The 'Stark barrel' described by J. L. Hom, D. M. Homan, C. S. Hwang,

W. L. Fuqua III and K. B. MacAdam, Rev. Sci. Istrum. vol 69 (1998) 4086-93. 

A cylindrical arrangement of electrodes that provides a nearly uniform electric field over a considerable volume.

Here there are 16 rods of diameter 1.58mm and length 70mm, enclosing an unobstructed volume of diameter 20mm.

The potentials applied to a rod is cos(theta), where theta is the angle between the xz plane and a line from the centre of the rod to the centre of the assembly.  The values of theta are j*11.25 degrees, where j= 1, 3, 5 and 7.

3 planes of reflection symmetry (or anti-symmetry) are used to give a total number of segments 8*960.  A larger number can easily be used to give higher accuracy.

The output information is given below.  We see that the field at the centre of the device is 9.43187E-02 V/mm.

The deviations from this field for a selection of non-central positions are:

Coordinate   Fractional deviation

x  y  z

0  3  0        +3.2E-6

0  4  0        +4.2E-6

0  5  0        -3.1E-5

2  0  0        +1.1E-6

4  0  0        +8.5E-6

0  0  2        -5.3E-6

0  0  4        -1.8E-5

It would not be difficult to improve the uniformity of the field at non-zero values of x and y by empirically adjusting the potentials applied to the rods.  It would also not be difficult to improve the field for non-zero values of z by replacing the ends of the rods by separate systems of rods that have higher applied potentials. 

Please see the contents of the output file temp70a.dat.