REVIEW OF SCIENTIFIC INSTRUMENTS 86, 015109 (2015)
A large-dynamic-range current probe for microsecond pulsed vacuum breakdown research Liang Zhao,a) Jian-cang Su, Xi-bo Zhang, Rui Li, Lei Zheng, Bo Zeng, Jie Cheng, Xi-yuan She, and Xiao-long Wu Science and Technology on High Power Microwave Laboratory, Northwest Institute of Nuclear Technology, Xi’an, Shaanxi 710024, China
(Received 25 August 2014; accepted 26 December 2014; published online 16 January 2015) A large-dynamic-range current probe for microsecond pulsed vacuum breakdown research is fabricated. The basic principle of this probe is to turn the current signal to a voltage one via a load of fixed impedance and to test the voltage signal via a voltage divider of adjustable voltage ratio. With a segment of 40-Ω coaxial line, which is connected to the experimental chamber, and a self-fabricated two-stage resistor-capacitor voltage divider, the current probe is realized and is applied to test the vacuum breakdown current for 3-cm parallel-plate electrodes under microsecond pulses. The results show that the current probe is capable of responding to current signals with an amplitude of 10−2-103 A and a duration of 10−2-101 µs. Based on the current probe, the characteristics of the vacuum breakdown current under 30-µs quasi-sinusoidal pulses are summarized. The potential mechanisms for each type of current are also discussed in this paper. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4905624]
I. INTRODUCTION
proportional to the current amplitude, I, the following relation holds true:
The amplitude of the current in vacuum breakdown process usually varies from several picoamperes (pA) to several kiloamperes (kA), and the time scale usually changes from nanosecond (ns) to millisecond (ms) time scale.1–3 The dynamic range of the vacuum breakdown current may get even larger when the applied voltage is a pulse. It is of importance to measure the current in vacuum breakdown process, since knowing the vacuum breakdown current characteristics can not only help to understand the vacuum breakdown mechanism but also to increase the vacuum insulation strength. Several methods are proposed to measure the pulsed breakdown current. The typical one is the Rogowski Coil, which is put forward in 1887.4–8 This coil is based on the Faraday’s Law of Induction, which can respond to a current signal with a duration in a wide range.9–11 It also has the advantages of easy assembly. However, the sensitivity (S) of a Rogowski Coil is usually limited by the configuration of the device to be tested. If the device is small, the S of a Rogowski Coil cannot be designed too large. Another method is the current divider, the principle of which is to employ a resistor of small resistance (R) to turn the current signal to a voltage one.12 The S of a current divider depends on the R and the power (P) of the resistor. An ideal resistor in a current divider should be of small R and large P. As a matter of fact, this type of resistor is usually unobtainable. A third method is the electro-optic sensor.12 This method employs the effect that the collimated light would get twisted in a dielectric when a magnetic field is imposed on the dielectric. The twisted angle, θ, is proportional to the applied magnetic field, M. Since M is
a)Author to whom correspondence should be addressed. Electronic mail:
[email protected]. Tel.: +86-29-84767631.
0034-6748/2015/86(1)/015109/9/$30.00
θ = k I,
(1)
where k is a constant. The advantage of an electro-optic sensor is that it is less affected by the external electromagnetic environment. But, it has a disadvantage that it needs a set of complicated optic devices. All these methods aforementioned are appropriate to measure a current signal with a fixed amplitude and a fixed duration. However, when the amplitude and the duration of the current signal change in a large dynamic range, these methods are not applicable and a new method should be devised. In our laboratory, when conducting the vacuum breakdown experiments using a pair of Bruce-profiled parallel-plate electrodes under microsecond pulses, we found that different changes had taken place on the main voltage waveform for different voltage amplitudes. The experimental chamber containing the Bruce electrodes is shown in Figure 1 in which the vacuum gap is set as 3 cm and the effective flat area of the Bruce electrode is 28.3 cm2 (effective diameter: 6 cm). The normal waveforms compared with the abnormal ones are shown in Figures 2(a)–2(d). For the normal waveform, it is quasi-sinusoidal with a full width at half maximum (FWHM) of 30 µs. This pulse is produced by a Tesla-type generator, TPG400. Detailed introduction on the TPG400 as well as on the Tesla-type generators can be seen in Refs. 13–21. For the abnormal waveform, it is found that they can be classified into two types: the “recessed” ones, such as those shown in Figures 2(a) and 2(c), and the “chopped” ones, such as those shown in Figures 2(b) and 2(d). We wonder what are the characteristics of the current waveforms corresponding to the abnormal waveforms and what types of physical mechanisms are hidden behind the current waveforms? To answer these
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A. Consideration on τ
For the τ, from Figures 2(a) and 2(c), it is seen that the recesses on the main waveforms are of a duration of tens of microseconds. So, it is believed that the τ of the current waveform corresponding to the recessed voltage waveforms is also about tens of microseconds. From Figures 2(b) and 2(d), it is seen that oscillations take place on the main waveforms. These oscillations are due to the wave reflection between the switch (vacuum chamber) and the load of the TPG400. Since the length of transmission line (TL, a segment coaxial line between the switch and the load) of the TPG400 is about 1 m, which corresponds to an electrical length of 10 ns (1-m transmission line corresponds to an electrical length of 10 ns), it is considered that the τ of the current waveform for chopped voltage waveforms is about 10 ns. FIG. 1. Bruce-profiled parallel-plate electrodes assembled in a vacuum experimental chamber.
B. Consideration on S
questions, a current probe, which can respond to a signal in a large dynamic range, is needed. In this paper, a current probe meeting both the sensitivity and the duration requirements is designed and fabricated. This probe has two features: (1) It has a large dynamic range that it can test a current with an amplitude of 10−2-103 A and a FWHM of 10−2-101 µs; (2) It is realized by simple common components such as a voltage divider and a segment of coaxial line. The general consideration for this probe is presented in Sec. II. The design on the probe is dealt with in Sec. III. The calibration results for this probe are given in Sec. IV. Section V is for the typical vacuum breakdown current waveforms obtained via this current probe and the potential mechanisms. The last section, e.g., Sec. VI, is for the conclusions in this paper.
II. GENERAL CONSIDERATIONS
The current probe is considered in two aspects: (1) time constant-τ and (2) sensitivity-S.
For S, it is calculated with the following formula: S=
Iv , Uout
(2)
where Iv is the vacuum breakdown current and Uout is the voltage displayed on the oscillograph. Assuming that Uout is fixed, the S of the current probe would only depend on Iv . For Iv , it is evaluated with the following formula: Iv = C
∆U , ∆t
(3)
where C is the capacitance of the equivalent capacitor of parallel-plate electrodes, which is simulated to be 6 pF; ∆U is the voltage decrement; and ∆t is the time duration or the time constant. For the recessed abnormal voltage waveforms, ∆U is about 10-100 kV and ∆t is about 10 µs. So, Iv is calculated to be 6-60 mA. For the chopped abnormal voltage waveforms, ∆U is about 400-800 kV and ∆t is about 10 ns. So, Iv is calculated to be 240-480 A. So, Iv is in the range of 6 mA-480
FIG. 2. Abnormal waveforms compared with the normal 30-µs quasi-sinusoidal pulses at different voltage amplitudes.
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A. Letting Uout be 1 V, S of the current probe would be in the range from 6 mA·V−1 to 480 A·V−1 according to Eq. (2).
