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if (present(ddpsidrr)) ddpsidrr = psi_spline%deriv(R, z, 2, 0)
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if (present(ddpsidzz)) ddpsidzz = psi_spline%deriv(R, z, 0, 2)
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if (present(ddpsidrz)) ddpsidrz = psi_spline%deriv(R, z, 1, 1)
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else
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! Outside
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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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end if
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end if
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end subroutine pol_flux
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! F(ψ) = B₀⋅R₀, a constant
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if (present(fpolv)) fpolv = model%B0 * model%R0
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if (present(dfpv)) dfpv = 0
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end subroutine equian
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subroutine pol_curr(psi_n, fpol, dfpol)
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! Computes the poloidal current function F(ψ_n)
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! and (optionally) its derivative dF/dψ given ψ_n.
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use gray_params, only : iequil
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implicit none
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! function arguments
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real(wp_), intent(in) :: psi_n ! normalised poloidal flux
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real(wp_), intent(out) :: fpol ! poloidal current
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real(wp_), intent(out), optional :: dfpol ! derivative
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if (iequil < 2) then
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! Analytical model
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! F(ψ) = B₀⋅R₀, a constant
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fpol = model%B0 * model%R0
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if (present(dfpol)) dfpol = 0
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else
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! Numerical data
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if(psi_n <= 1 .and. psi_n >= 0) then
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fpol = fpol_spline%eval(psi_n)
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if (present(dfpol)) dfpol = fpol_spline%deriv(psi_n) / psia
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else
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fpol = fpolas
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if (present(dfpol)) dfpol = 0
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end if
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end if
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end subroutine pol_curr
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function frhotor(rho_p)
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@ -1017,83 +1016,93 @@ contains
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end function fq
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subroutine bfield(rpsim, zpsim, bphi, br, bz)
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subroutine bfield(R, z, B_R, B_z, B_phi)
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! Computes the magnetic field as a function of
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! (R, z) in cylindrical coordinates
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!
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! Note: all output arguments are optional.
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use gray_params, only : iequil
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implicit none
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! subroutine arguments
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real(wp_), intent(in) :: rpsim, zpsim
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real(wp_), intent(out), optional :: bphi,br,bz
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real(wp_), intent(in) :: R, z
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real(wp_), intent(out), optional :: B_R, B_z, B_phi
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! local variables
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real(wp_) :: psin,fpol
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real(wp_) :: psi_n, fpol, dpsidr, dpsidz
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if (iequil < 2) then
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! Analytical model
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call equian(rpsim,zpsim,fpolv=bphi,dpsidr=bz,dpsidz=br)
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if (present(bphi)) bphi=bphi/rpsim
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else
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! Numerical data
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call equinum_psi(rpsim,zpsim,psi=bphi,dpsidr=bz,dpsidz=br)
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if (present(bphi)) then
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psin=bphi
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call equinum_fpol(psin,fpol)
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bphi=fpol/rpsim
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end if
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end if
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call pol_flux(R, z, psi_n, dpsidr, dpsidz)
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call pol_curr(psi_n, fpol)
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if (present(br)) br=-br/rpsim
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if (present(bz)) bz= bz/rpsim
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! The field in cocos=3 is given by
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!
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! B = F(ψ)∇φ + ∇ψ×∇φ.
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!
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! Writing the gradient of ψ=ψ(R,z) as
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!
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! ∇ψ = ∂ψ/∂R ∇R + ∂ψ/∂z ∇z,
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!
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! and carrying out the cross products:
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!
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! B = F(ψ)∇φ - ∂ψ/∂z ∇R/R + ∂ψ/∂R ∇z/R
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!
