2019-03-26 15:21:22 +01:00
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module multipass
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use const_and_precisions, only : wp_, zero, half, one, degree, czero
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use beamdata, only : dst, nray
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use gray_params, only : ipass
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2024-03-12 16:42:19 +01:00
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use polarization, only : pol_limit, field_to_ellipse
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2019-03-26 15:21:22 +01:00
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use reflections, only : wall_refl
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use equilibrium, only : bfield
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2024-01-27 12:09:56 +01:00
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2019-03-26 15:21:22 +01:00
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implicit none
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2019-03-28 10:50:28 +01:00
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integer, save :: nbeam_max ! max n of beams active at a time
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integer, save :: nbeam_tot ! total n of beams
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2019-03-26 15:21:22 +01:00
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contains
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fix coupling for subsequent beams
In situations when multiple beams are traced, either when allowing
multiple plasma crossings (raytracing.ipass > 0) or the initial polarisation
is mixed (raytracing.ipol == .true.), the couplings of all but the first
beam (with least index_rt) were invalid.
The bug is due to the re-use of the psipol,chipol variables as the beams
are traced sequentially over the beam_loop. For the first beam being
traced the psipol,chipol are correctly initialised to the user-defined
value and the resulting coupling is correct.
However, in each subsequent beam the values were not set to those of the
parent beam (or to the user-defined value in the case of the first X
mode beam), but to those of the previous beams (current index_rt - 1).
This change repurposes the psipv,chipv arrays to store the polarisation
of the parent beams, including the initial user-defined value and makes
plasma_in always use these to compute the coupling.
In addition, in the case the polarisation is not immediately known (i.e.
if raytracing.ipol == .false.), this change postpones the computation of
the Jones vector (ext, eyt) from the launch point, if the magnetic
equilibrium is available, to when the ray actually crosses the
plasma boundary.
The original code, besides being strictly incorrect, can lead to
non-negligible alterations to the coupling. This change also mean:
1. most of the functionality of `set_pol` has been merged with
`plasma_in`
2. the polarisation is undefined and the Jones vector is set to the
placeholder value [1, 0] till `plasma_im` is called
Finally, `polarcold` is removed because it's unused.
2024-03-02 17:32:03 +01:00
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subroutine plasma_in(i, x, N, Bres, sox, cpl, psi, chi, iop, ext, eyt, perfect)
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! Computes the ray polarisation and power couplings when it enteres the plasma
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use const_and_precisions, only: cm
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! subroutine arguments
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integer, intent(in) :: i ! ray index
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real(wp_), intent(in) :: x(3), N(3) ! position, refactive index
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real(wp_), intent(in) :: Bres ! resonant B field
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integer, intent(in) :: sox ! sign of polarisation mode: -1 ⇒ O, +1 ⇒ X
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real(wp_), intent(out) :: cpl(2) ! power coupling vector (O, X)
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real(wp_), intent(out) :: psi, chi ! polarisation ellipse angles
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integer, intent(inout), pointer :: iop(:) ! inside/outside plasma flag
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complex(wp_), intent(inout), pointer :: ext(:), eyt(:) ! ray polarisation vector (e_x, e_y)
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logical, intent(in) :: perfect ! whether to assume perfect coupling
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! local variables
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real(wp_) :: R, z, cosphi, sinphi, B_phi, B_R, B_z
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real(wp_) :: B(3)
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real(wp_) :: c
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complex(wp_) :: e_mode(2), e_ray(2)
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! Update the inside/outside flag
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iop(i) = iop(i) + 1
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! Compute B in cartesian coordinates
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R = norm2(x(1:2)) * cm
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z = x(3) * cm
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cosphi = x(1)/R * cm
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sinphi = x(2)/R * cm
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call bfield(R, z, B_R, B_z, B_phi)
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B(1) = B_R*cosphi - B_phi*sinphi
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B(2) = B_R*sinphi + B_phi*cosphi
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B(3) = B_z
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! Get the polarisation vector of the given mode
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call pol_limit(N, B, Bres, sox, e_mode(1), e_mode(2))
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if(i == 1) then
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! For the central ray, compute the polarization ellipse
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2024-03-12 16:42:19 +01:00
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call field_to_ellipse(e_mode(1), e_mode(2), psi, chi)
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2019-03-26 15:21:22 +01:00
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else
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fix coupling for subsequent beams
In situations when multiple beams are traced, either when allowing
multiple plasma crossings (raytracing.ipass > 0) or the initial polarisation
is mixed (raytracing.ipol == .true.), the couplings of all but the first
beam (with least index_rt) were invalid.
