REVIEW OF SCIENTIFIC INSTRUMENTS 81, 033302 共2010兲
A compact high-voltage pulse generator based on pulse transformer with closed magnetic core Yu Zhang, Jinliang Liu,a兲 Xinbing Cheng, Guoqiang Bai, Hongbo Zhang, Jiahuai Feng, and Bo Liang College of Optoelectronic Science and Engineering, National University of Defense Technology, Changsha 410073, China
共Received 16 November 2009; accepted 25 January 2010; published online 12 March 2010兲 A compact high-voltage nanosecond pulse generator, based on a pulse transformer with a closed magnetic core, is presented in this paper. The pulse generator consists of a miniaturized pulse transformer, a curled parallel strip pulse forming line 共PFL兲, a spark gap, and a matched load. The innovative design is characterized by the compact structure of the transformer and the curled strip PFL. A new structure of transformer windings was designed to keep good insulation and decrease distributed capacitance between turns of windings. A three-copper-strip structure was adopted to avoid asymmetric coupling of the curled strip PFL. When the 31 F primary capacitor is charged to 2 kV, the pulse transformer can charge the PFL to 165 kV, and the 3.5 ⍀ matched load can deliver a high-voltage pulse with a duration of 9 ns, amplitude of 84 kV, and rise time of 5.1 ns. When the load is changed to 50 ⍀, the output peak voltage of the generator can be 165 kV, the full width at half maximum is 68 ns, and the rise time is 6.5 ns. © 2010 American Institute of Physics. 关doi:10.1063/1.3321494兴
I. INTRODUCTION
Since 1960, pulsed power technology has been widely used in a good many fields, including high power microwave ultrawideband rf radiation,3,4 x-ray radiation,1,2 4–6 7–11 chemical reactions,11–13 radiography, radiation physics, and biological researches.14,15 In the future, the developments of the powerful pulse generators tend to be higher power,16,17 higher repetitive frequency,2,4–6,16,17 and more miniaturized volume.1,3–6,11 In view of these irreversible trends, a plan of compact structure and minimized volume has been adopted in this paper to construct a high-voltage nanosecond pulse generator. Marx generators and pulse forming networks 共PFNs兲 are usually used to construct high-voltage pulse generators. However, by contrast to pulse transformers, Marx generators are much huger and more complex, though both of them can boost voltage up to 100 kV grade.18,19 So, pulse transformers can be used to substitute Marx generators in many applications.20–22 There are also many types of pulse transformers, such as air-core transformers, Tesla transformers with open magnetic cores, closed magnetic-core transformers, and so on. An air-core transformer has advantages of simple structure and low cost but the effective coupling coefficient is usually low.23,24 A Tesla transformer with open magnetic core, having been developed to a high level by Russian scientists, has superiority on high coupling and high voltage output, but the structure and technologies are more complex, which lead to high cost.3–6,16,17 A pulse transformer with closed magnetic core, which also owns attributes of a兲
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high coupling and high efficiency, has usually been used to charge PFN to produce repetitive long microsecond pulses. However, researches on the closed magnetic-core transformer that charges the pulse forming line 共PFL兲 and produces short nanosecond pulses are much fewer.21 In this paper, a new design approach of integration of a pulse transformer with closed magnetic core and a small curled parallel PFL is presented to achieve goals of high coupling and high output voltage. The generator consists of pulse transformer, curled parallel strip PFL, spark gap, and a matched load. The output voltage pulse of the pulse generator has a peak amplitude of 20–80 kV with 9 ns duration and 5.1 ns rise time, and form the 3.5 ⍀ matched load. If the load is changed to 50 ⍀, the output peak voltage can be 165 kV, the duration of full width at half maximum 共FWHM兲 is 68 ns, and the rise time is 6.5 ns. The size of the system is about ⫻ 共22 cm兲2 ⫻ 80 cm and the weight is less than 30 kg. By contrast to Ref. 21, the pulse generator we produced is much more compact and portable, and the cost is much lower. It also provides another technical way for portable high-voltage pulsers at 10 ns range, by contrast to compact Tesla pulsers.3–6 This pulse generator has already been employed to trigger the trigatron in our laboratory. II. STRUCTURE OF THE GENERATOR
As shown in Fig. 1, the four parts of the pulse generator are in series to make a more compact structure. The input point, allocated at the bottom of the generator, connects with the primary charging capacitor and primary windings of pulse transformer. The output point of transformer’s second windings joints the high-voltage electrode of PFL so that the transformer can charge the PFL. The parallel strip PFL consists of three curled copper strips and 40 layers of Mylar
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FIG. 1. 共Color online兲 Compact high-voltage pulse generator system 关共1兲 pulse transformer, 共2兲 curled parallel strip PFL, 共3兲 spark gap, 共4兲 load resistor, and 共5兲 nylon support cylinder兴.
