!-----------------------------------------------------------------
!
!  This file is (or was) part of SPLASH, a visualisation tool
!  for Smoothed Particle Hydrodynamics written by Daniel Price:
!
!  http://users.monash.edu.au/~dprice/splash
!
!  SPLASH comes with ABSOLUTELY NO WARRANTY.
!  This is free software; and you are welcome to redistribute
!  it under the terms of the GNU General Public License
!  (see LICENSE file for details) and the provision that
!  this notice remains intact. If you modify this file, please
!  note section 2a) of the GPLv2 states that:
!
!  a) You must cause the modified files to carry prominent notices
!     stating that you changed the files and the date of any change.
!
!  Copyright (C) 2005-2009 Daniel Price. All rights reserved.
!  Contact: daniel.price@sci.monash.edu.au
!
!-----------------------------------------------------------------

! ----------------------------------------------------------------------
!  Plots solution for equilibrium torus of Papaloizou & Pringle
!  strictly valid for the midplane only (uses spherical r)
!
!  Added by D. Price 16.1.06
! ----------------------------------------------------------------------
module torus
 implicit none

contains

subroutine exact_torus(iplot,itorus,Mstar,Rtorus,AA,distortion,gamma,xplot,yplot,ierr)
 implicit none
 integer, intent(in) :: iplot,itorus
 real, intent(in) :: Mstar,Rtorus,AA,gamma,distortion
 real, intent(in), dimension(:) :: xplot
 real, intent(out), dimension(size(xplot)) :: yplot
 real :: term,densi,rxy
 integer, intent(out) :: ierr
 integer :: i,mytorus
 real :: ra2
 integer, parameter :: nu = 2
 real, parameter :: atorus = 0.2, currj0 = 1.0
!
! check for errors
!
 ierr = 0
 if (Mstar <= 0.) then
    print*,'error: mass <= 0 in exact_torus'
    ierr = 2
    return
 elseif (Rtorus < 0.) then
    print*,'error: rtorus < 0 in exact_torus'
    ierr = 3
    return
 endif

 mytorus = 1
 select case(mytorus)

!
!--Tokamak torus (in torus 'r' co-ordinate)
!
 case(2)
    if (nu <= 0 .or. (iplot < 4 .and. nu > 2)) then
       print*,'error: solution not found for nu value in tokamak torus'
       ierr = 5
       return
    endif
    print*,' plotting tokamak torus'

    do i=1,size(xplot)
       ra2 = xplot(i)**2/atorus**2
       if (nu==1) then
          term = currj0**2*atorus**2*(1. - ra2)*(7.*ra2**2 - 23.*ra2 + 13.)/96.
       elseif (nu==2) then
          term = currj0**2*atorus**2*(47. - 12.*ra2**5 + 75.*ra2**4 - 200.*ra2**3 + 270.*ra2**2 - 180*ra2)/720.
       endif
       if (abs(ra2) < tiny(ra2)) print*,'rho0 = ',term

       select case(iplot)
       case(1)
          !--density
          yplot(i) = Mstar*term**gamma
       case(2)
          !--pressure
          yplot(i) = term
       case(3)
          !--thermal energy
          yplot(i) = term
       case(4)
          !--Btheta
          if (xplot(i) > tiny(xplot(i))) then
             yplot(i) = 0.5*currj0*atorus**2/(nu+1)* &
                   (1.-(1.-ra2)**(nu+1))/xplot(i)
          else
             yplot(i) = 0.
          endif
       case(5)
          !--Jphi current
          yplot(i) = currj0*(1. - ra2)**nu
       end select
    enddo
!
!--Papaloizou & Pringle equilibrium torus
!
 case default
    if ((gamma-1.) <= 1e-4) then
       print*,'error: exact solution not valid for isothermal eos'
       ierr = 4
       return
    endif

    do i=1,size(xplot)
       if (iplot /= 4) then
          !--plot quantities vs spherical r (assume z = 0)
          term = Mstar/(AA*Rtorus)*(gamma-1.)/gamma* &
                (Rtorus/xplot(i) - 0.5*(Rtorus/xplot(i))**2 - 1./(2.*distortion))
       else
          !--plots with z (assume cyl r = Rtorus)
          rxy = sqrt(Rtorus**2 + xplot(i)**2)
          term = Mstar/(AA*Rtorus)*(gamma-1.)/gamma* &
                (Rtorus/rxy - 0.5 - 1./(2.*distortion))
       endif
       if (term > tiny(term)) then
          densi = term**(1./(gamma-1.))
       else
          densi = 0.
       endif
       select case(iplot)
       case(1)
          !--density
          yplot(i) = densi
       case(2,4)
          !--pressure
          yplot(i) = AA*densi**gamma
       case(3)
          !--thermal energy
          yplot(i) = AA/(gamma-1.)*densi**(gamma-1.)
       end select
    enddo
 end select
 return
end subroutine exact_torus

end module torus
