23a8caff37
While technically accepted by GRAY, these indices do not carry a special meaning, as wrongly implied by the documentation: they are equivalent to 8, 18 and specifically don't change the meaning of sgnbi,sgni.
576 lines
29 KiB
Markdown
576 lines
29 KiB
Markdown
# Input and output files {#sec:io-files}
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This section describes the input data required by GRAY and the output
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files that are saved and stored for the GRT-161 analysis. In [@tbl:io]
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the assigned unit numbers used for various input and output files in GRAY are
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listed. Shell scripts allow to run the code for various input data that are
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varied by means of suitable loops.
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---------------------------------------------------------------------------------------------------------------------------
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Unit Number I/O Content Filename
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------------- -------- ---------------------------------------------- -----------------------------------------------------
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2 I Input data `gray_params.data`
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99 I Equilibrium file EQDSK `filenmeqq.eqdsk`
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98 I Kinetic profiles `filenmeprf.prf`
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97 I Beam data `filenmebm.txt`
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4 O Data for central ray None
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7 O Global data and results None / assigned by shell script
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48 O ECRH&CD profiles None / assigned by shell script
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33 O Data for outmost rays None
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8 O Beam cross section shape None
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9 O Rays distribution at the end None
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of the integration path
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12 O Beam transverse sizes None
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17 O Beam tracing error on Hamiltonian None
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55 O Kinetic profiles None
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56 O Flux averaged quantities None
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70 O EC resonance surface at relevant harmonics None
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71 O Flux surface contours at None
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$\sqrt{\psi}=\text{const}$
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78 O Record of input parameters `headers.txt` / attached to output by shell script
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---------------------------------------------------------------------------------------------------------------------------
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Table: GRAY I/O Unit Numbers {#tbl:io}
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## Input Files {#sec:input-files}
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To run GRAY, the user must supply a `gray_params.data` file and two
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files, containing information about the MHD equilibrium and the kinetic
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profiles, respectively.
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The variables and quantities in `gray_params.data` are listed in
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[@tbl:input1;@tbl:input2;@tbl:input3], suitably grouped together.
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The equilibrium information is provided via a G-EQDSK file (with extension
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`.eqdsk`), with conventions specified as in [@cocos].
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The kinetic profiles are provided in an ASCII file (with extension `.prf`).
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The format of the G-EQDSK file is described in [@sec:eqdisk], while the format
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of the `.prf` file for the profiles is the following quantities defined in
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[@tbl:profiles1]:
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```fortran
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read (98,*) npp
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do i=1,npp
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read(98,*) psin(i),Te(i),ne(i),Zeff(i)
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end do
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```
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The beam parameters are read either from the `gray_params.data` file, or
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from an ASCII file (with extension `.txt`), depending on the value of the
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`ibeam` parameter as specified in [@tbl:input1]. If the ASCII file
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is used, the user can supply multiple launching conditions, and/or use a
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general astigmatic Gaussian beam. The format of the `.txt` file is the
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following, for `ibeam`=1 and `ibeam`=2 respectively (quantities defined
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in [@tbl:profiles2]):
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```fortran
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! +++ IBEAM=1 +++
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read(97,*) nsteer
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do i=1,nsteer
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read(97,*) gamma(i),alpha0(i),beta0(i),x0mm(i),y0mm(i),z0mm(i), &
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w0xi(i),d0eta(i),w0xi(i),d0eta(i),phiw(i)
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end do
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! +++ IBEAM=2 +++
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read(97,*) nsteer
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do i=1,nisteer
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read(97,*) gamma(i),alpha0(i),beta0(i),x0mm(i),y0mm(i),z0mm(i), &
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wxi(i),weta(i),rcixi(i),rcieta(i),phiw(i),phir(i)
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end do
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```
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## G-EQDSK format {#sec:eqdisk}
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The G EQDSK file provides information on:
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1. pressure,
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2. poloidal current function,
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3. $q$ profile,
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4. plasma boundary,
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5. limiter contour
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All quantities are defined on a uniform flux grid from the magnetic axis to the
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plasma boundary and the poloidal flux function on the rectangular computation
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grid. A right-handed cylindrical coordinate system $(R, φ, Ζ)$ is used.
