Differential-output $B$-dot and $D$-dot monitors for current and voltage measurements on a 20-MA, 3-MV pulsed-power accelerator

We have developed a system of differential-output monitors that diagnose current and voltage in the vacuum section of a 20-MA 3-MV pulsed-power accelerator. The system includes 62 gauges: 3 current and 6 voltage monitors that are fielded on each of the accelerator’s 4 vacuum-insulator stacks, 6 current monitors on each of the accelerator’s 4 outer magnetically insulated transmission lines (MITLs), and 2 current monitors on the accelerator’s inner MITL. The inner-MITL monitors are located 6 cm from the axis of the load. Each of the stack and outer-MITL current monitors comprises two separate $B$-dot sensors, each of which consists of four 3-mm-diameter wire loops wound in series. The two sensors are separately located within adjacent cavities machined out of a single piece of copper. The high electrical conductivity of copper minimizes penetration of magnetic flux into the cavity walls, which minimizes changes in the sensitivity of the sensors on the 100-ns time scale of the accelerator’s power pulse. A model of flux penetration has been developed and is used to correct (to first order) the $B$-dot signals for the penetration that does occur. The two sensors are designed to produce signals with opposite polarities; hence, each current monitor may be regarded as a single detector with differential outputs. Common-mode-noise rejection is achieved by combining these signals in a $50\mathrm{\text{−}}\Omega$ balun. The signal cables that connect the $B$-dot monitors to the balun are chosen to provide reasonable bandwidth and acceptable levels of Compton drive in the bremsstrahlung field of the accelerator. A single $50\mathrm{\text{−}}\Omega$ cable transmits the output signal of each balun to a double-wall screen room, where the signals are attenuated, digitized ($0.5\mathrm{\text{−}}\mathrm{ns}/\mathrm{sample}$), numerically compensated for cable losses, and numerically integrated. By contrast, each inner-MITL current monitor contains only a single $B$-dot sensor. These monitors are fielded in opposite-polarity pairs. The two signals from a pair are not combined in a balun; they are instead numerically processed for common-mode-noise rejection after digitization. All the current monitors are calibrated on a 76-cm-diameter axisymmetric radial transmission line that is driven by a 10-kA current pulse. The reference current is measured by a current-viewing resistor (CVR). The stack voltage monitors are also differential-output gauges, consisting of one 1.8-cm-diameter $D$-dot sensor and one null sensor. Hence, each voltage monitor is also a differential detector with two output signals, processed as described above. The voltage monitors are calibrated in situ at 1.5 MV on dedicated accelerator shots with a short-circuit load. Faraday’s law of induction is used to generate the reference voltage: currents are obtained from calibrated outer-MITL $B$-dot monitors, and inductances from the system geometry. In this way, both current and voltage measurements are traceable to a single CVR. Dependable and consistent measurements are thus obtained with this system of calibrated diagnostics. On accelerator shots that deliver 22 MA to a low-impedance $z$-pinch load, the peak lineal current densities at the stack, outer-MITL, and inner-MITL monitor locations are 0.5, 1, and $58\mathrm{MA}/\mathrm{m}$, respectively. On such shots the peak currents measured at these three locations agree to within 1%.

Figure 1

Cross-sectional view of the four-level vacuum-power-flow section of the $Z$ pulsed-power accelerator [1, 2, 4, 5, 6, 7, 8, 9]. Each level includes a vacuum-insulator stack and an outer MITL. This view shows the locations of the insulator-stack $D$-dot, outer-MITL $B$-dot, and inner-MITL $B$-dot monitors. The stack $B$-dots (which are not pictured here) are located at the same radial location as that of the stack $D$-dots, but at different azimuthal locations. The outer diameter of the insulator stack is 3.35 m.

Figure 2

Two cross-sectional views of the differential-output $B$-dot current monitor that is fielded on the outer MITLs of the $Z$ accelerator. Not shown here is the 0.005-mm-thick nichrome foil that is placed over the epoxy-filled volumes. The foil shields the epoxy and $B$-dot sensors from the high electric field in the MITL’s anode-cathode gap.

Figure 3

Lumped-circuit model of a single outer-MITL $B$-dot current sensor.

Figure 4

Cross-sectional view of the central region of the $B$-dot calibration system.

Figure 5

Result of the calibration of an outer-MITL $B$-dot current monitor. The reference current is that measured by a current-viewing resistor (CVR). The normalized standard deviation of the pointwise difference [Eq. (12)] between the two current-pulse shapes is less than 1%.

Figure 6

Cross-sectional view of the inner-MITL $B$-dot current monitor.

Figure 7

Result of the calibration of an inner-MITL $B$-dot current monitor. The reference current is that measured by a current-viewing resistor (CVR). The normalized standard deviation of the pointwise difference [Eq. (12)] between the two current-pulse shapes is less than 1%.

Figure 8

Location of a differential-output $D$-dot voltage monitor in the anode of the $Z$-accelerator’s B-level insulator stack. (All four stack levels are illustrated by Fig. 1.)

Figure 9

Cross-sectional view of the differential-output $D$-dot voltage monitor that is fielded on the insulator stack of the $Z$ accelerator.

Figure 10

Lumped-circuit model of an insulator-stack $D$-dot sensor [75].

Figure 11

Result of an in situ calibration of a differential-output $D$-dot voltage monitor. The reference voltage is generated using current measurements (made with calibrated $B$-dot current monitors) and the geometry of the stack-MITL-load system. The normalized standard deviation of the pointwise difference between the two voltage-pulse shapes is less than 1%. The standard deviation is calculated using an expression analogous to Eq. (12).

Figure 12

Measurements on $Z$-shot 1548 of the D-level insulator-stack voltage at 6 azimuthal locations.

Figure 13

Measurements on $Z$-shot 1548 of the A-level insulator-stack current at 3 azimuthal locations.

Figure 14

Measurements on $Z$-shot 1548 of the A-level MITL current at 6 azimuthal locations.

Figure 15

Measurements on $Z$-shot 1548 of the inner-MITL current at 2 azimuthal locations.

Figure 16

Measurements on $Z$-shot 1548 of the total insulator-stack, outer-MITL, and inner-MITL currents.

Figure 17

Result of a numerical cable compensation [79] that is performed using a step-function voltage pulse. The undegraded pulse has a 10%–90% rise time of 1.3 ns and a peak voltage of 0.5 V. When the pulse is transported through the coaxial-cable system delineated by Table , the pulse suffers a significant reduction of its high-frequency components. Both the undegraded and degraded pulses are used to generate a deconvolution function for the coaxial-cable system [79]. The numerically compensated pulse plotted above is obtained by deconvolving the degraded pulse [79]. (The waveforms have been time shifted to facilitate comparisons.)