films. As insulated material, every 20 layers of Mylar films fill in the interspace between every two copper strips. The PFL immerges in transformer oil. Because a large number of small air bubbles clinging to the films and copper strips can remarkably weaken the capability of insulation, the PFL will be broken down by high voltage before the spark gap discharges. So the transformer and the PEL need to be put in a hermetic hollow nylon cylinder, in order that the chamber inside can be vacuumized and then filled with transformer oil to keep superior insulation. There are two small holes in the wall between the chambers of spark gap and load, and insulated gas can be aerated into these two chambers at the same time. On the sides of these two chambers, high-voltage detectors are installed. The working principle of the pulse generator is described as follows. When the switch between the primary capacitor and transformer switches on, the pulse transformer boosts low voltage pulses and delivers much higher voltage pulses to the PFL due to its good coupling between windings. The PFL is charged to a high-voltage level until the spark gap is broken down. Then, the PFL discharges to the load resistor and the load delivers high-voltage nanosecond pulses. III. THEORETICAL DESIGN OF THE PULSE GENERATOR A. Pulse transformer
Pulse transformers are powerful devices which are used to boost voltage to several hundred kilovolts to charge the PFL.20,25–28 In order to increase effective coupling coefficient of transformer windings, a magnetic ring made from ironbased amorphous alloys was used as the closed magnetic core of pulse transformer. Then, the magnetic core was fixed into a bigger hollow insulated cylinder to enable good endurance to high voltage. The primary and secondary windings of the transformer, separately winded around the walls of the insulated cylinder without overlapping, and an essential distance between the two windings were needed to keep insulation. To get excellent effect of insulation, the one-turn primary winding consists of three wires in parallel to resist high pulse current. New consideration of the secondary winding is that it consists of two interlaced layers of wires. The second turn in the outer layer winds after the first turn in the inner layer, and then the third turn winds in the inner layer, the fourth one winds in the outer layer, and so on. This structure makes lower voltage and smaller distributed capacitance between turns. Lastly, the insulated cylinder and the magnetic core were both enclosed in the windings. The whole transformer immerged into transformer oil to keep insulation. The
FIG. 2. 共Color online兲 Pulse transformer with closed magnetic core 关共1兲 secondary winding, 共2兲 primary winding, 共3兲 support cylinder, and 共4兲 insulated films兴.
pulse transformer is shown in Fig. 2. In Fig. 3, the geometrical structure of the cross-section of the transformer is presented. For the sake of convenience, some geometrical parameters should be defined first. In Fig. 3, to the insulated cylinder, the longitudinal length is l0, the inner and outer transverse diameters are D1 and D2, the thickness of its inner wall is d2, the thickness of outer wall is d1, and the bottom thickness is d5. To the magnetic core, the longitudinal length is lm and the transverse diameters are D3 and D4. The distance between the front faces of insulated cylinder and magnetic core is d4, while the back counterpart is d3. To the primary winding, the diameter of the wire is d p and the number of turns is N1. ds and N2 are counterparts to the second winding. To the iron-based amorphous alloys, saturated magnetic inductive intensity 共Bs兲 is as large as 1.56 T and the residual magnetic inductive intensity is close to 0. The initial relative permeability of the material 共r兲 is about 2500. Lastly, the permittivity and permeability of vacuum are 0 and 0. According to geometrical parameters, the longitudinal cross-section area of the magnetic core 共S兲 is calculated as S = 共D4 − D3兲lm/2.
共1兲
To portray the characteristics of the pulse transformer, some important electromagnetic parameters need to be figured out. We define the magnetization inductance of the transformer as L, the leakage inductances of primary and secondary windings as Lps and Lss, and the self-inductances of primary and secondary windings as L1 and L2. Mutual inductance and
FIG. 3. 共Color online兲 Cross-section of the pulse transformer.
