The stepped-pressure equilibrium code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 , 112 502) is extended to enable free-boundary multi-region relaxed magnetohydrodynamic (MRxMHD) equilibrium calculations. The vacuum field surrounding the plasma inside an arbitrary ‘computational boundary’, ##IMG## [http://ej.iop.org/images/0741-3335/62/8/084002/ppcfab9a61ieqn1.gif] {${\mathcal{D}}$} , is computed, and the virtual-casing principle is used iteratively to compute the normal field on ##IMG## [http://ej.iop.org/images/0741-3335/62/8/084002/ppcfab9a61ieqn2.gif] {${\mathcal{D}}$} so that the equilibrium is consistent with an externally produced magnetic field. Recent modifications to SPEC are described, such as the use of Chebyshev polynomials to describe the radial dependence of the magnetic vector potential, and a variety of free-boundary verification calculations are presented.

中文翻译：

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使用阶跃压力平衡码的自由边界MRxMHD平衡计算

扩展了阶跃压力平衡代码（SPEC）（Hudson et al 2012 Phys.Plasmas 19，112 502），以实现自由边界的多区域松弛磁流体动力学（MRxMHD）平衡计算。任意“计算边界”内部等离子体周围的真空场，## IMG ## [http://ej.iop.org/images/0741-3335/62/8/084002/ppcfab9a61ieqn1.gif] {$ {\计算mathcal {D}} $}，并反复使用虚拟套管原理来计算## IMG ## [http://ej.iop.org/images/0741-3335/62/ 8/084002 / ppcfab9a61ieqn2.gif] {$ {\ mathcal {D}} $}，以便平衡与外部产生的磁场保持一致。描述了对SPEC的最新修改，例如使用Chebyshev多项式描述磁矢量势的径向依赖性，