From 78d68a08879c096e724324fdc6dd134b1e58280c Mon Sep 17 00:00:00 2001
From: Antoine Hoffmann <antoine.hoffmann@epfl.ch>
Date: Tue, 3 Oct 2023 11:50:09 +0200
Subject: [PATCH] implementation of global miller
---
src/geometry_mod.F90 | 11 +-
src/miller_mod.F90 | 246 +++++++++++++++++++++++++++++--------------
2 files changed, 175 insertions(+), 82 deletions(-)
diff --git a/src/geometry_mod.F90 b/src/geometry_mod.F90
index 5675ced4..cf3adae4 100644
--- a/src/geometry_mod.F90
+++ b/src/geometry_mod.F90
@@ -18,6 +18,8 @@ implicit none
REAL(xp), PUBLIC, PROTECTED :: s_delta = 0._xp ! '' sdelta = r/sqrt(1-delta2) ddelta/dr
REAL(xp), PUBLIC, PROTECTED :: zeta = 0._xp ! squareness
REAL(xp), PUBLIC, PROTECTED :: s_zeta = 0._xp ! '' szeta = r dzeta/dr
+ REAL(xp), PUBLIC, PROTECTED :: theta1 = 0._xp ! for Miller global
+ REAL(xp), PUBLIC, PROTECTED :: theta2 = 0._xp !
! to apply shift in the parallel z-BC if shearless
REAL(xp), PUBLIC, PROTECTED :: shift_y = 0._xp ! for Arno <3
REAL(xp), PUBLIC, PROTECTED :: Npol = 1._xp ! number of poloidal turns (real for 3D zpinch studies)
@@ -80,7 +82,8 @@ CONTAINS
! Read the input parameters
IMPLICIT NONE
NAMELIST /GEOMETRY/ geom, q0, shear, eps,&
- kappa, s_kappa,delta, s_delta, zeta, s_zeta,& ! For miller
+ kappa, s_kappa,delta, s_delta, zeta, s_zeta,& ! For Miller
+ theta1, theta2,& ! for Miller global
parallel_bc, shift_y, Npol, PB_PHASE
READ(lu_in,geometry)
PB_PHASE = .false.
@@ -139,15 +142,15 @@ CONTAINS
kappa = 1._xp
C_y = 1._xp
Cyq0_x0 = 1._xp
- CASE('miller','Miller')
+ CASE('miller','Miller','Miller_global','miller_global')
CALL speak('Miller geometry')
IF(FLOOR(Npol) .NE. CEILING(Npol)) ERROR STOP "ERROR STOP: Npol must be integer for Miller geometry"
IF(MODULO(FLOOR(Npol),2) .EQ. 0) THEN
write(*,*) "Npol must be odd for Miller, (Npol = ",Npol,")"
ERROR STOP
ENDIF
- call set_miller_parameters(kappa,s_kappa,delta,s_delta,zeta,s_zeta)
- call get_miller(eps,major_R,major_Z,q0,shear,FLOOR(Npol),alpha_MHD,edge_opt,&
+ call set_miller_parameters(kappa,s_kappa,delta,s_delta,zeta,s_zeta,theta1,theta2)
+ call get_miller(geom,eps,major_R,major_Z,q0,shear,FLOOR(Npol),alpha_MHD,edge_opt,&
C_y,C_xy,Cyq0_x0,xpdx_pm_geom,gxx,gxy,gxz,gyy,gyz,gzz,&
dBdx,dBdy,dBdz,hatB,jacobian,hatR,hatZ,dxdR,dxdZ)
CASE('circular','circ')
diff --git a/src/miller_mod.F90 b/src/miller_mod.F90
index 5f852843..705675f8 100644
--- a/src/miller_mod.F90
+++ b/src/miller_mod.F90
@@ -21,11 +21,12 @@ MODULE miller
real(xp) :: rho, kappa, delta, s_kappa, s_delta, drR, drZ, zeta, s_zeta
real(xp) :: thetaShift
real(xp) :: thetak, thetad
+ real(xp) :: asurf, theta1, theta2, theta3, delta2, delta3, Raxis, Zaxis
CONTAINS
!>Set defaults for miller parameters
- subroutine set_miller_parameters(kappa_,s_kappa_,delta_,s_delta_,zeta_,s_zeta_)
- real(xp), INTENT(IN) :: kappa_,s_kappa_,delta_,s_delta_,zeta_,s_zeta_
+ subroutine set_miller_parameters(kappa_,s_kappa_,delta_,s_delta_,zeta_,s_zeta_,theta1_,theta2_)
+ real(xp), INTENT(IN) :: kappa_,s_kappa_,delta_,s_delta_,zeta_,s_zeta_,theta1_,theta2_
rho = -1._xp
kappa = kappa_
s_kappa = s_kappa_
@@ -36,15 +37,24 @@ CONTAINS
drR = 0._xp
drZ = 0._xp
thetak = 0._xp
- thetad = 0._xp
+ thetad = 0._xp
+ asurf = 0.54_xp
+ theta1 = theta1_
+ theta2 = theta2_
+ theta3 = 0._xp
+ delta2 = 1._xp
+ delta3 = 1._xp
+ Raxis = 1._xp
+ Zaxis = 0._xp
end subroutine set_miller_parameters
!>Get Miller metric, magnetic field, jacobian etc.
