becoil.f90

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!> \file
!> \brief Compute the cylindrical components of the magnetic field due to external coils
!>        by bi-linear interpolation of the \c mgrid file.
 
!> \brief Compute the cylindrical components of the magnetic field due to external coils.
!>        by bi-linear interpolation of the \c mgrid file.
!>
!> @param rad \f$R\f$ at which to evaluate the external magnetic field
!> @param zee \f$Z\f$ at which to evaluate the external magnetic field
!> @param brvac cylindrical component of external magnetic field \f$B^R\f$
!> @param bpvac cylindrical component of external magnetic field \f$B^\varphi\f$
!> @param bzvac cylindrical component of external magnetic field \f$B^Z\f$
SUBROUTINE becoil(rad, zee, brvac, bpvac, bzvac)
 
  ! USE vparams, ONLY: nthreed
  USE vacmod
  USE mgrid_mod, ONLY: nr0b, np0b, nz0b, rminb, zminb, rmaxb, zmaxb, delrb, delzb
 
  use json
 
  IMPLICIT NONE
 
  REAL(rprec), DIMENSION(nuv2), INTENT(in) :: rad, zee
  REAL(rprec), DIMENSION(nr0b,nz0b,np0b), INTENT(in) :: brvac, bpvac, bzvac
 
  CHARACTER(LEN=50), PARAMETER :: warning = 'Plasma Boundary exceeded Vacuum Grid Size'
 
  INTEGER, SAVE :: icount = 0
  INTEGER :: i, kv, ir, jz, ir1, jz1
  REAL(rprec) :: rad0, zee0, ri, zj, pr, qz, w22, w21, w12, w11
 
  ! DETERMINE THE CYLINDRICAL COMPONENTS OF THE EXTERNAL
  ! MAGNETIC FIELD (BR, BP, BZ) AT A FIXED PHI PLANE BY
  ! USING 2-D INTERPOLATION BASED ON THE FOUR POINT FORMULA
  ! IN ABRAMOWITZ AND STEGUN, EQ. 25.2.66
  !
  ! BRVAC, BPVAC, BZVAC: CYLINDRICAL COMPONENTS OF VACUUM B-FIELD
  !                      STORED ON R, Z, PHI GRID
  !
  ! RAD, ZEE:            ARRAY OF R, Z VALUES (ON FLUX SURFACE)
  !                      AT WHICH B-FIELD IS TO BE DETERMINED
 
!   if (icount .eq. 0) then
!     ! dump MGRID contents to text file for comparison with re-created file
!
!     call open_dbg_out("mgrid.json")
!
!     call add_int("nr0b", nr0b)
!     call add_int("nz0b", nz0b)
!     call add_int("np0b", np0b)
!
!     call add_real_3d("brvac", nr0b, nz0b, np0b, brvac)
!     call add_real_3d("bpvac", nr0b, nz0b, np0b, bpvac)
!     call add_real_3d("bzvac", nr0b, nz0b, np0b, bzvac)
!
!     call close_dbg_out()
!   end if
 
  icount = icount + 1
 
  DO i = 1, nuv2
 
     ! CHECK THAT BOUNDARY POINTS ARE INSIDE VACUUM GRID.
     ! IF NOT, SET THEM EQUAL TO LARGEST (OR SMALLEST) VACUUM GRID POINTS
     rad0 = min(rad(i), rmaxb)
     rad0 = max(rad0,   rminb)
     zee0 = min(zee(i), zmaxb)
     zee0 = max(zee0,   zminb)
 
     ! DETERMINE PHI-PLANE, KV (MUST LIE IN FIRST FIELD PERIOD)
     kv = 1 + mod(i - 1,nv)
 
     ! Axi-symmetric special case
     kv = min(kv, np0b)
 
     ! DETERMINE INTEGER INDICES (IR,JZ) FOR LOWER LEFT R, Z CORNER GRID POINT
     ir = int((rad0 - rminb)/delrb) + 1
     jz = int((zee0 - zminb)/delzb) + 1
     ir1 = min(nr0b,ir + 1)
     jz1 = min(nz0b,jz + 1)
 
     ! COMPUTE RI, ZJ AND PR , QZ AT GRID POINT (IR , JZ)
     ! ALSO, COMPUTE WEIGHTS WIJ FOR 4 CORNER GRID POINTS
     ri = rminb + (ir - 1)*delrb
     zj = zminb + (jz - 1)*delzb
     pr = (rad0 - ri)/delrb
     qz = (zee0 - zj)/delzb
     w22 = pr*qz                   !    p *   q
     w21 = pr - w22                !    p *(1-q)
     w12 = qz - w22                ! (1-p)*   q
     w11 = 1 + w22 - (pr + qz)     ! (1-p)*(1-q)
 
     ! COMPUTE B FIELD AT R, PHI, Z BY INTERPOLATION
     brad(i) = w11*brvac(ir,jz,kv) + w22*brvac(ir1,jz1,kv) + w21*brvac(ir1,jz,kv) + w12*brvac(ir,jz1,kv)
     bphi(i) = w11*bpvac(ir,jz,kv) + w22*bpvac(ir1,jz1,kv) + w21*bpvac(ir1,jz,kv) + w12*bpvac(ir,jz1,kv)
     bz(i)   = w11*bzvac(ir,jz,kv) + w22*bzvac(ir1,jz1,kv) + w21*bzvac(ir1,jz,kv) + w12*bzvac(ir,jz1,kv)
 
  END DO
 
  IF (mod(icount,25).eq.0) THEN
     ! PRINT INFO IF R, Z OUT OF BOX
     i = 0
     rad0 = maxval(rad)
     zee0 = maxval(zee)
     IF (rad0 .gt. rmaxb) i = 1
     IF (zee0 .gt. zmaxb) i = i + 2
     ri   = minval(rad)
     zj   = minval(zee)
     IF (ri .lt. rminb) i = i + 4
     IF (zj .lt. zminb) i = i + 8
     IF (i .ne. 0) THEN
        print *, warning
        ! WRITE (nthreed, *) warning
        IF (i/8 .ne. 0) print *,' zmin = ', zj
        i = mod(i,8)
        IF (i/4 .ne. 0) print *,' rmin = ', ri
        i = mod(i,4)
        IF (i/2 .ne. 0) print *,' zmax = ', zee0
        i = mod(i,2)
        IF (i .ne. 0) print *,' rmax = ', rad0
     END IF
  ENDIF
 
END SUBROUTINE becoil