geometry_mod.F90

module geometry
! computes geometrical quantities
! Adapted from B.J.Frei MOLIX code (2021)
  use prec_const, ONLY: dp
implicit none
  PRIVATE
  ! Geometry input parameters
  CHARACTER(len=16), &
               PUBLIC, PROTECTED :: geom      = 's-alpha'
  REAL(dp),    PUBLIC, PROTECTED :: q0        = 1.4_dp  ! safety factor
  REAL(dp),    PUBLIC, PROTECTED :: shear     = 0._dp   ! magnetic field shear
  REAL(dp),    PUBLIC, PROTECTED :: eps       = 0.18_dp ! inverse aspect ratio
  REAL(dp),    PUBLIC, PROTECTED :: alpha_MHD = 0 ! shafranov shift effect alpha = -q2 R dbeta/dr
  ! parameters for Miller geometry
  REAL(dp),    PUBLIC, PROTECTED :: kappa     = 1._dp ! elongation (1 for circular)
  REAL(dp),    PUBLIC, PROTECTED :: s_kappa   = 0._dp ! r normalized derivative skappa = r/kappa dkappa/dr
  REAL(dp),    PUBLIC, PROTECTED :: delta     = 0._dp ! triangularity
  REAL(dp),    PUBLIC, PROTECTED :: s_delta   = 0._dp ! '' sdelta = r/sqrt(1-delta2) ddelta/dr
  REAL(dp),    PUBLIC, PROTECTED :: zeta      = 0._dp ! squareness
  REAL(dp),    PUBLIC, PROTECTED :: s_zeta    = 0._dp ! '' szeta = r dzeta/dr
  ! to apply shift in the parallel z-BC if shearless
  REAL(dp),    PUBLIC, PROTECTED :: shift_y   = 0._dp ! for Arno <3
  INTEGER,     PUBLIC, PROTECTED :: Npol      = 1         ! number of poloidal turns
  ! Chooses the type of parallel BC we use for the unconnected kx modes (active for non-zero shear only)
  !  'periodic'     : Connect a disconnected kx to a mode on the other cadran
  !  'dirichlet'    : Connect a disconnected kx to 0
  !  'disconnected' : Connect all kx to 0
  !  'shearless'    : Connect all kx to itself
  CHARACTER(len=256), &
               PUBLIC, PROTECTED :: parallel_bc

  ! GENE unused additional parameters for miller_mod
  REAL(dp), PUBLIC, PROTECTED :: edge_opt      = 0._dp ! meant to redistribute the points in z
  REAL(dp), PUBLIC, PROTECTED :: major_R       = 1._dp ! major radius
  REAL(dp), PUBLIC, PROTECTED :: major_Z       = 0._dp ! vertical elevation
  REAL(dp), PUBLIC, PROTECTED :: dpdx_pm_geom  = 0._dp ! amplitude mag. eq. pressure grad.
  REAL(dp), PUBLIC, PROTECTED ::          C_y  = 0._dp ! defines y coordinate : Cy (q theta - phi)
  REAL(dp), PUBLIC, PROTECTED ::         C_xy  = 1._dp ! defines x coordinate : B = Cxy Vx x Vy