- subroutine get_miller(trpeps,major_R,major_Z,q0,shat,Npol,amhd,edge_opt,&
+ subroutine get_miller(geom,trpeps,major_R,major_Z,q0,shat,Npol,amhd,edge_opt,&
C_y,C_xy,Cyq0_x0,xpdx_pm_geom,gxx_,gxy_,gxz_,gyy_,gyz_,gzz_,dBdx_,dBdy_,dBdz_,&
Bfield_,jacobian_,R_hat_,Z_hat_,dxdR_,dxdZ_)
!!!!!!!!!!!!!!!! GYACOMO INTERFACE !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+ CHARACTER(len=16), INTENT(IN) :: geom
real(xp), INTENT(INOUT) :: trpeps ! eps in gyacomo (inverse aspect ratio)
real(xp), INTENT(INOUT) :: major_R ! major radius
real(xp), INTENT(INOUT) :: major_Z ! major Z
@@ -73,8 +83,8 @@ CONTAINS
real(xp), dimension(500*(Npol+2)):: dtdtZcirc, dtdtZelong, dtdtZelongTilt, dtdtZtri, dtdtZtriTilt, dtRcirc, dtRelong
real(xp), dimension(500*(Npol+2)):: dtRelongTilt, dtRtri, dtRtriTilt, dtZcirc, dtZelong, dtZelongTilt, dtZtri, dtZtriTilt
real(xp), dimension(500*(Npol+2)):: Rcirc, Relong, RelongTilt, Rtri, RtriTilt, Zcirc, Zelong, ZelongTilt, Ztri, ZtriTilt
- ! real(xp), dimension(500*(Npol+2)):: drrShape, drrAng, drxAng, dryAng, dtdtrShape, dtdtrAng, dtdtxAng
- ! real(xp), dimension(500*(Npol+2)):: dtdtyAng, dtrShape, dtrAng, dtxAng, dtyAng, rShape, rAng, xAng, yAng
+ real(xp), dimension(500*(Npol+2)):: drrShape, drrAng, drxAng, dryAng, dtdtrShape, dtdtrAng, dtdtxAng
+ real(xp), dimension(500*(Npol+2)):: dtdtyAng, dtrShape, dtrAng, dtxAng, dtyAng, rShape, rAng, xAng, yAng
real(xp), dimension(500*(Npol+2)):: theta, thAdj, J_r, B, Bp, D0, D1, D2, D3, nu, chi, psi1, nu1
real(xp), dimension(500*(Npol+2)):: tmp_reverse, theta_reverse, tmp_arr
@@ -91,9 +101,9 @@ CONTAINS
real(xp), dimension(1:total_nz+ngz):: gxx_out,gxy_out,gxz_out,gyy_out,gyz_out,gzz_out,Bfield_out,jacobian_out, dBdx_out, dBdz_out, chi_out
real(xp), dimension(1:total_nz+ngz):: R_out, Z_out, dxdR_out, dxdZ_out
real(xp):: d_inv, drPsi, dxPsi, dq_dx, dq_dpsi, R0, Z0, B0, F, D0_full, D1_full, D2_full, D3_full
- !real(xp) :: Lnorm, Psi0 ! currently module-wide defined anyway
+ real(xp) :: Lnorm, Psi0 ! currently module-wide defined anyway
real(xp):: pprime, ffprime, D0_mid, D1_mid, D2_mid, D3_mid, dx_drho, pi, mu_0, dzprimedz
- ! real(xp):: rho_a, psiN, drpsiN, CN2, CN3, Rcenter, Zcenter, drRcenter, drZcenter
+ real(xp):: rho_a, psiN, drpsiN, CN2, CN3, Rcenter, Zcenter, drRcenter, drZcenter