The bug is due to the re-use of the psipol,chipol variables as the beams
are traced sequentially over the beam_loop. For the first beam being
traced the psipol,chipol are correctly initialised to the user-defined
value and the resulting coupling is correct.
However, in each subsequent beam the values were not set to those of the
parent beam (or to the user-defined value in the case of the first X
mode beam), but to those of the previous beams (current index_rt - 1).
This change repurposes the psipv,chipv arrays to store the polarisation
of the parent beams, including the initial user-defined value and makes
plasma_in always use these to compute the coupling.
In addition, in the case the polarisation is not immediately known (i.e.
if raytracing.ipol == .false.), this change postpones the computation of
the Jones vector (ext, eyt) from the launch point, if the magnetic
equilibrium is available, to when the ray actually crosses the
plasma boundary.
The original code, besides being strictly incorrect, can lead to
non-negligible alterations to the coupling. This change also mean:
1. most of the functionality of `set_pol` has been merged with
`plasma_in`
2. the polarisation is undefined and the Jones vector is set to the
placeholder value [1, 0] till `plasma_im` is called
Finally, `polarcold` is removed because it's unused.
2024-03-02 17:32:03 +01:00
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psi = 0
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chi = 0
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end if
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if (perfect) then
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! Ignore the given vector and use the expected one
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! Note: this will give 100% coupling to the current mode
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ext(i) = e_mode(1)
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eyt(i) = e_mode(2)
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2019-03-26 15:21:22 +01:00
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end if
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fix coupling for subsequent beams
In situations when multiple beams are traced, either when allowing
multiple plasma crossings (raytracing.ipass > 0) or the initial polarisation
is mixed (raytracing.ipol == .true.), the couplings of all but the first
beam (with least index_rt) were invalid.
The bug is due to the re-use of the psipol,chipol variables as the beams
are traced sequentially over the beam_loop. For the first beam being
traced the psipol,chipol are correctly initialised to the user-defined
value and the resulting coupling is correct.
However, in each subsequent beam the values were not set to those of the
parent beam (or to the user-defined value in the case of the first X
mode beam), but to those of the previous beams (current index_rt - 1).
This change repurposes the psipv,chipv arrays to store the polarisation
of the parent beams, including the initial user-defined value and makes
plasma_in always use these to compute the coupling.
In addition, in the case the polarisation is not immediately known (i.e.
if raytracing.ipol == .false.), this change postpones the computation of
the Jones vector (ext, eyt) from the launch point, if the magnetic
equilibrium is available, to when the ray actually crosses the
plasma boundary.
The original code, besides being strictly incorrect, can lead to
non-negligible alterations to the coupling. This change also mean:
1. most of the functionality of `set_pol` has been merged with
`plasma_in`
2. the polarisation is undefined and the Jones vector is set to the
placeholder value [1, 0] till `plasma_im` is called
Finally, `polarcold` is removed because it's unused.
2024-03-02 17:32:03 +01:00
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! Compute the power coupling with the current mode
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e_ray = [ext(i), eyt(i)]
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c = abs(dot_product(e_mode, e_ray))**2
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! Store both O and X couplings, in this order
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c = merge(c, 1-c, sox == -1)
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cpl = [c, 1-c]
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2019-03-26 15:21:22 +01:00
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end subroutine plasma_in
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fix coupling for subsequent beams
In situations when multiple beams are traced, either when allowing
multiple plasma crossings (raytracing.ipass > 0) or the initial polarisation
is mixed (raytracing.ipol == .true.), the couplings of all but the first
beam (with least index_rt) were invalid.
The bug is due to the re-use of the psipol,chipol variables as the beams
are traced sequentially over the beam_loop. For the first beam being
traced the psipol,chipol are correctly initialised to the user-defined
value and the resulting coupling is correct.
However, in each subsequent beam the values were not set to those of the
parent beam (or to the user-defined value in the case of the first X
mode beam), but to those of the previous beams (current index_rt - 1).
This change repurposes the psipv,chipv arrays to store the polarisation
of the parent beams, including the initial user-defined value and makes
plasma_in always use these to compute the coupling.
In addition, in the case the polarisation is not immediately known (i.e.
if raytracing.ipol == .false.), this change postpones the computation of
the Jones vector (ext, eyt) from the launch point, if the magnetic
equilibrium is available, to when the ray actually crosses the
plasma boundary.
