1. INTRODUCTION
Intense electron-beam accelerators (IEBA) based on the Blumlein line (Friedman et al., Reference Friedman, Limpaecher and Sirchis1988; Phelps et al., Reference Phelps, Franklin, Homeyer, Nerem and Overett1990; Liu et al., Reference Liu, Li, Zhang, Li and Wang2006) is widely used in a great variety of applications such as in lasers (Sethian et al., Reference Sethian, Myers, Smith, Carboni, Kishi, Morton, Pearce, Bowen, Schlitt, Barr and Webster2000; Apruzese et al., Reference Apruzese, Giuliani, Wolford, Sethian, Petrov, Hinshelwood, Myers and Ponce2006), high power microwave generators (HPMG) (Clark et al., Reference Clark, Mardar and Bacon1988; Fan et al., Reference Fan, Zhong, Shu and Li2008; He et al., Reference He, Cao, Zhang, Wang and Ling2011), X-pinch (Zou et al., Reference Zou, Liu, Zeng, Han, Yuan, Wang and Zhang2006; Li et al., 2008), X-ray generation (Coogan et al., Reference Coogan, Davanloo and Collins1990; Kuai et al., Reference Kuai, Wu, Qiu, Wang, Cong and Wang2009), and so on. At present, the increase of power and repetitive rate and the duration of the output pulse (Liu et al., Reference Liu, Yin, Ge, Zhan, Cheng, Feng, Shu, Zhang and Wang2007a; Yatsui et al., Reference Yatsui, Shimiya, Masugata, Shigeta and Shibata2005) are the important development trend for an accelerator. To increase the duration of the output pulse, spiral type pulse forming line was widely used (Korovin et al, 2001; Liu et al., Reference Liu, Yin, Ge, Zhan, Cheng, Feng, Shu, Zhang and Wang2007a). For the conventional Blumlein pulse forming line (BPFL), it consists of mainly three coaxial cylinders of different radii, named inner cylinder, middle cylinder, and outer cylinder, respectively. The inner cylinder and middle cylinder form inner pulse forming line (PFL), middle cylinder and outer cylinder form outer PFL. But for the spiral type BPFL, the middle cylinder is usually spiral type cylinder (Liu et al., Reference Liu, Cheng, Qian, Ge, Zhang and Wang2009), which may cause the distortion of the output voltage waveform and affect the quality of the electron beam, because the quality of the electron beam is directly affected by the output voltage waveform. Meanwhile, improving the electron-beam quality is very important for the requirement of the applications of the IEBA. Especially in the application of HPMG, the ideal pulse voltage is the flattop rectangular pulse, because the typical HPMG can operate at the highest of efficiency in this pulse voltage (Robert & Edl, Reference Robert and Edl2001). So the factors that affect the quality of the output voltage waveform of IEBA should be studied.
In the paper (Liu et al., Reference Liu, Cheng, Qian, Ge, Zhang and Wang2009), the design of a spiral type BPFL for the ideal output voltage pulse on a matched load is discussed. A good output voltage waveform is obtained when the radius of the middle cylinder is the geometric average of the inner and outer cylinder radii. Also, the effect of transition section between the main switch and the BPFL, BPFL and load on the output voltage of IEBA based on spiral type BPFL had also been discussed (Cheng et al., Reference Cheng, Liu, Qian and Zhang2009, Reference Cheng, Liu, Zhang, Feng and Qian2010). Recently, effects of radial dielectric discontinuity caused by the support dielectric and filling dielectric on the dispersion characteristics of tape helix PFL were analyzed, it was obtained that if the permittivity of support dielectric was smaller than that of filling dielectric, the electric length of the PFL was shortened, and the reverse condition corresponded to the reverse results (Zhang et al., Reference Zhang, Liu, Wang, Fan, Zhang and Feng2011). However, the effect on the fluctuation of output voltage waveform had not been analyzed. So, in this paper, the output voltage waveform of IEBA based on spiral type BPFL is analyzed, the reasons to cause the fluctuation of the output voltage waveform are discussed. In Section 2, the IEBA is introduced and the typically output voltage waveform is given. Then, the fluctuation of the output waveform is discussed in Section 3. Also, the factors that affect the fluctuation are obtained. And the combination of electromagnetic simulation software and PSpice circuit simulation software are used to calculate the output voltage waveform. Finally, the conclusion is given in Section 4.