  ! Geometrical auxiliary variables
  LOGICAL,     PUBLIC, PROTECTED :: SHEARED  = .false. ! flag for shear magn. geom or not
  ! Curvature
  REAL(dp),    PUBLIC, DIMENSION(:,:,:,:), ALLOCATABLE :: Ckxky  ! dimensions: kx, ky, z, odd/even p
  ! Jacobian
  REAL(dp),    PUBLIC, DIMENSION(:,:), ALLOCATABLE :: Jacobian ! dimensions: z, odd/even p
  COMPLEX(dp), PUBLIC, PROTECTED        :: iInt_Jacobian ! Inverse integrated Jacobian
  ! Metric
  REAL(dp),    PUBLIC, DIMENSION(:,:), ALLOCATABLE :: gxx, gxy, gxz, gyy, gyz, gzz ! dimensions: z, odd/even p
  REAL(dp),    PUBLIC, DIMENSION(:,:), ALLOCATABLE :: dxdr, dxdZ, Rc, phic, Zc
  ! derivatives of magnetic field strength
  REAL(dp),    PUBLIC, DIMENSION(:,:), ALLOCATABLE :: dBdx, dBdy, dBdz, dlnBdz
  ! Relative magnetic field strength
  REAL(dp),    PUBLIC, DIMENSION(:,:), ALLOCATABLE :: hatB
  ! Relative strength of major radius
  REAL(dp),    PUBLIC, DIMENSION(:,:), ALLOCATABLE :: hatR, hatZ
  ! Some geometrical coefficients
  REAL(dp),    PUBLIC, DIMENSION(:,:) , ALLOCATABLE :: gradz_coeff  ! 1 / [ J_{xyz} \hat{B} ]
  ! Array to map the index of mode (kx,ky,-pi) to (kx+2pi*s*ky,ky,pi) for sheared periodic boundary condition
  INTEGER,     PUBLIC, DIMENSION(:,:), ALLOCATABLE :: ikx_zBC_L, ikx_zBC_R
  ! Geometric factor in front of the parallel phi derivative (not implemented)
  ! REAL(dp),    PUBLIC, DIMENSION(:,:), ALLOCATABLE :: Gamma_phipar
  ! pb_phase, for parallel boundary phase, contains the factor that occurs when taking into account
  !   that q0 is defined in the middle of the fluxtube whereas the radial position spans in [0,Lx)
  !   This shift introduces a (-1)^(Nexc*iky) phase change that is included in GENE
  COMPLEX(dp), PUBLIC, DIMENSION(:),   ALLOCATABLE :: pb_phase_L, pb_phase_R

  ! Functions
  PUBLIC :: geometry_readinputs, geometry_outputinputs,&
            eval_magnetic_geometry, set_ikx_zBC_map
CONTAINS


  SUBROUTINE geometry_readinputs
    USE basic, ONLY: lu_in, speak
    ! Read the input parameters
    IMPLICIT NONE
    NAMELIST /GEOMETRY/ geom, q0, shear, eps,&
      kappa, s_kappa,delta, s_delta, zeta, s_zeta,& ! For miller
      parallel_bc, shift_y, Npol
    READ(lu_in,geometry)
    IF(shear .NE. 0._dp) SHEARED = .true.
    SELECT CASE(parallel_bc)
      CASE ('dirichlet')
      CASE ('periodic')
      CASE ('cyclic')
      CASE ('shearless')
      CASE ('disconnected')
      CASE DEFAULT
        ERROR STOP '>> ERROR << Parallel BC not recognized'
    END SELECT
    CALL speak('Parallel BC : '//parallel_bc)

  END SUBROUTINE geometry_readinputs

  subroutine eval_magnetic_geometry
    USE grid,     ONLY: total_nky, total_nz, local_nkx, local_nky, local_nz, Ngz,&
                        kxarray, kyarray, set_kparray, nzgrid, zweights_SR, ieven
    USE basic,    ONLY: speak
    USE miller,   ONLY: set_miller_parameters, get_miller
    USE calculus, ONLY: simpson_rule_z
    ! evalute metrix, elementwo_third_kpmaxts, jacobian and gradient
    implicit none
    REAL(dp) :: kx,ky
    COMPLEX(dp), DIMENSION(local_nz) :: integrant
    real(dp) :: G1,G2,G3,Cx,Cy
    INTEGER  :: eo,iz,iky,ikx

