29 KiB
Input and output files
This section describes the input data required by GRAY and the output files that are saved and stored for the GRT-161 analysis. In [@tbl:io] the assigned unit numbers used for various input and output files in GRAY are listed. Shell scripts allow to run the code for various input data that are varied by means of suitable loops.
Unit Number I/O Content Filename
2 I Input data gray_params.data
99 I Equilibrium file EQDSK filenmeqq.eqdsk
98 I Kinetic profiles filenmeprf.prf
97 I Beam data filenmebm.txt
4 O Data for central ray None
7 O Global data and results None / assigned by shell script
48 O ECRH&CD profiles None / assigned by shell script
33 O Data for outmost rays None
8 O Beam cross section shape None
9 O Rays distribution at the end None of the integration path
12 O Beam transverse sizes None
17 O Beam tracing error on Hamiltonian None
55 O Kinetic profiles None
56 O Flux averaged quantities None
70 O EC resonance surface at relevant harmonics None
71 O Flux surface contours at None
\sqrt{\psi}=\text{const}
78 O Record of input parameters headers.txt / attached to output by shell script
Table: GRAY I/O Unit Numbers {#tbl:io}
Input Files
To run GRAY, the user must supply a gray_params.data file and two
files, containing information about the MHD equilibrium and the kinetic
profiles, respectively.
The variables and quantities in gray_params.data are listed in
[@tbl:input1;@tbl:input2;@tbl:input3], suitably grouped together.
The equilibrium information is provided via a G-EQDSK file (with extension
.eqdsk), with conventions specified as in [@cocos].
The kinetic profiles are provided in an ASCII file (with extension .prf).
The format of the G-EQDSK file is described in [@sec:eqdisk], while the format
of the .prf file for the profiles is the following quantities defined in
[@tbl:profiles1]:
read (98,*) npp
do i=1,npp
read(98,*) psin(i),Te(i),ne(i),Zeff(i)
end do
The beam parameters are read either from the gray_params.data file, or
from an ASCII file (with extension .txt), depending on the value of the
ibeam parameter as specified in [@tbl:input1]. If the ASCII file
is used, the user can supply multiple launching conditions, and/or use a
general astigmatic Gaussian beam. The format of the .txt file is the
following, for ibeam=1 and ibeam=2 respectively (quantities defined
in [@tbl:profiles2]):
! +++ IBEAM=1 +++
read(97,*) nsteer
do i=1,nsteer
read(97,*) gamma(i),alpha0(i),beta0(i),x0mm(i),y0mm(i),z0mm(i), &
w0xi(i),d0eta(i),w0xi(i),d0eta(i),phiw(i)
end do
! +++ IBEAM=2 +++
read(97,*) nsteer
do i=1,nisteer
read(97,*) gamma(i),alpha0(i),beta0(i),x0mm(i),y0mm(i),z0mm(i), &
wxi(i),weta(i),rcixi(i),rcieta(i),phiw(i),phir(i)
end do
G-EQDSK format
The G EQDSK file provides information on:
- pressure,
- poloidal current function,
qprofile,- plasma boundary,
- limiter contour
All quantities are defined on a uniform flux grid from the magnetic axis to the
plasma boundary and the poloidal flux function on the rectangular computation
grid. A right-handed cylindrical coordinate system (R, φ, Ζ) is used.
