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Manuscript Title: The CHEASE code for toroidal MHD equilibria.
Authors: H. Lutjens, A. Bondeson, O. Sauter
Program title: CHEASE
Catalogue identifier: ADDH_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 97(1996)219
Programming language: Fortran.
Computer: CRAY.
Operating system: Unicos, SunOS, HP-UX.10.
RAM: 8M words
Word size: 64
Peripherals: disc.
Keywords: Plasma physics, Equilibrium, Grad-shafranov equation, Cubic hermite finite Elements, Mapping to magnetic Flux coordinates, Ballooning modes, Local interchange modes, Bootstrap current.
Classification: 19.6.

Nature of problem:
CHEASE [1] solves the Grad-Shafranov equation [2, 3, 4] for the MHD equilibrium of a Tokamak-like plasma with pressure and current profiles specified by analytic forms or sets of data points. Equilibria marginally stable to ballooning modes [5] or with a prescribed fraction of bootstrap current [6, 7, 8] can be computed. The code provides a mapping to magnetic flux coordinates, suitable for MHD stability calculations or global wave propagation studies. The code computes equilibrium quantities for the stability codes ERATO [9], MARS [10], PEST [11, 12], NOVA-W [13] and XTOR [14] and for the global wave propagation codes LION [15] and PENN [16].

Solution method:
The two-dimensional MHD equilibrium (Grad-Shafranov) equation is solved in variational form. The discretization uses bicubic Hermite finite element with continuous first order derivatives for the poloidal flux function Psi. The nonlinearity of the problem is handled by Picard iteration. The mapping to flux coordinates is carried out with a method which conserves the accuracy of the cubic finite elements.

Unusual features:
The code uses routines from the CRAY libsci.a program library. However, all these routines are included in the CHEASE package itself. If CHEASE computes equilibrium quantities for MARS with fast Fourier transforms, the NAG library is required. CHEASE is written in standard FORTRAN-77, except for the use of the input facility NAMELIST. CHEASE uses variable names with up to 8 characters, and therefore violates the ANSI standard. CHEASE transfers plot quantities through an external disk file to a plot program named PCHEASE using the UNIRAS or the NCAR plot package.

References:
[1] H. Lutjens, A. Bondeson, A. Roy, Comput. Phys. Commun. 69, 287 (1992).
[2] V.D. Shafranov, ZhETF 33, 710 (1957); Sov. Phys. JETP 8, 494 (1958).
[3] R. Lust, A. Schluter, Z. Naturforsch. 129, 850 (1957).
[4] H. Grad and H. Rubin, Proc. of 2nd Int. Conf. on the Peaceful Uses of Atomic Energy (United Nations, Geneva, 1958), Vol. 31, 190.
[5] J.W. Connor, R.J. Hastie, J.B. Taylor, Phys. Rev. Lett. 40, 396 (1978).
[6] M.N. Rosenbluth, R.D. Hazeltine, F.L. Hinton, Phys. Fluids 15, 116 (1972).
[7] R.D. Hazeltine, F.L. Hinton, M.N. Rosenbluth, Phys. Fluids 16, 1645 (1973).
[8] S.P. Hirshman, Phys. Fluids 31, 3150 (1988).
[9] R. Gruber, F. Troyon, D. Berger, L.C. Bernard, S. Rousset, R. Schreiber, W. Kerner, W. Schneider, K.V. Roberts, Comput. Phys. Commun. 21, 323 (1981).
[10] A. Bondeson, G. Vlad, H. Lutjens, Phys. Fluids B4, 1889 (1992).
[11] R.C. Grimm, J.M. Greene, J.L. Johnson, Methods Comput. Phys. 9, 253 (1976).
[12] R.C. Grimm, R.L. Dewar, J. Manickam, J. Comput. Phys. 49, 94 (1983).
[13] D.J. Ward, S.C. Jardin, Nucl. Fusion 32, 973 (1992).
[14] K. Lerbinger, J.F. Luciani, J. Comput. Phys. 97, 444 (1991).
[15] L. Villard, K. Appert, R. Gruber, J. Vaclavik, Comput. Phys. Reports 4, 95 (1986).
[16] A. Jaun, K. Appert, H. Lutjens, S. Brunner, J. Vaclavik, L. Villard, Theory of Fusion Plasmas, Proc. Int. Workshop, Varenna, 1994, (Editrice Compositori, Bologna, 1994), p.369.