Description of the element "mag3d" for a dipole magnet with external 3D fields

  Element entry in the lattice file "sclinac.dat":

    n   mag3d  f_len  rbend  theta  airgap  width  bet1  bet2  invr1  invr2  nstep
  
    n          : number of the mag3d file to use (n=1 --> mag3d.#01)
    f_len [cm] : field length in file including fringe fields (not real dipole length)
    rbend [cm] : bending radius  
    theta [deg]: bending angle
    airgap [cm]: airgap
    width [cm] : width 
    bet1  [deg]: entrance angle  
    bet2  [deg]: exit angle
    r1inv[1/cm]: entrance curvature radius (not used)  
    r2inv[2/cm]: exit curvature radius     (not used)
    nstep      : number of integration steps

  Example:

    1   mag3d  93.6   50.   60.  6.  12.   30.   30.   0.   0.   200

  Format of the 3D field file:

    The Z direction of the field data has an angle of "theta/2" with the incomming and 
   outgoing beam directions. So the field is a 3D box at half the bending angle from in 
   and out beam directions.

    The field file is ASCI and could be read in fortran as follow:     

      open(2, file=magfile, status='old')
      read(2,*) ngx, xmn, xmx      
      read(2,*) ngy, ymn, ymx      
      read(2,*) ngz, zmn, zmx
      do i = 1, ngx
        do j = 1, ngy
          do k = 1, ngz
            read(2,*) b1, b2, b3
            bx(i,j,k) = b1
            by(i,j,k) = b2
            bz(i,j,k) = b3
          enddo
        enddo
      enddo     
      close(2)

    where: ngx, ngy, ngz: number of data points in every direction
           xmn, ymn, zmn: field's lower limits in X, Y and Z
           xmx, ymx, zmx: field's upper limits in X, Y and Z
           bx , by , bz : field data arrays
    

  Central trajectory calculation:

    TRACK is z-based code; the integration is done with steps in the distance z, so we should
   first determine the length of the central trajectory. This is done using the input beam 
   energy (Win) and the reference partile mass and charge state (Adesign, Qdesign). Both the
   field strength and the central trajectory length are adjusted using a fit to have an exit
   point symmetric to the entrance point for the central trajectory.

    Once the central trajectory length is determined it'll be considered as the actual length
   of the magnet and will be divided into "nstep" integration step to track the real beam
   particles.