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if (present(B_R)) B_R = - 1/R * dpsidz * psia
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if (present(B_z)) B_z = + 1/R * dpsidr * psia
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if (present(B_phi)) B_phi = fpol / R
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end subroutine bfield
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function tor_curr(rpsim,zpsim) result(jphi)
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! Computes the toroidal current Jφ as a function of (R, z)
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use const_and_precisions, only : ccj=>mu0inv
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use gray_params, only : iequil
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function tor_curr(R, z) result(J_phi)
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! Computes the toroidal current J_φ as a function of (R, z)
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use const_and_precisions, only : mu0_
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implicit none
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! function arguments
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real(wp_), intent(in) :: rpsim, zpsim
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real(wp_) :: jphi
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real(wp_), intent(in) :: R, z
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real(wp_) :: J_phi
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! local variables
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real(wp_) :: bzz,dbvcdc13,dbvcdc31
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real(wp_) :: dpsidr,ddpsidrr,ddpsidzz
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real(wp_) :: dB_Rdz, dB_zdR ! derivatives of B_R, B_z
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real(wp_) :: dpsidr, ddpsidrr, ddpsidzz ! derivatives of ψ_n
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if(iequil < 2) then
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! Analytical model
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call equian(rpsim,zpsim,dpsidr=dpsidr, &
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ddpsidrr=ddpsidrr,ddpsidzz=ddpsidzz)
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else
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! Numerical data
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call equinum_psi(rpsim,zpsim,dpsidr=dpsidr, &
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ddpsidrr=ddpsidrr,ddpsidzz=ddpsidzz)
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end if
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bzz= dpsidr/rpsim
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dbvcdc13=-ddpsidzz/rpsim
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dbvcdc31= ddpsidrr/rpsim-bzz/rpsim
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jphi=ccj*(dbvcdc13-dbvcdc31)
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call pol_flux(R, z, dpsidr=dpsidr, ddpsidrr=ddpsidrr, ddpsidzz=ddpsidzz)
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! In the usual MHD limit we have ∇×B = μ₀J. Using the
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! curl in cylindrical coords the toroidal current is
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!
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! J_φ = 1/μ₀ (∇×B)_φ = 1/μ₀ [∂B_R/∂z - ∂B_z/∂R].
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!
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! Finally, from B = F(ψ)∇φ + ∇ψ×∇φ we find:
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!
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! B_R = - 1/R ∂ψ/∂z,
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! B_z = + 1/R ∂ψ/∂R,
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!
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! from which:
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!
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! ∂B_R/∂z = - 1/R ∂²ψ/∂z²
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! ∂B_z/∂R = + 1/R ∂²ψ/∂R² - 1/R² ∂ψ/∂R.
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!
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dB_Rdz = - 1/R * ddpsidzz * psia
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dB_zdR = + 1/R * (ddpsidrr - 1/R * dpsidr) * psia
