• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Design of an efficient collector for the HIAF electron cooling system

    2021-11-13 01:30:42MeiTangTangLiJunMaoHaiJiaoLuLiXiaZhaoJieLiXiaoPingShaFuMaYunBinZhouKaiMinYanXiaoMingMaXiaoDongYangJianChengYang
    Nuclear Science and Techniques 2021年10期

    Mei-Tang Tang· Li-Jun Mao · Hai-Jiao Lu · Li-Xia Zhao · Jie Li ·Xiao-Ping Sha · Fu Ma · Yun-Bin Zhou · Kai-Min Yan · Xiao-Ming Ma ·Xiao-Dong Yang · Jian-Cheng Yang

    Abstract A collector with high perveance, efficient recuperation, and low secondary emissions is required for the 450-keV electron cooler in the HIAF accelerator complex.To optimize the collection efficiency of the collector, a simulation program,based on the Monte Carlo simulations,was developed in the world’s first attempt to calculate the electron collection efficiency. In this program, the backscattering electrons and secondary electrons generated on the collector surface are calculated using a Monte Carlo approach, and all electron trajectories in the collector region are tracked by the Runge-Kutta method. In this paper, the features and structure of our program are described.The backscattering electron yields, with various collector surface materials, are calculated using our program. Moreover, the collector efficiencies for various collector structures and electromagnetic fields are simulated and optimized. The measurement results of the collection efficiency of the HIAF collector prototype and the CSRm synchrotron are also reported. These experimental results were in good agreement with the simulation results of our program.

    Keywords Electron cooler · Secondary electron ·Backscattering electron · Monte Carlo method · Dielectric function

    1 Introduction

    A high-intensity heavy-ion accelerator facility(HIAF)is currently constructed at the Institute of Modern Physics,Chinese Academy of Sciences (IMP) [1-3], to provide intense primary and radioactive ion beams for nuclear physics [4-6], atomic physics [7], and application research [8].A schematic of the HIAF accelerator complex is shown in Fig. 1. It is mainly composed of a superconducting heavy-ion linear accelerator(iLinac) [9],a booster synchrotron (BRing), the high-energy fragment separator(HFRS), and a high-precision spectrometer ring (SRing).

    Generally, BRing is used to accumulate and accelerate the primary heavy-ion beams provided by iLinac [10].SRing is used to collect the secondary ions produced by bombarding the target with primary ions extracted from BRing. The precision values of the atomic masses will be measured in SRing [11]. Several internal target experiments using these secondary ions have also been proposed for SRing. To improve the beam quality and compensate for the heating effect of the internal target experiment, an electron cooling system is required [12].

    Electron cooling is widely used to reduce the velocity diffusion, suppress the scattering, and compensate for the energy loss of the ion beam in the storage ring. A typical magnetized electron cooler was designed as the main cooling scheme for SRing. The maximum electron energy is up to 450 keV,and the DC current is 2.0 A.To minimize the power consumed by the high-voltage system, an electron energy recuperation method is adopted in the cooler. In this method, a DC electron beam is generated from a thermionic cathode and accelerated to the required energy by an electrostatic tube. After interacting with ions in the cooling section,the electron beam is decelerated and absorbed by the collector.

    Fig. 1 (Color online) Layout of the HIAF accelerator complex

    Inevitably, some electrons are reflected from the collector. The reflected electrons increase the load current of the high-voltage system, thereby reducing the stability of the power supply, or hit the vacuum chamber, destroying the vacuum condition, and causing radiation safety issues.Therefore, collection efficiency is the key parameter for collector design and should be optimized to the maximum possible extent.

    In general, the collection efficiency ηcol is defined as the ratio of the electron current reflected from the collector Ileak to the current of the main electron beam Ibeam:

    The maximum acceptable value of the collection efficiency ηcol is limited by the maximum load current that the highvoltage system can withstand and the primary electron beam current. For coolers of several hundred keV, such as the cooler in CSR (Lanzhou, China), the current of the high-voltage generator is usually limited to a few milliamperes, and the required collection efficiency ηcol should reach an order of magnitude of 10-4for severalampere primary electron beams. For high-energy coolers,such as the coolers for the COSY, HESE, and Fermilab synchrotrons, the maximum load current of the high-voltage generator is limited to a value of several hundred microamperes [13]; in this case, the required collection efficiency ηcol should reach 10-5.

