NoahH/CreateCoil | Paclet Repository

NoahH`CreateCoil`

FindEllipseCoil

FindEllipseCoil [{ i χ1 , i χ2 ,…},{n,m},{ χ cmin , χ cmax },{ ψ cmin , ψ cmax }]
	returns, for ellipse groups of turn ratios i χ1 , i χ2 , … , axial separations between χ c min and χ c max and ellipse extents between ψ c min and ψ c max optimised to generate the field harmonic of order n and degree m .

Details and Options



Examples

(14)

Basic Examples

(2)

Optimise a pair of ellipse groups to generate the

1, 1

(i.e.

n=1

m=1

) field harmonic, with a normalised separation between 0.01 and 1, and a normalised axial extent between 0.1 and 0.5:

In[1]:=

FindEllipseCoil

[{1},{1,1},{0.01,1},{0.1,0.5}]

Out[1]=

{{Coilχc[1]0.504209,Coilψc[1]0.493298,DesToErr5.48405},{Coilχc[1]0.502104,Coilψc[1]0.48875,DesToErr5.38526},{Coilχc[1]0.500193,Coilψc[1]0.484582,DesToErr5.29699},{Coilχc[1]0.498513,Coilψc[1]0.480891,DesToErr5.22056},{Coilχc[1]0.497226,Coilψc[1]0.478045,DesToErr5.16274},{Coilχc[1]0.4953,Coilψc[1]0.473754,DesToErr5.07731},{Coilχc[1]0.493239,Coilψc[1]0.46912,DesToErr4.98739},{Coilχc[1]0.491609,Coilψc[1]0.465425,DesToErr4.91735},{Coilχc[1]0.489069,Coilψc[1]0.459607,DesToErr4.81002},{Coilχc[1]0.488438,Coilψc[1]0.45815,DesToErr4.78369}}

Optimise two pairs of ellipse groups, of turn ratios 1 and -1, to generate the

2, 1

(i.e.

n=2

m=1

) field harmonic, with normalised separations between 0.1 and 1.32, and normalised axial extents between 0.1 and 0.5.

First, we can use

HarmonicFieldPlot

to examine the Cartesian components of the desired field along the

- and

-axes:

In[1]:=

HarmonicFieldPlot

[{2,1},ImageSizeSmall]

Out[1]=





Now find coils which aim to generate this field:

In[2]:=

sols=

FindEllipseCoil

[{1,-1},{2,1},{0.1,1.32},{0.1,0.5}]

Out[2]=

{{Coilχc[1]0.464584,Coilχc[2]0.596781,Coilψc[1]0.282267,Coilψc[2]0.499178,DesToErr3.51843},{Coilχc[1]0.465795,Coilχc[2]0.595184,Coilψc[1]0.283759,Coilψc[2]0.496138,DesToErr3.51223},{Coilχc[1]0.467115,Coilχc[2]0.593459,Coilψc[1]0.285394,Coilψc[2]0.492857,DesToErr3.50568},{Coilχc[1]0.468461,Coilχc[2]0.591715,Coilψc[1]0.287075,Coilψc[2]0.489542,DesToErr3.49921},{Coilχc[1]0.469696,Coilχc[2]0.590129,Coilψc[1]0.288627,Coilψc[2]0.486529,DesToErr3.49345},{Coilχc[1]0.470336,Coilχc[2]0.589311,Coilψc[1]0.289436,Coilψc[2]0.484977,DesToErr3.49054},{Coilχc[1]0.471115,Coilχc[2]0.588321,Coilψc[1]0.290424,Coilψc[2]0.483099,DesToErr3.48706},{Coilχc[1]0.471804,Coilχc[2]0.587449,Coilψc[1]0.291301,Coilψc[2]0.481446,DesToErr3.48404},{Coilχc[1]0.472612,Coilχc[2]0.586431,Coilψc[1]0.292334,Coilψc[2]0.479519,DesToErr3.48056},{Coilχc[1]0.472887,Coilχc[2]0.586085,Coilψc[1]0.292687,Coilψc[2]0.478864,DesToErr3.47939}}

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