III. DESIGN ON THE CURRENT PROBE
Taking into account that the TL assembled next to the vacuum chamber is a segment of coaxial line with a fixed impedance of 40 Ω, this line can be used as a “resistor” to turn the current signal to a voltage one. So, the question on how to measure a large-dynamic-range current is turned to that on how to measure the voltage signal in a large dynamic range. Since the voltage applied on the coaxial line, Uline, and current flowing through the line, Iv , conforms to the following relation: Iv =
Uline , Zline
(4)
where Zline is the impedance of the TL, S can be transformed into the following expressions by inserting Eq. (4) into Eq. (2): S=
1 Uline β = , Zline Uout Zline
(5)
where β is defined as the voltage ratio of the voltage divider assembled on the coaxial line. Letting Zline be equal to 40 Ω and S be equal to 0.006-480 A·V−1 as aforementioned, β would be in the range of 0.24 V·V−1-19.2 kV·V−1. Aside from the voltage ratio, the time constant should also be considered into. The common methods to test the voltage of the high-voltage (HV) pulses include the resistor voltage divider, the capacitor voltage divider, and the composed resistorcapacitor voltage divider,12 among which the composed resistor-capacitor voltage divider is a feasible approach due to its large voltage ratio and wide time constant. Figure 3 shows the equivalent circuit of a typical two-stage resistor-capacitor voltage divider, in which C1 and C2 are the HV-arm and the low-voltage-arm (LV-arm) capacitors of the first-stage voltage divider (also the capacitor voltage divider), respectively; R1 and R2 are the HV-arm and the LV-arm resistors of the second-stage voltage divider (also the resistor voltage divider), respectively. Subsections III A–III D are devoted to the calculation on a desired two-stage capacitor-resistor voltage divider. A. Calculations on the voltage ratio of the two-stage voltage divider
The voltage ratio of the first-stage voltage divider, β1, can be expressed as follows: C1 +C2 C2 ≈ (C2 >> C1), β1 = C1 C1
(6)
ε 0ε r A , Ro ln Ro /Ri
where ε 0 and ε r are the dielectric constant in vacuum and the relative dielectric constant of the insulation dielectric, respectively; Ri and Ro are the inner and the outer radii of the coaxial line, respectively; A is the area of the brass-covered thin dielectric film. As to C2, it can be calculated as follows: C2 = C0 A,
(8)
where C0 is the unit-area capacitance of a brass-covered thin dielectric film, which is a constant. For the coaxial line to turn the current signal to a voltage one assembled next to the vacuum chamber, Ri = 104 mm, Ro = 202 mm, and ε r = 1 (the insulation dielectric is vacuum). The thin brass-covered film is made of polyimide and is with a C0 of 60 pF·cm−2. With these values as well as Eqs. (6)–(8), β1 of the first-stage voltage divider is calculated to be 9.1 kV·V−1. The voltage ratio of the second-stage voltage divider, β2, is as follows: R1 R1 + R2 = 1+ . (9) β2 = R2 R2 Since β1 of the first-stage voltage divider is 9.1 kV·V−1, the total voltage ratio of the two-stage resistor-capacitor voltage divider, β, can be expressed as follows: ( ) R1 β = β1 β2 = 9.1 1 + (kV·V−1). (10) R2 Usually, R2 is the impedance of the cable, which is 50 Ω. So, β is only dependent on R1. Not only β is dependent on R1 but also the time constant of the two-stage voltage divider, τs, is dependent on R1. B. Calculations on the time constant of the two-stage voltage divider
According to Figure 3, τs can be expressed as follows:
where C1 is the equivalent capacitance of the device to be tested; C2 is the capacitance of a thin metal-covered dielectric film. If the tested device is with a standard structure, then β1 can be calculated theoretically. Taking a coaxial line as example, the exact expression of C1 of a capacitor voltage divider assembled on it is as follows: C1 =
FIG. 3. Typical equivalent circuit of a two-stage capacitor-resistor voltage divider. Ui-input voltage, also the high voltage to be tested; Uo-output voltage, also the low voltage displayed on the oscillograph.
(7)
τs = (R1 + R2)C2 = (R1 + R2)C0 A,
(11)
where C0 is as defined in Eq. (8). From Eq. (11), it is seen that two methods can be used to increase τs: one is to increase (R1 + R2), the other is to increase A. A is limited by two factors: the specific structure of the coaxial line and the area of the piece of thin brass-covered film. The maximum area of the brass-covered film, which can be used on the coaxial line, is
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FIG. 6. Simulation results (R 1 = 100 Ω).
FIG. 4. Curves of β and τs versus R 1 in one coordinate.
19×49 cm2. So, C2 is 56 nF. With R2 of 50 Ω and C2 of 56 nF, the curves of β and τs versus R1 can be plotted according to Eqs. (10) and (11), as shown in Figure 4. From this figure, it is seen that both β and τs increase linearly as R1 increases. It is also seen that if β is required to be 19.2 kV·V−1, R1 of 50 Ω would be enough. However, when R1 is 50 Ω, τs is only 5.6 µs, which is smaller than the FWHM of the quasi-sinusoidal waveform (30 µs). So, R1 should be increased “moderately.” C. Optimization on R1 via circuit simulation
R1 should not be designed to be too large, since a much larger R1 would correspond to a much larger β, which would result in a much smaller Uout ( β = Uline/Uout). So, optimization on R1 is conducted, which is realized via circuit simulation. The model of the circuit is shown in Figure 5. In this circuit, a trapezoidal pulse with an amplitude of 100 kV, a crest of 1 µs, and rise and fall time of 0.1 µs are imposed on the two-stage resistor-capacitor voltage divider to simulate the condition to test a microsecond signal. C2 is set as 56 nF as calculated previously; C1 is set as 6.15 pF (56 nF/9.1 k = 6.15 pF); R2 is set as 50 Ω (the impedance of the test cable); the cable length is set as 90 m to simulate the practical condition; the impedance of the oscillograph is set as low-impedance grade (50 Ω); and R1 is set as the variable which ranges from 50 to 1000 Ω. Figure 6 shows the simulation results when R1 is set as 100 Ω. This figure reveals that the output voltage would get distorted, if the R1 or τs is too small. The voltage error, Er , is
defined as Er =
U1 −U2 × 100%, U1
(12)
where U1 and U2 are as defined in Figure 6. It is believed that the R1 or τs is acceptable only when Er is smaller than a certain value, e.g., 3%. Figure 7 shows the curves of the simulated voltage ratio, βsim, and Er versus R1. This figure clearly shows that the βsim agrees with the analytical voltage ratio and that as R1 increases, Er decreases. In addition, when R1 is equal to 500 Ω and Er is equal to 3%. So, R1 is set as 500 Ω and the corresponding β and τs are 100 kV·V−1 and 30 µs, respectively. Taking Eq. (5) into account, the S is equal to be 2.5 kA·V−1. It is noted that the smaller the required S, the wider the τs. That (S, τs) are designed as (2.5 kA·V−1, 30 µs) is only suitable to test the “chopped” waveforms. For the “recessed” waveforms, since the time duration is much longer, the current amplitude would be much smaller, which means that a smaller S and a wider τs are needed. D. Circuit simulation for the recessed waveforms
Based on the above analysis, only the first-stage voltage divider (capacitor voltage divider) is used to test the current signal corresponding to the “recessed” waveforms. In addition, the oscillograph is set as high-impedance, which is 1 MΩ. In this condition, the time constant, τs′, should be as follows: τs ′ = Zosc (C2 +Ccable) = Zosc (C2 +C c0l),
FIG. 5. Circuit simulation for optimizing R 1.
