conductorFunc

conductorFunc

UserFuncs of kind = conductorFunc return a result with information about a Conductor Block in a cutCellPoisson updater, namely the voltage on the conductor, the total and absorbed charge on the conductor, or the capacitance of the conductor (with respect to other conductors).

UserFuncs of kind = conductorFunc take zero arguments.

conductorFunc parameters

conductor

The name of a Conductor Block to query for information. The name may need to be qualified, e.g., with the name of the MultiField and FieldUpdater containing the referenced conductor – e.g., myEsField.poissonUpdater.metalSphereC.

result (string, required)

Specifies what information the function should return; depending on result, different attributes may apply.

Following is a list of results and the extra attributes (if any) that pertain to each specific result. Each result is a scalar float.

voltage

result = voltage returns the voltage of the conductor (in Volts).

charge

result = charge returns the total charge on the conductor (in Coulombs). To calculate this, calculateCharge must be true in the Conductor Block (this is automatically true for floating conductors).

For floating conductors, this will be the absorbed charge (minus the emitted charge). For setVoltage conductors, this will be the induced charge, calculated from Gauss’s Law by integrating the electric field of the surface of the conductor.

absorbedCharge

result = absorbedCharge returns the absorbed charge on the conductor (in Coulombs). To calculate this, calculateCharge must be true in the Conductor Block (this is automatically true for floating conductors).

The absorbed charge is charge on the conductor resulting from absorbed/emitted particles as well as specified currents (cf. ptclAbsorbers, ptclSources, and <Expression current> in the Conductor Block). For floating conductors, the absorbed charge will be (nearly) equal to the total charge. For conductors with setVoltage, the absorbed charge will be zero.

capacitance

This result uses the following attribute:

otherConductor (string, optional, default: the same

as 'conductor')

which (like conductor) specifies the name of a Conductor Block.

result = capacitance returns the capacitance of the conductor with respect to another conductor (or itself). Unlike the other results, this does not typically change in time over the course of a simulation.

The capacitance of conductor C1 with respect to another conductor C2 is defined as the charge induced on C1 when 1V is placed on conductor C2 (while the voltage of all other conductors – including C1 if C1 and C2 are not the same – is maintained at zero). The units are C/V (or Farads).

Note: the otherConductor must be in the same cutCellPoisson block as the conductor.

Note: either conductor or otherConductor (or both) must be floating conductors (cf. Conductor Block) for the capacitance to be calculated.

Note: if conductor and otherConductor are the same, the capacitance is positive: 1 V on the conductor will generally induced a positive charge on that conductor. However, if the conductors are different, the resulting capacitance is negative: putting 1 V on C2 while C1 remains at 0 V will generally induce a negative charge on C1.

Note: the capacitance between two floating conductors C1 and C2 is symmetric; swapping conductor and otherConductor will yield the same result.

conductorFunc examples

In these examples, a conductorFunc is used within a functionOfTime TensorHistory to record charge, voltage, and capacitance of a conductor. These assume that there is a MultiField block ‘myEsField’ that contains a cutCellPoisson updater block ‘poissonUpdater’ that contains Conductor Block ‘sphereC’ and ‘plateC’, both of which are floating conductors.

<History sphereVoltageAndCharge>
  kind = functionOfTime
  <Expression histCalc>
    <UserFunc v>
      kind = conductorFunc
      conductor = myEsField.poissonUpdater.sphereC
      result = voltage
    </UserFunc>
    <UserFunc q>
      kind = conductorFunc
      conductor = myEsField.poissonUpdater.sphereC
      result = charge
    </UserFunc>
    expression = vector(v(), q())
  </Expression>
</History>
<History sphereCapacitance>
  kind = functionOfTime
  <Expression histCalc>
    <UserFunc c>
      kind = conductorFunc
      conductor = myEsField.poissonUpdater.sphereC
      # otherConductor = sphereC # default
      result = capacitance
    </UserFunc>
    expression = c()
  </Expression>
  applyPeriod = 0 # this doesn't change in time, so record just once
</History>
<History spherePlateCapacitance>
  kind = functionOfTime
  <Expression histCalc>
    <UserFunc c>
      kind = conductorFunc
      conductor = myEsField.poissonUpdater.sphereC
      otherConductor = plateC
      result = capacitance
    </UserFunc>
    expression = abs(c()) # c() < 0; for convenience, we record abs(c()).
  </Expression>
  applyPeriod = 0 # this doesn't change in time, so record just once
</History>