Study on the steady operating state of a micro-pulse electron gun Zhou Kui, Lu Xiangyang, Quan Shengwen, Zhao Jifei, Luo Xing, and Yang Ziqin Citation: Review of Scientific Instruments 85, 093304 (2014); doi: 10.1063/1.4895604 View online: http://dx.doi.org/10.1063/1.4895604 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/85/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Negative transconductance in apertured electron guns J. Appl. Phys. 103, 113301 (2008); 10.1063/1.2936972 Basic R&D Studies for Lower Emittance Polarized Electron Guns AIP Conf. Proc. 675, 1068 (2003); 10.1063/1.1607298 Characteristics of Ion Induced Secondary Emission Electron Gun AIP Conf. Proc. 650, 243 (2002); 10.1063/1.1530845 Electron pulse broadening due to space charge effects in a photoelectron gun for electron diffraction and streak camera systems J. Appl. Phys. 91, 462 (2002); 10.1063/1.1419209 Self-excitation and operational characteristics of the crossed-field secondary emission electron source Rev. Sci. Instrum. 70, 4502 (1999); 10.1063/1.1150103
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 093304 (2014)
Study on the steady operating state of a micro-pulse electron gun Zhou Kui,1,2 Lu Xiangyang,1 Quan Shengwen,1 Zhao Jifei,1 Luo Xing,1,2 and Yang Ziqin1 1 2
State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China Institute of Applied Electronics, Chinese Academy of Engineering Physics, Mianyang 621900, China
(Received 25 April 2014; accepted 30 August 2014; published online 17 September 2014) Micro-pulse electron gun (MPG) employs the basic concept of multipacting to produce high-current and short-pulse electron beams from a radio-frequency (RF) cavity. The concept of MPG has been proposed for more than two decades. However, the unstable operating state of MPG vastly obstructs its practical applications. This paper presents a study on the steady operating state of a micro-pulse electron gun with theory and experiments. The requirements for the steady operating state are proposed through the analysis of the interaction between the RF cavity and the beam load. Accordingly, a MPG cavity with the frequency of 2856 MHz has been designed, constructed, and tested. Some primary experiments have been finished. Both the unstable and stable operating states of the MPG have been observed. The stable output beam current has been detected at about 3.8 mA. Further experimental study is under way now. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4895604] I. INTRODUCTION
Multipacting is a resonant electron discharge phenomenon via secondary electron emission,1 which is frequently observed in microwave systems and usually undesirable. Micro-pulse electron gun (MPG)2 utilizes the basic concept of multipacting to produce pulsed electron beams from a radio-frequency (RF) cavity. Due to its self-bunching property, MPG is capable of providing high current and short pulse electron beams. In addition to that, its simple structure and high tolerance to contamination make it a potential electron source for accelerators and microwave systems. However, no record on its applications has been reported since the concept was proposed more than two decades ago.2 The main problem in the development of MPG is the stability of its output beam current. Most theoretical studies mainly focused on the analysis of the resonant condition and the saturation mechanism. The saturation process was thought to be the equilibrium result of self-bunching effect and space charge effect.1, 5 To get high beam current with high energy and low emittance, previous experimental studies on MPG always tried to feed high power into the cavity or employ cathodes with high secondary emission yield (SEY).4 However, we believe the beam loading effect also plays an important role in the forming process of the stable multipacting current, especially for high Q RF cavity. This paper presents a study