(13)
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simulated. Table I lists designed values for the current probe compared with the required values. From this table, it is seen that the time constant meets the requirements whereas the sensitivity is larger than the required values. This is due to the accuracy requirement of the probe as shown in Figure 7 and it can be overcome by choosing a finer grade of voltage division on the oscillograph.
IV. CALIBRATION ON THE CURRENT PROBE
FIG. 7. Curves of the simulated β and E r dependent on R 1.
where Zosc is the impedance of the oscillograph; Ccable is the capacitance of the cable; Cc0 is capacitance of the cable with unit length; and l is the length of the cable. With l of 90 m, Cc0 of 0.1 nF·m−1, Zosc of 1 MΩ, and C2 of 56 nF, τs′ is calculated to be 64 ms, which is far larger than the duration of the recessed waveforms (10 µs). So, the requirement of time constant is satisfied. The voltage ratio of the capacitor voltage divider, β1′, should be revised as follows: β1 ′ =
C2 +Ccable , C1
(14)
where C1 is 6.15 pF as calculated previously. So β1′ is calculated to be 10.6 kV·V−1 theoretically. With Eq. (5), the sensitivity, S ′, can be calculated to be 260 A·V−1. In other words (S ′, τs′) for the recessed waveforms are (260 A·V−1, 64 ms), respectively. Figure 8 shows the equivalent circuit of the current probe to test for the “recessed” waveforms. The imposed waveform is set as follows: amplitude 100 kV, creation 5 µs, rise and fall time 15 µs to simulate the quasi-sinusoidal waveform. Compared with the circuit shown in Figure 5, the differences in this circuit are that the impedance of the oscillograph is set as 1 MV and R1 is replaced with R1′(50 Ω), which matches the impedance the cable to absorb the reflected pulse. Figure 9 shows the simulation results, this figure reveals that the output waveform is basically the same as the input waveform, and the simulated β1′ is 10.6 kV·V−1 (100 kV ÷ 9.46 V) and S ′ is 260 A·V−1, which agrees with the theoretical value. As a summary for this section, a current probe with two grades of sensitivity and time constant is designed and
Calibration for the self-fabricated probe is also conducted. The calibration is realized via a HV probe, P6015A, which is with an attenuation coefficient of 1000. Figure 10 shows the calibration schematics, in which, the HV pulse is produced by the TPG400, the cable is with a length of 90 m, and the voltage-divider signal and signal tested by the P6015A are displayed on an oscillograph, DPO4104. The two grades of the voltage divider are calibrated, respectively. First is for the low-S grade. A small cylindrical polyimide (PI) insulator is placed between the two plate electrodes to simulate the condition of the “recessed” waveforms. Since the amplitude of the HV pulse is low, breakdown or surface flashover cannot occur. Therefore, a pulse with a FWHM of 30 µs can be imposed on the voltage divider. A 50-Ω resistor is used to absorb the reflected wave, and the oscillograph is set as high-impedance grade as aforementioned. Figure 11 shows the typical calibration waveform. From this figure, it is seen that the attenuated raw waveform and the waveform obtained by the voltage divider are consistent with each other, which means that the current probe can respond to a signal with a FWHM as long as 30 µs. Figure 12 shows the calibration results that are repeated by 6 times. This figure reveals that the standard error is low and the average voltage ratio is 10.5 kV·V−1, which agrees with the theoretical voltage ratio of 10.6 kV·V−1. Second is for the high-S grade. The PI insulator is removed and a small vacuum gap is left between the two plate electrodes. The gap is as small as possible to ensure that a vacuum breakdown can occur to produce the “chopped” waveforms under low voltages. A 500-Ω resistor is used as the HVarm resistor, and the oscillograph is set as low-impedance grade. Figure 13 shows the typical calibration waveform. This figure reveals that the pulse duration may decrease to tens of nanoseconds when vacuum breakdown occurs and that the waveform obtained by the voltage divider is the same as that
FIG. 8. Equivalent circuit to test the current signal corresponding to the “recessed” waveforms.
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FIG. 9. Simulation results for the “recessed” waveforms. FIG. 10. Calibration schematics for the voltage divider.
by the P6015A. Also, the calibration is repeated by 6 times. Figure 14 shows the results. From this figure, it is seen that the average voltage ratio is 111.8 kV·V−1, which is close to the theoretical voltage ratio obtained in Sec. III. Since the low-grade and the high-grade voltage ratios of the voltage divider are 10.5 kV·V−1 and 111.8 kV·V−1, respectively; the low-grade and the high-grade sensitivities of the current probe are 262 A·V−1 and 2.8 kA·V−1, respectively (S = β/Zline, Zline = 40 Ω).
V. DISCUSSIONS ON THE µs-PULSED VACUUM BREAKDOWN CURRENT
With the self-fabricated current probe, the vacuum breakdown current on a 3-cm parallel-plate gap under 30-µs quasisinusoidal pulses was tested for different voltage amplitudes. A number of current waveforms are obtained, and they are analyzed in perspective of statistics. It is found that these current waveforms can be classified into three types: the displacement current, the pre-breakdown current, and the breakdown current.
FIG. 11. Typical calibration waveform for the “recessed” waveforms.
A. The type of the displacement current
Figure 15 shows the typical current waveform corresponding to the normal voltage waveform, which is tested via the current probe at low-S grade. From this figure, it is seen that the current amplitude is 0.45 A (1.74 mV×262 A·V−1) and the FWHM is 20 µs. By summarizing the characteristics of this type of current waveforms, it is concluded that they are with an amplitude of 10-1000 mA and a FWHM of about 20 µs. There is no abnormal phenomenon between the electrodes for this type of current waveforms.
FIG. 12. Calibration result for the “recessed” waveforms.
TABLE I. The sensitivity and time constant for the designed current probe compared with the required values.
Grade Low-S grade High-S grade
Aim For the “recessed” voltage waveform For the “chopped” voltage waveform
Designed time constant (required values) 64 ms (>>10 µs) 30 µs (>>10 ns)
Designed sensitivity (required values) A·V−1,
260 (∼60 mA·V−1) 2.5 kA·V−1 (∼480 A·V−1)
Realization A one-stage capacitor voltage divider and a 40-Ω coaxial line A two-stage capacitor-resistor divider and a 40-Ω coaxial line
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FIG. 13. Typical calibration waveform for the “chopped” waveforms.