Variables
In order of appearance in the file:
Name Type Description
case String(6) Identification string
nw Integer Number of horizontal R grid points
nh Integer Number of vertical Z grid points
Table: Miscellanea {#tbl:eqdisk-misc}
Name Type Unit Description
rdim Real m Horizontal dimension of the computational box
zdim Real m Vertical dimension of the computational box
rleft Real m Minimum R of the rectangular computational box
zmid Real m Z of center of the computational box
rmaxis Real m R of the magnetic axis
zmaxis Real m Z of the magnetic axis
Table: Geometry {#tbl:eqdisk-geom}
Name Type Unit Description
simag Real Wb/rad Poloidal flux at the magnetic axis
sibry Real Wb/rad Poloidal flux at the plasma boundary
rcentr Real m R of vacuum toroidal magnetic field bcentr
bcentr Real T Vacuum toroidal magnetic field at rcentr
current Real A Plasma current
fpol Real mT Poloidal current function, F = RB_T on the flux grid
pres Real Pa Plasma pressure on a uniform flux grid
ffprim Real (mT²)/(Wb/rad) FF'(ψ) on a uniform flux grid
pprime Real Pa/(Wb/rad) P'(ψ) on a uniform flux grid
psizr Real Wb/rad Poloidal flux on the rectangular grid points
qpsi Real 1 q values on uniform flux grid from axis to boundary
Table: Magnetic equilibrium {#tbl:eqdisk-eq}
Name Type Unit Description
nbbbs Integer 1 Number of boundary points
limitr Integer 1 Number of limiter points
rbbbs Real m R of boundary points
zbbbs Real m Z of boundary points
rlim Real m R of surrounding limiter contour
zlim Real m Z of surrounding limiter contour
Table: Plasma boundary {#tbl:eqdisk-bound}
Toroidal Current Density
The toroidal current J_T (A/m²) is related to P'(ψ) and FF'(ψ) through
J_T = R P'(ψ) + FF'(ψ) / R
Example Fortran 77 code
The following snippet can be used to load a G-EQDSK file:
character*10 case(6)
dimension psirz(nw,nh),fpol(1),pres(1),ffprim(1),
. pprime(1),qpsi(1),rbbbs(1),zbbbs(1),
. rlim(1),zlim(1)
c
read (neqdsk,2000) (case(i),i=1,6),idum,nw,nh
read (neqdsk,2020) rdim,zdim,rcentr,rleft,zmid
read (neqdsk,2020) rmaxis,zmaxis,simag,sibry,bcentr
read (neqdsk,2020) current,simag,xdum,rmaxis,xdum
read (neqdsk,2020) zmaxis,xdum,sibry,xdum,xdum
read (neqdsk,2020) (fpol(i),i=1,nw)
read (neqdsk,2020) (pres(i),i=1,nw)
read (neqdsk,2020) (ffprim(i),i=1,nw)
read (neqdsk,2020) (pprime(i),i=1,nw)
read (neqdsk,2020) ((psirz(i,j),i=1,nw),j=1,nh)
read (neqdsk,2020) (qpsi(i),i=1,nw)
read (neqdsk,2022) nbbbs,limitr
read (neqdsk,2020) (rbbbs(i),zbbbs(i),i=1,nbbbs)
read (neqdsk,2020) (rlim(i),zlim(i),i=1,limitr)
c
2000 format (6a8,3i4)
2020 format (5e16.9)
2022 format (2i5)
Output Files
GRAY outputs are given in ASCII files at each GRAY execution. [@tbl:output7;@tbl:output48] describe the outputs reported in units 7 and 48, respectively.
Variable Type Units Valid range Definition
alpha0 Real deg -180 < x ≤ 180 Poloidal injection angle α, defined in [@eq:albt].
beta0 Real deg -90 < x ≤ 90 Toroidal injection angle β, defined in [@eq:albt].
fghz Real GHz x>0 EC frequency.
P0 Real MW x>0 EC injected power.
Nrayr Integer 1 1 ≤ n ≤ 31 Number of rays N_r in radial direction + 1 in
the center, {\tt Nrayr} = N_r +1.
Nrayth Integer 1 1 ≤ n ≤ 36 Number of rays N_{\theta} in angular direction.
rwmax Real x > 0 "cut-off" size \tilde ρ_{max} of the gaussian beam.
(typical 1 ≤ {\tt rwmax} ≤ 1.5), defined at page.
x0 Real cm X coordinate of the launching point.
y0 Real cm Y coordinate of the launching point.
z0 Real cm Z coordinate of the launching point.
w0xi Real cm x > 0 Beam waist w_{0,\xi} in beam reference system.
along \xi, defined in [@eq:rciw].
w0eta Real cm x > 0 Beam waist w_{0,\eta} in beam reference system.
along \eta, defined in [@eq:rciw].
d0xi Real cm \bar{z} coordinate of beam waist w_{0,\xi},.
defined in [@eq:rciw].
d0eta Real cm \bar{z} coordinate of beam waist w_{0,\eta},.
defined in [@eq:rciw].
phiw Real deg -90 < x ≤ 90 Rotation angle φ_w=φ_R of local beam coordinate.
system, defined in [@eq:phiwr].
ibeam Integer 0, 1, 2 Input source for beam data:.
0=simple astigmatic beam with parameters as above,.
1=simple astigmatic beam from filenmbm,.
2=general astigmatic beam from filenmbm.
filenmbm String len$(s)≤ 24$ Name of file (extension .txt appended) with beam.
parameters, used if {\tt ibeam} >0.
iox Integer 1, 2 1=Ordinary mode (OM), 2=Extraordinary (XM) mode.
psipol0 Real deg -90 < x ≤ 90 Wave polarisation angle \psi_p at the launching point.
chipol0 Real deg -45 ≤ x ≤ 45 Wave polarisation angle \chi_p at the launching point.