The original code, besides being strictly incorrect, can lead to
non-negligible alterations to the coupling. This change also mean:
1. most of the functionality of `set_pol` has been merged with
`plasma_in`
2. the polarisation is undefined and the Jones vector is set to the
placeholder value [1, 0] till `plasma_im` is called
Finally, `polarcold` is removed because it's unused.
2024-03-02 17:32:03 +01:00
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2019-03-26 15:21:22 +01:00
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subroutine plasma_out(i,xv,anv,bres,sox,iop,ext,eyt) ! ray exits plasma
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2019-03-28 10:50:28 +01:00
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! arguments
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2019-03-26 15:21:22 +01:00
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integer, intent(in) :: i ! ray index
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real(wp_), dimension(3), intent(in) :: xv,anv
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2022-05-20 13:10:49 +02:00
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real(wp_), intent(in) :: bres
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integer, intent(in) :: sox
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2019-03-28 10:50:28 +01:00
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integer, dimension(:), intent(inout), pointer :: iop ! in/out plasma flag
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2019-03-26 15:21:22 +01:00
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complex(wp_), dimension(:), intent(out), pointer :: ext,eyt
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2019-03-28 10:50:28 +01:00
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! local variables
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2019-03-26 15:21:22 +01:00
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real(wp_) :: rm,csphi,snphi,bphi,br,bz
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real(wp_), dimension(3) :: bv,xmv
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!
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2019-03-28 10:50:28 +01:00
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iop(i)=iop(i)+1 ! in->out
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2019-03-26 15:21:22 +01:00
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xmv=xv*0.01_wp_ ! convert from cm to m
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rm=sqrt(xmv(1)**2+xmv(2)**2)
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csphi=xmv(1)/rm
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snphi=xmv(2)/rm
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2023-10-22 10:32:27 +02:00
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call bfield(rm,xmv(3),br,bz,bphi)
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2019-03-26 15:21:22 +01:00
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bv(1)=br*csphi-bphi*snphi
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bv(2)=br*snphi+bphi*csphi
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bv(3)=bz
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call pol_limit(anv,bv,bres,sox,ext(i),eyt(i)) ! polarization at plasma exit
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end subroutine plasma_out
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! ------------------------------
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! subroutine wall_in(i) ! ray enters vessel
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! integer, intent(in) :: i ! ray index
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!
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! iow(i)=iow(i)+1
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! end subroutine wall_in
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! ------------------------------
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subroutine wall_out(i,ins,xv,anv,bres,sox,psipol1,chipol1,iow,iop,ext,eyt) ! ray exits vessel
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2019-03-28 10:50:28 +01:00
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! arguments
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2019-03-26 15:21:22 +01:00
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integer, intent(in) :: i ! ray index
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logical, intent(in) :: ins ! inside plasma? (ins=1 plasma/wall overlap)
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real(wp_), dimension(3), intent(inout) :: xv,anv
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2022-05-20 13:10:49 +02:00
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real(wp_), intent(in) :: bres
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integer, intent(in) :: sox
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2019-03-26 15:21:22 +01:00
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real(wp_), intent(out) :: psipol1,chipol1
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2019-03-28 10:50:28 +01:00
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integer, dimension(:), intent(inout), pointer :: iow,iop ! in/out vessel and plasma flags
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2019-03-26 15:21:22 +01:00
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complex(wp_), dimension(:), intent(inout), pointer :: ext,eyt
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2019-03-28 10:50:28 +01:00
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! local variables
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2019-03-26 15:21:22 +01:00
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integer :: irfl
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real(wp_), dimension(3) :: xvrfl,anvrfl,walln
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complex(wp_) :: ext1,eyt1
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2019-03-28 10:50:28 +01:00
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!