2. IEBA SYSTEMS AND TYPICAL WAVEFORM
Figure 1 shown the schematic of the IEBA, which was capable of generating a quasi-square wave with voltage of 100–600 kV by adjusting the gas pressure of the main switch, and full width at half maximum (FWHM) of 180 ns when connected to impedance-matched load of 10 Ω. The IEBA consisted of a 50 kV, 12 uF primary storage capacitor, a 50 kV field distortion trigger switch, a spiral strip type pulsed transformer (Liu et al., Reference Liu, Zhan, Zhang, Liu, Feng, Shu, Zhang and Wang2007b) with output voltage up to 600 kV, main switch with sulfur-hexafluoride (SF6) used as insulating medium, strip spiral type BPFL with impedance of about 10 Ω, vacuum chamber which was pumped by the combination of mechanical and molecular pumps to keep the vacuum degree up to 10−3 Pa, voltage and current diagnostic system.
(Color online) Schematic of the intense electron beam accelerator based on strip spiral type Blumlein line.
Just as shown in Figure 1, a resistant divider (A) that placed between the output terminal of the pulse transformer and main switch was used to measure the charging voltage of the BPFL, and resistant divider (B) was also placed on the output terminal of the BPFL in order to measure the load voltage. A Rogowski coil that was used to measure the load current.
The operating process of the IEBA was as follow. When the charging voltage of the primary storage capacitor reached a certain value, the field distortion trigger switch was triggered and closed, and then the primary storage capacitor discharged to the primary winding of the transformer consequently, the transformer started to charge the BPFL. Once the charging voltage of the BPFL reached the breakdown value of the main switch, the BPFL discharged to the load, and a quasi-square wave with a rise time approximately 30 ns and FWHM of 180 ns was formed. The amplitude of the quasi-square wave could be adjusted from 100 kV to 600 kV by changing the gas pressure (Pm = 0–0.50 MPa) of the main switch, so the output peak power could be up to 30 gigawatt.
The typical charging voltage, load voltage, and current waveform of the IEBA were shown in Figure 2 when a water load of 10 Ω was used. Figure 2a had shown the charging voltage. At point A, the triggered switch shown in Figure 1 was closed, the primary storage capacitor started discharging to the primary winding of the pulse transformer, and consequently, the transformer started charging the BPFL. And then at point B the main switch (gas pressure of the main switch was 0.30 MPa) was breakdown, a pulse with 180 ns FWHM would be formed on the water load. From Figure 2a, it was clearly shown that the charging time (Tc) was about 5.4 µs, and the output waveform was Quasi-square pulse wave with FWHM of 180 ns, load voltage of 350 kV and current of 30 kA (Fig. 2b).
(Color online) Typical waveform of the IEBA at gas pressure of 0.15 MPa when a water load of 10 Ohm was used (a) of charging voltage (b) load voltage and current.
3. DISCUSSION
3.1. Fluctuation of the Flattop of the Load Voltage
In Figure 2, there was obvious fluctuation on the flattop of the load voltage waveform, and several important points were labeled as t 1, t 2, t 3, t 4, t 5, and t 6. At t 1, the main pulse of the output voltage started, and the flattop of the pulse began at time of t 2. Consequently, the voltage of the flattop started increasing at time of t 3. The duration between t 2 and t 3 could be called as first flattop. Then, the output voltage was up to a maximum at time of t 4. Next, the waveform began dropping to a lower voltage until t 5 and a second flattop was formed, the duration was the subtractive value between t 6 and t 5. After t 6, the load voltage started decreasing. In fact, this kind of fluctuation was disadvantageous to the IEBA applications, such as HPMG. The typical HPMG can operate at the highest efficiency with a flattop rectangular pulse, and the microwave may collapse if there is fluctuation on the flattop of the load voltage.
The reason to form the first flattop was the transition section that is between the middle cylinder of BPFL and the load (Cheng et al., Reference Cheng, Liu, Zhang, Feng and Qian2010). Meanwhile, the electron emission of the cathode holder was one of the reasons that the load voltage was decreased from t 4 to t 5, because comparing with high voltage, this kind of decrement was not so obvious at lower voltage (Cheng et al., Reference Cheng, Liu, Fan, Hong and Qian2011).
3.2. Flatness of the Output Voltage
Figure 3 shows the output voltage waveform at different gas pressure of the main switch, and it was clearly shown that the load voltage was difference at different gas pressure of the main switch. To discuss the quality of the waveform, three points were labeled as V 1, V 2, and V 3, and the flatness h1 = |(V1 − V2)/V2| × 100% and h2 = |(V3 − V2)/V2| × 100% were defined. Obviously, if h 1 = h 2 = 0, the load voltage was a well shaped square wave pulse. Meanwhile, the flatness of different gas pressure of main switch could be obtained from Figure 3, and which was shown in Figure 4.