    ! Allocate arrays
    CALL geometry_allocate_mem(local_nky,local_nkx,local_nz,Ngz,nzgrid)
    !
    IF( (total_nky .EQ. 1) .AND. (total_nz .EQ. 1)) THEN !1D perp linear run
      CALL speak('1D perpendicular geometry')
      call eval_1D_geometry
    ELSE
      SELECT CASE(geom)
        CASE('s-alpha')
          CALL speak('s-alpha geometry')
          call eval_salpha_geometry
        CASE('Z-pinch','z-pinch','Zpinch','zpinch')
          CALL speak('Z-pinch geometry')
          call eval_zpinch_geometry
          SHEARED = .FALSE.
          shear   = 0._dp
        CASE('miller')
          CALL speak('Miller geometry')
          call set_miller_parameters(kappa,s_kappa,delta,s_delta,zeta,s_zeta)
          call get_miller(eps,major_R,major_Z,q0,shear,Npol,alpha_MHD,edge_opt,&
                          C_y,C_xy,dpdx_pm_geom,gxx,gyy,gzz,gxy,gxz,gyz,&
                          dBdx,dBdy,hatB,jacobian,dBdz,hatR,hatZ,dxdR,dxdZ,&
                          Ckxky,gradz_coeff)
        CASE DEFAULT
          ERROR STOP '>> ERROR << geometry not recognized!!'
        END SELECT
    ENDIF
    !
    ! Evaluate perpendicular wavenumber
    !  k_\perp^2 = g^{xx} k_x^2 + 2 g^{xy}k_x k_y + k_y^2 g^{yy}
    !  normalized to rhos_
    CALL set_kparray(gxx,gxy,gyy,hatB)
    DO eo = 1,nzgrid
      ! Curvature operator (Frei et al. 2022 eq 2.15)
      DO iz = 1,local_nz+Ngz
        G1 = gxx(iz,eo)*gyy(iz,eo)-gxy(iz,eo)*gxy(iz,eo)
        G2 = gxx(iz,eo)*gyz(iz,eo)-gxy(iz,eo)*gxz(iz,eo)
        G3 = gxy(iz,eo)*gyz(iz,eo)-gyy(iz,eo)*gxz(iz,eo)
        ! Here we divide by hatB because our equation is formulated with grad(lnB) terms (not gradB like in GENE)
        Cx =-(dBdy(iz,eo) + G2/G1*dBdz(iz,eo))/hatB(iz,eo)
        Cy = (dBdx(iz,eo) - G3/G1*dBdz(iz,eo))/hatB(iz,eo)
        DO iky = 1,local_nky
          ky = kyarray(iky)
           DO ikx= 1,local_nkx
             kx = kxarray(ikx)
             Ckxky(iky, ikx, iz,eo) = (Cx*kx + Cy*ky)/C_xy
           ENDDO
        ENDDO
        ! coefficient in the front of parallel derivative
        gradz_coeff(iz,eo) = 1._dp /(jacobian(iz,eo)*hatB(iz,eo))
        ! d/dz(ln B) to correspond to the formulation in paper 2023
        dlnBdz(iz,eo)      = dBdz(iz,eo)/hatB(iz,eo)
        ! Geometric factor in front to the maxwellian dzphi term (not implemented)
        ! Gamma_phipar(iz,eo) = G2/G1
      ENDDO
    ENDDO
    !
    ! set the mapping for parallel boundary conditions
    CALL set_ikx_zBC_map
    !
    ! Compute the inverse z integrated Jacobian (useful for flux averaging)
    integrant = Jacobian((1+ngz/2):(local_nz+ngz/2),ieven) ! Convert into complex array
    CALL simpson_rule_z(local_nz,zweights_SR,integrant,iInt_Jacobian)
    iInt_Jacobian = 1._dp/iInt_Jacobian ! reverse it
  END SUBROUTINE eval_magnetic_geometry
  !
  !--------------------------------------------------------------------------------
  !