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J_phi = 1/mu0_ * (dB_Rdz - dB_zdR)
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end function tor_curr
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function tor_curr_psi(psin) result(jphi)
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! Computes the toroidal current Jφ as a function of ψ
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function tor_curr_psi(psi_n) result(J_phi)
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! Computes the toroidal current J_φ as a function of ψ
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implicit none
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! function arguments
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real(wp_), intent(in) :: psin
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real(wp_) :: jphi
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real(wp_), intent(in) :: psi_n
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real(wp_) :: J_phi
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! local variables
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real(wp_) :: r1, r2
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call psi_raxis(psin, r1, r2)
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jphi = tor_curr(r2, zmaxis)
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real(wp_) :: R1, R2
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call psi_raxis(psi_n, R1, R2)
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J_phi = tor_curr(R2, zmaxis)
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end function tor_curr_psi
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@ -1178,7 +1187,7 @@ contains
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end if
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rf=xvec(1)
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zf=xvec(2)
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call equinum_psi(rf,zf,psinvf)
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call pol_flux(rf, zf, psinvf)
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end subroutine points_ox
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@ -1199,12 +1208,12 @@ contains
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select case(iflag)
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case(1)
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call equinum_psi(x(1),x(2),dpsidr=dpsidr,dpsidz=dpsidz)
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call pol_flux(x(1), x(2), dpsidr=dpsidr, dpsidz=dpsidz)
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fvec(1) = dpsidr
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fvec(2) = dpsidz
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case(2)
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call equinum_psi(x(1),x(2),ddpsidrr=ddpsidrr,ddpsidzz=ddpsidzz, &
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ddpsidrz=ddpsidrz)
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call pol_flux(x(1), x(2), ddpsidrr=ddpsidrr, ddpsidzz=ddpsidzz, &
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ddpsidrz=ddpsidrz)
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fjac(1,1) = ddpsidrr
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fjac(1,2) = ddpsidrz
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fjac(2,1) = ddpsidrz
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@ -1272,12 +1281,12 @@ contains
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select case(iflag)
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case(1)
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call equinum_psi(x(1),x(2),psinv,dpsidr)
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call pol_flux(x(1), x(2), psinv, dpsidr)
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fvec(1) = psinv-f0(1)
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fvec(2) = dpsidr-f0(2)
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case(2)
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call equinum_psi(x(1),x(2),dpsidr=dpsidr,dpsidz=dpsidz, &
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ddpsidrr=ddpsidrr,ddpsidrz=ddpsidrz)
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call pol_flux(x(1), x(2), dpsidr=dpsidr, dpsidz=dpsidz, &
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ddpsidrr=ddpsidrr, ddpsidrz=ddpsidrz)
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fjac(1,1) = dpsidr