on the steady operating state of a micro-pulse electron gun with theory and experiments. In Sec. II, a simplified model is set up to show the basic characteristics of the MPG. Theoretically, the requirements for the steady operating state are proposed through the analysis of the interaction between the RF cavity and the beam load. In particular, the working point should be set in the vicinity of the first crossover point on the total effective SEY curve. In Sec. III, a MPG cavity with the frequency of 2856 MHz has been designed, constructed, and tested. Some primary experiments have been done. Both the unstable and stable operating states of the MPG have been observed in the experiments. The 0034-6748/2014/85(9)/093304/4/$30.00
stable output beam current has been detected at about 3.8 mA. Finally, a summary of this paper is given. II. THEORETICAL ANALYSIS A. The MPG model
The MPG model (Fig. 1) consists of three parts: a RF cavity, working in the TM010 mode, a secondary emission surface, and a grid, which is opaque to the microwave electric field but partially transparent to the electrons in order to extract the electron beams.3 We suppose the secondary emission surface to be the cathode with SEY δ 1 and the grid to be the grid-anode with SEY δ 2 and transmission coefficient T. Actually, δ 1 and δ 2 are affected by many factors, such as the impact energy of the primary electrons, the incident angle, the roughness and cleanliness of the material surface, etc.1, 6 Here, for simplicity, we assume the primary electrons perpendicularly impact into the surfaces of the cathode and the grid-anode. So, for a given material, its secondary electron emission yield only depends on the impact energy of the primary electrons. We adopt Vaughan’s empirical formula for δ 1 and δ 2 7 k δ1 (Ei ) = δmax1 v1 e1−v1 , (1a) k δ2 (Ei ) = δmax2 v2 e1−v2 ,
(1b)
where Ei is the electrons impact energy, δ max1 and δ max2 being the maximum value of δ 1 and δ 2 , v1 = (Ei1 − E0 )/(Emax1 − E0 ), v2 = (Ei2 − E0 )/(Emax2 − E0 ), in which Emax1 and Emax2 are the impact energy corresponding to δ max1 and δ max2 , E0 being the initial energy of secondary electrons and k = 0.62 for v < 1; k = 0.25 for v > 1. For one RF period, the total effective secondary electron emission yield δ is δ = δ1 (Ei )δ2 (Ei )(1 − T ).
(2)
Here, T is the transmission coefficient of the grid-anode. The typical SEY curves for δ 1 , δ 2 , and δ are shown in
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FIG. 1. The schematic diagram of the MPG model.3
Fig. 2. Now, we consider a RF cavity operating at the resonant frequency ω0 . The gap distance between the cathode and the grid-anode is d. Under the force of the electric field, electrons in the cavity move back and forth between the cathode and the grid-anode. The transit time from one anode to the other is just one-half RF period.1 We obtain the resonant condition Vc =
m ω0 d(ω0 d − π v0 ) e 2 sin ϕ0 + π cos ϕ0
(3)
in which, m is the mass of electron, e is the elementary electric charge, v0 is the initial velocity of the emitted electrons, and ϕ 0 is the initial phase of the RF field. The MPG also needs to satisfy the requirement of the self-bunching property. The self-bunching property demands the secondary electrons emitted within an appropriate initial phase range. For electrons with emitted energy E0 = 0, the appropriate initial phase range is 0 to arctan 2/π (≈32.5◦ ).1 Substituting the phase range into the resonant condition (Eq. (3)), we get the corresponding resonant gap voltage range Vmin =
m ω02 d 2 , √ e π2 + 4
(4a)
m ω02 d 2 . e π
(4b)
Vmax =
FIG. 2. Typical SEY curves for δ 1 , δ 2 , and δ.
FIG. 3. The resonant gap voltage range versus the gap distance d when the cavity frequency is 2856 MHz. Different gap distance d1 , d2 , and d3 correspond to different resonant gap voltage ranges [Vmin1 ,Vmax1 ], [Vmin2 , Vmax2 ], and [Vmin3 , Vmax3 ].