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TABLE I. Geometrical parameters of the pulse transformer. l0 共mm兲
Lm 共mm兲
D1 共mm兲
D2 共mm兲
D3 共mm兲
D4 共mm兲
100.8 d1 10.05
50 d2 5.6
68.8 d3 25.4
170 d4 25.4
80 d5 10
150 ¯ ¯
effective coupling coefficient of windings are defined as M and Keff. From Ampere’s circuital law and principles of magnetic flux, the magnetization inductance can be calculated as L =
0rN21SKT ln共D4/D3兲 . 共D4 − D3兲
netic core. However, there are still a few that exist outside of the core and they are mainly concentrated in the insulated cylinder and the windings, which lead to leakage inductance of the windings. The volume of the primary winding itself is V1 and the volume of insulated cylinder section, which is enclosed only by the primary winding, is V2. The leakage magnetic fields of the primary winding mainly converge in volumes V1 and V2. All the same, Va and Vb correspond to the secondary winding’s two leakage volumes. From the relations between leakage inductance and energy of the leakage magnetic fields, the leakage inductances of primary and secondary windings are calculated as Eq. 共3兲. The forms of V1, V2, Va, and Vb are presented in Eq. 共4兲.
冦
共2兲
In Eq. 共2兲, KT represents the filling coefficient of the magnetic core. As we know, most of the magnetic fields, generated by the currents in the windings, converge in the mag-
冦
V1 = 3l0d p共d1 + d2兲 + 共D4 − D3兲3d p共d4 + d3兲/2 V2 = 6d2p共l0 + 共D2 − D1兲/2兲 Va = l0d1共D2 − d1兲 + l0d2共D1 + d2兲 + 共D24/4 − D23/4兲共d4 + d3兲 Vb = 2dsl0共D2/2 + D1 − 3ds/2兲 + ds共D22 − D21兲/2
Because the self-inductance of the primary winding represents all the magnetic energy generated by the primary current, L1 consists of L and Lps, which separately represent magnetic energy in the core and leakage magnetic energy outside the core. So does L2, the self-inductance of the secondary winding. Self-inductances are presented as
再
L1 = L + Lps L2 = L共N2/N1兲2 + Lss
.
冎
共5兲
In view of r Ⰷ 1, magnetic induction intensity in the core is much larger than the counterpart outside. The effective coupling coefficient and mutual inductance between primary and secondary windings are presented as follows:
冦
M = LN2/N1
Keff =
冑
1−
Lps + Lss共N1/N2兲2 . L
冧
共6兲
.
Lps =
冉
0N21 V2 2 V1 + 3 9d p
冉
冊
0N 2 Vb Lss = 2 2 2 2 Va + 3 共D1 + D2兲/4
冊冧
共3兲
.
冧
共4兲
voltage. Meanwhile, the primary winding consists of three shunt-wound wires to resist high current. So d p is designed as 4 mm and ds as 3 mm. In order to get a higher turns ratio of the two windings, N1 is designed as only one turn and N2 as 110 turns. According to Eqs. 共1兲–共6兲 and the data from Table I, the electromagnetic parameters can be calculated as shown in Table II. By comparison to the theoretical data in Table II, accurate meter “HP4284A” was used to test the electromagnetic parameters under a frequency of 100 kHz. Because the output pulse period of the transformer is about 10 s, the frequency for testing was fixed at 100 kHz. The measurement results are shown in Table III. Theoretical data are close to the tested data and the relative percentage errors of M and Keff are both less than 6%. B. Curled parallel strip PFL
Considering the limits of size and the capability of highvoltage endurance, geometrical parameters are designed in Table I. The wire diameter of secondary winding must be large enough so that the wire can endure 100 kV grade high
At present, there are many forms of pulse forming, such as PFNs,19 coaxial PFL,3–6 and spiral PFL.16,27–29 Usually, the insulated dielectric filling in the PFL is water or oil,
TABLE II. Electromagnetic parameters of the transformer.
TABLE III. Measurement results of electromagnetic parameters.