  SUBROUTINE eval_salpha_geometry
    USE grid, ONLY : local_nz,Ngz,zarray,nzgrid
  ! evaluate s-alpha geometry model
  implicit none
  REAL(dp) :: z
  INTEGER  :: iz, eo
  alpha_MHD = 0._dp

  DO eo = 1,nzgrid
   DO iz = 1,local_nz+Ngz
    z = zarray(iz,eo)

    ! metric
      gxx(iz,eo) = 1._dp
      gxy(iz,eo) = shear*z - alpha_MHD*SIN(z)
      gxz(iz,eo) = 0._dp
      gyy(iz,eo) = 1._dp + (shear*z - alpha_MHD*SIN(z))**2
      gyz(iz,eo) = 1._dp/eps
      gzz(iz,eo) = 1._dp/eps**2
      dxdR(iz,eo)= COS(z)
      dxdZ(iz,eo)= SIN(z)

    ! Poloidal plane coordinates
      hatR(iz,eo) = 1._dp + eps*COS(z)
      hatZ(iz,eo) = 1._dp + eps*SIN(z)

    ! toroidal coordinates
      Rc  (iz,eo) = hatR(iz,eo)
      phic(iz,eo) = z
      Zc  (iz,eo) = hatZ(iz,eo)

    ! Relative strengh of modulus of B
      hatB(iz,eo) = 1._dp/(1._dp + eps*COS(z))

    ! Jacobian
      Jacobian(iz,eo) = q0/hatB(iz,eo)

    ! Derivative of the magnetic field strenght
      dBdx(iz,eo) = -COS(z)*hatB(iz,eo)**2 ! LB = 1
      dBdy(iz,eo) =  0._dp
      dBdz(iz,eo) =  eps*SIN(z)*hatB(iz,eo)**2

    ! Curvature factor
      C_xy = 1._dp

   ENDDO
  ENDDO
  END SUBROUTINE eval_salpha_geometry
  !
  !--------------------------------------------------------------------------------
  !

  SUBROUTINE eval_zpinch_geometry
  USE grid, ONLY : local_nz,Ngz,zarray,nzgrid
  implicit none
  REAL(dp) :: z
  INTEGER  :: iz, eo
  alpha_MHD = 0._dp

  DO eo = 1,nzgrid
   DO iz = 1,local_nz+Ngz
    z = zarray(iz,eo)

    ! metric
      gxx(iz,eo) = 1._dp
      gxy(iz,eo) = 0._dp
      gxz(iz,eo) = 0._dp
      gyy(iz,eo) = 1._dp ! 1/R but R is the normalization length
      gyz(iz,eo) = 0._dp
      gzz(iz,eo) = 1._dp
      dxdR(iz,eo)= COS(z)
      dxdZ(iz,eo)= SIN(z)

    ! Relative strengh of radius
      hatR(iz,eo) = 1._dp ! R but R is the normalization length
      hatZ(iz,eo) = 1._dp

    ! toroidal coordinates
      Rc  (iz,eo) = hatR(iz,eo)
      phic(iz,eo) = z
      Zc  (iz,eo) = hatZ(iz,eo)

    ! Jacobian
      Jacobian(iz,eo) = 1._dp ! R but R is the normalization length

    ! Relative strengh of modulus of B
      hatB   (iz,eo) = 1._dp

    ! Derivative of the magnetic field strenght
      dBdx(iz,eo) = -hatB(iz,eo) ! LB = 1
      dBdy(iz,eo) = 0._dp
      dBdz(iz,eo) = 0._dp ! Gene put a factor hatB or 1/hatR in this

  ENDDO
  ENDDO

  ! Curvature factor
    C_xy = 1._dp
  END SUBROUTINE eval_zpinch_geometry
    !
    !--------------------------------------------------------------------------------
    ! NOT TESTED
  subroutine eval_1D_geometry
    USE grid, ONLY : local_nz,Ngz,zarray, nzgrid
    ! evaluate 1D perp geometry model
    implicit none
    REAL(dp) :: z
    INTEGER  :: iz, eo
    DO eo = 1,nzgrid
      DO iz = 1,local_nz+Ngz
      z = zarray(iz,eo)

      ! metric
      gxx(iz,eo) = 1._dp
      gxy(iz,eo) = 0._dp
      gyy(iz,eo) = 1._dp

      ! Relative strengh of radius
      hatR(iz,eo) = 1._dp

      ! Jacobian
      Jacobian(iz,eo) = 1._dp

      ! Relative strengh of modulus of B
      hatB(iz,eo) = 1._dp

      ENDDO
    ENDDO
   END SUBROUTINE eval_1D_geometry

   !
   !--------------------------------------------------------------------------------
   !