Figure 3 shows the resonant gap voltage region (gray area) varying with the gap distance d when the cavity frequency is 2856 MHz. If the gap voltage is outside of this resonant range, the electrons cannot gather together in the longitudinal direction so that the electron beam will break up. B. Analysis of the steady operating state
When electrons move back and forth in the cavity, the amount of energy gained will vary according to the electric field intensity or the gap voltage. Basically, the higher the gap voltage is, the more energy will be gained. According to the secondary emission property of common materials, we can map the total effective SEY curve versus the gap voltage qualitatively (Fig. 4). Supposing that the resonant gap voltage range is [Vmin1 , Vmax1 ], if the gap voltage Vc is greater (less) than V1 , more (fewer) secondary electrons will be released, so the number of electrons Ne will increase (decrease). As a result, more (less) microwave power will be drained from the cavity as it accelerates more (fewer) secondary electrons. This leads to a higher (lower) Pb and lower (higher) Pc as well as a lower (higher)
FIG. 4. The total effective SEY curve versus the gap voltage Vc . (E1 is the first crossover point and E2 is the second one. V1 and V2 are the gap voltages corresponding to E1 and E2 . In addition, it is supposed that V1 ∈ [Vmin1 ,Vmax1 ] and V2 ∈ [Vmin2 ,Vmax2 ].)
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gap voltage Vc , which makes Vc closer to V1 in subsequent RF periods. Similarly, Vc will move far away from V2 automatically if [Vmin2 ,Vmax2 ] is the resonant gap voltage range. Thus, E1 is the stable operating point for the MPG, not E2 . This conclusion is consistent with Kishek and Lau’s analysis on multipactor discharge in a closed RF cavity.8, 9 They also reached a conclusion from a circuit model of interaction between rf cavity and multipactor discharge8 that steady state multipactor saturates in a rf cavity as a result of loading. The image space charge force of the multipacting electrons is insignificant to alter the phase condition or the saturation condition whenever Q ≥ 10. However, if the resonant gap voltage range is set to be [Vmin3 , Vmax3 ] as many previous studies did, δ will be always greater than 1. When the gap voltage reaches the resonant range, the multipacting current will grow to a very large value in a very short time. A great deal of microwave power will be drained from the cavity to accelerate these multiplied electrons. So the gap voltage will eventually fall outside of the resonant range and the electron beam will break up due to the longitudinal debunching. Therefore, there is no stable working point in [Vmin3 , Vmax3 ]. This explains why previous MPGs could not work stablely. To obtain steady state multipacting current, the working point should be set in the vicinity of the first crossover point E1 and [Vmin1 , Vmax1 ] should be set as the resonant gap voltage range. Meanwhile, V1 must be included in this resonant range. Noting that the value of E1 depends on the secondary emission property of the cathode and the grid-anode as well as the transmission factor T (Eq. (2)), while the resonant gap voltage range [Vmin1 , Vmax1 ] is determined by ω0 and d. So, as long as the above requirements are satisfied, it is possible to realize the steady operating state for the MPG. III. PRIMARY EXPERIMENTS
Rev. Sci. Instrum. 85, 093304 (2014) TABLE I. RF parameters of the MPG cavity. Resonant frequency f0 (MHz) Cavity gap d (mm) Unloaded quality factor Q0 Shunt impedance rshunt () Unloaded coupling coefficient β 0
2853.6 1.95 ≈213 ≈10 946 1.1
can be replaced easily. The distributions of the magnetic field and the electric field are shown in Figs. 5(b) and 5(c). Obviously, the electric field is mainly concentrated in the region between the cathode and the grid-anode. Table I lists the measured RF parameters of the MPG cavity and the test stand is shown in Fig. 6. The microwave power is supplied by a solid-state power amplifier with 1 kW maximum output power. The output electron beams from the gridanode are collected by a faraday cup parallelly connected to a 50 resistance and the beam current is measured by a HP 54503A oscilloscope with 1 M input resistance.
