Floating Conductor

From SIMION

A floating conductor is a conductor that is isolated from ground. As a conductor, it has constant potential over the entire surface. The only difference in SIMION for the floating conductor is that you might not know a priori its potential since it is not held to a reference potential but rather depends on the surrounding potentials as calculated by the SIMION Refine process, which circularly depends again on the potential of the floating conductor. What you do (or should) know, however, about the floating conductor is the total charge Q on it (e.g. zero for neutral). After all, the total charge on a floating conductor is a constant because the charges are isolated from ground and have no other place to go.

The SIMION refine process does not directly provide for the specification of floating conductors. If it did, this would be just another variable to be solved inside the Refine process. However, there is a way to do this calculation in SIMION (at least since version 6.0):

(1) Model the system with a fast adjust potential array (PA# file). Make the floating conductor a separate fast adjust electrode.
(2) Refine the PA.
(3) Fast adjust the non-floating conductors to 0 V and the floating conductor to 1 V. Save the PA0 file and calculate the total charge Q1 on the floating conductor under these conditions as described in Charge-Capacitance Calculation.
(4) Repeat step #3 but fast adjust the non-floating conductors to appropriate values and the floating conductor to 0V. The calculated total charge will now be named Q2.
(5) The proper potential Vf on the floating conductor is then found by solving Vf * Q1 + (1 V) * Q2 = Q. This is a direct result from Gauss's Law given that the actual field is some (unknown) linear combination of the two cases above (i.e. principle of superposition or SIMION fast adjust). (*2) Fast adjust the floating conductor to this potential.
(6) As an optional check, you may repeat the total charge calculation with the final potentials to confirm that the total charge on the floating conductor is as expected.

An example of this is shown in Figure 1. This is a 2D planar parallel plate system with a floating conductor of zero charge placed in the middle at a 45 degree angle. The parallel plates are at 0V and 1V, and by symmetry alone we predict the floating conductor to be at 0.5V.

(Figure 1)

In fact, using the totalcharge.pl program around the perimeter box2d(20,20, 80,80) we obtain integration results of Q1 = 3.3517E-14 and Q2 = -1.6684E-14, and we already know that Q = 0. Solving the linear equation then gives Qf = 0.498 V, roughly as we expect. The resultant potential contours with the floating conductor fast-adjusted to this voltage are shown in Figure 2.

(Figure 2)

One practical remark by Marc (*1)--in working with charged particles, floating conductor surfaces will collect particles emitted from the source. This charge capture modifies the potential very fast until the beam is fully repelled. In most cases the floating conductor will finally reach a potential close to the potential of the emitting source. In electrostatic optical systems one should be aware of charge captures on insulating surfaces. Therefore the insulator should as far as possible from the optics' "active" elements.

Also noted by Frank (*2)--a similar approach has been used in simulating magnetic shields in SIMION. For mu -> infinity materials, the magnetic potential is constant at the surface. So SIMION's approach to magnetic fields is quite natural _if_ you know what potential to put on the PAs. Using the same logic above, one can set the potential so that a Gaussian integral around the shield PA is zero, which is the only choice satisfying div B = 0.

(*1) Marc Bernheim - SIMION User Group Discussion #367 - Floating Conductor (http://www.simion.com/discuss/viewtopic?p=1035)
(*2) Frank Crary - SIMION User Group Discussion #367 - Floating Conductor (http://www.simion.com/discuss/viewtopic?p=1037) + SIMION User Group Discussion - Mu-Metal simulation (http://www.simion.com/discuss/viewtopic?p=2190)

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Info: Floating Conductor

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