Table: GRAY input data gray_params.data - EC wave {#tbl:input1}
Variable Type Units Valid range Definition
iequil Integer 0, 1, 2 Magnetic equilibrium model:
0=vacuum (no plasma at all),
1=analytical
2=G-EQDSK.
ixp Integer -1, 0, 1 X point occurrence:
-1=bottom,
0=none,
+1=top.
iprof Integer 0, 1 Kinetic profiles:
0=analytical
1=numerical.
filenmeqq String len$(s)≤ 24$ Name of EQDSK file (extension .eqdsk appended).
ipsinorm Integer 0, 1 0=dimensional (default),
1=normalized (obsolete, for some old files
psi$(R,z)$ in filenmeqq.
sspl Real 1 x > 0 Tension of spline fit for psi ({\tt sspl} \ll 1 typical),
0=interpolation.
factb Real 1 x > 0 Numerical factor to rescale the magnetic field
B \rightarrow B \cdot {\tt factb}.
factt Real 1 x > 0 Numerical factor to rescale the electron temperature
$T_e \rightarrow T_e \cdot {\tt factt}
\cdot {\tt factb}^{\tt ab}$.
factn Real 1 x > 0 Numerical factor to rescale the electron density
$n_e \rightarrow n_e \cdot {\tt factn}
\cdot {\tt factb}^{\tt ab}$.
iscal Int 1, 2 Model for n_e, T_e scaling with B:
1=constant n_{Greenwald} (ab=1),
2=none (ab=0).
filenmprf String len$(s) ≤ 24$ Name of file for kinetic profiles
(extension .prf appended).
psdbnd Real 1 x > 0 Normalized psi value at the plasma boundary where
n_e is set to zero (typ. 1 ≤ {\tt psdbnd} ≤ 1.1).
sgnbphi Real 1 -1, +1 Signum of toroidal B, used if icocos=0.
sgniphi Real 1 -1, +1 Signum of toroidal plasma current I, used if icocos=0.
icocos Int 0-8, 10-18 COCOS index used in filenmeqq as defined in [@cocos]:
0=no COCOS convention and psi in Wb/rad,
10=means no convention and psi in Wb.
Table: GRAY input data gray_params.data - plasma data {#tbl:input2}
Variable Type Units Valid range Definition
iwarm Integer 0, 1, 2, 3 Absorption model:
0=none (α=0),
1=weakly relativistic,
2=fully relativistic (fast),
3=fully relativistic (slow).
ilarm Integer 1 n ≥ 1 Order of Larmor radius expansion for absorption
computation {\tt ilarm}> local EC harmonic number.
ieccd Integer 0, 1, 11 Current drive model:
0=none,
1=Cohen,
11=Marushchenko.
igrad Integer 0, 1 Ray-tracing model:
0=optical,
1=quasi-optical (requires {\tt nrayr} \ge 5).
idst Integer 0, 1, 2 Ray-tracing integration variable:
0=s,
e1=c \cdot t,
2=S_R,
(default=0).
dst Real cm x > 0 Spatial integration step.
nstep Integer 1 0 ≤ n ≤ 8000 Maximum number of integration steps.
istprj Integer 1 1 ≤ n ≤ {\tt nstep} Subsampling factor for beam cross section
data output (units 8, 12).
istpl Integer 1 1 ≤ n ≤ {\tt nstep} Subsampling factor for outmost rays
data output (unit 33).
ipec Integer 0, 1 Grid spacing for ECRH&CD profiles:
0=equispaced in \psi (obsolete),
1=equispaced in \sqrt{\psi}.
nnd Integer 1 2 ≤ n ≤ 5001 Number of points in the ECRH&CD profile grid.
ipass Integer -2,1, 2 $\vert{\tt ipass}\vert$=number of passes into plasma:
-2=reflection at rwallm,
+2=reflection at limiter.
Surface given in EQDSK.
rwallm Real m x > 0 Inner wall radius for 2nd pass calculations,
used only for ipass=-2.
Table: GRAY input data gray_params.data - ECRH&CD models and code parameters {#tbl:input3}
Variable Type Units Valid range Definition
npp Integer 1 2 ≤ n ≤ 250 Number of points in psin table
psin real 1 0 ≤ x ≤ psdbnd Poloidal flux \psi normalized over the value at the LCS
Te real keV x ≥ 0 Electron temperature
ne real 10¹⁹m⁻³ x ≥ 0 Electron density
Zeff real 1 x ≥ 0 Effective charge, Z_{\rm eff}
Table: GRAY input data filenmprf.prf - plasma profiles {#tbl:profiles1}
Variable Type Units Valid range Definition
nsteer Integer 1 n ≤ 50 Number launching conditions in table.