B. Experiment results and discussions
Two kinds of grid-anodes are tested in our experiments. The grid-anodes are made of stainless steel and their transmission coefficients are 6% and 18.3%, respectively. The macro-pulse signal of the output electron beams as well as the microwave pick-up signal and reflected signal are monitored. When the generator power increases to an appropriate range, the multipacting discharge occurs in the cavity. Figure 7 shows the primary experimental results. The macropulse width is 15 μs and the repetition rate is about 100 Hz. The vacuum pressure is below 10−5 Pa during the experiments. Both the unstable and stable states of the MPG have been observed. For the unstable state, the macro-pulse signal
A. The MPG cavity and the test stand
According to the analysis before, a micro-pulse electron gun working in the TM010 mode with the frequency of 2856 MHz has been designed. The micro-pulse electron gun consists of a RF cavity made of stainless steel, a cathode made of Cu–Al–Mg alloy, and a grid-anode (Fig. 5(a)). The impact energy corresponding to the maximum secondary emission yield is about 1 KeV for Cu–Al–Mg alloy.10 The diameter of the cathode is 8 mm. The cathode is connected to a position adjuster, while the grid-anode is fixed by screw thread on the other side of the cavity. So the gap between the cathode and the grid-anode is adjustable with the precision of 0.01 mm. The cathode and the grid-anode are also dismountable and
FIG. 5. (a) The cross section of the MPG, (b) the magnetic field distribution, (c) the electric field distribution.
FIG. 6. Photograph of the test stand.
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cavity will seek the next chance of multiplication and a new cycle keeps on. IV. SUMMARY
FIG. 7. Primary experimental results. (a) The unstable output beam current when T = 6%; (b) the pick-up and reflected signal corresponding to (a); (c) the stable output beam current when T = 18.3%; (d) the pick-up and reflected signal corresponding to (c).
is always fluctuating and no flat top exists during the macropulse. It is difficult to get a stable value of the output beam current. Meanwhile, there are a lot of “spikes” randomly and densely appearing on the pick-up signal and reflected signal. For the stable state, the macro-pulse signal is very steady. There exists a flat top during the macro-pulse and the “spikes” also disappear on both the pick-up signal and the reflected signal. So the output macro-pulse beam current can be measured by the oscilloscope easily. Presently, the stable output beam current has been measured at about 3.8 mA. The spikes appearing on the pick-up signal and the reflected signal have indicated the typical unstable multipacting processes in the cavity. In this situation, the total effective SEY is above 1, but the actual working point is not in the vicinity of E1 . So, the electrons in the cavity grows rapidly without restraint. The multiplied electrons absorb plenty of RF power, leading to the cavity voltage falling out of the resonant range. The multiplication condition is broken and the electron beam collapses. After that, the cavity voltage returns to the initial state and a “spike” appears on the pick-up signal as well as the reflected signal due to the variation of the loaded coupling coefficient. The remaining electrons in the
In conclusion, this paper presents a study on the steady operating state of a micro-pulse electron gun with theory and experiments. In theory, a simplified model is set up to show the basic characteristics of the MPG. The requirements for the steady operating state have been proposed through the analysis of the interaction between the RF cavity and the beam load. The working point should be set in the vicinity of the first crossover point E1 and [Vmin1 , Vmax1 ] should be set as the resonant gap voltage range. Meanwhile, V1 must be included in this range. As for experiments, a MPG cavity with the frequency of 2856 MHz has been designed, constructed, and tested. Some primary experiments have been done. Both the unstable and stable states of the MPG have been observed. Presently, the measured stable output beam current has reached 3.8 mA. Further experimental study is under way now. ACKNOWLEDGMENTS
We gratefully acknowledge the assistance of Li Ming and Yang Xingfan in providing the solid-state power amplifier. We also thank Wang Xinping for preparing the Cu–Al–Mg alloy. 1 J.
R. M. Vaughan, IEEE Trans. Electron Devices 35(7), 1172–1180 (1988). M. Mako and W. Peter, in Proceedings of the PAC’93, Washington (Institute of Electrical and Electronics Engineers (IEEE), 1993), Vol. 4, pp. 2702–2704. 3 L. K. Len and F. M. Mak, in Proceedings of the PAC’99, New York (Institute of Electrical and Electronics Engineers (IEEE), 1999), Vol. 1, pp. 70–74. 4 J. Y. Zhai, C. X. Tang, and S. X. Zheng, in Proceedings of the EPAC’06, Edinburgh, THPCH174 (European Physical Society Accelerator Group (EPSAG), 2006), pp. 3203–3205. 5 L. Lang, Z. Meng et al., Chin. Phys. C 37, 117004 (2013). 6 A. Shih and C. Hor, IEEE Trans. Electron Devices 40(4), 824–828 (1993). 7 J. R. M. Vaughan, IEEE Trans. Electron Devices 36(9), 1963–1967 (1989). 8 R. Kishek and Y. Y. Lau, Phys. Rev. Lett. 75(6), 1218–1221 (1995). 9 R. Kishek, Y. Y. Lau et al., Phys. Plasmas 5(5), 2120–2126 (1998). 10 P. Qihan, W. Xinping, L. Jielan et al., China patent CN1062608C (28 February 2001) (in Chinese). 2 F.
