×

zbMATH — the first resource for mathematics

The CHEASE code for toroidal MHD equilibria. (English) Zbl 0922.76240
Summary: We show that the CHEASE code (cubic Hermite element axisymmetric static equilibrium) solves the Grad-Shafranov equation for toroidal MHD equilibria using a Hermite bicubic finite element discretization with pressure, current profiles, and plasma boundaries specified by analytical forms or sets of experimental data points. Moreover, CHEASE allows the automatic generation of pressure profiles marginally stable to ballooning modes or with a prescribed fraction of bootstrap current. The code provides equilibrium quantities for several stability and global wave propagation codes.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
Software:
CHEASE; ERATO; XTOR
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Lütjens, H.; Bondeson, A.; Roy, A., Comput. phys. commun., 69, 287, (1992)
[2] Shafranov, V.D., Zhetf, Sov. phys. JETP, 8, 494, (1958)
[3] Lüst, R.; Schlüter, A., Z. naturforsch., 129, 850, (1957)
[4] Grad, H.; Rubin, H., (), 190
[5] Connor, J.W.; Hastie, R.J.; Taylor, J.B., Phys. rev. lett., 40, 396, (1978)
[6] Rosenbluth, M.N.; Hazeltine, R.D.; Hinton, F.L., Phys. fluids, 15, 116, (1972)
[7] Hazeltine, R.D.; Hinton, F.L.; Rosenbluth, M.N., Phys. fluids, 16, 1645, (1973)
[8] Hirshman, S.P., Phys. fluids, 31, 3150, (1988)
[9] Gruber, R.; Troyon, F.; Berger, D.; Bernard, L.C.; Rousset, S.; Schreiber, R.; Kerner, W.; Schneider, W.; Roberts, K.V., Comput. phys. commun., 21, 323, (1981)
[10] Bondeson, A.; Vlad, G.; Lütjens, H., Phys. fluids B, 4, 1889, (1992)
[11] Grimm, R.C.; Greene, J.M.; Johnson, J.L., Methods comput. phys., 9, 253, (1976)
[12] Grimm, R.C.; Dewar, R.L.; Manickam, J., J. comput. phys., 49, 94, (1983)
[13] Ward, D.J.; Jardin, S.C., Nucl. fusion, 32, 973, (1992)
[14] Lerbinger, K.; Luciani, J.F., J. comput. phys., 97, 444, (1991)
[15] Villard, L.; Appert, K.; Gruber, R.; Vaclavik, J., Comput. phys. reports, 4, 95, (1986)
[16] Jaun, A.; Appert, K.; Lütjens, H.; Brunner, S.; Vaclavik, J.; Villard, L., (), 369
[17] Lao, L.L., Nucl. fusion, 30, 1035, (1990)
[18] Rebut, P.H.; JET team, Plasma physics and controlled nuclear fusion research 1986, (), 31
[19] Rebut, P.H.; Chuyanov, V.; Huguet, M.; Perkins, F.; Barabaschi, P.; Bosia, G., Plasma physics and controlled nuclear fusion research 1994, ()
[20] Troyon, F.; Gruber, R.; Sauremann, H.; Semenzato, S.; Succi, S., Plasma physics and controlled fusion, 26, 209, (1984)
[21] Turnbull, A.D.; Secrétan, M.A.; Troyon, F.; Semenzato, S.; Gruber, R., Comput. phys. commun., 66, 391, (1986)
[22] Delucia, J.; Jardin, S.C.; Todd, A.M.M., J. comput. phys., 37, 183, (1980)
[23] Freidberg, J.P., Ideal magnetohydrodynamics, (1987), Plenum Press New York
[24] Mercier, C., Nucl. fusion suppl., 1, 47, (1960)
[25] Graeub, W., Die grundlehren der mathematischen wissenschaften, band XCVII, lineare algebra, (), 157
[26] Glasser, A.H.; Greene, J.M.; Johnson, J.L., Phys. fluids, 18, 875, (1975)
[27] Jardin, S.C.; Bhattacharjee, A.; Bondeson, A.; Chance, M.S.; Cowley, S.C.; Eriksson, G.; Greene, J.M.; Hofmann, F.; Hughes, M.; Iacono, R.; Ignat, D.W.; Kessel, C.; Lütjens, H.; Manickam, J.; Monticello, D.A.; Perkins, F.W.; Phillips, M.; Pomphrey, N.; Ramos, J.; Reiman, A.H.; Rutherford, P.H.; Valeo, E.J.; Villard, L.; Wang, C.; Ward, D.J., (), 285
[28] Strang, G.; Fix, G., An analysis of the finite element method, (1973), Prentice-Hall Englewood Cliffs, NJ · Zbl 0278.65116
[29] Morton, K.W., Comput. phys. report, 6, 1, (1987)
[30] Bondeson, A.; Fu, G.Y., Comput. phys. commun., 66, 167, (1991)
[31] Solovev, L.S., Zh. tekh. fiz., Jetp, 26, 400, (1968)
[32] Roy, A.; Troyon, F., Theory of fusion plasmas, (), 175
[33] Forsythe, G.E.; Malcolm, M.A.; Moler, C.B., Computer methods for mathematical computations, (), 70
[34] Press, W.H.; Flannery, B.P.; Teukolsky, S.A.; Vetterling, W.T., Numerical recipes, (), 86
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.