Hanyu WU (吴撼宇), Zhengzhong ZENG (曾正中), Mengtong QIU (邱孟通),Peitian CONG(丛培天),Jinhai ZHANG(张金海),Xinjun ZHANG(张信军)and Ning GUO (郭宁)

State Key Laboratory of Intense Pulsed Radiation Simulation and Effect, Northwest Institute of Nuclear Technology, Xi'an 710024, People's Republic of China

Abstract The post-hole convolute(PHC),which is used to transport and combine the pulse power flux,is a key component in huge pulsed power generators. Current loss at the PHC is a challenging problem for researchers. To explore a method of reducing the current loss, a single-hole PHC was designed for experiments on the current loss on the Qiang Guang I generator. The experimental results showed that the current loss at the single-hole PHC is related to the distance l between the vicinity of the cathode hole and the surface of the downstream side of the post.Meanwhile, a single-hole PHC with a blob cathode hole transmitted current more effectively than the PHC with a circle cathode hole.The relative current loss at the single-hole PHC with the cathode coated with gold foil was about 30%-50% of that with the cathode coated with nickel and titanium foil. The gap closing speed was also obtained from the current waveforms in the experiments. The speed was 5.74-14.52 cm μs−1 which was different from the classical plasma expansion velocity of 3 cm μs−1.

Keywords: plasma, post-hole convolute, magnetic insulation, current loss(Some figures may appear in colour only in the online journal)

1. Introduction

Experiments on a huge pulse power generator can provide new insights into high-energy-density physics [1], inertial confinement fusion [2, 3], shock physics [4], and isentropic compression [5]. At present, multi-module and parallel designs are commonly used for huge pulse generators such as the Z-machine [6, 7] and primary test stand (PTS) [8]. This concept is also used in the design of next generation huge pulse power generators [9, 10].

The generator is usually composed of a primary energy storage system, water transmission system, laser trigger gas switch,water-vacuum-insulator stacks,magnetically insulated transmission lines (MITLs), and load, for example the Z-machine generator [7]. The four-level MITLs are usually connected to a single inner MITL by a double post-hole convolute (PHC). However, significant current loss has been observed at the PHC and the inner MITL under the condition of high current density [8, 11, 12]. The peak value of the current loss is up to about 4 MA while the peak current value is 22 MA at the insulator stack in the Z1786 shot [11].The peak value of the electron current loss is up to 300 kA at the PTS generator when the load peak current value is about 8.8 MA [8]. While the understanding of the principle of current loss at the PHC is still unclear, the research on the current loss at the PHC is exigent for the design of the next pulse power driver in China.

In this paper,we would like to introduce an experimental study of the current loss of a PHC with a single hole. The input linear current density appears to be an important influential factor on current loss at the MITLs and PHC [13-15],so the linear current density of the PHC on the Qiang Guang I(QG I) generator will be designed to be close to that of the Z-machine.

2. Experimental setup

The QG I generator is designed for plasma and radiation effect experiments [16-19]. When the load is short circuit, it can produce voltage with about a 1 MV peak value current with about a 1.5 MA peak value, and 100 ns rise time at the vacuum transmission line [20]. The current from the QG I generator is far less than the current from the Z-machine generator. Therefore the design of the PHC based on QG I generator is challenging and interesting work, because the linear current density at the PHC should be close to the PHC of the Z-machine generator.

As shown in figure 1, the PHC comprises a tri-plate transmission line with open configuration. The transmission line cathode is a triangular plate, as shown in figure 2. The plates above and below the central cathode plate are transmission line anodes.The width of the anode plate is 350 mm.And the longest width of the triangular cathode plate is 200 mm.The edge of the cathode is milled into an arc-shaped structure to reduce the electron emission at this zone.The red cylinder connecting the anodes represents the convolute post which passes through a hole at the cathode. The cathodeanode (AK) gap distance of the plate transmission line is 10 mm.The diameter of the cathode hole and the post can be varied.The distance between the axis of the load and the posthole is about 54 mm.The short circuit load is a metal cylinder with a diameter of 20 mm.