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 093304 (2014)
Study on the steady operating state of a micro-pulse electron gun Zhou Kui,1,2 Lu Xiangyang,1 Quan Shengwen,1 Zhao Jifei,1 Luo Xing,1,2 and Yang Ziqin1 1 2
State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China Institute of Applied Electronics, Chinese Academy of Engineering Physics, Mianyang 621900, China
(Received 25 April 2014; accepted 30 August 2014; published online 17 September 2014) Micro-pulse electron gun (MPG) employs the basic concept of multipacting to produce high-current and short-pulse electron beams from a radio-frequency (RF) cavity. The concept of MPG has been proposed for more than two decades. However, the unstable operating state of MPG vastly obstructs its practical applications. This paper presents a study on the steady operating state of a micro-pulse electron gun with theory and experiments. The requirements for the steady operating state are proposed through the analysis of the interaction between the RF cavity and the beam load. Accordingly, a MPG cavity with the frequency of 2856 MHz has been designed, constructed, and tested. Some primary experiments have been finished. Both the unstable and stable operating states of the MPG have been observed. The stable output beam current has been detected at about 3.8 mA. Further experimental study is under way now. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4895604] I. INTRODUCTION
Multipacting is a resonant electron discharge phenomenon via secondary electron emission,1 which is frequently observed in microwave systems and usually undesirable. Micro-pulse electron gun (MPG)2 utilizes the basic concept of multipacting to produce pulsed electron beams from a radio-frequency (RF) cavity. Due to its self-bunching property, MPG is capable of providing high current and short pulse electron beams. In addition to that, its simple structure and high tolerance to contamination make it a potential electron source for accelerators and microwave systems. However, no record on its applications has been reported since the concept was proposed more than two decades ago.2 The main problem in the development of MPG is the stability of its output beam current. Most theoretical studies mainly focused on the analysis of the resonant condition and the saturation mechanism. The saturation process was thought to be the equilibrium result of self-bunching effect and space charge effect.1, 5 To get high beam current with high energy and low emittance, previous experimental studies on MPG always tried to feed high power into the cavity or employ cathodes with high secondary emission yield (SEY).4 However, we believe the beam loading effect also plays an important role in the forming process of the stable multipacting current, especially for high Q RF cavity. This paper presents a study on the steady operating state of a micro-pulse electron gun with theory and experiments. In Sec. II, a simplified model is set up to show the basic characteristics of the MPG. Theoretically, the requirements for the steady operating state are proposed through the analysis of the interaction between the RF cavity and the beam load. In particular, the working point should be set in the vicinity of the first crossover point on the total effective SEY curve. In Sec. III, a MPG cavity with the frequency of 2856 MHz has been designed, constructed, and tested. Some primary experiments have been done. Both the unstable and stable operating states of the MPG have been observed in the experiments. The 0034-6748/2014/85(9)/093304/4/$30.00
stable output beam current has been detected at about 3.8 mA. Finally, a summary of this paper is given. II. THEORETICAL ANALYSIS A. The MPG model
The MPG model (Fig. 1) consists of three parts: a RF cavity, working in the TM010 mode, a secondary emission surface, and a grid, which is opaque to the microwave electric field but partially transparent to the electrons in order to extract the electron beams.3 We suppose the secondary emission surface to be the cathode with SEY δ 1 and the grid to be the grid-anode with SEY δ 2 and transmission coefficient T. Actually, δ 1 and δ 2 are affected by many factors, such as the impact energy of the primary electrons, the incident angle, the roughness and cleanliness of the material surface, etc.1, 6 Here, for simplicity, we assume the primary electrons perpendicularly impact into the surfaces of the cathode and the grid-anode. So, for a given material, its secondary electron emission yield only depends on the impact energy of the primary electrons. We adopt Vaughan’s empirical formula for δ 1 and δ 2 7 k δ1 (Ei ) = δmax1 v1 e1−v1 , (1a) k δ2 (Ei ) = δmax2 v2 e1−v2 ,
(1b)
where Ei is the electrons impact energy, δ max1 and δ max2 being the maximum value of δ 1 and δ 2 , v1 = (Ei1 − E0 )/(Emax1 − E0 ), v2 = (Ei2 − E0 )/(Emax2 − E0 ), in which Emax1 and Emax2 are the impact energy corresponding to δ max1 and δ max2 , E0 being the initial energy of secondary electrons and k = 0.62 for v < 1; k = 0.25 for v > 1. For one RF period, the total effective secondary electron emission yield δ is δ = δ1 (Ei )δ2 (Ei )(1 − T ).
