Poloidal toroidal decomposition
Encyclopedia
In vector analysis, a mathematical discipline, a three-dimensional solenoidal vector field F can be considered to be generated by a pair of scalar potential
s Ψ and Φ:
where k is a unit vector.
This decomposition
is analogous to a Helmholtz decomposition
, and has been used in dynamo theory
.
Scalar potential
A scalar potential is a fundamental concept in vector analysis and physics . The scalar potential is an example of a scalar field...
s Ψ and Φ:
where k is a unit vector.
This decomposition
Vector decomposition
Vector decomposition refers to decomposing a vector of Rn into several vectors, each linearly independent .-Vector decomposition in two dimensions:...
is analogous to a Helmholtz decomposition
Helmholtz decomposition
In physics and mathematics, in the area of vector calculus, Helmholtz's theorem, also known as the fundamental theorem of vector calculus, states that any sufficiently smooth, rapidly decaying vector field in three dimensions can be resolved into the sum of an irrotational vector field and a...
, and has been used in dynamo theory
Dynamo theory
In geophysics, dynamo theory proposes a mechanism by which a celestial body such as the Earth or a star generates a magnetic field. The theory describes the process through which a rotating, convecting, and electrically conducting fluid can maintain a magnetic field over astronomical time...
.