L1 共H兲
Lps 共H兲
L2 共mH兲
Lss 共H兲
M 共mH兲
Keff
L1 共H兲
Lps 共H兲
L2 共mH兲
Lss 共H兲
M 共mH兲
Keff
13.02
0.41
153
152.7
1.39
0.984
11.93
0.36
129.5
8.8
1.31
0.945
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FIG. 5. 共Color online兲 Simplified geometric structure of the PFL. FIG. 4. 共Color online兲 Unfolded parallel strip PFL and its support.
sometimes even the mixture of water and glycol. Coaxial PFL and spiral PFL are often made of materials of iron and steel, which lead to high costs and big weights. Since we only need short pulses, PFL method is still prior to PFN method. So the parallel strip PFL, as a simple and low-cost method for pulse forming, is designed in this paper. As Fig. 4 shows, the parallel strip PFL consists of three 1-m-long copper strips and 40 layers of 1.2-m-long insulated films. The structure of three-copper-strip is a new consideration to reject asymmetric coupling that appears when the copper strips are curled in a two-copper-strip structure. The material of the insulated films is polyester film and polyester fiber, which is usually called as Mylar films. The width of Mylar films is 200 mm, which is twice as large as the width of copper strips. The thickness of each film is 0.15 mm and the thickness of each copper strip is 0.2 mm. To each layer of film, the voltage of surface flashover is about 10 kV in air but more than 16 kV in transformer oil. The inner copper strip and the outer one are jointed together as ground electrodes of the PFL. The middle strip connects with the secondary winding of pulse transformer as high-voltage electrode. Every 20 layers of Mylar films fill in the interspace between every two copper strips as dielectric. The distance between adjacent long edges of the strips and the films is 50 mm, which is enough to prevent surface flashover. To get smaller size and compact structure, the parallel strip PFL is tightly curled up around a hollow support cylinder as a capacitance to store electrical energy. All parts of the PFL immerge in transformer oil in a hermetic chamber to keep good insulation. Unfortunately, this is far from enough because enormous small air bubbles stick to the walls of the films and strips. We define the relative permittivity of air, oil, and the films as 1, 2 共2.3兲, and 3 共2.5兲 in order. As 3, 2 ⬎ 1, these air bubbles 共1 = 1兲 obviously change the electric field intensity around its borders so that dielectric films can be broken down easily. So the hermetic chamber of the PFL must be vacuumized first and then filled with transformer oil. The simplified geometric structure, which represents a single transmission line, is presented in Fig. 5. If the distance between the middle strip 共high-voltage electrode兲 and the ground strip is d, and the width and length of copper strips are a and l, then capacitance, inductance, characteristic impedance, and pulse delay time of the PFL are orderly defined
as C, L, Z0, and 0. These electric parameters can be calculated as follows. According to the definition of capacitance, C is listed as C = 203al/d.
共7兲
As a Ⰷ d, we assume that the traveling waves in the PFL are mainly transmission electron microscopy 共TEM兲 waves. From Ampere’s circuital law and conservation of magnetic energy, L is presented as L = 0dl/共2a兲.
共8兲
The length of the PFL is so short 共l = 1 m兲 that the PFL can be viewed as a lossless transmission line. The characteristic impedance is like this Z0 = 冑L/C.
共9兲
If the phase velocity of TEM wave in the PFL is V p, V p = 共LC兲−0.5, the pulse delay time of the PFL can be calculated as
0 = l/V p = l冑LC.
共10兲
So the pulse duration of the PFL is like this: = 20. From Eqs. 共7兲–共10兲, the electric parameters of the curled parallel strip PFL can be figured out as shown in Table IV. Actually, C and Z0 are tested at the frequency of 100 kHz for reference. The tested C was 1.38 nF and tested Z0 was 3.5 ⍀. In a word, the theoretical data in Table IV correspond to the tested data, which proves that theoretical design is reasonable. C. Spark gap and load resistor
In order to get sharp front edges of pulse, a spark gap was used to sharpen the pulses coming form the transformer. Together with the spark gap, the PFL can produce short highvoltage pulses of 10 ns duration and deliver them to the load resistor. Figure 1 shows the structure of the spark gap and load resistor. The walls of the hermetic chambers were made from insulated material. Half-sphere copper electrodes were used to minimize the asymmetric effects of electric fields. The distance between two electrodes was 1 cm. According to TABLE IV. Electric parameters of the PFL. C 共nF兲
L 共nH兲
Z0 共⍀兲
共ns兲
1.36
18.9
3.73
10.1
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FIG. 6. 共Color online兲 Geometric structure of the load resistor and its equivalent circuit.