(2)
Here, T is the transmission coefficient of the grid-anode. The typical SEY curves for δ 1 , δ 2 , and δ are shown in
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FIG. 1. The schematic diagram of the MPG model.3
Fig. 2. Now, we consider a RF cavity operating at the resonant frequency ω0 . The gap distance between the cathode and the grid-anode is d. Under the force of the electric field, electrons in the cavity move back and forth between the cathode and the grid-anode. The transit time from one anode to the other is just one-half RF period.1 We obtain the resonant condition Vc =
m ω0 d(ω0 d − π v0 ) e 2 sin ϕ0 + π cos ϕ0
(3)
in which, m is the mass of electron, e is the elementary electric charge, v0 is the initial velocity of the emitted electrons, and ϕ 0 is the initial phase of the RF field. The MPG also needs to satisfy the requirement of the self-bunching property. The self-bunching property demands the secondary electrons emitted within an appropriate initial phase range. For electrons with emitted energy E0 = 0, the appropriate initial phase range is 0 to arctan 2/π (≈32.5◦ ).1 Substituting the phase range into the resonant condition (Eq. (3)), we get the corresponding resonant gap voltage range Vmin =
m ω02 d 2 , √ e π2 + 4
(4a)
m ω02 d 2 . e π
(4b)
Vmax =
FIG. 2. Typical SEY curves for δ 1 , δ 2 , and δ.
FIG. 3. The resonant gap voltage range versus the gap distance d when the cavity frequency is 2856 MHz. Different gap distance d1 , d2 , and d3 correspond to different resonant gap voltage ranges [Vmin1 ,Vmax1 ], [Vmin2 , Vmax2 ], and [Vmin3 , Vmax3 ].
Figure 3 shows the resonant gap voltage region (gray area) varying with the gap distance d when the cavity frequency is 2856 MHz. If the gap voltage is outside of this resonant range, the electrons cannot gather together in the longitudinal direction so that the electron beam will break up. B. Analysis of the steady operating state
When electrons move back and forth in the cavity, the amount of energy gained will vary according to the electric field intensity or the gap voltage. Basically, the higher the gap voltage is, the more energy will be gained. According to the secondary emission property of common materials, we can map the total effective SEY curve versus the gap voltage qualitatively (Fig. 4). Supposing that the resonant gap voltage range is [Vmin1 , Vmax1 ], if the gap voltage Vc is greater (less) than V1 , more (fewer) secondary electrons will be released, so the number of electrons Ne will increase (decrease). As a result, more (less) microwave power will be drained from the cavity as it accelerates more (fewer) secondary electrons. This leads to a higher (lower) Pb and lower (higher) Pc as well as a lower (higher)
FIG. 4. The total effective SEY curve versus the gap voltage Vc . (E1 is the first crossover point and E2 is the second one. V1 and V2 are the gap voltages corresponding to E1 and E2 . In addition, it is supposed that V1 ∈ [Vmin1 ,Vmax1 ] and V2 ∈ [Vmin2 ,Vmax2 ].)