It is considered that this type of current is the displacement current. The reason lies in the following: when the pulse generator is boosting the voltage, the parallel-plate electrodes can be considered as a capacitor, which can couple the voltage of the pulse generator. So, displacement current can flow through the electrodes. In addition, the current and the charging voltage should conform to a differential relation, as shown in Eq. (3). Based on this consideration, the differential waveform of the charging voltage is acquired, which is also shown in Figure 15. By comparing the differential waveform with the current waveform, it can be seen that they are basically the same as each other for the first peak. Therefore, it is believed that this type of current is the displacement current. B. The type of the pre-breakdown current
Figure 16 shows the pre-breakdown current corresponding to the “recessed” voltage waveform, which is also tested by the current probe with low-S grade. From this figure, it is seen that when the voltage is recessed, the current would increase as large as 11 A (44 mV×262 A·V−1). The characteristics of this type of current are also summarized, which are that the current amplitude is in the range of 1-10 A and the FWHM is 5-10 µs. It is found that there are haloes covering both the surfaces of the electrodes when the recessed waveform appears, as shown in Figure 17 (the specific dimensions of electrodes can be clearly
FIG. 14. Calibration result for the “chopped” waveforms.
FIG. 15. The current waveform corresponding to the normal voltage waveform.
seen in Figure 1). After the haloes fade, the vacuum insulation recovers again. As to the mechanism of the pre-breakdown current, it is conjectured that it is due to field electron emission (FEE). According to the Fowler-Nordheim formula,12 the current flowing from the cathode surface can be expressed as follows: β p2E 2 t 2( y)φ m 7 3/2 6.85 × 10 φ m × exp − θ( y) , βpE
Iv = j (E)·Ae = Ae × 1.55 × 10−6
(15)
where j(E) is the current density in A·cm−2; Ae is the effective emission area of the micro-protrusion on the cathode surface in cm2; β p is the field enhancement factor of the microprotrusions; φ m is the work function of the cathode in eV; θ( y) and y are the middle parameters, which are θ( y) = 0.956 √ -1.06 y 2 and y = 3.8×10−4 E/φ m , respectively. According to Ref. 22, Ae is in the range of 0.01-1 µm2, β p is in the range of 100-1000.22 Letting φ m be 4.5 eV, Iv is calculated to be 10−28 -102 A, when E is 100-200 kV·cm−2. This current range covers the amplitude of the pre-breakdown current (1-10 A). So, it is considered that this type of the current is due to FEE.
FIG. 16. The pre-breakdown current corresponding to the “recessed” voltage waveform.
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FIG. 19. Beams ejected from cathode to anode when vacuum breakdown occurs. FIG. 17. Haloes covered on the surfaces of the electrodes for the “recessed” waveform.
Figure 18 shows the breakdown current flowing through vacuum gap tested by the current probe with high-S grade, which corresponds to the “chopped” voltage waveforms. This figure shows that the current amplitude increases as large as 2 kA (688 mV × 2.8 AA·V−1) and the pulse duration decreases as short as tens of nanoseconds. The characteristics of this type of current are summarized as follows: amplitude, 100-3000 kA and FWHM, 40-200 ns. When vacuum breakdown occurs, there is obviously a bunch of beam ejected from the cathode to the anode, as shown in Figure 19. It is conjectured that the breakdown current is due to “electron explosion emission” (EEE). The conception of EEE was put forward by G. A. Mesyats in 1966,22,23 which emphasizes that the micro protrusions can explode to form a plasma in high field, and the plasma serves as the electron source or electron sea. According to Ref. 24, the cathode based on EEE is the only type of cathode, which can supply high-current and high-current-density beams, and the amplitude of an EEE current is usually as large as several kilo-amperes. Aside from
that, there is always a small peak before the main peak of the main EEE current peak, and the duration between the small peak and the main peak is about tens of nanoseconds. For the vacuum breakdown current waveforms in our experiments, it is observed that small peaks emerge ahead of the main peaks, as shown in Figure 18. This is the first proof that the vacuum breakdown current is due to EEE. Another proof is the local configuration on the cathode surface, as shown in Figure 20. This figure reveals that there are obvious traces of eroded metal. These traces are totally the same as the EEE traces reported in Ref. 25. It is considered that the traces are due to the exploded micro-protrusion, which has been cooled down. So, it is believed that the breakdown current is owing to the EEE. As a summary for this section, the 3-cm vacuum-gap breakdown current under 30-µs quasi-sinusoidal pulses was tested under different voltage amplitudes based on the selffabricated current probe. It is summarized the current waveforms can be classified into the displacement current, the prebreakdown current, and the breakdown current. The characteristics for each type of current are summarized and the potential mechanisms are also explored, as listed in Table II.
FIG. 18. The breakdown current corresponding to the “chopped” voltage waveform.
FIG. 20. Eroded metal traces on the cathode surface.
C. The type of the breakdown current
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TABLE II. Characteristics and potential mechanisms of the 3-cm vacuum-gap breakdown current under 30-µs quasi-sinusoidal pulses. Current types Displacement current Pre-breakdown current Breakdown current
Amplitude range
FWHM
Phenomenon between electrodes
Potential mechanisms
0.01-1 A 1-10 A 100-3000 A
20 µs 5-10 µs 40-200 ns
No abnormal phenomenon Halos covering the electrode surfaces Beams ejected from cathode to anode
I v = C ∆U ∆t FEE EEE
VI. CONCLUSIONS
A large-dynamic-range current probe for microsecond pulsed vacuum breakdown research is fabricated in this paper. This probe features large-dynamic measurement range and simple composition structure. As main components of this probe, a 40-Ω coaxial line is used to turn the current signal to a voltage one and a two-stage resistor-capacitor voltage divider is used to test the voltage in a large-dynamic range. The breakdown current for a 3-cm parallel-plate vacuum gap under 30-µs quasi-sinusoidal pulses was tested based on this current probe. The test results show that the probe is capable of responding to the current signals of an amplitude of 10−2103 A and a FWHM of 10−2-101 µs. Future work is to research the mechanisms of the vacuum breakdown current deeply with this probe.
ACKNOWLEDGMENTS
This work is supported by the National Natural Science Foundation of China (NNSFC) under Grant No. 51377135. The authors wish to express thanks to Y. F. Pan for his helpful discussions on this paper. 1O.