Paschen’s law, high pressure insulated gas, such as nitrogen or SF6, filled in the gap chamber to increase the voltage of breakdown. The voltage test point of the PFL is allocated at the side wall of the gap chamber, connected by a narrow copper strip inside the chamber. Usually, high power resistors with low parasitic parameters, which can take the place of vacuum diodes,28 were used in test experiments of pulse generators. As shown in Fig. 6, load resistors with wavy surface were designed to test the output voltage of the pulse generator. The main component of the water solution inside the load resistor was bluestone. The voltage test point of the load resistor is also allocated at the side wall of the hollow cylinder, which enclosed the load resistor. The geometric structure of load resistor and its equivalent circuit of parasitic parameters are presented in Fig. 6. In Fig. 6, l0 represents the length of the water solution of bluestone and ⌽0 is the inner diameter. The lengths of the electrodes on the two sides of load resistor are l1 and l2. Relative permittivity of the solution is 4. The parasitic inductance and parasitic capacitance of load resistor are LR and CR, while the resistance is R0. The parasitic capacitance can be calculated as CR = 0420/共4l0兲.
FIG. 8. 共Color online兲 Output voltage of the pulse transformer in simulation.
was designed to 3.5 ⍀ to match with the characteristic impedance of the PFL 共Z0兲, or the pulse transformer will be broken down easily at the situation of low load resistance.28 When the temperature is 20 ° C, 4 is about 40. According to Eqs. 共11兲 and 共12兲, CR is 23.1 pF and LR is 16.8 nH from theoretical calculation. IV. CIRCUIT SIMULATION OF THE SYSTEM PSPICE circuital analysis was used to simulate the highvoltage pulse generator system based on a curled parallel strip PFL and pulse transformer with closed magnetic core. Figure 7 shows the equivalent circuital schematics of the pulse generator system. In the schematics, C1 represents primary energy-storage capacitor, of which the capacitance and maximum charging voltage are 31 F and 3 kV. In the primary circuit of the transformer, L1 and R1 represent stray inductance and stray resistance. L2 stands for stray inductance between pulse
共11兲
As we know, the magnetic field induced by line-distributed current weakens when distance from the current increases. To estimate LR for reference, we assume the magnetic field is close to 0 when the distance from the center of the resistor is farther than 5⌽0. Actually, by contrast to the intense magnetic field near load resistor, the approximate estimation is reasonable. With reference to Ref. 30, LR can be calculated from magnetic flux induced by the current of load resistor. LR = 5.1700l0 .
共12兲
Equation 共12兲 infers that a longer resistor has larger parasitic inductance. However, a shorter resistor may have trouble on high-voltage endurance for a long time because the flashover distance becomes shorter. Meanwhile, large ⌽0 causes large CR, which leads to inferior waveforms of output voltage pulse. In view of these limits, these geometric parameters were designed like this: l0 is 30 mm and ⌽0 is 50 mm. R0
FIG. 7. 共Color online兲 Equivalent schematics of the pulse generator system.
FIG. 9. 共Color online兲 PSPICE simulation results 关共a兲 output voltages of load resistor; 共b兲 output currents of load resistor; 共c兲 output voltage of load resistor 共U0 = 1.5 kV兲; 共d兲 output current of load resistor 共U0 = 1.5 kV兲; 共e兲 output voltages of pulse transformer and load resistor 共U0 = 1.5 kV and R0 = 50 ⍀兲; and 共f兲 output current and voltage of load resistor 共U0 = 1.5 kV and R0 = 50 ⍀兲兴.
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FIG. 10. 共Color online兲 Compact pulse generator system in experiment.
