A differential equation for the ambipolar electric field in a multiple-helicity torsatron

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Abstract
In a torsatron, the ambipolar electric field is obtained by equating the ion and electron fluxes. This formulation, when solved simultaneously with the density and temperature rate equations, gives continuous electric fields but may lead to the radial derivative of the electric field being discontinuous. This unphysical situation arises from the neglect of the finite orbit deviation from the flux surfaces. If the fluxes are calculated to higher order in inverse aspect ratio to include the finite orbit deviation, then a second-order differential equation is obtained that will give a continuous first derivative for the electric field.