 SUBROUTINE set_ikx_zBC_map
   USE grid,       ONLY: local_nky,total_nkx,contains_zmin,contains_zmax, Nexc,&
                         local_nky_offset
   USE prec_const, ONLY: imagu, pi
   IMPLICIT NONE
   ! REAL(dp) :: shift
   INTEGER :: ikx,iky, mn_y
   ALLOCATE(ikx_zBC_L(local_nky,total_nkx))
   ALLOCATE(ikx_zBC_R(local_nky,total_nkx))
   ALLOCATE(pb_phase_L(local_nky))
   ALLOCATE(pb_phase_R(local_nky))
   !! No shear case (simple id mapping) or not at the end of the z domain
   !3            | 1    2    3    4    5    6 |  ky = 3 dky
   !2   ky       | 1    2    3    4    5    6 |  ky = 2 dky
   !1   A        | 1    2    3    4    5    6 |  ky = 1 dky
   !0   | -> kx  | 1____2____3____4____5____6 |  ky = 0 dky
   !(e.g.) kx =    0   0.1  0.2  0.3 -0.2 -0.1  (dkx=free)
   DO iky = 1,local_nky
     DO ikx = 1,total_nkx
       ikx_zBC_L(iky,ikx) = ikx ! connect to itself per default
       ikx_zBC_R(iky,ikx) = ikx
     ENDDO
     pb_phase_L(iky) = 1._dp ! no phase change per default
     pb_phase_R(iky) = 1._dp
   ENDDO
   ! Parallel boundary are not trivial for sheared case and if
   !  the user does not ask explicitly for shearless bc
   IF(SHEARED .AND. (parallel_bc .NE. 'shearless')) THEN
     !!!!!!!!!! LEFT PARALLEL BOUNDARY
     ! Modify connection map only at border of z (matters for MPI z-parallelization)
     IF(contains_zmin) THEN ! Check if the process is at the start of the fluxtube
       DO iky = 1,local_nky
        ! get the real mode number (iky starts at 1 and is shifted from paral)
        mn_y = iky-1+local_nky_offset
        ! Formula for the shift due to shear after Npol turns
        ! shift = 2._dp*PI*shear*kyarray(iky)*Npol
          DO ikx = 1,total_nkx
            ! Usual formula for shifting indices using that dkx = 2pi*shear*dky/Nexc
            ikx_zBC_L(iky,ikx) = ikx-mn_y*Nexc
            ! Check if it points out of the kx domain
            ! IF( (kxarray(ikx) - shift) .LT. kx_min ) THEN
            IF( (ikx-mn_y*Nexc) .LT. 1 ) THEN ! outside of the frequ domain
              SELECT CASE(parallel_bc)
                CASE ('dirichlet')! connected to 0
                  ikx_zBC_L(iky,ikx) = -99
                CASE ('periodic')
                  ikx_zBC_L(iky,ikx) = ikx
                CASE ('cyclic')! reroute it by cycling through modes
                  ikx_zBC_L(iky,ikx) = MODULO(ikx_zBC_L(iky,ikx)-1,total_nkx)+1
              END SELECT
            ENDIF
          ENDDO
          ! phase present in GENE from a shift of the x origin by Lx/2 (useless?)
          ! We also put the user defined shift in the y direction (see Volcokas et al. 2022)
          pb_phase_L(iky) = (-1._dp)**(Nexc*mn_y)*EXP(imagu*REAL(mn_y,dp)*2._dp*pi*shift_y)