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K. Paul, P. K. Chattopadhyay, and D. Bora, Meas. Sci. Technol. 18(6), 2673–2680 (2007). 11Q. Zhang, J. Zhu, J. Jia, F. Tao, and L. Yang, Meas. Sci. Technol. 17(4), 895–900 (2006). 12H. Bluhm, Pulsed Power Systems (Springer, Karlsruhe, Germany, 2006). 13J. Cheng, J. C. Su, X. B. Zhang, W. Y. Liu, B. Zeng, X. L. Wu, J. P. Fang, X. Sun, L. M. Wang, and L. Zhao, in Annual Report Conference on Electrical Insulation and Dielectric Phenomena (IEEE, Shenzhen, China, 2013), Vol. 1, pp. 464–469. 14J. C. Su, X. B. Zhang, G. Z. Liu, X. X. Song, Y. F. Pan, L. M. Wang, J. C. Peng, and Z. J. Ding, IEEE Trans. Plasma Sci. 37(10), 1954–1958 (2009). 15B. Zeng, J. C. Su, X. B. Zhang, J. Cheng, X. L. Wu, J. P. Fang, L. M. Wang, X. Sun, and L. Zhao, in Annual Report Conference on Electrical Insulation and Dielectric Phenomena (IEEE, Shenzhen, China, 2013), Vol. 1, pp. 460–463. 16S. D. Korovin, V. P. Gubanov, A. V. Gunin, I. V. Pegel, and A. S. Stepchenko, in Proceedings of 13th IEEE International Pulsed Power Conference (IEEE, Las Vegas, NV, 2001), Vol. 2, pp. 1249–1251. 17S. D. Korovin, V. V. Rostov, S. D. Polevin, I. V. Pegel, E. Schamiloglu, M. I. Fuks, and R. J. Barker, Proc. IEEE 92(7), 1082–1095 (2004). 18J. C. Su, J. C. Peng, X. X. Zhu, X. X. Song, and L. Zhao, Appl. Phys. 1(2), 165–172 (2010). 19L. Zhao, G. Z. Liu, J. C. Su, Y. F. Pan, and X. B. Zhang, IEEE Trans. Plasma Sci. 39(7), 1613–1618 (2011). 20L. Zhao, Y. F. Pan, J. C. Su, X. B. Zhang, L. M. Wang, J. P. Fang, X. Sun, and R. Lui, Rev. Sci. Instrum. 84, 105114 (2013). 21J. C. Su, X. B. Zhang, R. Li, L. Zhao, X. Sun, L. M. Wang, B. Zeng, J. Cheng, Y. Wang, J. C. Peng, and X. X. Song, Rev. Sci. Instrum. 85(06), 063303 (2014). 22G. A. Mesyats, Pulsed Power (Kluwer Academic/Plenum Publishers, New York, Boston, Dordrecht, London, Moscow, 2005). 23G. A. Mesyats, Explosive Electron Emission (URO-Press, Ekaterinburg, 1998). 24J. Sun and G. Z. Liu, IEEE Trans. Plasma Sci. 33(5), 1487–1490 (2005). 25G. A. Mesyats and D. I. Proskurovsky, Pulsed Electrical Discharge in Vacuum (Springer-Verlag, Berlin, New York, 1989).
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A large-dynamic-range current probe for microsecond pulsed vacuum breakdown research Liang Zhao,a) Jian-cang Su, Xi-bo Zhang, Rui Li, Lei Zheng, Bo Zeng, Jie Cheng, Xi-yuan She, and Xiao-long Wu Science and Technology on High Power Microwave Laboratory, Northwest Institute of Nuclear Technology, Xi’an, Shaanxi 710024, China
(Received 25 August 2014; accepted 26 December 2014; published online 16 January 2015) A large-dynamic-range current probe for microsecond pulsed vacuum breakdown research is fabricated. The basic principle of this probe is to turn the current signal to a voltage one via a load of fixed impedance and to test the voltage signal via a voltage divider of adjustable voltage ratio. With a segment of 40-Ω coaxial line, which is connected to the experimental chamber, and a self-fabricated two-stage resistor-capacitor voltage divider, the current probe is realized and is applied to test the vacuum breakdown current for 3-cm parallel-plate electrodes under microsecond pulses. The results show that the current probe is capable of responding to current signals with an amplitude of 10−2-103 A and a duration of 10−2-101 µs. Based on the current probe, the characteristics of the vacuum breakdown current under 30-µs quasi-sinusoidal pulses are summarized. The potential mechanisms for each type of current are also discussed in this paper. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4905624]
I. INTRODUCTION
proportional to the current amplitude, I, the following relation holds true:
The amplitude of the current in vacuum breakdown process usually varies from several picoamperes (pA) to several kiloamperes (kA), and the time scale usually changes from nanosecond (ns) to millisecond (ms) time scale.1–3 The dynamic range of the vacuum breakdown current may get even larger when the applied voltage is a pulse. It is of importance to measure the current in vacuum breakdown process, since knowing the vacuum breakdown current characteristics can not only help to understand the vacuum breakdown mechanism but also to increase the vacuum insulation strength. Several methods are proposed to measure the pulsed breakdown current. The typical one is the Rogowski Coil, which is put forward in 1887.4–8 This coil is based on the Faraday’s Law of Induction, which can respond to a current signal with a duration in a wide range.9–11 It also has the advantages of easy assembly. However, the sensitivity (S) of a Rogowski Coil is usually limited by the configuration of the device to be tested. If the device is small, the S of a Rogowski Coil cannot be designed too large. Another method is the current divider, the principle of which is to employ a resistor of small resistance (R) to turn the current signal to a voltage one.12 The S of a current divider depends on the R and the power (P) of the resistor. An ideal resistor in a current divider should be of small R and large P. As a matter of fact, this type of resistor is usually unobtainable. A third method is the electro-optic sensor.12 This method employs the effect that the collimated light would get twisted in a dielectric when a magnetic field is imposed on the dielectric. The twisted angle, θ, is proportional to the applied magnetic field, M. Since M is
a)Author to whom correspondence should be addressed. Electronic mail:
[email protected]. Tel.: +86-29-84767631.
0034-6748/2015/86(1)/015109/9/$30.00
θ = k I,
(1)
where k is a constant. The advantage of an electro-optic sensor is that it is less affected by the external electromagnetic environment. But, it has a disadvantage that it needs a set of complicated optic devices. All these methods aforementioned are appropriate to measure a current signal with a fixed amplitude and a fixed duration. However, when the amplitude and the duration of the current signal change in a large dynamic range, these methods are not applicable and a new method should be devised. In our laboratory, when conducting the vacuum breakdown experiments using a pair of Bruce-profiled parallel-plate electrodes under microsecond pulses, we found that different changes had taken place on the main voltage waveform for different voltage amplitudes. The experimental chamber containing the Bruce electrodes is shown in Figure 1 in which the vacuum gap is set as 3 cm and the effective flat area of the Bruce electrode is 28.3 cm2 (effective diameter: 6 cm). The normal waveforms compared with the abnormal ones are shown in Figures 2(a)–2(d). For the normal waveform, it is quasi-sinusoidal with a full width at half maximum (FWHM) of 30 µs. This pulse is produced by a Tesla-type generator, TPG400. Detailed introduction on the TPG400 as well as on the Tesla-type generators can be seen in Refs. 13–21. For the abnormal waveform, it is found that they can be classified into two types: the “recessed” ones, such as those shown in Figures 2(a) and 2(c), and the “chopped” ones, such as those shown in Figures 2(b) and 2(d). We wonder what are the characteristics of the current waveforms corresponding to the abnormal waveforms and what types of physical mechanisms are hidden behind the current waveforms? To answer these
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A. Consideration on τ
For the τ, from Figures 2(a) and 2(c), it is seen that the recesses on the main waveforms are of a duration of tens of microseconds. So, it is believed that the τ of the current waveform corresponding to the recessed voltage waveforms is also about tens of microseconds. From Figures 2(b) and 2(d), it is seen that oscillations take place on the main waveforms. These oscillations are due to the wave reflection between the switch (vacuum chamber) and the load of the TPG400. Since the length of transmission line (TL, a segment coaxial line between the switch and the load) of the TPG400 is about 1 m, which corresponds to an electrical length of 10 ns (1-m transmission line corresponds to an electrical length of 10 ns), it is considered that the τ of the current waveform for chopped voltage waveforms is about 10 ns. FIG. 1. Bruce-profiled parallel-plate electrodes assembled in a vacuum experimental chamber.
B. Consideration on S
questions, a current probe, which can respond to a signal in a large dynamic range, is needed. In this paper, a current probe meeting both the sensitivity and the duration requirements is designed and fabricated. This probe has two features: (1) It has a large dynamic range that it can test a current with an amplitude of 10−2-103 A and a FWHM of 10−2-101 µs; (2) It is realized by simple common components such as a voltage divider and a segment of coaxial line. The general consideration for this probe is presented in Sec. II. The design on the probe is dealt with in Sec. III. The calibration results for this probe are given in Sec. IV. Section V is for the typical vacuum breakdown current waveforms obtained via this current probe and the potential mechanisms. The last section, e.g., Sec. VI, is for the conclusions in this paper.
