Modifying the geometry of stellarator coils in order to minimize the inter-coil electromagnetic forces

The three-dimensional shaping of external current-carrying coils needed to confine plasmas in stellarators can result in complicated coil geometry, making it difficult to design economically attractive fusion power plants based on the stellarator concept. We aim to lessen the inter-coil electromagnetic forces by minimizing the magnetic field present outside of the plasma volume through modifying the geometry of the stellarator coils. The objective function is the sum of (i) the traditional quadratic flux passing through a given boundary, so that a desired plasma boundary is achieved, (ii) a coil-length term, so that the coils do not become too long, and (iii) a magnetic energy term. Using the Julia coding language, we calculate these quantities as either surface or line integrals, and we use auto differentiation (AD) to compute the gradient of the objective function in terms of the stellarator coil geometry. The gradient information allows, for example, the steepest descent algorithm to be used to find the minimum. By minimizing the magnetic field outside of the plasma volume, we reduce the amount of energy needed to confine the plasma, and we potentially decrease inter-coil repulsion. Thus the cost of constructing and operating fusion power plants is lowered.