Direct use of input magnetic equilibrium

This option is selected with LEVGEO=8

The information that must be provided to TRANSP to represent an equilibrium solution includes the 2D flux surface geometry as a function of minor radius (toroidal flux), poloidal angle, and time; 1D profiles for $q$, $R\cdot Btoroidal$, and pressure $p$ as functions of minor radius and time; and 0D time histories of total toroidal and poloidal flux. A TRANSP utility called scrunch2 can extract this data from EFIT equilibria in an MDS+ database tree and write them to legacy format UFiles that can be read by the TRANSP preprocessor trdat. The trdat utility now also has the ability to retrieve this information from an IMAS database, without the need for scrunch2 or UFiles. Because TRANSP was co-developed with PPPL’s TFTR tokamak, which had a circular plasma cross-section, it made sense at the time to use a moments representation of the equilibrium geometry, with cylindrical $R$ and $Z$ for a plasma surface provided as cosine and sine expansions in poloidal mode number respectively (or full sine and cosine for both $R$ and $Z$ for non-up-down-symmetric surfaces). This moments representation is still supported by the code. Since 2002, however, TRANSP has also supported the alternative to read in and use $R(x,\theta,t)$ and $Z(x,\theta,t)$, which avoids truncation errors in the representation of the more highly-shaped cross-sections of modern tokamaks. TRANSP can also read the poloidal flux function $\psi $𝜓(R,Z,t), which provides the field solution outside the last closed flux surface. These last three functions are always present in the representation read from IMAS.

When $\psi(R,Z,t)$ is provided, TRANSP performs additional analysis on the equilibrium. It attempts to locate all X-points, the magnetic axis, and the bounding point of the plasma, which may be either an X-point or a location on the limiter. For X-point-bounded plasmas, it has the option to trace the separatrix for interface with scrape-off-layer codes. It can also compute the normalized inductances at the analysis boundary and the separatrix.

In addition, if logical variable NLPSIRZ_FLUX is set to .TRUE. in the input namelist, the function $\psi(R,Z,t)$ will be used to compute the locations of the flux surfaces (overriding the provided geometry data) and the enclosed poloidal flux within each surface. When this poloidal flux profile is combined with the provided $q$ and $R\cdot B_{toroidal}$ profiles, the equilibrium is overdetermined, which can be resolved in a number of ways determined by the choice of input variable NPSIRZ_MODE. By default (NPSIRZ_MODE=102), TRANSP will use its self-evolved q profile combined with $\psi(R,Z,t)$ to recalculate the toroidal flux profile, which in turn affects the geometry mapping. If instead NPSIRZ_MODE=-102, the input $q$ profile will be used for this calculation. To give priority to $R\cdot B_{toroidal}$, choose NPSIRZ_MODE=103, which will recompute q based on the poloidal and toroidal fluxes; or NPSIRZ_MODE=-103, which uses the provided $R\cdot B_{toroidal}$ and $q$ and recomputes the equilibrium to match $\psi(R,Z,t)$, ignoring the provided pressure profile.

The input UFILES can be generated running scrunch2. LEVGEO=8 needs either the PREMMX/EXTMMX UFILE or the {RFS,ZFS} UFILES for the magnetic equilibrium evolution, but not both.
Below is a list of the UFILES and namelist variables. Out of all UFILES generated by scrunch2, only the MMX, QPR and LIM files are needed to run LEVGEO=8, others are optional.

NOTE: the output of scrunch2 is in MKS units, unless otherwise specified. Need to set LFIXUP=2 in the namelist to inform TRANSP that units must be converted and that the radial and time coordinates sequence in the UFILE should be checked and swapped, if needed (i.e. whether the profile array needs to be transposed).

PREMMX/EXTMMX
Magnetic equilibrium moments.
PRERFS,EXTRFS
Magnetic equilibrium geometry described with explicit flux surfaces R(t,theta,x)
PREZFS,EXTZFS
Magnetic equilibrium geometry described with explicit flux surfaces Z(t,theta,x)
PREQPR/EXTPQR
Safety factor profile. Define also NRIQPR=5 in the namelist. Important: Contrary to other profiles, the q profile in TRANSP MUST be provided as a function of the sqrt of normalized toroidal flux. No other coordinate is accepted when using LEVGEO=8.
PREGBR/EXTGBR
(RBT) profile. If this UFILES is provided together with the 1D UFILE PRERBZ/EXTRBZ, the 2D data will overwrite the 1D data. Include also NRIGRB=5 in the namelist. This UFILE is optional.
PREPRS/EXTPRS
Pressure profile generated by scrunch2. If density and temperature profiles from Thomson scattering are available, then it is advised to use these, since the pressure profiles generated by scrunch2 come directly from EFIT or equivalent. Unless the EFIT (or equivalent) equilibrium has been contrained by kinetic profiles and MSE data, it is not advised to use the PREPRS/EXTPRS UFILE. Also, this file is not necessary to use LEVGEO=8.
PRETRF/EXTTRF
Total enclosed toroidal flux vs time.
PREPLF/EXTPLF
Total enclosed poloidal flux vs time.
PREPSI/EXTPSI
External field evolution from EFIT (or equivalent equilibrium reconstruction), ψ(t,R,Z). By convention ψ=0 on the magnetic axis. This UFILE is optional.
PREPF0/EXTPF0
ψ(t) on the magnetic axis. Together with the PREPSI/EXTPSI for ψ(t,R,Z), this file is used to generate the poloidal flux ψ=RAφ. This file is optional, but is required if the PREPSI/EXTPSI UFILE is provided.
PRELIM/EXTLIM
Limiter location from EFIT, time invariant contour (R,z) expressed as a Z vs R UFILE.

Output profiles and metrics

When running with the option LEVGEO=8, a full metric solution to the MHD fixed boundary equilibrium problem is generated. This includes the location of the closed flux surfaces and the para/diamagnetic correction to the toroidal field due to poloidal plasma current (g function).

Note that when using LEVGEO=8, it is still possible to turn-on the poloidal field diffusion calculations. In this case, it is important to understand what effect this has when comparing the equilibrium calculated by TRANSP and the input equilibrium calculated by EFIT (or an equivalent free-boundary magnetic equilibrium solver).

The pressure profile used by TRANSP is not the same used by EFIT. The contribution from the fast ion pressure and from the rotation are included in the calculation of the magnetic equilibrium. The contribution of the bootstrap current is also included in the calculation. The internal g=(RBT) profile is obtained from a surface-averaged Grad-Shafranov solution, which will be slightly different than that in EFIT.

If the poloidal field diffusion is calculated, then also the q profile is different from the input profile. Thus, comparison of input and output profiles of q, g and pressure quantify the magnitude of deviation with EFITprofiles and total flux. Note that - if the input q profile is enforced in TRANSP when evolving the poloidal field diffusion, there are still differences at the edge when comparing with the input profile. This is a consequence of TRANSP having to satisfy the boundary conditions for total current, which cause the edge q values to be modified.