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3.5 Vacuum magnetic field (not finished)

In the vacuum region that is between the plasma and the first wall, there is no current, i.e.,

∇ × B = 0.
(68)

Next, let us examine what constraint this condition imposes on the magnetic field. Using expression  (10), the above equation is written as

∇ × (∇Ψ × ∇ϕ )+ ∇g × ∇ϕ = 0,
(69)

It is not obvious how to draw useful information from the above equation.

In the above, we use the vector potential approach. Next, let us try the scalar potential approach:

B = ∇ Φ,
(70)

then the constraint ∇⋅ B = 0 is written as

∇2Φ = 0.
(71)

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