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The boundary term in the energy integral (105) is superfluous and should be dropped. If we use the Jacobian relation (86) to transform the dummy variables of integration from ψ, θ, to x, y (recalling that B = Bmax = const. at the ends), we see that this term reduces to the integral of a fixed function of x and y over a fixed region of the (x, y) plane. In other words, it reduces to a pure constant.
A study is made of the equilibrium and stability of a magnetically confined collisionless plasma in the paraxial or ‘long, thin’ limit. The main field is poloidalaxisymmetric, and a stabilizing quadrupole field is superimposed.