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### Variables
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In order of appearance in the file:
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-------- --------- -------------------------------------
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Name Type Description
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--------- --------- -------------------------------------
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`case` String(6) Identification string
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`nw` Integer Number of horizontal $R$ grid points
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`nh` Integer Number of vertical $Z$ grid points
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---------------------------------------------------------
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Table: **Miscellanea** {#tbl:eqdisk-misc}
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--------- --------- --------------- -----------------------------------------------
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Name Type Unit Description
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--------- --------- --------------- -----------------------------------------------
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`rdim` Real m Horizontal dimension of the computational box
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`zdim` Real m Vertical dimension of the computational box
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`rleft` Real m Minimum R of the rectangular computational box
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`zmid` Real m Z of center of the computational box
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`rmaxis` Real m R of the magnetic axis
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`zmaxis` Real m $Z$ of the magnetic axis
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-----------------------------------------------------------------------------
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Table: **Geometry** {#tbl:eqdisk-geom}
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--------- --------- --------------- -------------------------------------------------------
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Name Type Unit Description
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--------- --------- --------------- -------------------------------------------------------
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`simag` Real Wb/rad Poloidal flux at the magnetic axis
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`sibry` Real Wb/rad Poloidal flux at the plasma boundary
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`rcentr` Real m $R$ of vacuum toroidal magnetic field `bcentr`
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`bcentr` Real T Vacuum toroidal magnetic field at `rcentr`
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`current` Real A Plasma current
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`fpol` Real mT Poloidal current function, $F = RB_T$ on the flux grid
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`pres` Real Pa Plasma pressure on a uniform flux grid
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`ffprim` Real (mT²)/(Wb/rad) $FF'(ψ)$ on a uniform flux grid
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`pprime` Real Pa/(Wb/rad) $P'(ψ)$ on a uniform flux grid
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`psizr` Real Wb/rad Poloidal flux on the rectangular grid points
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`qpsi` Real 1 $q$ values on uniform flux grid from axis to boundary
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-------------------------------------------------------------------------------------------
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Table: **Magnetic equilibrium** {#tbl:eqdisk-eq}
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--------- --------- --------------- -------------------------------------------------------
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Name Type Unit Description
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--------- --------- --------------- -------------------------------------------------------
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`nbbbs` Integer 1 Number of boundary points
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`limitr` Integer 1 Number of limiter points
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`rbbbs` Real m $R$ of boundary points
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`zbbbs` Real m $Z$ of boundary points
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`rlim` Real m $R$ of surrounding limiter contour
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`zlim` Real m $Z$ of surrounding limiter contour
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--------------------------------------------------------------
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Table: **Plasma boundary** {#tbl:eqdisk-bound}
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### Toroidal Current Density
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The toroidal current $J_T$ (A/m²) is related to $P'(ψ)$ and $FF'(ψ)$ through
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$$
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J_T = R P'(ψ) + FF'(ψ) / R
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$$
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### Example Fortran 77 code
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The following snippet can be used to load a G-EQDSK file:
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```fortran
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character*10 case(6)
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dimension psirz(nw,nh),fpol(1),pres(1),ffprim(1),
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. pprime(1),qpsi(1),rbbbs(1),zbbbs(1),
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. rlim(1),zlim(1)
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c
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read (neqdsk,2000) (case(i),i=1,6),idum,nw,nh
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read (neqdsk,2020) rdim,zdim,rcentr,rleft,zmid
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read (neqdsk,2020) rmaxis,zmaxis,simag,sibry,bcentr
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read (neqdsk,2020) current,simag,xdum,rmaxis,xdum
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read (neqdsk,2020) zmaxis,xdum,sibry,xdum,xdum
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read (neqdsk,2020) (fpol(i),i=1,nw)
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read (neqdsk,2020) (pres(i),i=1,nw)
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read (neqdsk,2020) (ffprim(i),i=1,nw)
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read (neqdsk,2020) (pprime(i),i=1,nw)
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read (neqdsk,2020) ((psirz(i,j),i=1,nw),j=1,nh)
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read (neqdsk,2020) (qpsi(i),i=1,nw)
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read (neqdsk,2022) nbbbs,limitr
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read (neqdsk,2020) (rbbbs(i),zbbbs(i),i=1,nbbbs)
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read (neqdsk,2020) (rlim(i),zlim(i),i=1,limitr)
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c
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2000 format (6a8,3i4)
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2020 format (5e16.9)
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2022 format (2i5)
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```
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## Output Files
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GRAY outputs are given in ASCII files at each GRAY execution.
