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Manuscript Title: ERATO stability code.
Authors: R. Gruber, F. Troyon, D. Berger, L.C. Bernard, S. Rousset, R. Schreiber, W. Kerner, W. Schneider, K.V. Roberts
Program title: ERATO
Catalogue identifier: ABVS_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 21(1981)323
Programming language: Fortran.
Computer: CDC CYBER 170-720.
Operating system: NOS BE.
RAM: 35K words
Word size: 60
Peripherals: disc.
Keywords: Plasma physics, Ideal mhd, Variational principle, Finite elements, Spectrum, Instabilities, Eigenfunctions, Equilibrium.
Classification: 19.6.

Nature of problem:
This computer code treats the stability of a Tokamak-like plasma described by the ideal linearized magnetohydrodynamic (MHD) equations. The plasma is considered to be in an equilibrium state. After perturbation of such an equilibrium, the evolution of the normal modes can be calculated by linearizing the ideal MHD equations. Any mode (unstable or stable) of the spectrum can be examined.

Solution method:
The variational form of the 2D ideal MHD equations is treated by a finite hybrid element approach, which proves to be well suited to describe the features of the problem with sufficient accuracy. The eigenvalue problem Ax= Omega squared Bx is solved by VEKIT (an inverse vector iteration), a subprogram of the block matrix library HYMNIABLOCK. The code consists of 5 main programs (ERATO 1 to ERATO 5) linked together by disk files.

Unusual features:
The code uses subroutines from two program libraries, the utility routines of the CDC OLYMPUS package and the eigenvalue package HYMNIABLOCK. However, all the required subroutines are included in the ERATO package itself. ERATO is written in STANDARD FORTRAN, except for use of the input facility NAMELIST which is available on most computers, and the CDC statement ENCODE which is used in ERATO 5. The plotting routines PLOTS, PLOT and SYMBOL used in ERATO 5 must be written to suit the local computer system and details of their arguments given. ERATO also uses the CDC function subprogram DATE which picks up the actual date for plotting, and LOCF which gives the base address of an array. The programs ERATO 1-5 are arranged so that they can readily be combined into a single program if sufficient storage is available.

Running time:
The running time is proportional to the number of poloidal flux surfaces N Psi, and to the cube of the number of angular intervals Nx when Nx>20. A typical case with 24*24 intervals in Psi and x takes 15 min per eigenvalue on a CDC 6500.