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A study of two-fields (B,rotB) of conservative flux (div B = 0), which admits a family of toroidal surfaces of parameter OE on a domain limited by a given surface S, suggests their construction by a Cauchy Arzel method of step by step. Taking into account the Newcomb condition: INTEGRAL f/B ds-B = C**const (OE), which is inherent in a further relation B-$4HrotB = f"DEL"OE, this method is consistent with force-free magnetic fields and with helical equilibria with scalar pressure (P = OE and f = - 1). The method supposes that B is of class C**1. In a minor class B ELEMENT C**2, the equation div B = 0 would introduce an additional Newcomb condition which is generally not satisfied. This construction makes use of the remarkable property of the field B to be the surface gradient of a generating multivalued function Q on a closed surface. Consequently, the initial surface will be given with its normal metric coefficient K; that is to say, B admits a family F* of homotopic surfaces on an infinitesimal domain about S, an element of F*. From this, the periodic part of Q is a solution of a Beltrami equation for the flux conservation of which the numerical resolution is envisaged. The study of these fields is made in a bi-orthogonal system of coordinates. The coefficients of the two fundamental metric forms of magnetic surfaces vary with OE and are interrelated by a sixth order differential system of equations which gives their variation.

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Bibliographic Reference: WRITE TO CEA MENTIONING EUR-CEA-FC 1184 FR, 1983
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