Dual-Waveform Ringing Gain Analysis and its Application to Pre-Pulse Reduction on Blumlein-Based X-ray Machines

Summary form only given. Pulsed-power machines at AWE are routinely used for flash X-ray radiographic applications in the 1-10 MV range to drive high-and low-impedance e-beam diodes. During the pulse-forming line (PFL) charging phase, certain diode types are sensitive to pre-pulse voltages as low as a few tens of kilovolts due to small anode-cathode gaps and geometries that enhance electric fields. This results in electron emission before the main pulse is applied which can prevent the diode from operating properly. It is therefore crucial to limit the pre-pulse voltage appearing at the diode to below the emission level. A Blumlein PFL, as used on all AWE machines at present, comprises three co-axial cylindrical conductors, the outer one of which is grounded. The intermediate conductor, of voltage V_in, is charged from the output of a Marx bank. An output pulse is created on the inner conductor on closure of an oil-switch which shorts the inner and intermediate Blumlein conductors. Prior to closure of this switch, the voltage of the inner Blumlein conductor, denoted by V_i, which is actually the pre-pulse voltage, must be kept as close to ground as possible. This can be accomplished using a balance circuit, comprising two inductors (L_i & L_o) and two damping resistors (R_i & R_o) which connect to the base of the Marx bank. For ideal electrical balance, the ratios L_i:L_o and R_i:R_o must equal the ratio C_o:C_i where C_o is the capacitance between the outer and intermediate Blumlein conductors and C_i is the capacitance between the inner and intermediate Blumlein conductors. Practical circuits will likely have some level of imbalance and non-zero pre-pulse voltage (V_i). This situation cannot be dealt with by the standard AWE ringing gain analysis method which applies solely to the charging waveform (V_{i- n}) and gives values only for such parameters as: Marx parallel resistance (R_p), series resistance (R_s) and inductance (L_s), based on the match between analytical and machine waveforms. By extending the analysis to the pre-pulse voltage (V_i), values of the balance circuit components (L_i, L_o, R_i & R_o) can also be obtained. The Laplace transform technique is used, taking into account non-zero initial conditions, and the solution in the time domain obtained by applying Heaviside´s expansion theorem. Theory predicts that, when there is electrical imbalance, an oscillatory perturbation to the charging waveform (V_in) will result and give rise to pre-pulse voltage (V_i) which can be high. These findings are consistent with experimental observations. On Blumlein-based machines, dual-waveform ringing gain analysis should assist in: (i) keeping the electrical system balanced, (ii) reducing pre-pulse voltage levels, and (iii) allowing ringing gain analysis to be performed on machines with serious electrical imbalance.