    The energy of the electron cooler for HIAF is designed to be 450 keV, and the load current of the high-voltage system is limited to 1 mA. Therefore, the collection efficiency of the HIAF electron cooler must be designed to be<5×10-4at a maximum current of 2 A. The required collection efficiency is better than that of the coolers for CSRe and CSRm and worse than that of the coolers for COSY, HESR, and Fermilab. The main parameters and design requirements are listed in Table 1.

    Generally,the collection efficiency of a collector can be estimated by a simple formula:

    where Ucoll is the potential in the collector, Umin is the potential minimum in front of the collector, Bc and B0are the magnetic field strengths at the potential minimum and at the collector surface, respectively, and k is the coefficient of reflection from the collector. However, it is impossible to use this formula to optimize the collection efficiency of the collector.

    Tracking the movement of electrons in the collector region is an effective method for calculating the collection efficiency.Many computer programs,such as Opera,CST,and Geant4, can be used to calculate beam motion and secondary electron emissions. In Opera and CST, the secondary electrons are generated by the Furman emission model [14] or the Vaughan emission model [15]. In these models, true secondary electrons and backscattering electrons can be generated by probability distribution functions that depend on the incident energy and angle.

    However, in these programs, the angular distribution of the emitted electrons, especially that of the backscattered electrons, is not well considered. In CST and Opera, the polar angle is considered to satisfy the cosine distribution,when it does not, in fact, do so. For a collector with a potential barrier and magnetic mirror, the majority of the escaped electrons are small-angle backscattered electrons,and the angular distribution should be dealt with in detail.In Geant4,the Monte Carlo method is used to calculate thesecondary electron emissions, and the obtained secondary electron distribution is more reliable. However, the beam space-charge field, which is very important in the beam motion of the collector, is not considered in the beam transportation process in Geant4. In short, these programs cannot be used to optimize our collector.

    Table 1 Basic parameters and requirements for the HIAF cooler collector

    A computer program was developed to simulate the movement of the primary and secondary electrons in the HIAF cooler collector and to conveniently optimize the collector. In this program, the electron scattering process on the surface of the collector was calculated using a Monte Carlo model. The electron motion in an electromagnetic field in the collector region was solved using the fourth-order Runge-Kutta numerical algorithm.

    In this study, the details of this program are presented.The backscattering electron yields and secondary electron yields are calculated to choose an appropriate material for the collector. The magnetic mirror field, collector shape,and electric field are optimized according to the simulation results. Finally, the experimental results for the prototype collector are summarized and compared with the simulated results.

    2 Electron beam motion in the collector and the Monte Carlo procedures

    Generally, an axisymmetric structure is used in the collector design. Therefore, the Lorentz force equation in the cylindrical coordinate system(R,θ,Z)is adopted in our software to calculate the electronic motion in the collector area [16]:

    where E and B are the strengths of the electric and magnetic fields,respectively.m is the rest mass of the electron,γ is the Lorentz factor,and e is the elementary charge.The fourth-order Runge-Kutta method was used to solve Eq. (3).

    Initially, a certain number of model electrons were generated using the primary electron beam parameters at the entrance to the collector. The electromagnetic field in the collector region was calculated using the Ultra-SAM software, which is widely used for simulations of cylindrically symmetric electron guns and collectors, and the space-charge field was considered in the software. The movement of these electrons in the field is tracked using the solution of Eq.(3).When the primary electrons collide with the collector surface,the Monte Carlo method is used to simulate the interaction process.

    There are two different scattering processes: elastic and inelastic. In the elastic process, electrons are scattered by atomic nuclei, and the momentum is transferred without any energy loss. In the inelastic process, electrons interact with the extranuclear electrons of the solid, and the extranuclear electrons are excited.The excited extranuclear electrons have the opportunity to escape from the collector surface and become real secondary electrons. The primary electron also has the opportunity to escape from the collector surface, after many scatterings, and become a backscattering electron. The numbers of primary and escaped electrons are used to estimate the collection efficiency.

    Because the energy of the primary electrons, after deceleration in front of the collector, is less than 3.0 keV,the Monte Carlo simulation model is used in our program.It is based on the optical dielectric function and Mott’s elastic cross section, which are suitable for low-energy situations. The scattering process was calculated step by step. The step length was calculated as follows:

    where R1is a uniform random number in the range of 0-1.λm is the total mean free pass calculated from the elastic mean free pass λe and the inelastic mean free pass: λin

    In the inelastic scattering process, a secondary electron can be excited. In the case of ΔE<EB, the valence electron will be excited. The energy of the excited electron is E=ΔE+E′, the polar angle θ′=πR7, and the azimuthal angle φ′=2πR8, where EB is the binding energy of the outermost inner-shell edge and E′is the energy of a Fermi sea electron.

