Your handwavy claims about his model are 0/10. He clearly explained where and why he simplified he model for purposes of his papers. None of your criticisms are even *remotely* valid.
I note when you are on the defensive you mirror my criticisms word for word which forms part of your spin story which doesn’t even try to *remotely* explain why Scott’s model is right by addressing the seven points in the rebuttal.
If Scott’s equations are correct then why are they contradicted in the very Wiegelmann link he references in his paper.
The equation mentioned is µ₀jz₀ = ∂By₀∂x − ∂Bx₀∂y at a particular point in space.
This equation meaningless to you is the mathematical relationship between
B and
j in Cartesian coordinates where the current density
j is in the direction z.
The authors of the reference assume the reader has the mathematical knowledge so I will derive the general equation to fill in the gaps to show another reason why Scott’s algebra and his equations are nonsensical.
First of all we have the force free equation;
∇×
B = α
B
Since this is a Beltrami vector field
∇×
B is parallel to
B.
Furthermore since
B is parallel to
j for the force free condition, then
∇×
B is also parallel to
j which also forms part of the Beltrami vector field.
Hence we can define an equation of the form
∇×
B = µ₀
j
To anyone familiar with vector analysis
∇×
B can be expressed as the determinant;
e₁,
e₂,
e₃ are the orthogonal unit vectors.
Expanding the determinant gives;
∇×
B = (∂Bz/∂y-∂By/∂z)
e₁ - (∂Bz/∂x-∂Bx/∂z)
e₂ + (∂By/∂x-∂Bx/∂y)
e₃
Also µ₀
j = (µ₀j
)e₁ + (µ₀j
)e₂ + (µ₀j
)e₃
Since
∇×
B is parallel to
j.
(∂Bz/∂y-∂By/∂z)
e₁ - (∂Bz/∂x-∂Bx/∂z)
e₂ + (∂By/∂x-∂Bx/∂y)
e₃ =
(µ₀j
)e₁ + (µ₀j
)e₂ + (µ₀j
)e₃
In the
z or
e₃ direction;
µ₀j = (∂By/∂x
- ∂Bx/∂y) which is the general equation in the link for the z direction.
In Scott’s model however cylindrical coordinates are used with unit vectors
R,
Φ and
Z where;
∇×
B = ((1/r)∂Bz/∂ϕ-∂Bϕ/∂z)
R + (∂Br/∂z-∂Bz/∂r)
Φ + 1/r(∂(rBϕ)/∂r − ∂Br∂ϕ)
Z
µ₀
j = (µ₀j
)R + (µ₀j
)Φ + (µ₀j
)Z
In the
Z direction the equation reduces to;
jz(r) = (1/µ₀r)(∂(rBϕ)/∂r − ∂Br∂ϕ)
Even though you do not understand the maths this equation looks nothing like Scott’s equation
jz(r) = (α/μ)Bz(0)J0(αr).
Furthermore the mathematics used to derive the equation is at odds with Scott’s algebra.
So therefore the algebra used to derive Scott’s equation is wrong.
To anyone with even a basic knowledge of algebra the error is obvious and one would not have to go down this convoluted path.
What is disturbing is Scott seems to suffer from your disease; using a reference he not only doesn’t understand but also contradicts his equations.