logical:: bMaxShift
integer:: i, k, iBmax
@@ -124,76 +134,156 @@ CONTAINS
do while (bMaxShift)
!flux surface parametrization
thAdj = theta + thetaShift
- if (zeta/=0._xp .or. s_zeta/=0._xp) then
- R = R0 + rho*Cos(thAdj + d_inv*Sin(thAdj))
- Z = Z0 + kappa*rho*Sin(thAdj + zeta*Sin(2*thAdj))
-
- R_rho = drR + Cos(thAdj + d_inv*Sin(thAdj)) - s_delta*Sin(thAdj)*Sin(thAdj + d_inv*Sin(thAdj))
- Z_rho = drZ + kappa*s_zeta*Cos(thAdj + zeta*Sin(2*thAdj))*Sin(2*thAdj) &
- + kappa*Sin(thAdj + zeta*Sin(2*thAdj)) + kappa*s_kappa*Sin(thAdj + zeta*Sin(2*thAdj))
-
- R_theta = -(rho*(1 + d_inv*Cos(thAdj))*Sin(thAdj + d_inv*Sin(thAdj)))
- Z_theta = kappa*rho*(1 + 2*zeta*Cos(2*thAdj))*Cos(thAdj + zeta*Sin(2*thAdj))
-
- R_theta_theta = -(rho*(1 + d_inv*Cos(thAdj))**2*Cos(thAdj + d_inv*Sin(thAdj))) &
- + d_inv*rho*Sin(thAdj)*Sin(thAdj + d_inv*Sin(thAdj))
- Z_theta_theta = -4*kappa*rho*zeta*Cos(thAdj + zeta*Sin(2*thAdj))*Sin(2*thAdj) &
- - kappa*rho*(1 + 2*zeta*Cos(2*thAdj))**2*Sin(thAdj + zeta*Sin(2*thAdj))
- else
- Rcirc = rho*Cos(thAdj - thetad + thetak)
- Zcirc = rho*Sin(thAdj - thetad + thetak)
- Relong = Rcirc
- Zelong = Zcirc + (-1 + kappa)*rho*Sin(thAdj - thetad + thetak)
- RelongTilt = Relong*Cos(thetad - thetak) - Zelong*Sin(thetad - thetak)
- ZelongTilt = Zelong*Cos(thetad - thetak) + Relong*Sin(thetad - thetak)
- Rtri = RelongTilt - rho*Cos(thAdj) + rho*Cos(thAdj + delta*Sin(thAdj))
- Ztri = ZelongTilt
- RtriTilt = Rtri*Cos(thetad) + Ztri*Sin(thetad)
- ZtriTilt = Ztri*Cos(thetad) - Rtri*Sin(thetad)
- R = R0 + RtriTilt
- Z = Z0 + ZtriTilt
-
- drRcirc = Cos(thAdj - thetad + thetak)
- drZcirc = Sin(thAdj - thetad + thetak)
- drRelong = drRcirc
- drZelong = drZcirc - (1 - kappa - kappa*s_kappa)*Sin(thAdj - thetad + thetak)
- drRelongTilt = drRelong*Cos(thetad - thetak) - drZelong*Sin(thetad - thetak)
- drZelongTilt = drZelong*Cos(thetad - thetak) + drRelong*Sin(thetad - thetak)
- drRtri = drRelongTilt - Cos(thAdj) + Cos(thAdj + delta*Sin(thAdj)) &
- - s_delta*Sin(thAdj)*Sin(thAdj + delta*Sin(thAdj))
- drZtri = drZelongTilt
- drRtriTilt = drRtri*Cos(thetad) + drZtri*Sin(thetad)
- drZtriTilt = drZtri*Cos(thetad) - drRtri*Sin(thetad)
- R_rho = drR + drRtriTilt
- Z_rho = drZ + drZtriTilt