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[@tbl:output7;@tbl:output48] describe the outputs reported in units 7 and 48,
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respectively.
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----------------------------------------------------------------------------------------------------------------------------
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Variable Type Units Valid range Definition
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---------------- ----------- --------- ----------------------- ------------------------------------------------------------
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`alpha0` Real deg $-180 < x ≤ 180$ Poloidal injection angle $α$, defined in [@eq:albt].
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`beta0` Real deg $-90 < x ≤ 90$ Toroidal injection angle $β$, defined in [@eq:albt].
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`fghz` Real GHz $x>0$ EC frequency.
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`P0` Real MW $x>0$ EC injected power.
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`Nrayr` Integer 1 $1 ≤ n ≤ 31$ Number of rays $N_r$ in radial direction + 1 in
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the center, ${\tt Nrayr} = N_r +1$.
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`Nrayth` Integer 1 $1 ≤ n ≤ 36$ Number of rays $N_{\theta}$ in angular direction.
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`rwmax` Real $x > 0$ "cut-off" size $\tilde ρ_{max}$ of the gaussian beam.
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(typical $1 ≤ {\tt rwmax} ≤ 1.5$), defined at page.
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`x0` Real cm $X$ coordinate of the launching point.
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`y0` Real cm $Y$ coordinate of the launching point.
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`z0` Real cm $Z$ coordinate of the launching point.
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`w0xi` Real cm $x > 0$ Beam waist $w_{0,\xi}$ in beam reference system.
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along $\xi$, defined in [@eq:rciw].
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`w0eta` Real cm $x > 0$ Beam waist $w_{0,\eta}$ in beam reference system.
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along $\eta$, defined in [@eq:rciw].
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`d0xi` Real cm $\bar{z}$ coordinate of beam waist $w_{0,\xi}$,.
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defined in [@eq:rciw].
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`d0eta` Real cm $\bar{z}$ coordinate of beam waist $w_{0,\eta}$,.
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defined in [@eq:rciw].
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`phiw` Real deg $-90 < x ≤ 90$ Rotation angle $φ_w=φ_R$ of local beam coordinate.
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system, defined in [@eq:phiwr].
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`ibeam` Integer 0, 1, 2 Input source for beam data:
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0=simple astigmatic beam with parameters as above,
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1=simple astigmatic beam from `filenmbm`,
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2=general astigmatic beam from `filenmbm`.
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`irho` Integer 0, 1, 2 Coordinate of the input profiles:
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0=$ρ_t$,
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1=$ρ_p$,
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2=$ψ$.
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`filenmbm` String len$(s)≤ 24$ Name of file (extension `.txt` appended) with beam.
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parameters, used if ${\tt ibeam} >0$.
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`iox` Integer 1, 2 1=Ordinary mode (OM), 2=Extraordinary (XM) mode.
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`ipol` Integer 0, 1 Whether to compute the mode at the launcher from the
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polarisation:
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0=use `iox`,
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1=use `psipol0`, `chipol0` angles.
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`psipol0` Real deg $-90 < x ≤ 90$ Wave polarisation angle $\psi_p$ at the launching point.
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`chipol0` Real deg $-45 ≤ x ≤ 45$ Wave polarisation angle $\chi_p$ at the launching point.