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gap voltage Vc , which makes Vc closer to V1 in subsequent RF periods. Similarly, Vc will move far away from V2 automatically if [Vmin2 ,Vmax2 ] is the resonant gap voltage range. Thus, E1 is the stable operating point for the MPG, not E2 . This conclusion is consistent with Kishek and Lau’s analysis on multipactor discharge in a closed RF cavity.8, 9 They also reached a conclusion from a circuit model of interaction between rf cavity and multipactor discharge8 that steady state multipactor saturates in a rf cavity as a result of loading. The image space charge force of the multipacting electrons is insignificant to alter the phase condition or the saturation condition whenever Q ≥ 10. However, if the resonant gap voltage range is set to be [Vmin3 , Vmax3 ] as many previous studies did, δ will be always greater than 1. When the gap voltage reaches the resonant range, the multipacting current will grow to a very large value in a very short time. A great deal of microwave power will be drained from the cavity to accelerate these multiplied electrons. So the gap voltage will eventually fall outside of the resonant range and the electron beam will break up due to the longitudinal debunching. Therefore, there is no stable working point in [Vmin3 , Vmax3 ]. This explains why previous MPGs could not work stablely. To obtain steady state multipacting current, the working point should be set in the vicinity of the first crossover point E1 and [Vmin1 , Vmax1 ] should be set as the resonant gap voltage range. Meanwhile, V1 must be included in this resonant range. Noting that the value of E1 depends on the secondary emission property of the cathode and the grid-anode as well as the transmission factor T (Eq. (2)), while the resonant gap voltage range [Vmin1 , Vmax1 ] is determined by ω0 and d. So, as long as the above requirements are satisfied, it is possible to realize the steady operating state for the MPG. III. PRIMARY EXPERIMENTS
Rev. Sci. Instrum. 85, 093304 (2014) TABLE I. RF parameters of the MPG cavity. Resonant frequency f0 (MHz) Cavity gap d (mm) Unloaded quality factor Q0 Shunt impedance rshunt () Unloaded coupling coefficient β 0
2853.6 1.95 ≈213 ≈10 946 1.1
can be replaced easily. The distributions of the magnetic field and the electric field are shown in Figs. 5(b) and 5(c). Obviously, the electric field is mainly concentrated in the region between the cathode and the grid-anode. Table I lists the measured RF parameters of the MPG cavity and the test stand is shown in Fig. 6. The microwave power is supplied by a solid-state power amplifier with 1 kW maximum output power. The output electron beams from the gridanode are collected by a faraday cup parallelly connected to a 50 resistance and the beam current is measured by a HP 54503A oscilloscope with 1 M input resistance.
B. Experiment results and discussions
Two kinds of grid-anodes are tested in our experiments. The grid-anodes are made of stainless steel and their transmission coefficients are 6% and 18.3%, respectively. The macro-pulse signal of the output electron beams as well as the microwave pick-up signal and reflected signal are monitored. When the generator power increases to an appropriate range, the multipacting discharge occurs in the cavity. Figure 7 shows the primary experimental results. The macropulse width is 15 μs and the repetition rate is about 100 Hz. The vacuum pressure is below 10−5 Pa during the experiments. Both the unstable and stable states of the MPG have been observed. For the unstable state, the macro-pulse signal
A. The MPG cavity and the test stand
According to the analysis before, a micro-pulse electron gun working in the TM010 mode with the frequency of 2856 MHz has been designed. The micro-pulse electron gun consists of a RF cavity made of stainless steel, a cathode made of Cu–Al–Mg alloy, and a grid-anode (Fig. 5(a)). The impact energy corresponding to the maximum secondary emission yield is about 1 KeV for Cu–Al–Mg alloy.10 The diameter of the cathode is 8 mm. The cathode is connected to a position adjuster, while the grid-anode is fixed by screw thread on the other side of the cavity. So the gap between the cathode and the grid-anode is adjustable with the precision of 0.01 mm. The cathode and the grid-anode are also dismountable and
FIG. 5. (a) The cross section of the MPG, (b) the magnetic field distribution, (c) the electric field distribution.
