We also need to keep both the scales y, Y in ∇2 ⊥, ∇2 ⊥ → ∂2 x + (∂y + ϵ∂Y )2 = ∇2 ⊥ + 2ϵ∂Y ∂y + ϵ2∂2 Y (B16) Finally, we note that (B15) has to be evaluated at z = 1 + ϵη

Kinematic boundary condition order by order The KBC is obtained from the equation ∇Φ · ∇ψ = 0 with B = ∇Φ, ψ = z − ϵη, is given by φ,z = ϵη,x(1 + ϵφ,x) + ϵ2φ,yη,y (B15) Owing to

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Periodic Korteweg-de Vries soliton potentials generate quasisymmetric magnetic fields

physics.plasm-ph · 2023-02-27 · unverdicted · novelty 7.0

Quasisymmetric stellarator magnetic fields are generated by periodic KdV soliton potentials, with B approaching the 1-soliton reflectionless form near the outermost surface.

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Periodic Korteweg-de Vries soliton potentials generate quasisymmetric magnetic fields physics.plasm-ph · 2023-02-27 · unverdicted · none · ref 5
Quasisymmetric stellarator magnetic fields are generated by periodic KdV soliton potentials, with B approaching the 1-soliton reflectionless form near the outermost surface.

We also need to keep both the scales y, Y in ∇2 ⊥, ∇2 ⊥ → ∂2 x + (∂y + ϵ∂Y )2 = ∇2 ⊥ + 2ϵ∂Y ∂y + ϵ2∂2 Y (B16) Finally, we note that (B15) has to be evaluated at z = 1 + ϵη

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