Move psi functions of Solov'ev equilibria to Solov'ev module.

src/analytic/solovev.jl

@@ -16,7 +16,60 @@ module Solovev
 
     export  SolovevEquilibrium, SolovevXpointEquilibrium
 
-    include("solovev_psi.jl")
+
+    function ψ₀(x::AbstractVector{T}, a) where {T <: Number}
+        x[1]^4 / 8 + a * (x[1]^2 * log(x[1]) / 2 - x[1]^4 / 8 )
+    end
+
+    function ψ₁(x::AbstractVector{T}) where {T <: Number}
+        one(T)
+    end
+
+    function ψ₂(x::AbstractVector{T}) where {T <: Number}
+        x[1]^2
+    end
+
+    function ψ₃(x::AbstractVector{T}) where {T <: Number}
+        x[2]^2 - x[1]^2 * log(x[1])
+    end
+
+    function ψ₄(x::AbstractVector{T}) where {T <: Number}
+        x[1]^4 - 4 * x[1]^2 * x[2]^2
+    end
+
+    function ψ₅(x::AbstractVector{T}) where {T <: Number}
+        2 * x[2]^4 - 9 * x[2]^2 * x[1]^2 + 3 * x[1]^4 * log(x[1]) - 12 * x[1]^2 * x[2]^2 * log(x[1])
+    end
+
+    function ψ₆(x::AbstractVector{T}) where {T <: Number}
+        x[1]^6 - 12 * x[1]^4 * x[2]^2 + 8 * x[1]^2 * x[2]^4
+    end
+
+    function ψ₇(x::AbstractVector{T}) where {T <: Number}
+        8 * x[2]^6 - 140 * x[2]^4 * x[1]^2 + 75 * x[2]^2 * x[1]^4 - 15 * x[1]^6 * log(x[1]) +
+                    180 * x[1]^4 * x[2]^2 * log(x[1]) - 120 * x[1]^2 * x[2]^4 * log(x[1])
+    end
+
+    function ψ₈(x::AbstractVector{T}) where {T <: Number}
+        x[2]
+    end
+
+    function ψ₉(x::AbstractVector{T}) where {T <: Number}
+        x[2] * x[1]^2
+    end
+
+    function ψ₁₀(x::AbstractVector{T}) where {T <: Number}
+        x[2]^3 - 3 * x[2] * x[1]^2 * log(x[1])
+    end
+
+    function ψ₁₁(x::AbstractVector{T}) where {T <: Number}
+        3 * x[2] * x[1]^4 - 4 * x[2]^3 * x[1]^2
+    end
+
+    function ψ₁₂(x::AbstractVector{T}) where {T <: Number}
+        8 * x[2]^5 - 45 * x[2] * x[1]^4 - 80 * x[2]^3 * x[1]^2 * log(x[1]) + 60 * x[2] * x[1]^4 * log(x[1])
+    end
+
 
     @doc raw"""
     Axisymmetric Solov'ev equilibra in (R/R₀,Z/R₀,ϕ) coordinates.