       ENDDO
     ENDIF
     ! Option for disconnecting every modes, viz. connecting all boundary to 0
     IF(parallel_bc .EQ. 'disconnected') ikx_zBC_L = -99
     !!!!!!!!!! RIGHT PARALLEL BOUNDARY
     IF(contains_zmax) THEN ! Check if the process is at the end of the flux-tube
       DO iky = 1,local_nky
        ! get the real mode number (iky starts at 1 and is shifted from paral)
        mn_y = iky-1+local_nky_offset
        ! Formula for the shift due to shear after Npol
        ! shift = 2._dp*PI*shear*kyarray(iky)*Npol
          DO ikx = 1,total_nkx
            ! Usual formula for shifting indices
            ikx_zBC_R(iky,ikx) = ikx+mn_y*Nexc
            ! Check if it points out of the kx domain
            ! IF( (kxarray(ikx) + shift) .GT. kx_max ) THEN ! outside of the frequ domain
            IF( (ikx+mn_y*Nexc) .GT. total_nkx ) THEN ! outside of the frequ domain
              SELECT CASE(parallel_bc)
                CASE ('dirichlet') ! connected to 0
                  ikx_zBC_R(iky,ikx) = -99
                CASE ('periodic') ! connected to itself as for shearless
                  ikx_zBC_R(iky,ikx) = ikx
                CASE ('cyclic')
                  ! write(*,*) 'check',ikx,iky, kxarray(ikx) + shift, '>', kx_max
                  ikx_zBC_R(iky,ikx) = MODULO(ikx_zBC_R(iky,ikx)-1,total_nkx)+1
              END SELECT
            ENDIF
          ENDDO
          ! phase present in GENE from a shift ofthe x origin by Lx/2 (useless?)
          ! We also put the user defined shift in the y direction (see Volcokas et al. 2022)
          pb_phase_R(iky) = (-1._dp)**(Nexc*mn_y)*EXP(-imagu*REAL(mn_y,dp)*2._dp*pi*shift_y)
       ENDDO
     ENDIF
     ! Option for disconnecting every modes, viz. connecting all boundary to 0
     IF(parallel_bc .EQ. 'disconnected') ikx_zBC_R = -99
    ENDIF
    ! write(*,*) kxarray
    ! write(*,*) kyarray
    ! write(*,*) 'ikx_zBC_L :-----------'
    ! DO iky = ikys,ikye
    !   print*, ikx_zBC_L(iky,:)
    ! enddo
    ! print*, pb_phase_L
    ! write(*,*) 'ikx_zBC_R :-----------'
    ! DO iky = ikys,ikye
    !   print*, ikx_zBC_R(iky,:)
    ! enddo
    ! print*, pb_phase_R
    ! print*, shift_y
    ! stop
    !!!!!!! Example of maps ('x' means connected to 0 value, in the table it is -99)
    ! dirichlet connection map BC of the RIGHT boundary (z=pi*Npol-dz)
    !3            | 4    x    x    x    2    3 |  ky = 3 dky
    !2   ky       | 3    4    x    x    1    2 |  ky = 2 dky
    !1   A        | 2    3    4    x    6    1 |  ky = 1 dky
    !0   | -> kx  | 1____2____3____4____5____6 |  ky = 0 dky
    !kx =           0   0.1  0.2  0.3 -0.2 -0.1  (dkx=2pi*shear*npol*dky)