gamma Real deg Steering angle w.r.t. a reference position (unused).
alpha0 Real deg -180 < x ≤ 180 Poloidal injection angle α.
beta0 Real deg -90 ≤ x ≤ 90 Toroidal injection angle β.
x0mm Real mm X coordinate of the launching point.
y0mm Real mm Y coordinate of the launching point.
z0mm Real mm Z coordinate of the launching point.
w0xi Real mm x > 0 Beam waist w_{0,\xi} along \xi.
w0eta Real mm x > 0 Beam waist w_{0,\eta} along \eta.
d0xi Real mm \bar z coordinate of beam waist w_{0,\xi},
$\bar z=0$ at launching point.
d0eta Real mm \bar z coordinate of beam waist w_{0,\eta},
$\bar z=0$ at launching point.
wxi Real mm x > 0 Beam width w_{\xi} at the launching point.
weta Real mm x > 0 Beam width w_{\eta} at the launching point.
rcixi Real mm⁻¹ Inverse of phase front curvature radius $1/R_{\xi}$
at the launching point.
rcieta Real mm⁻¹ Inverse of phase front curvature radius $1/R_{\eta}$
at the launching point.
phiw Real deg Rotation angle φ_w of the (\xi_w,\eta_w) reference
system, defined in [@eq:phiwr].
phir Real deg Rotation angle φ_R of the (\xi_R,\eta_R) reference
system, defined in [@eq:phiwr].
Table: GRAY input data filenmbm.prf - launched beam parameters {#tbl:profiles2}
Variable Type Units Definition
Icd Real kA EC total driven current I_{cd}.
Pa Real MW EC total absorbed power P_{abs}.
Jphimx Real MA⋅m⁻² EC peak current density J_{φ}= dI_{cd}/dA.
dPdVmx Real MW⋅m⁻³ EC peak power density dP/dV.
rhotj Real 1 ρ value corresponding to Jphimx.
rhotp Real 1 ρ value corresponding to dPdVmx.
drhotj Real 1 Full width at 1/e of driven current density profile.
drhotp Real 1 Full width at 1/e of power density profile.
Jphip Real MA⋅m⁻² EC peak current density J_{φ 0} from Gaussian profile,
defined in [@eq:pjgauss].
dPdVp Real MW⋅m⁻³ EC peak power density p_0 from Gaussian profile,
defined in [@eq:pjgauss].
rhotjava Real 1 ρ value averaged over current density profile,
defined in [@eq:rav].
rhotpav Real 1 ρ value averaged over power density profile,
defined in [@eq:rav].
drhotjava Real 1 Full width of the driven current density profile,
defined in [@eq:drav].
drhotpav Real 1 Full width of the driven power density profile,
defined in [@eq:drav].
ratjbmx Real 1 Ratio J_{cd}/J_{φ} at $ρ=$rhotjava,
with $J_{cd}=\langle \bold{J}\cdot \bold{B} \rangle
/\langle \mathbf{B} \rangle$.
ratjamx Real 1 Ratio J_{cd}/J_{φ} at $ρ=$rhotjava,
with J_{cd}=\langle \bold{J}\cdot \bold{B} \rangle/B_0
stmx Real cm Path from the launching point and peak $dP/dV$
for the central ray.
psipol Real deg \psi polarisation angle at vacuum-plasma boundary.
chipol Real deg \chi polarisation angle at vacuum-plasma boundary.
index_rt Integer Index encoding mode and pass number, see [@sec:index_rt].
Table: GRAY output data - unit 7 {#tbl:output7}
Variable Type Units Definition
psin Real 1 Normalized poloidal flux.
rhot Real 1 Normalized minor radius ρ.
Jphi Real MA⋅m⁻² EC current density J_{φ}= dI_{cd}/dA,
with A the area of the poloidal section labelled by ρ.
Jcdb Real MA⋅m⁻² EC current density
$J_{cd}=\langle \bold{J}\cdot\bold{B} \rangle
/\langle \mathbf{B} \rangle$.
dPdV Real MW⋅m⁻³ EC power density p(ρ)=dP/dV.
Icdins Real kA EC current driven inside surface of radius ρ,
I_{ins}(ρ)=\int_0^{ρ} J_{cd} dA.
Pins Real MW EC power absorbed inside surface of radius ρ,
P_{ins}(ρ)=\int_0^{ρ}p dV.
P% Real 1 Fraction of power deposited inside radius ρ,
P%(ρ)=P_{ins}/P_{abs}.
index_rt Integer Index encoding mode and pass number, see [@sec:index_rt].
Table: GRAY output data - unit 48 {#tbl:output48}