The configuration of the cathode at the QG I generator can help the linear current density near the cathode hole get close to that of the PHC in the Z-machine. By examining a single-pole PHC, we can understand the character of the whole PHC, because the PHC on the Z-machine [6, 7] and other similar devices [8] has a rotational symmetry configuration. And the single-hole PHC can be obtained by magnetic insulation based on the laminar flow theory [21].

The electron emission at the cathode edge from the single-hole PHC should be avoided or diminished as far as possible. Fortunately, the experiments on the tapered convolute [22] on the MITE generator which is also a tri-plate transmission line showed that the loss at the plane is dominated (approximately 85% is to the sides) by the loss at the sides [22], because the area of the plane is larger than that of the sides. In our experiments, there is also no obvious discharged channel observed at the cathode sides.

There are two kinds of the cathodes for the single-hole PHC in the experiments,as shown in figure 2.In figure 2,l is the distance between the downstream edge of the cathode hole and the surface of the post, along the line from the center of load to the post.In figure 2(b),D1is the diameter of the small circle hole, D2is the diameter of the big circle hole, and the distance between the center of the small and big circle holes d is 20 mm.The post is placed in the center of the big circle of the cathode with a blob hole.

The experiments are operated at the QG I generator.B-dots are used to measure the upstream and downstream current of the single-hole PHC. The relative standard deviations of their scale factors are all less than 2%. A copper shielding cover is used to protect the B-dot from the plasma bombardment. There is a gap with a suitable width on the cover for the measurement of magnetic field. Because the pulse high power flow will destroy the load and the post,the single-hole PHC needs to be set up after each experiment.

3. Experimental results

3.1. Current loss of the single-hole PHC with different configurations

Figure 3 shows the current waveforms of Shot 18124. The cathode hole and post are both made of stainless steel. The diameter of the cathode hole is 30 mm, and the diameter of the anode post is 8 mm. In figure 3, the waveforms of the upstream and the downstream currents are consistent with each other until there are obvious differences of current waveforms after the current peak value.The result in figure 3 indicates that there is no obvious current loss near the cathode hole before the current peak.

The linear current density near the cathode hole can be seen in figure 3. The maximum value of the downstream current is about 1.25 MA while the time is about 100 ns.The minimum width of the cathode near the hole is about 2 cm.The linear current density is about 625 kA cm−1, and the linear current density near the PHC in the Z-machine is about 570-670 kA cm−1calculated from its experimental data [6,23-25]. The two values are close to each other.

On the other hand,the current on the post is estimated to be about 625 kA just half of 1.25 MA. The linear current density on the post can also be estimated as 249 kA cm−1.It is also close to the linear current density of 250-300 kA cm−1of the post in the Z-machine [6, 23-25].

Figure 4 shows the voltage and current waveforms at the single-hole PHC.The voltage at the single-hole PHC is about 100 kV.There is obvious current loss near the cathode hole in Shot 19039.The diameters of the cathode hole and the anode post are 18 and 8 mm, respectively. The peak values of the upstream and the downstream currents are respectively about 1.19 and 1.06 MA. The loss current is about 0.13 MA at the current peak. In figure 4, the current waveforms indicate an obvious deviation after 25 ns. Because of the high electromagnetic interference, the waveforms from the B-dots after the peak are of greater uncertainty. In this paper, only the current waveforms before the peak are used in the analysis.

The current loss in the experiments is related to the configuration of the single-hole PHC.Other experimental data are listed in table 1.Here,Dkand Dpare the diameters of the cathode hole and the post, respectively. Iupis the upstream current peak. ILis the loss current which is the difference between the upstream and downstream current peaks. l is the gap distance,as shown in figure 2.The relative current loss is a ratio of the current loss to the upstream current. In table 1,the maximum relative current loss is larger than 50%, while the diameters of the cathode hole and the post are 15 and 8 mm, respectively. The minimum relative current loss is smaller than 1%,while the diameters of the cathode hole and the post are 30 and 6 mm, respectively. Considering the relative standard deviations of the B-dots, the experimental results show that the relative current loss is smaller than 5%and are all considered to have no current loss.