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iow(i)=iow(i)+1 ! out->in
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if(ins) call plasma_out(i,xv,anv,bres,sox,iop,ext,eyt) ! plasma-wall overlapping
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call wall_refl(xv-dst*anv,anv,ext(i),eyt(i),xvrfl,anvrfl,ext1,eyt1,walln,irfl) ! ray reflects at wall
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ext(i) = ext1 ! save parameters at wall reflection
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2019-03-26 15:21:22 +01:00
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eyt(i) = eyt1
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xv = xvrfl
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anv = anvrfl
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2024-03-12 16:42:19 +01:00
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if(i == 1) then ! polarization angles at wall reflection for central ray
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call field_to_ellipse(ext1, eyt1, psipol1, chipol1)
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2019-03-26 15:21:22 +01:00
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else
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psipol1 = zero
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chipol1 = zero
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end if
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end subroutine wall_out
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! ------------------------------
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subroutine initbeam(i,iroff,iboff,iwait,stv,jphi_beam,pins_beam,currins_beam, &
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dpdv_beam,jcd_beam) ! initialization at beam propagation start
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2021-12-18 18:57:38 +01:00
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use logger, only : log_info, log_warning
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2019-03-28 10:50:28 +01:00
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! arguments
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2019-03-26 15:21:22 +01:00
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integer, intent(in) :: i ! beam index
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2019-03-28 10:50:28 +01:00
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logical, dimension(:,:), intent(in), pointer :: iroff ! global ray status (F = active, T = inactive)
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2019-03-26 15:21:22 +01:00
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logical, intent(out) :: iboff
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logical, dimension(:), intent(out), pointer :: iwait
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real(wp_), dimension(:), intent(out), pointer :: jphi_beam,pins_beam, &
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currins_beam,dpdv_beam,jcd_beam,stv
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2021-12-18 18:57:38 +01:00
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character(256) :: msg ! buffer for formatting log messages
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2019-03-26 15:21:22 +01:00
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iboff = .false. ! beam status (F = active, T = inactive)
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iwait = iroff(:,i) ! copy ray status for current beam from global ray status
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if(all(iwait)) then ! no rays active => stop beam
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iboff = .true.
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2023-03-26 16:08:03 +02:00
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else if (any(iwait)) then
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! only some rays active
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write (msg,'(" beam ",g0,": only some rays are active!")') i
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2021-12-18 18:57:38 +01:00
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call log_warning(msg, mod='multipass', proc='initbeam')
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2019-03-26 15:21:22 +01:00
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end if
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stv = zero ! starting step
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jphi_beam = zero ! 1D beam profiles
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pins_beam = zero
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currins_beam = zero
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dpdv_beam = zero
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jcd_beam = zero
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end subroutine initbeam
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! ------------------------------
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subroutine initmultipass(i,iox,iroff,yynext,yypnext,yw0,ypw0,stnext,p0ray, &
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taus,tau1,etau1,cpls,cpl1,lgcpl1,psipv,chipv) ! initialization before pass loop
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2019-03-28 10:50:28 +01:00
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! arguments
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2024-01-29 01:08:28 +01:00
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logical, intent(in) :: i ! ipol
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integer, intent(in) :: iox ! mode active on 1st pass
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2019-03-28 10:50:28 +01:00
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logical, dimension(:,:), intent(out), pointer :: iroff ! global ray status (F = active, T = inactive)
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2019-03-26 15:21:22 +01:00
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real(wp_), dimension(:), intent(out), pointer :: p0ray,tau1,etau1,cpl1,lgcpl1, &
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psipv,chipv
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real(wp_), dimension(:,:), intent(out), pointer :: yw0,ypw0,stnext,taus,cpls
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real(wp_), dimension(:,:,:), intent(out), pointer :: yynext,yypnext
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!
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iroff = .false. ! global ray status (F = active, T = inactive)
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2024-01-29 01:08:28 +01:00
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if(.not. i) call turnoffray(0,1,3-iox,iroff) ! !ipol => stop other mode (iox=1/2 -> stop ib=2/1 at first pass)
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2019-03-26 15:21:22 +01:00
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yynext = zero ! starting beam coordinates (1)
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yypnext = zero ! starting beam coordinates (2)
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yw0 = zero ! temporary beam coordinates (1)
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ypw0 = zero ! temporary beam coordinates (2)
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stnext = zero ! starting beam step
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p0ray = zero ! starting beam power
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2019-03-28 10:50:28 +01:00
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taus = zero ! beam tau from previous passes
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tau1 = zero
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2019-03-26 15:21:22 +01:00
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etau1 = one
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2019-03-28 10:50:28 +01:00
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cpls = one ! beam coupling from previous passes
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2019-03-26 15:21:22 +01:00
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cpl1 = one
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lgcpl1 = zero
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psipv = zero ! psi polarization angle at vacuum-plasma boundary
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chipv = zero ! chi polarization angle at vacuum-plasma boundary
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end subroutine initmultipass
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! ------------------------------
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subroutine turnoffray(jk,ip,ib,iroff) ! turn off ray propagation
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2019-03-28 10:50:28 +01:00
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! arguments
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2019-03-26 15:21:22 +01:00
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integer, intent(in) :: jk, ip, ib ! ray (0=all rays), pass, beam indexes
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2019-03-28 10:50:28 +01:00
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logical, dimension(:,:), intent(out), pointer :: iroff ! global ray status (F = active, T = inactive)
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! local variables
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2019-03-26 15:21:22 +01:00
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integer :: ipx, i1, i2
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!
