Short DescriptionThe relativistic Collisional/QuasiLinear 3D code CQL3D solves a Bounce-Averaged Fokker-Planck equation to obtain the 3 1/2-D distributions of electrons and multispecies ions, resulting from the balance between collisions, RF/neutral beam sources and applied toroidal electric field, in toroidal geometry. (3 1/2-D refers to 2 velocity, 1 radius, and implicit treatment of the poloidal variation through the bounce-averaging.) Steady-state and time-dependent solutions are supported.
Dates/Active Use1985 to present
AuthorsR.W. Harvey and M.G. McCoy, Yu. Petrov
Purpose/Function/Special FeaturesThe overall aim for CQL3D is to create a general facility for the accurate calculation of heating and current drive in tokamaks. To the extent possible, all the physics effects which are known to be important in such calculations should be included. CQL3D is a multi-species, 2D-in-momentum-space, 1D in noncircular plasma radial cooordinate, fully relativistic, bounce-averaged, collisional/quasilinear Fokker-Planck equation solver. It is run in combination with LH, FW, EC and EBW ray tracing or full-wave (AORSA and TORIC-LH) rf data, the FREYA neutral beam deposition package, and a given toroidal electric field, thereby providing a general model for the distortion of the electron and ion distribution functions resulting from auxiliary heating and current drive injected from the plasma periphery. The distributions are taken to be toroidally symmetric and independent of azimuthal angle about the ambient magnetic field. Radial drifts are neglected. With the bounce-average, account is taken of variations as a function of (non-circular) radial coordinate, poloidal angle, and two momentum-space directions. A kinetic bootstrap current calculation is included. The code may be run with separate 2D momentum space solves on each flux surface, on in 3D mode including radial transport according to prescribed diffusion and pinch terms.
Although the focus of the code has been on electrons, it is a multispecies code, i.e., it can treat electron and multiple ion distributions simultaneously. The NFREYA neutral beam deposition module is coupled in for modeling of neutral beam current drive.
Further description of the code is available in Ref. , essentially The CQL3D Manual, below. It is founded on the 2D-in-velocity bounce-averaged Fokker-Planck CQL code, with RF/ray tracing methods first appearing in  . An early application of the code, indicating its versatility, was synergy studies between fast wave, lower hybrid, and electron cyclotron waves , and below.
Basic AlgorithmsThe steady state distributions and the radial rf absorption profile are obtained by iteration between (1) the Guassian elimination solution of the Fokker-Planck equation for the steady state on each flux surface, and (2) the rf energy transport equation integrated along a ray.
The computational scheme for time advancement consists of an alternating direction implicit scheme, between the two momentum-space variables and the radial variable. The momentum-space equation is solved in a fully implicit, direct gaussian elimination scheme previously developed for the 2D in momentum-space CQL code. Similarly, the radial variable is advanced fully implicitly, presently by a splitting algorithm alternating with the velocity-space advancement. More recently, sparse-matrix iterative techniques have been used for a fully-implicit solution of the 3D (2V,1R) equations.
Coupled DiagnosticsThe distribution functions from CQL3D are coupled to calculations of:
Key ResultsCQL3D results have strongly influenced the course of several important rf current drive experiments and proposals, specifically (1) experiments at GA and collaboration with Kurchatov Institute, Moscow, (2) implementation and interpretation of the lower hybrid current profile control experiments on the ASDEX experiment and the associated planning for the PBX lower hybrid current profile control- MHD second stability region-experiment, (3) interpretation of fast wave current drive (FWCD) and ECCD experiments at GA[7,8], and (4) consideration of FWCD synergy with electron cyclotron resonance heating (ECRH), and electron cycltron CD  in tokamak reactor environments.
An ECCD result first obtained unambiguously by CQL3D(), is that current drive by outside (i.e., outboard side) launch of the rf power is strongly preferred to inside launch, based on current drive efficiency. For inside launch, ECCD efficiency at low power is about one-half of that for the outside launch; as rf power increased, the inside launch efficiency can decrease and even pass through zero. In addition, outside launch efficiency doubles at high rf power. As a result of CQL3D, a new outside launch configuration was implemented in DIII-D.
CQL3D current drive results have since been shown to agree in detail with DIII-D experimental data near both the first and second cylcotron harmonics.[7,8].
The code has provided detailed estimates of EC current drive in ITER, contributing strongly to the advancment of this scheme for current profile control .
Application of the code has been made to several additional tokamak experiments: FT-1 (Joffe), Tore Supra, T-10, TdeV, Versator-II. The code has lead in devolpment of similar codes in Europe and Japan.
New applications are being made to the disruption/runaway electron problem.
Radial transport modeling proved to be a decisive factor in interpretation of the TCV ECCD experiment  and the MST reversed field pinch. The CQL3D code incorporates a variant, CQLP, which solves the 3D Fokker-Planck collisional problem along magnetic field lines, including the parallel streaming term, one flux surface at a time[16, 17].
Further work is being carried out on the parallel-transport Fokker-Planck resulted in the FPET code (renamed STELLA, after further additions) which models parallel electron transportthe electron streaming term along field lines, and obtains the self-consistent parallel electric field under the condition of equal electron and ion fluxes to divertor plate. Additional boundary conditions and RF quasilinear diffusion have been incorporated.
The fully nonlinear and fully relativistic collision operator option has been benchmarked. Current work  includes addition of a finite-orbit-width (FOW) option in the code, based on theory developed by Kupfer. Ref.  reports validation work with the NSTX spherical tokamak at Princeton Plasma Physics Laboratory. Report  provides a detailed description of the FOW enhancement of CQL3D, and is submitted for publication.
New work (2015) is aimed at a time-dependent continuum 2D-in-V, 2D-in-space Fokker-Planck code for axisymmetric mirror devices, coupling in neutral beam and RF heating, and a neutrals code. This work is extending Ref.  to multispecies, and is combined with the self-consistent parallel electric field and divertor boundary conditions as employed in Ref. .