Xmpl3d29, 29th 'example' data file for CPO3D

Field and potential penetration through a flat mesh of crossed flat wires.

The file was written when the memory and speed of PC's was much more limited than at present, so the available number of segments was small and the requested inaccuracies were fairly high to give a quick demonstration.

One of a set of files:

test2d18.dat: Field penetration through a flat mesh of flat strips.

xmpl2d19.dat: Field penetration through a cylindrical mesh of round wires.

xmpl2d20.dat: Field penetration through a flat mesh of round wires.

xmpl3d23.dat: Field and potential penetration through a flat mesh of crossed round wires.

xmpl3d29.dat: Field and potential penetration through a flat mesh of crossed flat wires.

For further details see the papers:

Short and long range penetration of fields and potentials through meshes, grids or gauzes, by F H Read, N J Bowring, P D Bullivant and R R A Ward Nucl. Instr. Meth. A427, 363-367 (1999).

Penetration of electrostatic fields and potentials through meshes, grids or gauzes, by F H Read, N J Bowring, P D Bullivant and R R A Ward, Rev. Sci. Instrum. 69, 2000-2006 (1998).

A flat mesh is composed of thin crossed strips that form an array of square holes, and has a transparency of 90 percent.

The objective of this study is to measure the penetration of the field and potential through the mesh. To do this the field on one side of the mesh (z>0) is set up as non-zero while the other side is set up as a nominally field-free region.

The mesh is at zero potential and fields are created on both sides of it by means of continuous end plates at a different potential, which is established iteratively.

The number N of segments is extrapolated to infinity, using either 1/N3 or 1/N3.5.

Final results:

r |
dv |
nseg |
vm |
vc |
ec |

.0125 |
.2642 |
inf |
0.2644 |
0.3634 |
-0.4983 |

.025 |
.216 |
inf |
0.2159 |
0.3064 |
-0.4982 |

.05 |
.1728 |
inf |
0.17041 |
0.24905 |
-0.49919 |

.10 |
.1290 |
558 |
0.1290 |
0.1903 |
-0.4964 |

where dv is applied to surround at z=0, vm is average found over z=0, vc, ec are potenetial, field at origin.

Investigation of fourier components of potential:

The 1st step is to find the coefficients a10, a20, a30 by eliminating the earlier y components by taking the combination pot(x,0,z)+2*pot(x,0.25,z)+pot(x,0.5,z) (which removes y components for m=1 to 3). See note at end of xmpl3d23.dat.

The 2nd step is to find the coefficient a11 by taking the combination

(pot(0,0,z)-2*pot(x,0.5,z)+pot(0.5,0.5,z))

Summary of fourier coefficients:

r |
a10 |
a20 |
a30 |
a11 |

0.0125 |
0.072 |
-0.037 |
0.024 |
0.033 |

0.025 |
0.070 |
-0.036 |
0.023 |
0.040 |

0.050 |
0.066 |
-0.033 |
0.019 |
0.046 |

Compare with analogous 3D results for round wire mesh:

r a10 a20 a30 a11

r |
a10 |
a20 |
a30 |
a11 |

0.0125 |
0.070 |
-0.037 |
0.025 |
0.028 |

0.025 |
0.067 |
-0.035 |
0.024 |
0.033 |

0.050 |
0.061 |
-0.031 |
0.020 |
0.040 |

For the program used in the analysis see program 18.