Ringing Gain Analysis for Calibrating X-Ray Machines: Detailing A New Approach and Some Problems

At AWE, ringing-gain voltage waveforms are analysed to calibrate pulsed-power machines in which electrical energy, stored in a Marx generator, is switched into a Blumlein pulse-forming line (PFL) via inductance and in the presence of serial and parallel resistive losses. Traditionally, an equivalent circuit comprising lumped capacitors, inductors and resistors is used which allows the determination of three unknown electrical parameters from two decay constants and the frequency of an oscillatory component calculated from the ringing-gain waveform. The Blumlein transmission line can be represented as a lumped capacitor since its transit time is much smaller than the time to reach peak voltage. Generally, the serial inductance and resistance of the Marx generator and its parallel resistance are assumed unknown whereas the Marx-generator capacitance, Blumlein capacitance and voltage-monitor resistance are assumed known. The ringing-gain analysis also yields the sensitivity of the voltage monitor. A new approach to ringing-gain analysis allows the determination of one of the decay constants from the current waveform and the other from the voltage waveform. This should improve the calibration accuracy of X-ray machines with relatively few ´rings´ on their ringing-gain waveforms, such as the PIM inductive voltage adder (IVA) machine at AWE. The dynamic resistance associated with Marx generator spark-gaps, which reduces with time, is also considered. This can cause the first cycle of the ringing-gain waveform to deviate from that predicted by the equivalent circuit unless time variability of the serial resistance is properly accounted for. Coupling the Blumlein output of an AWE prototype IVA machine to ground via an inductor, to reduce pre- pulse voltage, is found to affect adversely the ringing-gain waveform. The complexity of the equivalent circuit is increased since the two capacitive elements of the Blumlein must be considered separately. However, including a furthe- - r inductor in a balance circuit minimises adverse effects on the ringing-gain waveform.