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----------------------------------------------------------------------------------------------------------------------------
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Table: GRAY input data `gray_params.data` - EC wave {#tbl:input1}
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----------------------------------------------------------------------------------------------------------------------------
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Variable Type Units Valid range Definition
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---------------- ----------- --------- ----------------------- ------------------------------------------------------------
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`iequil` Integer 0, 1, 2 Magnetic equilibrium model:
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0=vacuum (no plasma at all),
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1=analytical
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2=G-EQDSK.
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`ixp` Integer -1, 0, 1 X point occurrence:
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-1=bottom,
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0=none,
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+1=top.
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`iprof` Integer 0, 1 Kinetic profiles:
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0=analytical
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1=numerical.
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`filenmeqq` String len$(s)≤ 24$ Name of EQDSK file (extension `.eqdsk` appended).
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`ipsinorm` Integer 0, 1 0=dimensional (default),
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1=normalized (obsolete, for some old files
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psi$(R,z)$ in `filenmeqq`.
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`sspl` Real 1 $x > 0$ Tension of spline fit for psi (${\tt sspl} \ll 1$ typical),
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0=interpolation.
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`factb` Real 1 $x > 0$ Numerical factor to rescale the magnetic field
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$B \rightarrow B \cdot {\tt factb}$.
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`factt` Real 1 $x > 0$ Numerical factor to rescale the electron temperature
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$T_e \rightarrow T_e \cdot {\tt factt}
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\cdot {\tt factb}^{\tt ab}$.
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`factn` Real 1 $x > 0$ Numerical factor to rescale the electron density
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$n_e \rightarrow n_e \cdot {\tt factn}
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\cdot {\tt factb}^{\tt ab}$.
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`iscal` Int 1, 2 Model for $n_e$, $T_e$ scaling with $B$:
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1=constant $n_{Greenwald}$ (`ab`=1),
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2=none (`ab`=0).
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`filenmprf` String len$(s) ≤ 24$ Name of file for kinetic profiles
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`psdbnd` Real 1 $x > 0$ Normalized psi value at the plasma boundary where
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$n_e$ is set to zero (typ. $1 ≤ {\tt psdbnd} ≤ 1.1$).
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`sgnbphi` Real 1 -1, +1, 0 Force signum of toroidal B, used if nonzero
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`sgniphi` Real 1 -1, +1, 0 Force Signum of toroidal plasma current $I$, used if nonzero
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`icocos` Int 1-8, 11-18 COCOS index used in the EQDSK equilibrium as defined in [@cocos]:
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----------------------------------------------------------------------------------------------------------------------------
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Table: GRAY input data `gray_params.data` - plasma data {#tbl:input2}
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----------------------------------------------------------------------------------------------------------------------------
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Variable Type Units Valid range Definition
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---------------- ----------- --------- ----------------------- ------------------------------------------------------------
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`iwarm` Integer 0, 1, 2, 3 Absorption model:
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0=none (α=0),
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1=weakly relativistic,
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2=fully relativistic (fast),
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3=fully relativistic (slow).
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`ilarm` Integer 1 $n ≥ 1$ Order of Larmor radius expansion for absorption
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computation ${\tt ilarm}>$ local EC harmonic number.
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`ieccd` Integer 0, 1, 11 Current drive model:
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0=none,
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1=Cohen,
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2=No trapping
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3=Neoclassical.
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`igrad` Integer 0, 1 Ray-tracing model:
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0=optical,
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1=quasi-optical (requires ${\tt nrayr} \ge 5$).
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`idst` Integer 0, 1, 2 Ray-tracing integration variable:
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0=$s$,
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e1=$c \cdot t$,
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2=$S_R$,
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(default=0).
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`dst` Real cm $x > 0$ Spatial integration step.
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`nstep` Integer 1 $0 ≤ n ≤ 8000$ Maximum number of integration steps.
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`istpr` Integer 1 $1 ≤ n ≤ {\tt nstep}$ Subsampling factor for beam cross section
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data output (units 8, 12).
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`istpl` Integer 1 $1 ≤ n ≤ {\tt nstep}$ Subsampling factor for outmost rays
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data output (unit 33).
