Seminar on Plasma Focus Experiments SPFE2010. In-situ measurement of Capacitor Bank Parameters Using Lee model code S H Saw 1,2 & S Lee 1,2,3 1 INTI International University, Nilai, Malaysia 2 Institute for Plasma Focus Studies, Melbourne, Malaysia, Singapore
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In-situ measurement of Capacitor Bank Parameters Using Lee model code
S H Saw1,2 & S Lee1,2,3
1INTI International University, Nilai, Malaysia
2Institute for Plasma Focus Studies, Melbourne, Malaysia, Singapore
3Nanyang Technological University, NIE, Singapore
FIG. 1. Showing the plasma focus with representative current sheet positions in the axial phase and the radial phase. The plasma focus acts in the following way: A capacitor bank C0 discharges a large current into the coaxial tube. The current flows in a current sheath CS which is driven by the JxB force, axially down the tube.
At the end of the axial phase the CS implodes radially, forming an elongating pinch. The static resistance r0 of the discharge circuit is not shown.
Analyse by L-C-R theory to obtain L0 and r0
However even at ‘safe’ high pressure, there is still significant motion and L0, r0 estimated using L-C-R not accurate. Hence fitting by the Lee Model code is necessary to account for motion and accurately determine L0 and r0.
FIG. 2. Measured discharge current waveform at 10 kV, 20 Torr neon; for INTI PF with C0=30mF
The waveform may be treated as sinusoid with period T the following approximate equns hold:a
where f is the reversal ratio obtained from the successive current peaks I1, I2, I3, I4, and I5 with f1= I2 / I1, f2= I3 / I2, f3= I4 / I3, f4=I5 / I4, and f =(1/4) (f1+ f2+ f3+ f4); and I0 the highest peak current is written here as I1, the peak current of
the first half cycle
3T = 36.6 ms, (measured from Fig 2)
giving T=12.2 ms and with C0=30mF
Also f1=0.737, f2=0.612, f3=0.760, and f4=0.524, (measured from Fig 2)
giving f =0.658; and
and peak current I0=128 kA.
The coil gives a peak first half cycle output of 24 V (measured from Fig 2)
Checking validity of Step 1: sheet positions in the axial phase and the radial phase. The plasma focus acts in the following way: A capacitor bank 1/3 Correction required if the current sheet had moved
FIG. 3. Discharge current waveform at 11 kV, 2 Torr neon.
So it takes 3.9ms for the current sheet to travel 16 cm, the length of the axial phase.
The average speed in this axial phase is 4.1 cm/ms for this shot at 11 kV, 2 Torr neon.
proportional to the charging voltage. Here r is the density which is proportional to the pressure for a fixed gas.
Step 2: Fitting the computed current trace to the measured current trace to determine the static inductance L0 1/7
FIG. 4. Fitting the computed current trace to the measured current trace by varying model parameters fm and fc. This good fit was obtained after several operations described in the following
by the addition of a small time delay.
Computed rising slope too shallow indicating L current trace to determine the static inductance L0 too large (also consistent with too low a current peak) [left figure] Correct by increasing L0 in steps until best fit; then small adjustments needed for r0 & fm & fc [right figure] 6/7
Note: The method is so sensitive that it picks up (see devaition feature at lower right of fitted figure) a current looping feature that occurs as the voltage across the tube drops to zero at t~5 us. The closing of that loop suddenly removes the remnant flux of the original current, from the capacitor bank circuit, thus reducing total inductance; resulting in shortening the discharge periodic time starting at t~5us.