Plasma Composition

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TRANSP can accommodate up to 7 thermal ion species which may be isotopes of Hydrogen, Helium or Lithium:

NG: The initial number of thermal ion species to be used.

NGMAX: The maximum number of thermal ion species to be used at any point in the run. This accommodates the possibility that the number of ion species present may be increased from its initial value via the use of pellets or neutral beams comprising new species.

APLASM(i): The atomic weight of bulk ion species i in units of the proton mass.

BACKZ(i): The nuclear charge of bulk ion species i. As TRANSP only accepts isotopes of Hydrogen, Helium or Lithium, this may take the values 1,2 or 3.

Single Impurity Model

AIMP : The atomic weight of the impurity species in units of the proton mass.

XZIMP : The charge of the impurity species.

Multiple Impurity Model

TRANSP can include up to 8 impurity species at a time. In this case it is necessary to either provide profile data via a Ufile or to manually fix the relative composition of the different species. The total impurity concentration is then rescaled to be consistent with the $Z_{\mathrm{Eff}}$ input data. The Ufile data is input using the PRESIM and EXTSIM variables which, unlike other TRDAT namelist entries, can take a comma separated list of values indicating the sources of data for the different impurity species present. For more details on how to use this feature, see the PPPL TRANSP help pages.

AIMPS : A comma separated list giving the atomic weights of the impurity species to be used.

XZIMPS : A comma separated list giving the charges of the impurity species to be used.

If Ufile data is being used for N species, these N species should be listed first and obviously in the same order for all variables. If no Ufile data is present for some of the impurities then their density must be specified as a fraction of the electron density using the following variables. If all impurities are being specified in this way then these variables can be passed comma separated lists in the same way as the variables above:

DENSIM(i) : The density of impurity species i on axis as a fraction of the electron density on axis. If DENSIMA(i) is unset this sets the density of this impurity species as a fraction of the electron density everywhere. If Ufile data is provided for this species it is renormalised to this value on axis.

DENSIMA(i) : The density of impurity species i at the plasma boundary as a fraction of the electron density at the boundary. If DENSIM(i) is unset this sets the density of this impurity species as a fraction of the electron density everywhere. If Ufile data is provided for this species it is renormalised to this value at the edge.

If both DENSIMA(i) and DENSIM(i) are set for a particular impurity species and no Ufile data is provided then the following functional form for the impurity profile is used, matching the specified values at the core and edge:

N_x( χ ) = DENSIM + χ^XZFA1 × (1 + (XZFA2-XZFA1) × (χ-1)) × ( DENSIMA - DENSIM )

Where χ = $\sqrt{{\Psi }_{\mathrm{Tor}}(Normalised)}$. The default values are XZFA1=2 and XZFA2=0.

Different Ufile data can be provided for each impurity species. If a 1D Ufile is provided, the impurity density profile is considered independent of time. If a 2D Ufile is provided a time dependent profile for a single charge state either specified in the Ufile or via XZIMPS is read. If a 3D Ufile is provided the third axis is considered to specify the charge state of the impurity. The flag NADVSIM can be set to 1 to instead set the distribution over charge states for the impurity from coronal equilibrium. If Ufile data is not being used, this setting is forced.

$Z_{\mathrm{Eff}}$

$Z_{\mathrm{Eff}}$ is used in two different ways during the course of a TRANSP run. Firstly it is used in conjunction with quasi-neutrality and input data for the species densities in determining the composition of the plasma, this is referred to as composition $Z_{\mathrm{Eff}}$. Secondly it is used in the calculation of the plasma resistivity when solving the poloidal field diffusion equation, this is referred to as the resistivity $Z_{\mathrm{Eff}}$. It is important to remember that TRANSP need not treat these two parameters in the same way and can use different prescriptions for determining them. It is only the composition $Z_{\mathrm{Eff}}$ that necessarily obeys

n_e Z_Eff = ∑ _s Z_s ² n_s

If the poloidal field diffusion equation is not being solved due to, for instance, input data for q being given, then only composition $Z_{\mathrm{Eff}}$ is used.

Composition $Z_{\mathrm{Eff}}$

NLZEFM : Set this to TRUE in order to use the calculated value of the resistivity $Z_{\mathrm{Eff}}$ for the composition $Z_{\mathrm{Eff}}$. Set CZEFFM to a non-zero constant to use a multiple of the resistivity $Z_{\mathrm{Eff}}$. This option is only available when solving the PFDE predictively.

NLZFIN : Set this flag to TRUE to read in a 1D Ufile of $Z_{\mathrm{Eff}}$ as a function of time using trigraph ZEF. The $Z_{\mathrm{Eff}}$ profile will be considered flat in this instance.

NLZFI2 : Set this flag to TRUE to read in a 2D Ufile containing $Z_{\mathrm{Eff}}$ profile data using trigraph ZF2.

NLZEFA : Set this flag to TRUE to read in a 1D Ufile of edge $Z_{\mathrm{Eff}}$ as a function of time using trigraph ZFA or to use a constant value for the edge $Z_{\mathrm{Eff}}$ specified by namelist entry XZEFFAI. For this to be used it is required that either NLZFIN=TRUE or NLVISB=TRUE & NLZVBR=TRUE. In the former case the input data provides the value of $Z_{\mathrm{Eff}}$ on axis directly, in the latter case a value consistent with the input visible Bremsstrahlung data is determined. The profile used for $Z_{\mathrm{Eff}}$ then has the form:

$Z_{\mathrm{Eff}}$( χ ) = $Z_{\mathrm{Eff}}$(0) + χ^XZFA1 × (1 + (XZFA2-XZFA1) × (χ-1)) × ( $Z_{\mathrm{Eff}}$(1) - $Z_{\mathrm{Eff}}$(0) )

Where χ = $\sqrt{{\Psi }_{\mathrm{Tor}}(Normalised)}$. The default values are XZFA1=2 and XZFA2=0.