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if(jk==0) then ! stop all rays
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2019-03-28 10:50:28 +01:00
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do ipx=ip,ipass ! from pass ip to last pass
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i1 = 2**ipx-2+2**(ipx-ip)*(ib-1)+1 ! first derived beam at pass ipx
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i2 = 2**ipx-2+2**(ipx-ip)*ib ! last derived beam at pass ipx (i1=i2 for ipx=ip)
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2019-03-26 15:21:22 +01:00
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iroff(:,i1:i2) = .true.
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end do
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else ! only stop ray jk
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do ipx=ip,ipass
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i1 = 2**ipx-2+2**(ipx-ip)*(ib-1)+1
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i2 = 2**ipx-2+2**(ipx-ip)*ib
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iroff(jk,i1:i2) = .true.
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end do
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end if
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end subroutine turnoffray
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! ------------------------------
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|
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subroutine alloc_multipass(dim,iwait,iroff,iop,iow,yynext,yypnext,yw0,ypw0,stnext, &
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|
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stv,p0ray,taus,tau1,etau1,cpls,cpl1,lgcpl1,jphi_beam, &
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pins_beam,currins_beam,dpdv_beam,jcd_beam,psipv,chipv)
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integer :: dim
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logical, dimension(:), intent(out), pointer :: iwait
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logical, dimension(:,:), intent(out), pointer :: iroff
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integer, dimension(:), intent(out), pointer :: iop,iow
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real(wp_), dimension(:), intent(out), pointer :: jphi_beam,pins_beam,currins_beam, &
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|
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dpdv_beam,jcd_beam,stv,tau1,etau1,cpl1,lgcpl1,p0ray,psipv,chipv
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|
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real(wp_), dimension(:,:), intent(out), pointer :: taus,cpls,stnext,yw0,ypw0
|
|
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real(wp_), dimension(:,:,:), intent(out), pointer :: yynext,yypnext
|
|
|
|
|
|
|
|
|
|
call dealloc_multipass(iwait,iroff,iop,iow,yynext,yypnext,yw0,ypw0,stnext,stv, &
|
|
|
|
|
p0ray,taus,tau1,etau1,cpls,cpl1,lgcpl1,jphi_beam,pins_beam,currins_beam, &
|
|
|
|
|
dpdv_beam,jcd_beam,psipv,chipv)
|
|
|
|
|
|
|
|
|
|
nbeam_max = 2**ipass ! max n of beams active at a time
|
|
|
|
|
nbeam_tot = 2**(ipass+1)-2 ! total n of beams
|
|
|
|
|
|
|
|
|
|
allocate(iwait(nray),iroff(nray,nbeam_tot),iop(nray),iow(nray), &
|
|
|
|
|
yynext(6,nray,nbeam_max-2),yypnext(6,nray,nbeam_max-2), &
|
|
|
|
|
yw0(6,nray),ypw0(6,nray),stnext(nray,nbeam_tot),stv(nray), &
|
|
|
|
|
p0ray(nray),taus(nray,nbeam_tot),tau1(nray),etau1(nray), &
|
|
|
|
|
cpls(nray,nbeam_tot),cpl1(nray),lgcpl1(nray),jphi_beam(dim), &
|
|
|
|
|
pins_beam(dim),currins_beam(dim),dpdv_beam(dim),jcd_beam(dim), &
|
fix coupling for subsequent beams
In situations when multiple beams are traced, either when allowing
multiple plasma crossings (raytracing.ipass > 0) or the initial polarisation
is mixed (raytracing.ipol == .true.), the couplings of all but the first
beam (with least index_rt) were invalid.
The bug is due to the re-use of the psipol,chipol variables as the beams
are traced sequentially over the beam_loop. For the first beam being
traced the psipol,chipol are correctly initialised to the user-defined
value and the resulting coupling is correct.