II. GENERAL CONSIDERATIONS
The current probe is considered in two aspects: (1) time constant-τ and (2) sensitivity-S.
For S, it is calculated with the following formula: S=
Iv , Uout
(2)
where Iv is the vacuum breakdown current and Uout is the voltage displayed on the oscillograph. Assuming that Uout is fixed, the S of the current probe would only depend on Iv . For Iv , it is evaluated with the following formula: Iv = C
∆U , ∆t
(3)
where C is the capacitance of the equivalent capacitor of parallel-plate electrodes, which is simulated to be 6 pF; ∆U is the voltage decrement; and ∆t is the time duration or the time constant. For the recessed abnormal voltage waveforms, ∆U is about 10-100 kV and ∆t is about 10 µs. So, Iv is calculated to be 6-60 mA. For the chopped abnormal voltage waveforms, ∆U is about 400-800 kV and ∆t is about 10 ns. So, Iv is calculated to be 240-480 A. So, Iv is in the range of 6 mA-480
FIG. 2. Abnormal waveforms compared with the normal 30-µs quasi-sinusoidal pulses at different voltage amplitudes.
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A. Letting Uout be 1 V, S of the current probe would be in the range from 6 mA·V−1 to 480 A·V−1 according to Eq. (2).
III. DESIGN ON THE CURRENT PROBE
Taking into account that the TL assembled next to the vacuum chamber is a segment of coaxial line with a fixed impedance of 40 Ω, this line can be used as a “resistor” to turn the current signal to a voltage one. So, the question on how to measure a large-dynamic-range current is turned to that on how to measure the voltage signal in a large dynamic range. Since the voltage applied on the coaxial line, Uline, and current flowing through the line, Iv , conforms to the following relation: Iv =
Uline , Zline
(4)
where Zline is the impedance of the TL, S can be transformed into the following expressions by inserting Eq. (4) into Eq. (2): S=
1 Uline β = , Zline Uout Zline
(5)
where β is defined as the voltage ratio of the voltage divider assembled on the coaxial line. Letting Zline be equal to 40 Ω and S be equal to 0.006-480 A·V−1 as aforementioned, β would be in the range of 0.24 V·V−1-19.2 kV·V−1. Aside from the voltage ratio, the time constant should also be considered into. The common methods to test the voltage of the high-voltage (HV) pulses include the resistor voltage divider, the capacitor voltage divider, and the composed resistorcapacitor voltage divider,12 among which the composed resistor-capacitor voltage divider is a feasible approach due to its large voltage ratio and wide time constant. Figure 3 shows the equivalent circuit of a typical two-stage resistor-capacitor voltage divider, in which C1 and C2 are the HV-arm and the low-voltage-arm (LV-arm) capacitors of the first-stage voltage divider (also the capacitor voltage divider), respectively; R1 and R2 are the HV-arm and the LV-arm resistors of the second-stage voltage divider (also the resistor voltage divider), respectively. Subsections III A–III D are devoted to the calculation on a desired two-stage capacitor-resistor voltage divider. A. Calculations on the voltage ratio of the two-stage voltage divider
The voltage ratio of the first-stage voltage divider, β1, can be expressed as follows: C1 +C2 C2 ≈ (C2 >> C1), β1 = C1 C1
(6)
ε 0ε r A , Ro ln Ro /Ri
where ε 0 and ε r are the dielectric constant in vacuum and the relative dielectric constant of the insulation dielectric, respectively; Ri and Ro are the inner and the outer radii of the coaxial line, respectively; A is the area of the brass-covered thin dielectric film. As to C2, it can be calculated as follows: C2 = C0 A,
(8)
where C0 is the unit-area capacitance of a brass-covered thin dielectric film, which is a constant. For the coaxial line to turn the current signal to a voltage one assembled next to the vacuum chamber, Ri = 104 mm, Ro = 202 mm, and ε r = 1 (the insulation dielectric is vacuum). The thin brass-covered film is made of polyimide and is with a C0 of 60 pF·cm−2. With these values as well as Eqs. (6)–(8), β1 of the first-stage voltage divider is calculated to be 9.1 kV·V−1. The voltage ratio of the second-stage voltage divider, β2, is as follows: R1 R1 + R2 = 1+ . (9) β2 = R2 R2 Since β1 of the first-stage voltage divider is 9.1 kV·V−1, the total voltage ratio of the two-stage resistor-capacitor voltage divider, β, can be expressed as follows: ( ) R1 β = β1 β2 = 9.1 1 + (kV·V−1). (10) R2 Usually, R2 is the impedance of the cable, which is 50 Ω. So, β is only dependent on R1. Not only β is dependent on R1 but also the time constant of the two-stage voltage divider, τs, is dependent on R1. B. Calculations on the time constant of the two-stage voltage divider
According to Figure 3, τs can be expressed as follows:
where C1 is the equivalent capacitance of the device to be tested; C2 is the capacitance of a thin metal-covered dielectric film. If the tested device is with a standard structure, then β1 can be calculated theoretically. Taking a coaxial line as example, the exact expression of C1 of a capacitor voltage divider assembled on it is as follows: C1 =
FIG. 3. Typical equivalent circuit of a two-stage capacitor-resistor voltage divider. Ui-input voltage, also the high voltage to be tested; Uo-output voltage, also the low voltage displayed on the oscillograph.
(7)
τs = (R1 + R2)C2 = (R1 + R2)C0 A,
(11)
where C0 is as defined in Eq. (8). From Eq. (11), it is seen that two methods can be used to increase τs: one is to increase (R1 + R2), the other is to increase A. A is limited by two factors: the specific structure of the coaxial line and the area of the piece of thin brass-covered film. The maximum area of the brass-covered film, which can be used on the coaxial line, is
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FIG. 6. Simulation results (R 1 = 100 Ω).
FIG. 4. Curves of β and τs versus R 1 in one coordinate.