From the data in table 1, more information can be obtained as shown in figure 5.Figure 5 shows that the relative current loss will decrease nonlinearly as the ratio Raof the distance l to the distance Dgapof the tri-plate transmission line increases. The Dgapis 10 mm and distance l is just(Dk− Dp)/2 for the circular cathode hole.The relative current loss decreases from 57.4% to 5% while the l/Dgapincreases from 0.35 to 0.6.The results suggest that the distance l should be over 60%of the distance of the Dgap,if the relative current loss is required to be less than 5%.

Table 2 shows the experimental data of the single-hole PHC with the cathode blob hole, as shown in figure 2. The results show that there is no current loss in the experiments on the single-hole PHC with the cathode blob hole. The configuration of the single-hole PHC with the cathode blob hole is better than that with the cathode circular hole for current transmission.

The distance l as shown in figure 2 seems to be the most important parameter. Comparing shots 19037, 19035, and 19041, the distance l of Shot 19041 is the largest, and thecurrent loss is the smallest.The results suggest that the region where the distance l is located is the easiest to form a discharged channel in the experiments. The reason may be that the magnetic field topology of the single-hole PHC is beneficial to the concentration plasma here.

Table 1. Data of the different single-hole PHCs with cathode circular holes. The electrodes are made of stainless steel.

3.2.Current loss of the single-hole PHC with different materials

The plasma source is the gas absorbed on the electrode surface [9, 13, 25-28]. There are different absorption capacities with different electrode materials. Experiments on the singlehole PHC with different materials are also operated. The materials are gold (Au) [29], titanium (Ti) [30], and nickel(Ni) [29], respectively. The absorption capacity of the Au is weaker than the capacity of the Ti and the Ni.The metals are respectively plated on the surface of the stainless steel cathode holes and posts by electroplating. The metal foil is used to prevent air from contacting electrodes. The thickness of the metal foil is about 5 μm in the experiments for exploring which metal can isolate the gas from the electrodes better.The question of how the thickness of the metal foil is better will be beyond the scope of this study.

Table 2. Data of the single-hole PHC with the cathode blob hole. The electrodes are made of stainless steel.

Figure 6 shows that the relative current losses are different as the materials change.The experiments include three configurations. The first configuration is diameters of the cathode hole and post of 15 and 8 mm, respectively. The second configuration is diameters of 15 and 6 mm, respectively. The third configuration is diameters of 18 and 8 mm,respectively.

In figure 6,the variation trend of the relative current loss with the distance l is consistent with the results above.Besides, it is obvious that there is the least relative current loss while the single-hole PHC is plated with the Au foil.The relative current losses of the single-hole PHC plated with the Ni and the Ti foils are close to that of the single-hole PHC made of stainless steel.The relative current loss of the singlehole PHC coated with the Au foil is just 30%-50% of those coated with other materials. The results indicate that the Au foil can help decrease the current loss of the single-hole PHC [29].

As known, the electrode plasma comes from the electrode surface where the neutral gas adsorbed will discharge based on the high electric field and the ohmic heat[12, 13, 24, 25]. Because of the inactive nature of Au, the neutral gas desorbed from the Au surface is far less than that from the other material surfaces in the experiments. Then the plasma density in the gap between the cathode hole and the post would be so small that the impedance of the current loss channel in the convolute is larger than the load impedance.Compared with the single-hole PHC plated with other materials,the single-hole PHC plated with Au has the best current transmission efficiency in the experiments.

3.3. The AK gap closing speed

The plasma expansion velocity is an interesting parameter.The AK gap is closed when the plasma in the vicinity of the convolute is up to the post. Then the current would be shunted, which should be transmitted to the load. During the experimental study, we define a gap closing speed to study the current loss of the single-hole PHC. It can also help researchers indirectly understand the expansion characteristics of the plasma in the gap between the vicinity of the cathode hole and the anode post.