-
- dtRcirc = -(rho*Sin(thAdj - thetad + thetak))
- dtZcirc = rho*Cos(thAdj - thetad + thetak)
- dtRelong = dtRcirc
- dtZelong = dtZcirc + (-1 + kappa)*rho*Cos(thAdj - thetad + thetak)
- dtRelongTilt = dtRelong*Cos(thetad - thetak) - dtZelong*Sin(thetad - thetak)
- dtZelongTilt = dtZelong*Cos(thetad - thetak) + dtRelong*Sin(thetad - thetak)
- dtRtri = dtRelongTilt + rho*Sin(thAdj) - rho*(1 + delta*Cos(thAdj))*Sin(thAdj + delta*Sin(thAdj))
- dtZtri = dtZelongTilt
- dtRtriTilt = dtRtri*Cos(thetad) + dtZtri*Sin(thetad)
- dtZtriTilt = dtZtri*Cos(thetad) - dtRtri*Sin(thetad)
- R_theta = dtRtriTilt
- Z_theta = dtZtriTilt
-
- dtdtRcirc = -(rho*Cos(thAdj - thetad + thetak))
- dtdtZcirc = -(rho*Sin(thAdj - thetad + thetak))
- dtdtRelong = dtdtRcirc
- dtdtZelong = dtdtZcirc - (-1 + kappa)*rho*Sin(thAdj - thetad + thetak)
- dtdtRelongTilt = dtdtRelong*Cos(thetad - thetak) - dtdtZelong*Sin(thetad - thetak)
- dtdtZelongTilt = dtdtZelong*Cos(thetad - thetak) + dtdtRelong*Sin(thetad - thetak)
- dtdtRtri = dtdtRelongTilt + rho*Cos(thAdj) - rho*(1 + delta*Cos(thAdj))**2*Cos(thAdj + delta*Sin(thAdj)) &
- + delta*rho*Sin(thAdj)*Sin(thAdj + delta*Sin(thAdj))
- dtdtZtri = dtdtZelongTilt
- dtdtRtriTilt = dtdtRtri*Cos(thetad) + dtdtZtri*Sin(thetad)
- dtdtZtriTilt = dtdtZtri*Cos(thetad) - dtdtRtri*Sin(thetad)
- R_theta_theta = dtdtRtriTilt
- Z_theta_theta = dtdtZtriTilt
- endif
+ SELECT CASE (geom)
+ CASE('Miller','miller')
+ if (zeta/=0._xp .or. s_zeta/=0._xp) then
+ R = R0 + rho*Cos(thAdj + d_inv*Sin(thAdj))
+ Z = Z0 + kappa*rho*Sin(thAdj + zeta*Sin(2*thAdj))
+
+ R_rho = drR + Cos(thAdj + d_inv*Sin(thAdj)) - s_delta*Sin(thAdj)*Sin(thAdj + d_inv*Sin(thAdj))
+ Z_rho = drZ + kappa*s_zeta*Cos(thAdj + zeta*Sin(2*thAdj))*Sin(2*thAdj) &
+ + kappa*Sin(thAdj + zeta*Sin(2*thAdj)) + kappa*s_kappa*Sin(thAdj + zeta*Sin(2*thAdj))
+
+ R_theta = -(rho*(1 + d_inv*Cos(thAdj))*Sin(thAdj + d_inv*Sin(thAdj)))
+ Z_theta = kappa*rho*(1 + 2*zeta*Cos(2*thAdj))*Cos(thAdj + zeta*Sin(2*thAdj))
+
+ R_theta_theta = -(rho*(1 + d_inv*Cos(thAdj))**2*Cos(thAdj + d_inv*Sin(thAdj))) &
+ + d_inv*rho*Sin(thAdj)*Sin(thAdj + d_inv*Sin(thAdj))
+ Z_theta_theta = -4*kappa*rho*zeta*Cos(thAdj + zeta*Sin(2*thAdj))*Sin(2*thAdj) &
+ - kappa*rho*(1 + 2*zeta*Cos(2*thAdj))**2*Sin(thAdj + zeta*Sin(2*thAdj))