However, in each subsequent beam the values were not set to those of the
parent beam (or to the user-defined value in the case of the first X
mode beam), but to those of the previous beams (current index_rt - 1).
This change repurposes the psipv,chipv arrays to store the polarisation
of the parent beams, including the initial user-defined value and makes
plasma_in always use these to compute the coupling.
In addition, in the case the polarisation is not immediately known (i.e.
if raytracing.ipol == .false.), this change postpones the computation of
the Jones vector (ext, eyt) from the launch point, if the magnetic
equilibrium is available, to when the ray actually crosses the
plasma boundary.
The original code, besides being strictly incorrect, can lead to
non-negligible alterations to the coupling. This change also mean:
1. most of the functionality of `set_pol` has been merged with
`plasma_in`
2. the polarisation is undefined and the Jones vector is set to the
placeholder value [1, 0] till `plasma_im` is called
Finally, `polarcold` is removed because it's unused.
2024-03-02 17:32:03 +01:00
|
|
|
psipv(0:nbeam_tot),chipv(0:nbeam_tot))
|
2019-03-26 15:21:22 +01:00
|
|
|
|
|
|
|
|
end subroutine alloc_multipass
|
|
|
|
|
! ------------------------------
|
|
|
|
|
subroutine dealloc_multipass(iwait,iroff,iop,iow,yynext,yypnext,yw0,ypw0,stnext, &
|
|
|
|
|
stv,p0ray,taus,tau1,etau1,cpls,cpl1,lgcpl1,jphi_beam, &
|
|
|
|
|
pins_beam,currins_beam,dpdv_beam,jcd_beam,psipv,chipv)
|
|
|
|
|
logical, dimension(:), intent(out), pointer :: iwait
|
|
|
|
|
logical, dimension(:,:), intent(out), pointer :: iroff
|
|
|
|
|
integer, dimension(:), intent(out), pointer :: iop,iow
|
|
|
|
|
real(wp_), dimension(:), intent(out), pointer :: stv,p0ray,tau1,etau1,cpl1,lgcpl1, &
|
|
|
|
|
jphi_beam,pins_beam,currins_beam,dpdv_beam,jcd_beam,psipv,chipv
|
|
|
|
|
real(wp_), dimension(:,:), intent(out), pointer :: yw0,ypw0,stnext,taus,cpls
|
|
|
|
|
real(wp_), dimension(:,:,:), intent(out), pointer :: yynext,yypnext
|
|
|
|
|
|
|
|
|
|
if (associated(iwait)) deallocate(iwait)
|
|
|
|
|
if (associated(iroff)) deallocate(iroff)
|
|
|
|
|
if (associated(iop)) deallocate(iop)
|
|
|
|
|
if (associated(iow)) deallocate(iow)
|
|
|
|
|
if (associated(yynext)) deallocate(yynext)
|
|
|
|
|
if (associated(yypnext)) deallocate(yypnext)
|
|
|
|
|
if (associated(yw0)) deallocate(yw0)
|
|
|
|
|
if (associated(ypw0)) deallocate(ypw0)
|
|
|
|
|
if (associated(stnext)) deallocate(stnext)
|
|
|
|
|
if (associated(stv)) deallocate(stv)
|
|
|
|
|
if (associated(p0ray)) deallocate(p0ray)
|
|
|
|
|
if (associated(taus)) deallocate(taus)
|
|
|
|
|
if (associated(tau1)) deallocate(tau1)
|
|
|
|
|
if (associated(etau1)) deallocate(etau1)
|
|
|
|
|
if (associated(cpls)) deallocate(cpls)
|
|
|
|
|
if (associated(cpl1)) deallocate(cpl1)
|
|
|
|
|
if (associated(lgcpl1)) deallocate(lgcpl1)
|
|
|
|
|
if (associated(jphi_beam)) deallocate(jphi_beam)
|
|
|
|
|
if (associated(pins_beam)) deallocate(pins_beam)
|
|
|
|
|
if (associated(currins_beam)) deallocate(currins_beam)
|
|
|
|
|
if (associated(dpdv_beam)) deallocate(dpdv_beam)
|
|
|
|
|
if (associated(jcd_beam)) deallocate(jcd_beam)
|
|
|
|
|
if (associated(psipv)) deallocate(psipv)
|
|
|
|
|
if (associated(chipv)) deallocate(chipv)
|
|
|
|
|
end subroutine dealloc_multipass
|
|
|
|
|
|
|
|
|
|
end module multipass
|