NLVISB : Set this flag to TRUE to read in a 1D Ufile of chordal visible Bremsstrahlung data using trigraph VSB. If NLZVBR is also set to TRUE a value of $Z_{\mathrm{Eff}}$ is calculated which is consistent with the input Bremsstrahlung data. In this case the following inputs can also be set to define the viewing chord:

• RVISB : The radial start point of the chord (cm)
• YVISB : The elevation of the start point of the chord (cm)
• THVISB : The poloidal angle of the chord (degrees - +ve values indicate 'up')
• PHVISB : The toroidal angle of the chord (degrees)

NLVB2 : Set this flag to TRUE to read in a 2D Ufile of Bremsstrahlung emissivity data using trigraph VB2. If NLZVB2 is also set to TRUE a profile of $Z_{\mathrm{Eff}}$ is calculated which is consistent with the input Bremsstrahlung data.

XZEFFI : In the absence of any other input data, this namelist entry can be set to a constant to be used for $Z_{\mathrm{Eff}}$.

It is possible to switch in time between different methods of calculating the composition $Z_{\mathrm{Eff}}$. For information on this see the PPPL TRANSP website.

Time Switching

The following controls allow the user to switch between different schemes for determining the composition Z_Eff profile over the course of the run. Be aware that these controls effectively overwrite the ones in the previous section when set (by default there is no time switching and the previous controls apply). The scheme to be used for determining the Z_Eff profile in the i^th time interval between times TZEFMOD(i-1) and TZEFMOD(i) is set using the switch NZEFMOD(i). The following options are available:

• -1 : Freeze Z_Eff in time at the previous value (not valid for the first time period).


• 0 : Use a flat Z_Eff profile with a constant value given by XZEFFI.


• 1 : Use the resistivity Z_Eff which may be a profile or a scale. This sets NLZEFM=TRUE.


• 2 : Use a flat Z_Eff profile with a time dependent value given by data input using trigraph ZEF. This sets NLZFIN=TRUE.


• 3 : Use a time dependent Z_Eff profile taken from input data using the trigraph ZF2. This sets NLZFI2=TRUE.


• 4 : Use a flat Z_Eff profile with a time dependent value calculated from visible Bremsstrahlung data input using trigraph VSB. This sets NLZVBR=TRUE.


• 5 : Use a time dependent Z_Eff profile calculated from input visible Bremsstrahlung profile data input using the trigraph VB2. This sets NLZVB2=TRUE.


• 6 : Reads a 2D Ufile of impurity density data for a single species and then calculates the Z_Eff profile. This sets NLZFXI=TRUE.


• 7 : Use the analytic Z_Eff profile specified above constrained using edge and axis data. This sets NLZFIN=TRUE and NLZEFA=TRUE


• 8 : Use the analytic Z_Eff profile specified above constrained using edge and chordal visble Bremsstrahlung data. This sets NLZVBR=TRUE and NLZEFA=TRUE


• 9 : Reads a 2D Ufile of impurity density data for a single species and then calculates the Z_Eff profile. It then renormalises the profile based on chordal visible Bremsstrahlung data. This sets NLZFXI=TRUE and NLZVBR=TRUE.


• 10 : Z_Eff is computed from multiple impurities. This sets NLZSIM=TRUE.


• 11 : Z_Eff is computed from multiple impurity data and then scaled by chordal visible Bremsstrahlung data. This sets NLZSIM=TRUE and NLZVBR=TRUE.

DTZEFMOD(i) : This sets the timescale over which the Z_Eff profile is smoothly merged from its value calculated using scheme i to its value calculated using scheme i+1. The default is 0.01s.

Resisitivity $Z_{\mathrm{Eff}}$

As described in more detail in the Magnetics section, one can use the measured surface voltage and plasma current to constrain the value of the resistivity $Z_{\mathrm{Eff}}$. This is achieved by setting NLMDIF=TRUE to turn on predictive solution of the PFDE, NLPCUR=TRUE to match the input plasma current data in the solution of the PFDE and NLVSUR=TRUE to also match the surface voltage. The following switch controls how the profile of the resistivity $Z_{\mathrm{Eff}}$ is determined.

NLZFIM=FALSE : The resistivity $Z_{\mathrm{Eff}}$ is made proporional to the composition $Z_{\mathrm{Eff}}$. If NLVSUR=TRUE then the proporionality constant is fixed so as to match the surface voltage, otherwise the relation between the two is given by:

$Z_{\mathrm{Eff}}$ (Composition) = CZEFFM × $Z_{\mathrm{Eff}}$ (Resistivity)

NLZFIM=TRUE : In this case the $Z_{\mathrm{Eff}}$ profile is given by:

$Z_{\mathrm{Eff}}$( χ ) = $Z_{\mathrm{Eff}}$(1) + ( $Z_{\mathrm{Eff}}$(ζ) - $Z_{\mathrm{Eff}}$(1) ) × ( 1 - χ² )^XPZEFF

The value of XPZEFF must be given in the namelist as well as a value for

XPZEFRAT = (Z_Eff(1)-1)/(Z_Eff(ζ)-1)

If NLVSUR=TRUE then the resistivity Z_Eff will be adjusted to match the surface voltage data, otherwise the namelist value XZEFIM sets the central resistivity Zeff value.

If NLVSUR=FALSE, a constant resistivity Z_Eff can be specified by selecting NLZFIM=TRUE and setting XZEFIM to the desired value.

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