General information on applied voltages.

This note deals with:

The voltage numbers (that is, addresses)

The voltage values

Time-dependent voltages

Varying voltages iteratively to focus a beam.

Defining relationships between voltages.

The voltage numbers

The number (that is, address) of the voltage that is applied to an electrode is specified separately from the value of the voltage.

(The reason for this is that when the electrode is specified the program needs to know the voltage number of the voltage that will applied to the electrode, but does not need to know the value of the voltage until later.)

See the relevant note for information on the maximum number of different voltages.

The voltage values

The values of the voltages are initially specified in the input data file, but they can be changed interactively at run-time. The voltage values can be constant, or can vary sinusoidally with time, or can vary with time in a way specified by a user-supplied program.

See the relevant note for further information on specifying the values of the voltages.

Remember that if 2 touching electrodes have different voltages, then the charges near the touching point will be very large AND THE RESULTS WILL BE INACCURATE OR MEANINGLESS.

Remember this if the voltages are changed at run time.

Two different voltage numbers can be specified for an electrode, in order to indicate that there is a voltage gradient along the electrode. This gradient is linear and can only be in the z direction. But if you want to apply the gradient in another direction (for example the x direction) then slope the electrode very slightly in the z direction (and make sure that the allowed reading error is small enough). (The voltage gradient is of course not physically possible for a real conducting electrode, but is included as an option to allow systems such as that in the 3rd 2D test to be set up.)

See the relevant note for information on voltage gradients.

Time-dependent voltages

The sinusoidal variation has the form

v(t) = v0+v1*sin(phi+2*pi*t/tau),

where tau is in milliseconds and phi is in radians.

The zero of time for each separate ray is specified when the rays themselves are specified.

See the relevant note.

When the voltages are time-dependent the fields are dealt with in the 'quasi-static' approximation. In other words, the program ignores any magnetic fields that are generated from the time variations of the electric fields (that is, electromagnetic effects), and so the user must ensure that the frequency of the field is not too high and that the wavelength is much longer than the electrode lengths.

Varying voltages iteratively to focus a beam.

See the relevant note for information on the option for varying voltages iteratively to focus a beam.

Defining relationships between voltages.

Any voltage can be defined to be linearly dependent on 3 other voltages. See the relevant note for further information.