+ else
+ Rcirc = rho*Cos(thAdj - thetad + thetak)
+ Zcirc = rho*Sin(thAdj - thetad + thetak)
+ Relong = Rcirc
+ Zelong = Zcirc + (-1 + kappa)*rho*Sin(thAdj - thetad + thetak)
+ RelongTilt = Relong*Cos(thetad - thetak) - Zelong*Sin(thetad - thetak)
+ ZelongTilt = Zelong*Cos(thetad - thetak) + Relong*Sin(thetad - thetak)
+ Rtri = RelongTilt - rho*Cos(thAdj) + rho*Cos(thAdj + delta*Sin(thAdj))
+ Ztri = ZelongTilt
+ RtriTilt = Rtri*Cos(thetad) + Ztri*Sin(thetad)
+ ZtriTilt = Ztri*Cos(thetad) - Rtri*Sin(thetad)
+ R = R0 + RtriTilt
+ Z = Z0 + ZtriTilt
+
+ drRcirc = Cos(thAdj - thetad + thetak)
+ drZcirc = Sin(thAdj - thetad + thetak)
+ drRelong = drRcirc
+ drZelong = drZcirc - (1 - kappa - kappa*s_kappa)*Sin(thAdj - thetad + thetak)
+ drRelongTilt = drRelong*Cos(thetad - thetak) - drZelong*Sin(thetad - thetak)
+ drZelongTilt = drZelong*Cos(thetad - thetak) + drRelong*Sin(thetad - thetak)
+ drRtri = drRelongTilt - Cos(thAdj) + Cos(thAdj + delta*Sin(thAdj)) &
+ - s_delta*Sin(thAdj)*Sin(thAdj + delta*Sin(thAdj))
+ drZtri = drZelongTilt
+ drRtriTilt = drRtri*Cos(thetad) + drZtri*Sin(thetad)
+ drZtriTilt = drZtri*Cos(thetad) - drRtri*Sin(thetad)
+ R_rho = drR + drRtriTilt
+ Z_rho = drZ + drZtriTilt
+
+ dtRcirc = -(rho*Sin(thAdj - thetad + thetak))
+ dtZcirc = rho*Cos(thAdj - thetad + thetak)
+ dtRelong = dtRcirc
+ dtZelong = dtZcirc + (-1 + kappa)*rho*Cos(thAdj - thetad + thetak)
+ dtRelongTilt = dtRelong*Cos(thetad - thetak) - dtZelong*Sin(thetad - thetak)
+ dtZelongTilt = dtZelong*Cos(thetad - thetak) + dtRelong*Sin(thetad - thetak)
+ dtRtri = dtRelongTilt + rho*Sin(thAdj) - rho*(1 + delta*Cos(thAdj))*Sin(thAdj + delta*Sin(thAdj))
+ dtZtri = dtZelongTilt
+ dtRtriTilt = dtRtri*Cos(thetad) + dtZtri*Sin(thetad)
+ dtZtriTilt = dtZtri*Cos(thetad) - dtRtri*Sin(thetad)
+ R_theta = dtRtriTilt
+ Z_theta = dtZtriTilt
+
+ dtdtRcirc = -(rho*Cos(thAdj - thetad + thetak))
+ dtdtZcirc = -(rho*Sin(thAdj - thetad + thetak))
+ dtdtRelong = dtdtRcirc
+ dtdtZelong = dtdtZcirc - (-1 + kappa)*rho*Sin(thAdj - thetad + thetak)
+ dtdtRelongTilt = dtdtRelong*Cos(thetad - thetak) - dtdtZelong*Sin(thetad - thetak)
+ dtdtZelongTilt = dtdtZelong*Cos(thetad - thetak) + dtdtRelong*Sin(thetad - thetak)