    ! periodic connection map BC of the RIGHT boundary (z=pi*Npol-dz)
    !3            | 4    2    3    4    2    3 |  ky = 3 dky
    !2   ky       | 3    4    3    4    1    2 |  ky = 2 dky
    !1   A        | 2    3    4    4    6    1 |  ky = 1 dky
    !0   | -> kx  | 1____2____3____4____5____6 |  ky = 0 dky
    !kx =           0   0.1  0.2  0.3 -0.2 -0.1  (dkx=2pi*shear*npol*dky)

    ! cyclic connection map BC of the LEFT boundary (z=-pi*Npol)
    !3            | 4    5    6    1    2    3 |  ky = 3 dky
    !2   ky       | 5    6    1    2    3    4 |  ky = 2 dky
    !1   A        | 6    1    2    3    4    5 |  ky = 1 dky
    !0   | -> kx  | 1____2____3____4____5____6 |  ky = 0 dky
    !(e.g.) kx =    0   0.1  0.2  0.3 -0.2 -0.1  (dkx=2pi*shear*npol*dky)

    ! shearless connection map BC of the LEFT/RIGHT boundary (z=+/-pi*Npol)
    !3            | 1    2    3    4    5    6 |  ky = 3 dky
    !2   ky       | 1    2    3    4    5    6 |  ky = 2 dky
    !1   A        | 1    2    3    4    5    6 |  ky = 1 dky
    !0   | -> kx  | 1____2____3____4____5____6 |  ky = 0 dky
    !(e.g.) kx =    0   0.1  0.2  0.3 -0.2 -0.1  (dkx=2pi*shear*npol*dky)

    ! disconnected connection map BC of the LEFT/RIGHT boundary (z=+/-pi*Npol)
    !3            | x    x    x    x    x    x |  ky = 3 dky
    !2   ky       | x    x    x    x    x    x |  ky = 2 dky
    !1   A        | x    x    x    x    x    x |  ky = 1 dky
    !0   | -> kx  | x____x____x____x____x____x |  ky = 0 dky
    !(e.g.) kx =    0   0.1  0.2  0.3 -0.2 -0.1  (dkx=2pi*shear*npol*dky)
END SUBROUTINE set_ikx_zBC_map

!
!--------------------------------------------------------------------------------
!

   SUBROUTINE geometry_allocate_mem(local_nky,local_nkx,local_nz,Ngz,nzgrid)
     INTEGER, INTENT(IN) :: local_nky,local_nkx,local_nz,Ngz,nzgrid
       ! Curvature and geometry
       ALLOCATE( Ckxky(local_nky,local_nkx,local_nz+Ngz,nzgrid))
       ALLOCATE(   Jacobian(local_nz+Ngz,nzgrid))
       ALLOCATE(        gxx(local_nz+Ngz,nzgrid))
       ALLOCATE(        gxy(local_nz+Ngz,nzgrid))
       ALLOCATE(        gxz(local_nz+Ngz,nzgrid))
       ALLOCATE(        gyy(local_nz+Ngz,nzgrid))
       ALLOCATE(        gyz(local_nz+Ngz,nzgrid))
       ALLOCATE(        gzz(local_nz+Ngz,nzgrid))
       ALLOCATE(       dBdx(local_nz+Ngz,nzgrid))
       ALLOCATE(       dBdy(local_nz+Ngz,nzgrid))
       ALLOCATE(       dBdz(local_nz+Ngz,nzgrid))
       ALLOCATE(     dlnBdz(local_nz+Ngz,nzgrid))
       ALLOCATE(       hatB(local_nz+Ngz,nzgrid))
       ! ALLOCATE(Gamma_phipar,(local_nz+Ngz,nzgrid)) (not implemented)
       ALLOCATE(       hatR(local_nz+Ngz,nzgrid))
       ALLOCATE(       hatZ(local_nz+Ngz,nzgrid))
       ALLOCATE(         Rc(local_nz+Ngz,nzgrid))
       ALLOCATE(       phic(local_nz+Ngz,nzgrid))
       ALLOCATE(         Zc(local_nz+Ngz,nzgrid))
       ALLOCATE(       dxdR(local_nz+Ngz,nzgrid))
       ALLOCATE(       dxdZ(local_nz+Ngz,nzgrid))
       ALLOCATE(gradz_coeff(local_nz+Ngz,nzgrid))

   END SUBROUTINE geometry_allocate_mem

   SUBROUTINE geometry_outputinputs(fid)
     ! Write the input parameters to the results_xx.h5 file
     USE futils, ONLY: attach, creatd
     IMPLICIT NONE
     INTEGER, INTENT(in) :: fid
     CHARACTER(len=256)  :: str
     WRITE(str,'(a)') '/data/input/geometry'
     CALL creatd(fid, 0,(/0/),TRIM(str),'Geometry Input')
     CALL attach(fid, TRIM(str),"geometry",  geom)
     CALL attach(fid, TRIM(str),      "q0",    q0)
     CALL attach(fid, TRIM(str),   "shear", shear)
     CALL attach(fid, TRIM(str),     "eps",   eps)
   END SUBROUTINE geometry_outputinputs
end module geometry