(Color online) Output load voltage at different gas pressure of the main switch.
(Color online) The flatness for different gas pressure of the main switch.
It was found the flatness h 1 was almost the same for different gas pressure of the main switch, about 8.5%. However, the flatness h 2 was about 9.5% at lower gas pressure, but when the gas pressure was up to 0.30 MPa, h 2 was quickly increased to 15.2%. So, the output voltage waveform was affected by the amplitude of the load voltage. At higher voltage, the distortion of the output voltage waveform was much serious. In the paper (Cheng et al., Reference Cheng, Liu, Fan, Hong and Qian2011), this kind of phenomenon had been discussed and the electron emission of the cathode holder was the one of the reasons to cause this phenomenon.
3.3. Electron Emission of Cathode Holder
In order to clearly show the electron emission of the cathode holder, a digital camera was placed at the view port in Figure 1 to record the image during the experiment. The time integrated pictures of the electron emission event were taken with the digital camera.
At lower gas pressure of the main switch (0 and 0.10 MPa), the load voltage was much lower, and only two pictures were recorded for each shot, so the duration of the light was very short. The typical pictures for each shot were shown in Figure 5. It was shown that the luminous intensity was different. At gas pressure of 0 MPa, the purple light was very dark (A1), and than after 0.033 s, the purple light was changed to white light (A2). Meanwhile, the insulator and water load was clearly observed in the picture. But when the gas pressure of the main switch was up to 0.10 MPa, the luminous intensity of the purple light (B1) was much stronger than that in (A1), there ware two purple light spots, also after 0.033 s, the white light (B2) was appeared. But now, the water load was all enveloped by the white light. Obviously, the luminous intensity of the light in picture B2 was much stronger than that in picture A2.
(Color online) Photograph from the view port during the experiment at lower gas pressure, the duration between picture A1 and A2 (B1 and B2) was about 0.033 second, (a) Pm = 0 MPa, (b) Pm = 0.10 MPa.
At higher gas pressure of the main switch (0.20 and 0.30 MPa), pictures were difference with that in Figure 5, and eight or nine pictures were recorded for each shot. In other words, the duration of the light was much longer, about 0.260 s. Figure 6 showed the typically three pictures for gas pressure of 0.20 and 0.30 MPa, respectively. There was no obvious purple light in Figure 6a, and the vacuum chamber was full of white light (C1), it was because of that the electron emission of the cathode holder was very intense at higher voltage, and the luminous intensity was too strong to observe the purple light. But after 0.033 s, the light became weak and weak (C2, C3). After about 0.260 s, the light disappeared. The same result was obtained in Figure 6b, and the luminous intensity in picture D1 was much stronger than that in picture C1.
(Color online) Photograph from the view port during the experiment at higher gas pressure, the duration between picture C1, C2 and C3 (D1, D2 and D3) was about 0.033 second, (a) Pm = 0.20 MPa, (b) Pm = 0.30 MPa.
In a word, at higher load voltage, the intensity of the electron emission of the cathode was much stronger. So the load voltage became lower after point t 4 in Figure 3 and the distortion of the load voltage was much obvious.
3.4. Effect of Spiral Type BPFL on the Flatness of the Flattop of the Output Voltage
The electron emission of the cathode holder had a great effect on the flatness of the flattop of the output voltage pulse, and this kind of effect was much obvious at higher voltage. However, at low voltage, the flatness h 1 and h 2 was also up to 8.5% and 9.5%, respectively. So, it was very important to decreases the flatness and to improve the quality of the output voltage waveform. According to Chernin et al. (Reference Chernin, Antonsen and Levush1999), the current along the spiral type cylinder was not uniform, while the spiral type Blumlein line was usually done as uniform. So the uniformity of the current along the spiral type middle cylinder may be the reason to cause the fluctuation of the output voltage, because of that the impedance of the Blumlein line was not a constant value while the current was not uniform. To calculate the current density along the spiral middle cylinder, a three-dimensional model was built by electromagnetic simulation software in Figure 7. A voltage path with 1 V was added on the spiral cylinder, and the current density along the arrow could be obtained in Figure 8.
(Color online) Structure of the strip spiral type middle cylinder of the Blumlein line.
(Color online) Current density along the strip spiral type middle cylinder of the Blumlein line.