+ dtdtRtri = dtdtRelongTilt + rho*Cos(thAdj) - rho*(1 + delta*Cos(thAdj))**2*Cos(thAdj + delta*Sin(thAdj)) &
+ + delta*rho*Sin(thAdj)*Sin(thAdj + delta*Sin(thAdj))
+ dtdtZtri = dtdtZelongTilt
+ dtdtRtriTilt = dtdtRtri*Cos(thetad) + dtdtZtri*Sin(thetad)
+ dtdtZtriTilt = dtdtZtri*Cos(thetad) - dtdtRtri*Sin(thetad)
+ R_theta_theta = dtdtRtriTilt
+ Z_theta_theta = dtdtZtriTilt
+ endif
+ CASE('Miller_global','miller_global')
+ rho_a = rho/aSurf
+
+ CN2 = (-1._xp + Delta2**2)/(1._xp + Delta2**2)
+ CN3 = (-1._xp + Delta3**2)/(1._xp + Delta3**3)
+
+ psiN = rho_a**2 + CN2*rho_a**2 + CN3*rho_a**3
+ drpsiN = 2._xp*rho_a + 2._xp*CN2*rho_a + 3._xp*CN3*rho_a**2
+
+ xAng = 2*(1._xp + CN2*Cos(2._xp*(thAdj + theta2)))**3 - 27._xp*CN3**2*Cos(3._xp*(thAdj + theta3))**2*psiN
+ drxAng = -27._xp*CN3**2*Cos(3._xp*(thAdj + theta3))**2*drpsiN
+ dtxAng = -12._xp*CN2*(1._xp + CN2*Cos(2._xp*(thAdj + theta2)))**2*Sin(2._xp*(thAdj + theta2)) &
+ + 162._xp*CN3**2*Cos(3._xp*(thAdj + theta3))*psiN*Sin(3._xp*(thAdj + theta3))
+ dtdtxAng = 486._xp*CN3**2*Cos(6._xp*(thAdj + theta3))*psiN + 24._xp*CN2*(1._xp + CN2*Cos(2._xp*(thAdj + theta2))) &
+ *(-(Cos(2._xp*(thAdj + theta2))*(1._xp + CN2*Cos(2._xp*(thAdj + theta2)))) + 2._xp*CN2*Sin(2._xp*(thAdj + theta2))**2)
+
+ yAng = 3._xp*Sqrt(3._xp)*CN3*Cos(3._xp*(thAdj + theta3))*Sqrt(psiN)*Sqrt(2._xp*(1._xp + CN2*Cos(2._xp*(thAdj + theta2)))**3 + xAng)
+ dryAng = (yAng*(drpsiN/psiN + drxAng/(2._xp*(1._xp + CN2*Cos(2._xp*(thAdj + theta2)))**3 + xAng)))/2._xp
+ dtyAng = yAng*(-3._xp*Tan(3._xp*(thAdj + theta3)) &
+ + (-12._xp*CN2*(1._xp + CN2*Cos(2._xp*(thAdj + theta2)))**2*Sin(2._xp*(thAdj + theta2)) + dtxAng) &
+ /(2._xp*(2*(1._xp + CN2*Cos(2*(thAdj + theta2)))**3 + xAng)))
+ dtdtyAng = dtyAng**2/yAng + yAng*(-9._xp/Cos(3._xp*(thAdj + theta3))**2 &
+ - (-12._xp*CN2*(1._xp + CN2*Cos(2._xp*(thAdj + theta2)))**2*Sin(2._xp*(thAdj + theta2)) + dtxAng)**2 &
+ /(2._xp*(2._xp*(1._xp + CN2*Cos(2._xp*(thAdj + theta2)))**3 + xAng)**2) &
+ + (-24._xp*CN2*Cos(2._xp*(thAdj + theta2))*(1._xp + CN2*Cos(2._xp*(thAdj + theta2)))**2 &
+ + 48._xp*CN2**2*(1._xp + CN2*Cos(2._xp*(thAdj + theta2)))*Sin(2._xp*(thAdj + theta2))**2 + dtdtxAng) &
+ /(2._xp*(2._xp*(1._xp + CN2*Cos(2._xp*(thAdj + theta2)))**3 + xAng)))
+
+ rAng = atan2(yAng,xAng)/3.
