{ VECTOR_MAGNET_COIL.PDE
AXI-SYMMETRIC MAGNETIC FIELDS
This example is a modification of MAGNET_COIL.PDE using vector variables.
See that example for discussion of the problem formulation.
}
Title 'AXI-SYMMETRIC MAGNETIC FIELD - Vector Variables'
Coordinates
{ Cylindrical coordinates, with cylinder axis along Cartesian X direction }
xcylinder(Z,R)
Variables
A = vector(0,0,Aphi) { the azimuthal component of the vector potential }
Definitions
mu = 1 { the permeability }
rmu = 1/mu
current = 0 { the source defaults to zero }
J = vector(0,0,current)
Bz = dr(r*Aphi)/r
Initial Values
Aphi = 2 { unimportant unless mu varies with H }
Equations
{ FlexPDE expands CURL in proper coordinates }
A : curl(rmu*curl(A)) = J
Boundaries
Region 1
start(-10,0)
value(Aphi) = 0 { specify A=0 along axis }
line to (10,0)
natural(Aphi) = 0 { H<dot>n = 0 on distant sphere }
arc(center=0,0) angle 180 to close
Region 2
current = 10 { override source value in the coil }
start (-0.25,1)
line to (0.25,1) to (0.25,1.5) to (-0.25,1.5) to close
Monitors
contour(Bz) zoom(-2,0,4,4) as 'FLUX DENSITY B'
contour(Aphi) as 'Potential'
Plots
grid(z,r)
contour(Bz) as 'FLUX DENSITY B'
contour(Bz) zoom(-2,0,4,4) as 'FLUX DENSITY B'
elevation(Aphi,dr(Aphi),Aphi/r,dr(Aphi)+Aphi/r,Aphi+r*dr(Aphi))
from (0,0) to (0,1) as 'Bz'
vector(dr(Aphi)+Aphi/r,-dz(Aphi)) as 'FLUX DENSITY B'
vector(dr(Aphi)+Aphi/r,-dz(Aphi)) zoom(-2,0,4,4) as 'FLUX DENSITY B'
contour(Aphi) as 'MAGNETIC POTENTIAL'
contour(Aphi) zoom(-2,0,4,4) as 'MAGNETIC POTENTIAL'
surface(Aphi) as 'MAGNETIC POTENTIAL' viewpoint (-1,1,30)
End
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