It was obtained that the current density along the arrow in Figure 7 was not a constant value actually. If linear fit of the current density, the tendency of the current density was decreased. So, it was proved that the impedance of the Blumline was not a constant value. According to the theory of the pulse forming line, the voltage was continuous along the line, and the product of the current and impedance of the line was a constant value. So the impedance was increased along the arrow in Figure 7. The impedance of inner line and outer line was about 6.4 and 4 Ω by the formula in this paper (Liu et al., Reference Liu, Cheng, Qian, Ge, Zhang and Wang2009); it was regard as the average impedance of the pulse forming line. From Figure 8, it could be induced that the minimal and maximal of impedance of inner line was 5.8 and 6.9 Ω, and 3.6 and 4.4 Ω for outer line, respectively. Also, considering the distribution of the current density in Figure 8, the transmission time could be obtained for different impedance. Then, the load voltage could be calculated by PSpice Circuit analysis software, and Figure 9 showed the schematically the circuit model when the nonuniformity of the BPFL was take into account.
(Color online) PSpice model of IEBA for calculating the output voltage when the nonuniformity of the strip spiral middle cylinder of Blumlein was taken into account.
As shown in Figure 9, C1 is the primary energy-storage capacitance, and R1 and L1 are the resistance and inductance of primary winding circuit, high voltage pulse transformer and the main switch are modeled and indicated by XForm1 and GAP1 in the circuit, respectively. T_in_1, T_in_2, and T_in_3 were connected to simulate the nonuniformity of the inner line, T_out_1, T_out_2, and T_out_3 were used to simulate the nonuniformity of the outer line, and also, the inner line and outer line are connected in parallel to simulate the BPFL. T_T was used to simulate the transition section between the Blumline line and load. R2 and R3 are the resistors of the resistant divider in Figure 1; L2 is the inductor that connects the inner cylinder of the BPFL to the ground. RL is the load of the IEBA. The whole circuit is connected with components built in PSpice component storage or modeled by the authors according to the performance of the device. In the circuit, the operation voltage of the IEBA is controlled by the main switch, GAP1.
Figure 10 shows the PSpice simulation result of the voltage waveform at the matching load. When the non-uniformity of the BPFL was taken into account, the actual theoretical result waveform was the simulation results. Meanwhile, when the non-uniformity of the BPFL was not taken into account (Impedance of T_in_1, T_in_2, and T_in_3 are all 6.4 Ω, T_out_1, T_out_2, and T_out_3 are all 4.0 Ω), the ideal theoretical result waveform stands for the simulation results.
(Color online) Comparison between the experimental results and theoretical calculation results.
In Figure 10, comparison between the experimental result and ideal theoretical results, there was first flattop, and the duration of the first flattop was almost the same. However, after the first flattop, the load voltage was a constant value for the ideal theoretical result, and there was no fluctuation on the flat part of the main pulse. Obviously, the ideal theoretical result did not agree with the experimental results well. Meanwhile, if the nonuniformity of the BPFL was taken into account, the actual theoretical result was obtained and which shown reasonable agreement with the experimental result. First, the first flattop was obtained from the actual theoretical results, and then, the output voltage was up to a maximum, next the waveform began decreasing to a low voltage and a second flattop was formed. So, it was proved that the nonuniformity of the BPFL was one of the reasons to cause the fluctuation of the output voltage waveform.
4. CONCLUSIONS
The output waveform of an intense electron beam accelerator based on strip spiral BPFL was analyzed, and the reason to cause the fluctuation of the flattop of the main pulse was discussed. Through the theoretical analysis, simulation results, and experiments results above, some conclusions can be lead to the following: (1) there was fluctuation for the flattop of the main pulse, at lower voltage, the flatness h 1 and h 2 was about 8.5% and 9.5%. However, at high voltage, the flatness h 1 was unchanged, but flatness h 2 was increased, when the gas pressure was up to 0.30 MPa, h 2 was quickly increased to 15.2%. (2) According to the analysis of the flatness h 2 and time integrated pictures of the electron emission event, the electron emission of the cathode holder was the main reason to cause the increment of the flatness h 2 at higher voltage. (3) According to the electromagnetic simulation and PSpice circuit simulation, the nonuniformity of the BPFL based on strip spiral type middle cylinder was one of the reasons to cause the fluctuation of the main pulse of the output voltage. So, to improve the quality of the output waveform of IEBA, the uniformity of the spiral middle cylinder should be improved, and the electron emission of the cathode holder should be avoided.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the support from the Fund of innovation, Graduate school of NUDT under Grand No. B090701. This work is also supported by Hunan Provincial Innovation Foundation for Postgraduate under Grand No.CX2009B007.