+ drrAng = (-(yAng*drxAng) + xAng*dryAng)/(3._xp*(xAng**2 + yAng**2))
+ dtrAng = (-(yAng*dtxAng) + xAng*dtyAng)/(3._xp*(xAng**2 + yAng**2))
+ dtdtrAng = (-6._xp*dtrAng**2*yAng)/xAng &
+ + ((2._xp*yAng*dtxAng**2)/xAng - 2._xp*dtxAng*dtyAng - yAng*dtdtxAng + xAng*dtdtyAng)/(3._xp*(xAng**2 + yAng**2))
+
+ rShape = (aSurf*(1._xp + CN2*Cos(2._xp*(thAdj + theta2)))/Cos(3._xp*(thAdj + theta3))*&
+ &(-1._xp + Cos(rAng) + Sqrt(3._xp)*Sin(rAng)))/(3._xp*CN3)
+ drrShape = (aSurf*(1._xp + CN2*Cos(2._xp*(thAdj + theta2)))/Cos(3._xp*(thAdj + theta3))*&
+ &(Sqrt(3._xp)*Cos(rAng) - Sin(rAng))*drrAng)/(3._xp*CN3)
+ dtrShape = rShape*((-2._xp*CN2*Sin(2._xp*(thAdj + theta2)))/(1._xp + CN2*Cos(2._xp*(thAdj + theta2)))&
+ &+ 3._xp*Tan(3._xp*(thAdj + theta3)) &
+ &+ ((Sqrt(3._xp)*Cos(rAng) - Sin(rAng))*dtrAng)/(-1._xp + Cos(rAng) + Sqrt(3._xp)*Sin(rAng)))
+ dtdtrShape = dtrShape**2/rShape + rShape*(9._xp - (4._xp*CN2*Cos(2._xp*(thAdj + theta2)))/(1._xp + CN2*Cos(2._xp*(thAdj + theta2))) &
+ - (4._xp*CN2**2*Sin (2._xp*(thAdj + theta2))**2)/(1._xp + CN2*Cos(2._xp*(thAdj + theta2)))**2 + 9._xp*Tan (3._xp*(thAdj + theta3))**2 &
+ + ((-4._xp + Cos(rAng) + Sqrt(3._xp)*Sin(rAng))*dtrAng**2)/(-1._xp + Cos(rAng) + Sqrt(3._xp)*Sin(rAng))**2 &
+ + ((Sqrt(3._xp)*Cos(rAng) - Sin(rAng))*dtdtrAng)/(-1._xp + Cos(rAng) + Sqrt(3._xp)*Sin(rAng)))
+
+ do i=1._xp,np
+ if (abs(CN3*cos(3._xp*(thAdj(i)+theta3)))<1e-8) then
+ rShape(i) = aSurf*Sqrt(psiN/(1._xp + CN2*Cos(2*(thAdj(i) + theta2))))
+ drrShape(i) = (rShape(i)*drpsiN)/(2._xp*psiN)
+ dtrShape(i) = (CN2*rShape(i)*Sin(2._xp*(thAdj(i) + theta2)))/(1._xp + CN2*Cos(2._xp*(thAdj(i) + theta2)))
+ dtdtrShape(i) = dtrShape(i)**2/rShape(i) &
+ + (2*(CN2**2 + CN2*Cos(2._xp*(thAdj(i) + theta2)))*rShape(i))/(1._xp + CN2*Cos(2._xp*(thAdj(i) + theta2)))**2
+ endif
+
+ if (abs(1._xp + CN2*Cos(2._xp*(thAdj(i) + theta2)))<1e-8) then
+ rShape(i) = aSurf*Sqrt(psiN)
+ drrShape(i) = 1._xp
+ dtrShape(i) = 0._xp
+ dtdtrShape(i) = 0._xp
+ endif
+ enddo
+
+ Rcenter = Raxis - (-R0 + Raxis)*rho_a**2
+ Zcenter = Zaxis - rho_a**2*(-Z0 + Zaxis)
+ drRcenter = -2._xp*(-R0 + Raxis)*rho_a
+ drZcenter = -2._xp*rho_a*(-Z0 + Zaxis)
+
+ R = Rcenter + Cos(thAdj)*rShape
+ Z = rShape*Sin(thAdj) + Zcenter
+ R_rho = (drRcenter + Cos(thAdj)*drrShape)/aSurf ! Adjust for rho deriv, not rho_a deriv
+ Z_rho = (drZcenter + Sin(thAdj)*drrShape)/aSurf ! Adjust for rho deriv, not rho_a deriv
+ R_theta = -(rShape*Sin(thAdj)) + Cos(thAdj)*dtrShape
+ Z_theta = Cos(thAdj)*rShape + Sin(thAdj)*dtrShape
+ R_theta_theta = -(Cos(thAdj)*rShape) - 2._xp*Sin(thAdj)*dtrShape + Cos(thAdj)*dtdtrShape
+ Z_theta_theta = -(rShape*Sin(thAdj)) + 2._xp*Cos(thAdj)*dtrShape + Sin(thAdj)*dtdtrShape
+
+ END SELECT
!dl/dtheta
dlp=(R_theta**2+Z_theta**2)**0.5_xp
--
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