conservación y manejo urbano en el contexto cultural mexicano
CONSIDERACIONES DEL CONTEXTO CULTURAL
Current and voltage
The current was measured using the current monitor. The sensitivity is 1 V ↔
1 A± 1%, meaning that for each ampere detected, the probe output produced 1 volt. The probe was connected to an oscilloscope and the signal was saved using a floppy disc then load into Origin to plot and analyse. The voltage was measured by connecting a high voltage probe to the wire between the power supply and the
electrode. The probes used were either the Pintek HVP-15HF or the Tektronix P6015A, both have a reading of 1 V↔1000 V, meaning that for each thousand volts measured the probes produce 1 volt. The voltage signals were taken in the same manner as the current signals. The sample interval used by the oscilloscope was 2 ns with a precision of 1µV. The behaviour of the voltage, the current, and the power as a function of the plasmas parameters is explained in the next paragraph. An example of voltage and current of a positive pulsed DC signal is shown in figure 4.1.
Figure 4.1: Current (black) and voltage (blue) of a 10 kHz, 10 % duty cycle at∼4 kV of ampli- tude. The quick rise of voltage creates a high displacement current clearly seen at -100µs and 0µs, the oscilloscope peak is saturated in this figure, the peak value was∼10 A. The quick drop of voltage creates an identical phenomenon with an opposite sign for the generated current. The positive bump visible at∼0.8µs corresponds to the plasma bullet current. A negative plasma bullet current is also recorded at∼10.7µs, however, it is hidden in the noise of the signal and is cut by the y-axis of the oscilloscope
Power measurement of Pulse DC
The high current signal at the rising and falling edge of the voltage in figure 4.1 is the displacement current given by the following equation:
Idisp(t) = ε
dΦE
dt (4.1)
where Idisp is the displacement current, ε is the relative permittivity, and ΦE
the electric flux. The displacement current (Idisp) can be related to the so-called
capacitor equation (4.2). In order to simplify things, the apparatus (electrode and front cone of mass spectrometer) can be assumed to correspond to a parallel plate capacitor with an area of A, thus ΦE =A·E where E is the electric field
between the plates and with E =V /L with Land V being the distance and the potential between the plates. Therefore equation (4.1) becomes,
I(t) =εd (A·E) dt =C
dV(t)
dt (4.2)
whereC =εA/L. The plasma bullet current can be seen on figure 4.1 at∼0.8µs visible on the higher magnification. A negative bullet current trace is also present, however, it is harder to detect on figure 4.1 due to a noisy current signal, fur- thermore, the oscilloscope y-axis signal was chosen to be between -15 and 40 mA slightly cutting the negative bullet current in this particular example.
The power is calculated usingP(t) = I(t)·V(t) where current and voltage are recorded by the probes. Instant power is presented in figure 4.2 using the current and voltage from figure 4.1. As expected, the instant power is zero for most of the signal duration, the only non-zero values are at 100n µs and (100n + 10µs) with n∈ Z. The power contributing to the plasma is the positive plasma bullet power which is the bump seen between 0.6µs and 1.1µs in figure 4.2, the negative bullets do not contribute to the power as it occurs when the voltage is zero. The average power is the integral of I(t)·V(t) over the period duration. To calculate the average power, first the energy of the plasma bullet (Ebullet) is estimated using
the following formula:
Ebullet= Z tend
tstart
(I(t)·V(t))dt (4.3)
where tstart and tend are the starting and the end time of the plasma bullet,
the plasma power the following equation has been used to evaluate the average plasma power (Pavg):
Pavg = 1 T Z t0+T t0 (I(t)·V(t))dt = Ebullet T (4.4)
whereT is the period. ThusPavg is the power of the plasma jet averaged over the
period. As the power is mostly zero over the period,I(t)·V(t) is integrated over a reduced the time step. In this way, integration of the noise is greatly reduced.
Figure 4.2: Power of a 10 kHz, 10 % duty cycle at ∼4 kV of amplitude. Power is calculated using current and voltage displayed on figure 4.1.
Power measurement of continuous wave
For continuous wave, the displacement current, as given by equation figure 4.2, is also sinusoidal. As in [80], plasma current can be observed after removing the displacement current (see figure 4.3). As opposed to the pulsed DC mode where
the variation in the voltage appears on a very short time scale, displacement currents of continuous wave in the range of 10 kHz, are very stable through time.
Figure 4.3: Plots of typical driving voltage (a) current signals, (b) total and discharge currents. In this case the driving frequency is 10 kHz. The currents have been intentionally delay by the authors to remove the 90 degree shift between current and voltage, taken from [80].
Power is measured similarly to the pulsed DC mode. By calculating the integral of I(t)·V(t) averaged over one period, Pavg can be achieved, given as:
Pavg = 1 T Z t0+T t0 ((I(t)−Idisp(t))·V(t))dt = 1 T Z t0+T t0 (Ibullet(t)·V(t))dt (4.5)
where Idisp(t) can be measured by removing the helium and thus turning the
plasma off whilst keeping the signal unchanged.