19×49 cm2. So, C2 is 56 nF. With R2 of 50 Ω and C2 of 56 nF, the curves of β and τs versus R1 can be plotted according to Eqs. (10) and (11), as shown in Figure 4. From this figure, it is seen that both β and τs increase linearly as R1 increases. It is also seen that if β is required to be 19.2 kV·V−1, R1 of 50 Ω would be enough. However, when R1 is 50 Ω, τs is only 5.6 µs, which is smaller than the FWHM of the quasi-sinusoidal waveform (30 µs). So, R1 should be increased “moderately.” C. Optimization on R1 via circuit simulation
R1 should not be designed to be too large, since a much larger R1 would correspond to a much larger β, which would result in a much smaller Uout ( β = Uline/Uout). So, optimization on R1 is conducted, which is realized via circuit simulation. The model of the circuit is shown in Figure 5. In this circuit, a trapezoidal pulse with an amplitude of 100 kV, a crest of 1 µs, and rise and fall time of 0.1 µs are imposed on the two-stage resistor-capacitor voltage divider to simulate the condition to test a microsecond signal. C2 is set as 56 nF as calculated previously; C1 is set as 6.15 pF (56 nF/9.1 k = 6.15 pF); R2 is set as 50 Ω (the impedance of the test cable); the cable length is set as 90 m to simulate the practical condition; the impedance of the oscillograph is set as low-impedance grade (50 Ω); and R1 is set as the variable which ranges from 50 to 1000 Ω. Figure 6 shows the simulation results when R1 is set as 100 Ω. This figure reveals that the output voltage would get distorted, if the R1 or τs is too small. The voltage error, Er , is
defined as Er =
U1 −U2 × 100%, U1
(12)
where U1 and U2 are as defined in Figure 6. It is believed that the R1 or τs is acceptable only when Er is smaller than a certain value, e.g., 3%. Figure 7 shows the curves of the simulated voltage ratio, βsim, and Er versus R1. This figure clearly shows that the βsim agrees with the analytical voltage ratio and that as R1 increases, Er decreases. In addition, when R1 is equal to 500 Ω and Er is equal to 3%. So, R1 is set as 500 Ω and the corresponding β and τs are 100 kV·V−1 and 30 µs, respectively. Taking Eq. (5) into account, the S is equal to be 2.5 kA·V−1. It is noted that the smaller the required S, the wider the τs. That (S, τs) are designed as (2.5 kA·V−1, 30 µs) is only suitable to test the “chopped” waveforms. For the “recessed” waveforms, since the time duration is much longer, the current amplitude would be much smaller, which means that a smaller S and a wider τs are needed. D. Circuit simulation for the recessed waveforms
Based on the above analysis, only the first-stage voltage divider (capacitor voltage divider) is used to test the current signal corresponding to the “recessed” waveforms. In addition, the oscillograph is set as high-impedance, which is 1 MΩ. In this condition, the time constant, τs′, should be as follows: τs ′ = Zosc (C2 +Ccable) = Zosc (C2 +C c0l),
FIG. 5. Circuit simulation for optimizing R 1.
(13)
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simulated. Table I lists designed values for the current probe compared with the required values. From this table, it is seen that the time constant meets the requirements whereas the sensitivity is larger than the required values. This is due to the accuracy requirement of the probe as shown in Figure 7 and it can be overcome by choosing a finer grade of voltage division on the oscillograph.
IV. CALIBRATION ON THE CURRENT PROBE
FIG. 7. Curves of the simulated β and E r dependent on R 1.
where Zosc is the impedance of the oscillograph; Ccable is the capacitance of the cable; Cc0 is capacitance of the cable with unit length; and l is the length of the cable. With l of 90 m, Cc0 of 0.1 nF·m−1, Zosc of 1 MΩ, and C2 of 56 nF, τs′ is calculated to be 64 ms, which is far larger than the duration of the recessed waveforms (10 µs). So, the requirement of time constant is satisfied. The voltage ratio of the capacitor voltage divider, β1′, should be revised as follows: β1 ′ =
C2 +Ccable , C1
(14)
where C1 is 6.15 pF as calculated previously. So β1′ is calculated to be 10.6 kV·V−1 theoretically. With Eq. (5), the sensitivity, S ′, can be calculated to be 260 A·V−1. In other words (S ′, τs′) for the recessed waveforms are (260 A·V−1, 64 ms), respectively. Figure 8 shows the equivalent circuit of the current probe to test for the “recessed” waveforms. The imposed waveform is set as follows: amplitude 100 kV, creation 5 µs, rise and fall time 15 µs to simulate the quasi-sinusoidal waveform. Compared with the circuit shown in Figure 5, the differences in this circuit are that the impedance of the oscillograph is set as 1 MV and R1 is replaced with R1′(50 Ω), which matches the impedance the cable to absorb the reflected pulse. Figure 9 shows the simulation results, this figure reveals that the output waveform is basically the same as the input waveform, and the simulated β1′ is 10.6 kV·V−1 (100 kV ÷ 9.46 V) and S ′ is 260 A·V−1, which agrees with the theoretical value. As a summary for this section, a current probe with two grades of sensitivity and time constant is designed and
Calibration for the self-fabricated probe is also conducted. The calibration is realized via a HV probe, P6015A, which is with an attenuation coefficient of 1000. Figure 10 shows the calibration schematics, in which, the HV pulse is produced by the TPG400, the cable is with a length of 90 m, and the voltage-divider signal and signal tested by the P6015A are displayed on an oscillograph, DPO4104. The two grades of the voltage divider are calibrated, respectively. First is for the low-S grade. A small cylindrical polyimide (PI) insulator is placed between the two plate electrodes to simulate the condition of the “recessed” waveforms. Since the amplitude of the HV pulse is low, breakdown or surface flashover cannot occur. Therefore, a pulse with a FWHM of 30 µs can be imposed on the voltage divider. A 50-Ω resistor is used to absorb the reflected wave, and the oscillograph is set as high-impedance grade as aforementioned. Figure 11 shows the typical calibration waveform. From this figure, it is seen that the attenuated raw waveform and the waveform obtained by the voltage divider are consistent with each other, which means that the current probe can respond to a signal with a FWHM as long as 30 µs. Figure 12 shows the calibration results that are repeated by 6 times. This figure reveals that the standard error is low and the average voltage ratio is 10.5 kV·V−1, which agrees with the theoretical voltage ratio of 10.6 kV·V−1. Second is for the high-S grade. The PI insulator is removed and a small vacuum gap is left between the two plate electrodes. The gap is as small as possible to ensure that a vacuum breakdown can occur to produce the “chopped” waveforms under low voltages. A 500-Ω resistor is used as the HVarm resistor, and the oscillograph is set as low-impedance grade. Figure 13 shows the typical calibration waveform. This figure reveals that the pulse duration may decrease to tens of nanoseconds when vacuum breakdown occurs and that the waveform obtained by the voltage divider is the same as that
FIG. 8. Equivalent circuit to test the current signal corresponding to the “recessed” waveforms.
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FIG. 9. Simulation results for the “recessed” waveforms. FIG. 10. Calibration schematics for the voltage divider.
by the P6015A. Also, the calibration is repeated by 6 times. Figure 14 shows the results. From this figure, it is seen that the average voltage ratio is 111.8 kV·V−1, which is close to the theoretical voltage ratio obtained in Sec. III. Since the low-grade and the high-grade voltage ratios of the voltage divider are 10.5 kV·V−1 and 111.8 kV·V−1, respectively; the low-grade and the high-grade sensitivities of the current probe are 262 A·V−1 and 2.8 kA·V−1, respectively (S = β/Zline, Zline = 40 Ω).
V. DISCUSSIONS ON THE µs-PULSED VACUUM BREAKDOWN CURRENT
With the self-fabricated current probe, the vacuum breakdown current on a 3-cm parallel-plate gap under 30-µs quasisinusoidal pulses was tested for different voltage amplitudes. A number of current waveforms are obtained, and they are analyzed in perspective of statistics. It is found that these current waveforms can be classified into three types: the displacement current, the pre-breakdown current, and the breakdown current.
FIG. 11. Typical calibration waveform for the “recessed” waveforms.
A. The type of the displacement current
Figure 15 shows the typical current waveform corresponding to the normal voltage waveform, which is tested via the current probe at low-S grade. From this figure, it is seen that the current amplitude is 0.45 A (1.74 mV×262 A·V−1) and the FWHM is 20 µs. By summarizing the characteristics of this type of current waveforms, it is concluded that they are with an amplitude of 10-1000 mA and a FWHM of about 20 µs. There is no abnormal phenomenon between the electrodes for this type of current waveforms.