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`ipec` Integer 1, 2 Grid spacing for ECRH&CD profiles:
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1=equispaced in $ρ_p$,
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2=equispaced in $ρ_t$,
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`nnd` Integer 1 $2 ≤ n ≤ 5001$ Number of points in the ECRH&CD profile grid.
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`ipass` Integer $-2,1, 2$ $\vert{\tt ipass}\vert$=number of passes into plasma:
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-2=reflection at `rwallm`,
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+2=reflection at limiter.
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Surface given in EQDSK.
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`rwallm` Real m $x > 0$ Inner wall radius for 2nd pass calculations,
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used only for `ipass`=$-2$.
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----------------------------------------------------------------------------------------------------------------------------
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Table: GRAY input data `gray_params.data` - ECRH&CD models and code parameters {#tbl:input3}
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----------------------------------------------------------------------------------------------------------------------------
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Variable Type Units Valid range Definition
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---------------- ----------- --------- ----------------------- ------------------------------------------------------------
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`npp` Integer 1 $2 ≤ n ≤ 250$ Number of points in `psin` table
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`psin` real 1 $0 ≤ x ≤$ `psdbnd` Poloidal flux $\psi$ normalized over the value at the LCS
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`Te` real keV $x ≥ 0$ Electron temperature
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`ne` real 10¹⁹m⁻³ $x ≥ 0$ Electron density
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`Zeff` real 1 $x ≥ 0$ Effective charge, $Z_{\rm eff}$
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----------------------------------------------------------------------------------------------------------------------------
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Table: GRAY input data `filenmprf.prf` - plasma profiles {#tbl:profiles1}
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----------------------------------------------------------------------------------------------------------------------------
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Variable Type Units Valid range Definition
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---------------- ----------- --------- ----------------------- ------------------------------------------------------------
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`nsteer` Integer 1 $n ≤ 50$ Number launching conditions in table.
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`gamma` Real deg Steering angle w.r.t. a reference position (unused).
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`alpha0` Real deg $-180 < x ≤ 180$ Poloidal injection angle $α$.
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`beta0` Real deg $-90 ≤ x ≤ 90$ Toroidal injection angle $β$.
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`x0mm` Real mm $X$ coordinate of the launching point.
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`y0mm` Real mm $Y$ coordinate of the launching point.
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`z0mm` Real mm $Z$ coordinate of the launching point.
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`w0xi` Real mm $x > 0$ Beam waist $w_{0,\xi}$ along $\xi$.
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`w0eta` Real mm $x > 0$ Beam waist $w_{0,\eta}$ along $\eta$.
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`d0xi` Real mm $\bar z$ coordinate of beam waist $w_{0,\xi}$,
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$\bar z=0$ at launching point.
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`d0eta` Real mm $\bar z$ coordinate of beam waist $w_{0,\eta}$,
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$\bar z=0$ at launching point.
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`wxi` Real mm $x > 0$ Beam width $w_{\xi}$ at the launching point.
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`weta` Real mm $x > 0$ Beam width $w_{\eta}$ at the launching point.
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`rcixi` Real mm⁻¹ Inverse of phase front curvature radius $1/R_{\xi}$
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at the launching point.
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`rcieta` Real mm⁻¹ Inverse of phase front curvature radius $1/R_{\eta}$
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at the launching point.
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`phiw` Real deg Rotation angle $φ_w$ of the $(\xi_w,\eta_w)$ reference
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system, defined in [@eq:phiwr].
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`phir` Real deg Rotation angle $φ_R$ of the $(\xi_R,\eta_R)$ reference
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system, defined in [@eq:phiwr].
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----------------------------------------------------------------------------------------------------------------------------
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Table: GRAY input data `filenmbm.prf` - launched beam parameters {#tbl:profiles2}
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---------------------------------------------------------------------------------------------------
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Variable Type Units Definition
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---------------- ----------- --------- ------------------------------------------------------------
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`Icd` Real kA EC total driven current $I_{cd}$.
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`Pa` Real MW EC total absorbed power $P_{abs}$.
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`Jphimx` Real MA⋅m⁻² EC peak current density $J_{φ}= dI_{cd}/dA$.
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|
||
`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}
|