Analysis of free-boundary plasma equilibrium in a conventional stellarator shows [1] that the pressure-induced shift Δ_β of the plasma column (total plasma shift) must be fairly large at high β:
β/(2β_eq⁰) < Δ_β/b < β₀/(2β_eq⁰). (1)
Here β_eq⁰=μ_b²b/R, μ_b is the rotational transform at the plasma edge, b is the averaged minor radius of the plasma, R is the major radius, β is the volume-averaged ratio 2p/B₀² with p being the plasma pressure and B₀ the toroidal magnetic field at r=R, and β₀=2p(0)/B₀² is the β value at the magnetic axis.

For Large Helical Device (LHD) with R = 3.9 m, b = 0.6 m, μ_b =1 [2] we have β_eq⁰=0.15, and the lower bound in (1) is 0.1 for β=3%, which is equivalent to 6 cm outward shift.

If such a large shift would appear in LHD, it certainly could be observed, for example, when the Shafranov shift was measured with soft X-ray CCD camera [3]. However, there is no mentioning of observations of large 'global' plasma shift in [3]. Therefore a question arises why the plasma column shift in LHD is actually smaller than the above estimate.

Theoretically, the plasma shift can be suppressed by the vertical magnetic field [1]. Such a field can appear due to the currents induced in the ideal conductors near the plasma. We consider this possibility using analytical methods described in [1]. The obtained expression for the plasma shift, incorporating both the finite beta expansion and the opposing reaction of the nearby ideal wall, can be used for interpreting the observable high-β equilibrium effects in LHD and other helical devices.

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