FIG. 12. Calibration result for the “recessed” waveforms.
TABLE I. The sensitivity and time constant for the designed current probe compared with the required values.
Grade Low-S grade High-S grade
Aim For the “recessed” voltage waveform For the “chopped” voltage waveform
Designed time constant (required values) 64 ms (>>10 µs) 30 µs (>>10 ns)
Designed sensitivity (required values) A·V−1,
260 (∼60 mA·V−1) 2.5 kA·V−1 (∼480 A·V−1)
Realization A one-stage capacitor voltage divider and a 40-Ω coaxial line A two-stage capacitor-resistor divider and a 40-Ω coaxial line
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FIG. 13. Typical calibration waveform for the “chopped” waveforms.
It is considered that this type of current is the displacement current. The reason lies in the following: when the pulse generator is boosting the voltage, the parallel-plate electrodes can be considered as a capacitor, which can couple the voltage of the pulse generator. So, displacement current can flow through the electrodes. In addition, the current and the charging voltage should conform to a differential relation, as shown in Eq. (3). Based on this consideration, the differential waveform of the charging voltage is acquired, which is also shown in Figure 15. By comparing the differential waveform with the current waveform, it can be seen that they are basically the same as each other for the first peak. Therefore, it is believed that this type of current is the displacement current. B. The type of the pre-breakdown current
Figure 16 shows the pre-breakdown current corresponding to the “recessed” voltage waveform, which is also tested by the current probe with low-S grade. From this figure, it is seen that when the voltage is recessed, the current would increase as large as 11 A (44 mV×262 A·V−1). The characteristics of this type of current are also summarized, which are that the current amplitude is in the range of 1-10 A and the FWHM is 5-10 µs. It is found that there are haloes covering both the surfaces of the electrodes when the recessed waveform appears, as shown in Figure 17 (the specific dimensions of electrodes can be clearly
FIG. 14. Calibration result for the “chopped” waveforms.
FIG. 15. The current waveform corresponding to the normal voltage waveform.
seen in Figure 1). After the haloes fade, the vacuum insulation recovers again. As to the mechanism of the pre-breakdown current, it is conjectured that it is due to field electron emission (FEE). According to the Fowler-Nordheim formula,12 the current flowing from the cathode surface can be expressed as follows: β p2E 2 t 2( y)φ m 7 3/2 6.85 × 10 φ m × exp − θ( y) , βpE
Iv = j (E)·Ae = Ae × 1.55 × 10−6
(15)
where j(E) is the current density in A·cm−2; Ae is the effective emission area of the micro-protrusion on the cathode surface in cm2; β p is the field enhancement factor of the microprotrusions; φ m is the work function of the cathode in eV; θ( y) and y are the middle parameters, which are θ( y) = 0.956 √ -1.06 y 2 and y = 3.8×10−4 E/φ m , respectively. According to Ref. 22, Ae is in the range of 0.01-1 µm2, β p is in the range of 100-1000.22 Letting φ m be 4.5 eV, Iv is calculated to be 10−28 -102 A, when E is 100-200 kV·cm−2. This current range covers the amplitude of the pre-breakdown current (1-10 A). So, it is considered that this type of the current is due to FEE.
FIG. 16. The pre-breakdown current corresponding to the “recessed” voltage waveform.
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FIG. 19. Beams ejected from cathode to anode when vacuum breakdown occurs. FIG. 17. Haloes covered on the surfaces of the electrodes for the “recessed” waveform.
Figure 18 shows the breakdown current flowing through vacuum gap tested by the current probe with high-S grade, which corresponds to the “chopped” voltage waveforms. This figure shows that the current amplitude increases as large as 2 kA (688 mV × 2.8 AA·V−1) and the pulse duration decreases as short as tens of nanoseconds. The characteristics of this type of current are summarized as follows: amplitude, 100-3000 kA and FWHM, 40-200 ns. When vacuum breakdown occurs, there is obviously a bunch of beam ejected from the cathode to the anode, as shown in Figure 19. It is conjectured that the breakdown current is due to “electron explosion emission” (EEE). The conception of EEE was put forward by G. A. Mesyats in 1966,22,23 which emphasizes that the micro protrusions can explode to form a plasma in high field, and the plasma serves as the electron source or electron sea. According to Ref. 24, the cathode based on EEE is the only type of cathode, which can supply high-current and high-current-density beams, and the amplitude of an EEE current is usually as large as several kilo-amperes. Aside from
that, there is always a small peak before the main peak of the main EEE current peak, and the duration between the small peak and the main peak is about tens of nanoseconds. For the vacuum breakdown current waveforms in our experiments, it is observed that small peaks emerge ahead of the main peaks, as shown in Figure 18. This is the first proof that the vacuum breakdown current is due to EEE. Another proof is the local configuration on the cathode surface, as shown in Figure 20. This figure reveals that there are obvious traces of eroded metal. These traces are totally the same as the EEE traces reported in Ref. 25. It is considered that the traces are due to the exploded micro-protrusion, which has been cooled down. So, it is believed that the breakdown current is owing to the EEE. As a summary for this section, the 3-cm vacuum-gap breakdown current under 30-µs quasi-sinusoidal pulses was tested under different voltage amplitudes based on the selffabricated current probe. It is summarized the current waveforms can be classified into the displacement current, the prebreakdown current, and the breakdown current. The characteristics for each type of current are summarized and the potential mechanisms are also explored, as listed in Table II.
FIG. 18. The breakdown current corresponding to the “chopped” voltage waveform.
FIG. 20. Eroded metal traces on the cathode surface.
C. The type of the breakdown current
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Rev. Sci. Instrum. 86, 015109 (2015)
TABLE II. Characteristics and potential mechanisms of the 3-cm vacuum-gap breakdown current under 30-µs quasi-sinusoidal pulses. Current types Displacement current Pre-breakdown current Breakdown current
Amplitude range
FWHM
Phenomenon between electrodes
Potential mechanisms
0.01-1 A 1-10 A 100-3000 A
20 µs 5-10 µs 40-200 ns
No abnormal phenomenon Halos covering the electrode surfaces Beams ejected from cathode to anode
I v = C ∆U ∆t FEE EEE
VI. CONCLUSIONS
A large-dynamic-range current probe for microsecond pulsed vacuum breakdown research is fabricated in this paper. This probe features large-dynamic measurement range and simple composition structure. As main components of this probe, a 40-Ω coaxial line is used to turn the current signal to a voltage one and a two-stage resistor-capacitor voltage divider is used to test the voltage in a large-dynamic range. The breakdown current for a 3-cm parallel-plate vacuum gap under 30-µs quasi-sinusoidal pulses was tested based on this current probe. The test results show that the probe is capable of responding to the current signals of an amplitude of 10−2103 A and a FWHM of 10−2-101 µs. Future work is to research the mechanisms of the vacuum breakdown current deeply with this probe.
ACKNOWLEDGMENTS
This work is supported by the National Natural Science Foundation of China (NNSFC) under Grant No. 51377135. The authors wish to express thanks to Y. F. Pan for his helpful discussions on this paper. 1O.
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