Highly elongated field-reversed configuration (FRC) equilibria are computed in a straight conducting cylinder for the pressure profile p′(ψ) = cH(ψ), where H(x) is the Heaviside function. The equilibria are found by inverting the Grad–Shafranov equation by means of a Green’s function and by solving the resulting nonlinear integral equation. Long equilibria are obtained only for values of the constant c very near a critical value: the equilibria change from 2:1 elongated to infinitely long as c varies by only 0.3%. This criticial value of c is predicted by the average beta condition.
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Spencer et al. (1982) studied this question.
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