FIG. 6. Photograph of the test stand.
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Rev. Sci. Instrum. 85, 093304 (2014)
cavity will seek the next chance of multiplication and a new cycle keeps on. IV. SUMMARY
FIG. 7. Primary experimental results. (a) The unstable output beam current when T = 6%; (b) the pick-up and reflected signal corresponding to (a); (c) the stable output beam current when T = 18.3%; (d) the pick-up and reflected signal corresponding to (c).
is always fluctuating and no flat top exists during the macropulse. It is difficult to get a stable value of the output beam current. Meanwhile, there are a lot of “spikes” randomly and densely appearing on the pick-up signal and reflected signal. For the stable state, the macro-pulse signal is very steady. There exists a flat top during the macro-pulse and the “spikes” also disappear on both the pick-up signal and the reflected signal. So the output macro-pulse beam current can be measured by the oscilloscope easily. Presently, the stable output beam current has been measured at about 3.8 mA. The spikes appearing on the pick-up signal and the reflected signal have indicated the typical unstable multipacting processes in the cavity. In this situation, the total effective SEY is above 1, but the actual working point is not in the vicinity of E1 . So, the electrons in the cavity grows rapidly without restraint. The multiplied electrons absorb plenty of RF power, leading to the cavity voltage falling out of the resonant range. The multiplication condition is broken and the electron beam collapses. After that, the cavity voltage returns to the initial state and a “spike” appears on the pick-up signal as well as the reflected signal due to the variation of the loaded coupling coefficient. The remaining electrons in the
In conclusion, this paper presents a study on the steady operating state of a micro-pulse electron gun with theory and experiments. In theory, a simplified model is set up to show the basic characteristics of the MPG. The requirements for the steady operating state have been proposed through the analysis of the interaction between the RF cavity and the beam load. The working point should be set in the vicinity of the first crossover point E1 and [Vmin1 , Vmax1 ] should be set as the resonant gap voltage range. Meanwhile, V1 must be included in this range. As for experiments, a MPG cavity with the frequency of 2856 MHz has been designed, constructed, and tested. Some primary experiments have been done. Both the unstable and stable states of the MPG have been observed. Presently, the measured stable output beam current has reached 3.8 mA. Further experimental study is under way now. ACKNOWLEDGMENTS
We gratefully acknowledge the assistance of Li Ming and Yang Xingfan in providing the solid-state power amplifier. We also thank Wang Xinping for preparing the Cu–Al–Mg alloy. 1 J.
R. M. Vaughan, IEEE Trans. Electron Devices 35(7), 1172–1180 (1988). M. Mako and W. Peter, in Proceedings of the PAC’93, Washington (Institute of Electrical and Electronics Engineers (IEEE), 1993), Vol. 4, pp. 2702–2704. 3 L. K. Len and F. M. Mak, in Proceedings of the PAC’99, New York (Institute of Electrical and Electronics Engineers (IEEE), 1999), Vol. 1, pp. 70–74. 4 J. Y. Zhai, C. X. Tang, and S. X. Zheng, in Proceedings of the EPAC’06, Edinburgh, THPCH174 (European Physical Society Accelerator Group (EPSAG), 2006), pp. 3203–3205. 5 L. Lang, Z. Meng et al., Chin. Phys. C 37, 117004 (2013). 6 A. Shih and C. Hor, IEEE Trans. Electron Devices 40(4), 824–828 (1993). 7 J. R. M. Vaughan, IEEE Trans. Electron Devices 36(9), 1963–1967 (1989). 8 R. Kishek and Y. Y. Lau, Phys. Rev. Lett. 75(6), 1218–1221 (1995). 9 R. Kishek, Y. Y. Lau et al., Phys. Plasmas 5(5), 2120–2126 (1998). 10 P. Qihan, W. Xinping, L. Jielan et al., China patent CN1062608C (28 February 2001) (in Chinese). 2 F.
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