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fjac(1,2) = dpsidz
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fjac(2,1) = ddpsidrr
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||||
@ -1260,7 +1260,7 @@ contains
|
||||
xg, yg, derxg, deryg, psinv_opt)
|
||||
use const_and_precisions, only : zero, cm
|
||||
use gray_params, only : iequil
|
||||
use equilibrium, only : psia, equinum_fpol, equinum_psi, equian, sgnbphi
|
||||
use equilibrium, only : psia, pol_flux, pol_curr, sgnbphi
|
||||
use coreprofiles, only : density
|
||||
|
||||
implicit none
|
||||
@ -1322,13 +1322,8 @@ contains
|
||||
zzm = 1.0e-2_wp_*zz
|
||||
rrm = 1.0e-2_wp_*rr
|
||||
|
||||
if(iequil==1) then
|
||||
call equian(rrm,zzm,psinv,fpolv,dfpv,dpsidr,dpsidz, &
|
||||
ddpsidrr,ddpsidzz,ddpsidrz)
|
||||
else
|
||||
call equinum_psi(rrm,zzm,psinv,dpsidr,dpsidz,ddpsidrr,ddpsidzz,ddpsidrz)
|
||||
call equinum_fpol(psinv,fpolv,dfpv)
|
||||
end if
|
||||
call pol_flux(rrm, zzm, psinv, dpsidr, dpsidz, ddpsidrr, ddpsidzz, ddpsidrz)
|
||||
call pol_curr(psinv, fpolv, dfpv)
|
||||
|
||||
! copy optional output
|
||||
if (present(psinv_opt)) psinv_opt = psinv
|
||||
@ -1886,7 +1881,7 @@ contains
|
||||
rm=sqrt(xmv(1)**2+xmv(2)**2)
|
||||
csphi=xmv(1)/rm
|
||||
snphi=xmv(2)/rm
|
||||
call bfield(rm,xmv(3),bphi,br,bz)
|
||||
call bfield(rm,xmv(3),br,bz,bphi)
|
||||
! bv(i) = B_i in cartesian coordinates
|
||||
bv(1)=br*csphi-bphi*snphi
|
||||
bv(2)=br*snphi+bphi*csphi
|
||||
@ -2266,7 +2261,7 @@ bb: do
|
||||
zzk = zv(k)
|
||||
do j = 1, q_spline%ndata
|
||||
rrj = rv(j)
|
||||
call bfield(rrj, zzk, bbphi, bbr, bbz)
|
||||
call bfield(rrj, zzk, bbr, bbz, bbphi)
|
||||
btotal(j,k) = sqrt(bbr**2 + bbz**2 + bbphi**2)
|
||||
if(btotal(j,k) >= btmx) btmx = btotal(j,k)
|
||||
if(btotal(j,k) <= btmn) btmn = btotal(j,k)
|
||||
@ -2295,9 +2290,8 @@ bb: do
|
||||
subroutine print_maps(bres, xgcn, r0, anpl0)
|
||||
! Prints several input quantities on a regular grid (unit 72)
|
||||
|
||||
use gray_params, only : iequil
|
||||
use equilibrium, only : rmnm, rmxm, zmnm, zmxm, equian, equinum_psi, &
|
||||
equinum_fpol, q_spline
|
||||
use equilibrium, only : rmnm, rmxm, zmnm, zmxm, &
|
||||
pol_flux, pol_curr, q_spline
|
||||
use coreprofiles, only : density, temp
|
||||
use units, only : umaps, unit_active
|
||||
|
||||
@ -2327,12 +2321,8 @@ bb: do
|
||||
anpl = anpl0 * r0/rj
|
||||
do k = 1, q_spline%ndata
|
||||
zk = z(k)
|
||||
if (iequil < 2) then
|
||||
call equian(rj, zk, psin=psin, fpolv=bphi, dpsidr=bz, dpsidz=br)
|
||||
else
|
||||
call equinum_psi(rj, zk, psi=psin, dpsidr=bz, dpsidz=br)
|
||||
call equinum_fpol(psin, fpol=bphi)
|
||||
end if
|
||||
call pol_flux(rj, zk, psin, dpsidr=bz, dpsidz=br)
|
||||
call pol_curr(psin, fpol=bphi)
|
||||
br = -br/rj
|
||||
bphi = bphi/rj
|
||||
bz = bz/rj
|
||||
|
||||
@ -101,9 +101,8 @@ contains
|
||||
|
||||
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,psia
|
||||
bfield,frhotor,fq,tor_curr,psia,pol_flux
|
||||
use dierckx, only : regrid,coeff_parder
|
||||
implicit none
|
||||
|
||||
@ -170,11 +169,7 @@ contains
|
||||
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
|
||||
call pol_flux(rmaxis, zmaxis, ddpsidrr=ddpsidrr, ddpsidzz=ddpsidzz)
|
||||
qq=abs(btaxis)/sqrt(ddpsidrr*ddpsidzz)/psia
|
||||
ajphiav=-ccj*(ddpsidrr+ddpsidzz)*psia/rmaxis
|
||||
|
||||
@ -230,7 +225,7 @@ contains
|
||||
bmmn=1.0e+30_wp_
|
||||
|
||||
ajphi0 = tor_curr(rctemp(1),zctemp(1))
|
||||
call bfield(rctemp(1),zctemp(1),bphi,br=brr,bz=bzz)
|
||||
call bfield(rctemp(1), zctemp(1), brr, bzz, bphi)
|
||||
fpolv=bphi*rctemp(1)
|
||||
btot0=sqrt(bphi**2+brr**2+bzz**2)
|
||||
bpoloid0=sqrt(brr**2+bzz**2)
|
||||
@ -256,7 +251,7 @@ contains
|
||||
! 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 bfield(rpsim, zpsim, brr, bzz)
|
||||
ajphi = tor_curr(rpsim,zpsim)
|
||||
bphi=fpolv/rpsim
|
||||
btot=sqrt(bphi**2+brr**2+bzz**2)
|
||||
|
||||
@ -37,7 +37,7 @@ contains
|
||||
rm=sqrt(xmv(1)**2+xmv(2)**2)
|
||||
csphi=xmv(1)/rm
|
||||
snphi=xmv(2)/rm
|
||||
call bfield(rm,xmv(3),bphi,br,bz)
|
||||
call bfield(rm,xmv(3),br,bz,bphi)
|
||||
bv(1)=br*csphi-bphi*snphi
|
||||
bv(2)=br*snphi+bphi*csphi
|
||||
bv(3)=bz
|
||||
@ -82,7 +82,7 @@ contains
|
||||
rm=sqrt(xmv(1)**2+xmv(2)**2)
|
||||
csphi=xmv(1)/rm
|
||||
snphi=xmv(2)/rm
|
||||
call bfield(rm,xmv(3),bphi,br,bz)
|
||||
call bfield(rm,xmv(3),br,bz,bphi)
|
||||
bv(1)=br*csphi-bphi*snphi
|
||||
bv(2)=br*snphi+bphi*csphi
|
||||
bv(3)=bz
|
||||
|
||||
Loading…
Reference in New Issue
Block a user