The beginning of the plasma is hard to measure, so the beginning of the gap closing is defined as the time which is at 10%of the upstream current peak.We assume that there is no or few plasma, and can be neglected before that, because the pre-pulse current is smaller than 100 kA. The ending of the gap closing is defined as the time when there are obvious differences between the upstream and the downstream currents. In figure 7, the closing time of the gap is about 40 ns,and the distance l is 4.5 mm. The gap closing speed is about 11.25 cm μs−1. The 17 experimental data of the gap closing speed are illustrated in figure 8. The speed values are 5.74-14.52 cm μs−1.

The experimental value is larger than the classical plasma expansion velocity 3 cm μs−1[24-28]. The classical plasma expansion velocity is only related to the electrode material[28],and its value varies little when the plasma temperature is 3-5 eV [28]. There must be some unknown reasons which can make the plasma motion faster.We guess that the cathode negative ions [13, 26] may be a potential competitor in all possible principles. In a particle-in-cell simulation of the single-hole PHC,we obtain the expansion velocity of cathode negative ion flow of about 10 cm μs−1[31] which is close to our experimental results.

Besides, the gap closing speed is less than the measured 35-50 cm μs−1plasma closing velocity [12]. The reasons may be that(a)the electric field intensity in the Z-machine is larger than that in the QG I generator, (b) the optic measurement method [12] can achieve a mean velocity in a shorter time ∼10 ns,but the method in our study can estimate a mean speed during the whole process of the plasma expansion, (c) the plasma motion is not in linear evolution,for the plasma motion may experience multi-state including high velocity, low velocity, and even transient stagnation,(d) the factors of current loss are not only the plasma closing velocity,but also the plasma density.When the plasmas reach the anode, there may be no obvious difference between the upstream and downstream current waveforms if there is not enough plasma density.

4. Conclusions

In this paper, experiments on single-hole PHC based on the QG I generator are introduced. The linear current density of the single-hole PHC is close to that of the PHCs in the Z-machine in order to understand the characteristics of the PHC under the condition of high linear current density.

The results of the experiments show that there are different current losses for a variety of single-hole PHCs when the load is a copper rod with a diameter of 20 mm.According to the experimental data, the single-hole PHC has only a 5%current loss when the distance l is longer than 0.6Dgapand the cathode hole is circular hole,and there is no loss current when the gap distance l is larger than the Dgap.

The results also show that the cathode with a blob hole is better than the cathode with a circular hole for the transmission efficiency of the current, because the distance l of the cathode with a blob hole is larger than others.

The electrode material also has an effect on the current transmission efficiency of the single-hole PHC. Compared to the stainless steel, Ti, and Ni, the convolute plated with Au foil has better current transmission efficiency.

The gap closing speed is obtained from the current waveforms.In this paper,the gap closing speed is 5.74-14.52 cm μs−1,and can show information on the plasma motion. The results indicate that the gap closing speed is related to the configuration of the convolute. The speed is faster than expected for a rough 3-5 eV plasma[24,25],and is closed to the expansion velocity of the cathode negative ion flow [31], but less than the plasma closing velocity [12]. The results suggest that there should be a new principle to explain the contradiction.

Despite the progress made in this paper, there are still many questions to be studied. The appropriate thickness of Au foil is unknown. The geometric parameter of a blob hole in which the current loss turns on is still unclear. The correlation between the impedance of the current loss channel near the convolute and the plasma density is unclear.The principle of the motion of the plasma including the cathode negative ions near the convolute under high electromagnetic field is uncertain.A more detailed study on current loss at the singlehole PHC will be conducted in future experiments.

Acknowledgments

This work is supported by National Natural Science Foundation of China (Nos. 51790521, 11875224) and the Foundation of State Key Laboratory of Intense Pulsed Radiation Simulation and Effect (Nos. SKLIPR1701Z, SKLIPR1901).