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FIG. 12. 共Color online兲 Output voltage and current pulse of the matched load resistor in experiment.
transformer and the PFL, while R2 represents the resistant divider. L3 is the connective inductance between the spark gap and load resistor. Resistant divider R3 is in parallel with the load resistor. Parameters of the pulse transformer, the PFL, and the load resistor are set up according to theoretical calculations and tested values. Parameters of other parts are listed in Fig. 7. When the switch is closed, C1 discharges to the transformer and then the transformer charges the PFL and boosts the voltage. If the initial voltage of C1 is defined as U0, the output voltage waveforms of the transformer are presented in Fig. 8. When U0 equals to 1 kV, the spark gap can be broken down at 100 kV with 8 s charge time. The step-up ratio is about 100. When U0 becomes 1.5 kV, the breakdown voltage is 160 kV and the step-up ratio is about 106, with 8.6 s charge time. When U0 changes from 0.5 to 1 and 1.5 kV, output voltages and currents of load resistor are presented in Figs. 9共a兲 and 9共b兲. Different locations of waveforms attribute to different times when the spark gap breaks down. When U0 is 1.5 kV, the output voltage pulse of the load resistor has an amplitude of 78 kV, FWHM of 10 ns, and rise time of 4.5 ns, as shown in Figs. 9共c兲 and 9共d兲. However, if R0 changes to 50 ⍀, the pulse generator can match with many microwave components. Then the maximum output voltages and currents of load resistor are presented in Figs. 9共e兲 and 9共f兲. As Fig. 9共e兲 shows, the output voltage of PFL is almost completely delivered to the load resistor because R0 is far more than characteristic impedance of the PFL. Lastly, a sawtooth voltage pulse with an amplitude of 165 kV and FWHM of 75 ns is generated.
In experiments, fast responsive Rogowski coil and resistant dividers were developed to detect high pulse currents and voltages of the transformer and load resistor. Insulated gases, such as nitrogen and SF6, were pressed into the chambers of the spark gap and load resistor to increase breakdown voltage. The compact pulse generator system is presented in Fig. 10. First, the generator was tested for reference without any insulated gas. The 1-cm-wide air gap was broken down when U0 was 350 V. The output voltage of transformer was 38 kV and voltage of matched load resistor was 20 kV. Then, nitrogen was pressed into spark gap to increase the pressure inside. According to the increase in the pressure inside, U0 varied from 0.35 to 2 kV so that the load resistor can deliver voltage pulses with different amplitudes. When U0 was 2 kV and the pressure was 3 atm, the highest output voltage appeared. As shown in Fig. 11, the peak voltage of transformer 共Um兲 was about 150 kV with 8.6 s charge time. In Fig. 12, the amplitude of the current pulse 共I0兲 of the matched load resistor is 25 kA. The voltage pulse 共U0兲 has an amplitude of 84 kV, FWHM of 9 ns, and rise time of 5.1 ns. When R0 was changed to 50 ⍀, the typical results are shown in Fig. 13. The amplitude of voltage signal 共U0兲 is about 155 kV and the amplitude of current signal 共I0兲 is 3.1 kA. The load resistor can deliver the highest voltage pulse with an amplitude of 165 kV, FWHM of 68 ns, and rise time of 6.5 ns. The experiment results basically correspond to PSPICE simulation results and theoretical design.
FIG. 11. 共Color online兲 Output voltage pulse of the pulse transformer in experiment.
FIG. 13. 共Color online兲 Output voltage and current of the 50 ⍀ load resistor in experiment.
V. EXPERIMENTS AND RESULTS
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VI. CONCLUSIONS
A high-voltage pulse generator, based on a curled parallel strip PFL and pulse transformer with closed magnetic core, is developed in this paper. Theoretical analyses and calculations of the PFL and pulse transformer are presented. Moreover, the equivalent circuit analyses on parasitic parameters of the load resistor are also considered. Results of experiments, circuit simulations, and theoretical designs basically correspond to one another. The generator can deliver voltage pulses with peak amplitude from 20 to 80 kV, FWHM of 9 ns, and rise time of 5.1 ns to a 3.5 ⍀ matched load. Pulses with a peak amplitude of 165 kV and FWHM of 68 ns can also be delivered to a 50 ⍀ load. Characterized by the compact and miniature structure of the transformer and the PFL, the generator has good stability with very low costs. At present, the pulse generator has been employed to trigger the trigatron in our laboratory. In the future, researches on repetitive work mode of the pulse generator will be carried out. ACKNOWLEDGMENTS
This work was supported by the National Natural Science Foundation of China under Grant No. 10675168. 1
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