130
The European Physical Journal Applied Physics
(A)
:
t(s)
5.2.2 Current source supply
10000.0
0.02
0.01
Isupply
Idischarge
As the previous simulations have proved the possibility to
control the shape of the waveform and the magnitude of
the current in the discharge by mean of the power supply,
we propose to investigate in the following simulations the
possibility of direct control of the current in the discharge;
this is achieved with a current source supply. We consider
the case of nitrogen.
(V)
:
t(s)
Vsupply
0.0
0.0
−0.01
−0.02
Square current supply.
Simulations of Figures 14
and 15 have pointed out that triangle voltage supply per-
mits to obtain (when the discharge is in on-state) square
currents; more generally, they prove that one can control
the pattern of the current in the discharge by mean of a
well chosen supply’s voltage waveform. We propose now
to consider a square current supply, applied to the whole
apparatus (gas + ceramics electrodes) Figure 16b; as will
be shown, the current in the discharge is flowing during
quite the whole of each half-period and one can expect
from this solution an interesting power transfer to the
discharge and controlled current peaks at turn-on, thus
avoiding filamentary regime risks.
−10000.0
0.0022
0.0023
0.0024
0.0025
0.0026
0.0027
t(s)
Fig. 15. Triangular voltage supply in nitrogen at 2 kHz, with
10 kV peak values and K2 × Rgen = 180 kΩ ( (simulations):
supply’s voltage and current (I, V ) and current in the dis-
charge.
turns on, as the gas voltage ripple can be neglected, the
dielectric barrier limits the current of the discharge and
imposes the following value:
We can remark that the current which flows in the
discharge (Fig. 16d) does not exactly correspond to the
supply’s one (Fig. 16b); indeed, the discharge turns off
when the supply’s current matches a null value and volt-
age conditions related to Vgas (Fig. 16e) have to be met
for the discharge to turn-on again: | Vgas |> Vbr. During
the necessary time interval to invert the gas voltage, the
supply’s current flows into the gas capacitor (Fig. 16c).
These two sequences, appearing on each half-period of the
supply, can be observed on the supply’s voltage waveform
(Fig. 16a). The strongest slope corresponds to the time
interval where the discharge is in off state; the supply’s
current flows in the serial association of the capacitors:
Cceram and Cgas. The lowest slope corresponds to the on-
state of the discharge: the voltage across the gas has a
very small ripple (as stated in the relations Eq. (1) and
Eq. (2)) and the supply’s current, flowing through the
Cceram capacitor in serial with the gas, defines the sup-
ply’s voltage: considering the energy transfer to the gas,
we have to note that only the risk of transition to fila-
mentary regime (which the model presented in this paper
is unable to detect), may limit the supply’s current mag-
nitude. When this parameter is increased, the duration
of the off state of the discharge decreases. Another way
to match the same optimal behaviour is to minimise the
value of the gas capacitor, Cgas, (but one should remind
that the value of the breakdown voltage, Vbr, should not
be considerably increased).
d(Vgen − Vgas
dt
)
dVgen
dt
Igas = Cceram
×
' Cceram
×
·
As the supply’s voltage, Vgen, is a triangle, the gas current,
when the discharge is in on state, has a rectangular shape.
As it can be observed by comparison of the obtained
waveforms of Figure 14, the magnitude of the rectangular
part of the gas current is proportional to the slope of the
supply’s voltage. The discharge naturally turns off when
the gas current, Igas, cancels; this event corresponds to
the extremum of the supply’s voltage, Vgen
.
These simulations point out that the choice of the sup-
ply is of crucial importance; the shape of the supply’s volt-
age permits the control of the waveform of the current in
the discharge, and thus the energy it receives. In order
to evaluate the importance of the parasitic parameters of
the supply, we have introduced in the simulated circuit
the internal impedance of the generator; the simulation’s
results are presented in Figure 15.
One can observe that the voltage, which can be mea-
sured across the terminals of the supply, presents a voltage
drop when the discharge turns on; its value corresponds
to the product of the discharge current peak, by the value
of the internal resistance of the generator. The value of
the internal resistance of the supply (8 Ω in the previ-
ous example) corresponds to the actual equipment used
in the experimental device (a linear amplifier associated Sine current supply. A practical realisation of a sup-
with low frequency generator); this parameter is showing ply apparatus able to generate pure square currents and
a negative influence on the control of the discharge cur- high voltages (Fig. 16a) is a rather hard to fulfil challenge;
rent. As especially designed power supplies are able to parasitic elements (and at first rank parasitic capacitors)
present very low values of their internal impedance, this drastically decay the performances. Static converters, us-
element will not be introduced in the investigations of the ing resonance technology, permit to deliver such high volt-
following paragraphs.
ages and to generate quasi-sine currents. This solution is
Haller
