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Manuscript Title: BALDUR: a one-dimensional plasma transport code.
Authors: C.E. Singer, D.E. Post, D.R. Mikkelsen, M.H. Redi, A. McKenney, A. Silverman, F.G.P. Seidl, P.H. Rutherford, R.J. Hawryluk, W.D. Langer, L. Foote, D.B. Heifetz, W.A. Houlberg, M.H. Hughes, R.V. Jensen, G. Lister, J. Ogden
Program title: BALDUR
Catalogue identifier: ABBS_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 49(1988)399
Programming language: Fortran.
Computer: CRAY-1.
Operating system: CRAY TIMESHARING SYSTEM.
RAM: 721K words
Word size: 64
Peripherals: disc.
Keywords: Plasma physics, Thermonuclear fusion, Tokamak, One-dimensional, Transport.
Classification: 19.11.

Nature of problem:
The purpose of the version of the BALDUR code documented here is to calculate the evolution of plasma parameters in an MHD equilibrium which can be approximated by concentric circular flux surfaces. Transport of up to six species of ionized particles, of electron and ion energy, and of poloidal magnetic field is computed. A wide variety of source terms are calculated including those due to neutral gas, fusion and auxiliary heating. The code is primarily designed for modeling tokamak plasmas but could be adapted to other toroidal confinement systems.

Solution method:
The plasma and the poloidal magnetic field encircling the plasma column are described by up to nine dependent variables, including up to six particle densities, ion energy, electron energy, and poloidal magnetic field. These variables are functions of time vector t and vector r. The code was designed for a circular poloidal cross section but can be applied to constant ellipticity ellipses with neutral beam injection. The basic equations form a set of parabolic initial value equations with nonlinear coefficients and source terms. The equations are differenced with a conservative Crank-Nicholson scheme with an adjustable degree of implicitness. Time centering of the source terms and transport coefficients is accomplished using a predictor-corrector scheme or by extrapolation methods. Convective terms are handled with a variety of up-stream and down-stream weighting schemes. Monte Carlo techniques are used to compute (1) alpha-particle heating, (2) neutral gas transport, and (3) the ionization of neutral beams. The evolution of the fast ion distribution, resulting from neutral beam injection, is computed as a function of energy and pitch angle using a simple multigroup Fokker-Planck scheme.

Restrictions:
BALDUR has been applied to a wide variety of tokamak simulations, and contains a variety of checks which terminate the computation if it goes outside the range of validity of the model. The most commonly encountered of these gives a message that the thermal velocity of the ions exceeds the neutral beam injection energy. Thermal collapse of the plasma edge will often drive the time step below a prescribed minimum. However, care must be taken to provide physically reasonable initial and boundary conditions and to examine carefully the assumptions used in modeling a given device, especially when operating outside the range of parameters covered by published applications. For example, line radiation losses assume coronal equilibrium, and users must use the output to support their own calculations to assess the validity of this assumption. A number of common input errors are checked at the beginning of each computation.

Unusual features:
The majority of BALDUR is written in OLYMPUS Fortran. NAMELIST is used for specifying input parameters. A choice among a variety of graphical and printed outputs is provided. The code also accesses U.S. Magnetic Energy Fusion Computer Center library subroutines such as their random number generator, which must be used to exactly reproduce the test case given below.

Running time:
Execution time is typically but not exclusively between three and ten minutes on the MFECC CRAY, depending on the complexity and length of the discharge simulation, and the sophistication of the physical models taken from among the various choices available in BALDUR.