    In another case, ΔE >EB, the inner-shell electron will be excited;in this case,the energy of the excited secondary electron will be ΔE-EB, the polar angle θ′=arcsin(cos(θ)), and the azimuthal angle φ′=π+φ.After the secondary electron is generated, its energy,position,and movement direction are stored in a file;it will be recalled and simulated in the same manner as the primary electron.In this process,secondary electrons will also be excited, which are the so-called cascade of secondary electrons. The above-mentioned scattering process is repeated until the kinetic energy of the penetrating electron is lower than the cutoff energy or the electron escapes from the surface.

    In our program, the cutoff energy is adjustable. When calculating the collection efficiency of the HIAF collector,the cutoff energy was set to be 50 eV less than the depth of the collector potential well to save CPU time. When the secondary and backscattering yields were calculated to check the reliability of the software, the cutoff energy was set to the internal potential of the target material, which is equal to the sum of the Fermi energy and the work function.

    In the Monte Carlo process, many electrons are calculated together, and the number of electrons N can be changed, according to the memory of the used computer.When the energy of each electron is lower than the cutoff energy or the electron leaves the solid, the simulation will terminate and start the simulation of another N electrons.After completing the simulation for all the primary and cascade electrons, the Monte Carlo process is completed.Then, the movement of the knocked-out electrons is simulated to obtain the collection efficiency.

    3 Collector materials

    Secondary electron emissions from the collector surface could severely perturb the collection efficiency. To select the available collector surface materials and check the reliability of the program, the secondary electron emission coefficients of different collector materials were simulated and compared with the existing experimental results from several laboratories.

    First, the backscattering yields η, which are defined as the ratios between the number of backscattering electrons and the number of incident electrons, are calculated. The simulation results of the backscattering yields with different materials are shown as lines in Fig. 2. In addition, the experimental results from different groups are shown as dots in the figure [23]. It can be seen that the backscattering yield is in good agreement with the experimental yield. For a certain initial electron energy, the yield increases with an increase in the atomic number.When the initial electron energy is greater than 1 keV, the backscattering yield does not change significantly with the initial electron energy.

    The secondary electron yield of copper δ is also calculated. It is defined as the ratio of the number of real secondary electrons to the number of incident electrons, and the results are shown as a line in Fig. 3. The experimental results from several measurements by different groups are shown as dots in that figure.

    The experimental data were collected by D.C. Joy [23]from the literature published over several decades, and the reliability of the data was not judged. Therefore, the discrepancy in the experimental data in Fig. 3 is large.Although this discrepancy is large at lower energies, the simulation results have the same trend as the experimental results. It can be observed that for the experimental data and simulation results, δ has a maximum value of approximately 0.5 keV, and the simulated yield is covered by the experimental data area.

    Figure 4 shows the energy spectra of the backscattering electrons and secondary electrons produced by primary electrons with an energy of 0.8 keV.It is observed that the energy of the secondary electrons generated by inelastic scattering is low,and the energy of backscattered electrons is high,with the maximum value reaching the energy of the primary electrons.

    A suppression electrode was installed at the entrance to the collector of the HIAF electronic cooler to create an electric potential barrier. This can reflect secondary electrons and backscattered electrons with lower energies into the collector. From this perspective, the collection efficiency is mainly contributed by backscattered electrons with higher energy. Materials with low backscattered electron yields are good choices for collector designs.Figure 2 shows that carbon has the smallest backscattering yield. Unfortunately, it is difficult to build a collector with carbon, owing to mechanical challenges. Based on experience with existing coolers, the collector for the HIAF electron cooler is made of copper.

    Fig. 2 (Color online) Primary electron energy dependence of backscattering yields η

    Fig. 3 (Color online) Primary electron energy dependence of secondary electron yields δ

    Fig. 4 (Color online) Energy spectra of the backscattering electrons(green) and secondary electrons (blue) for the 800-eV incident electrons at normal incidence.The distributions are normalized by the maximum value of the distributions

    To further examine the reliability of the program, the angular distribution of the backscattering coefficients at two different incident angles was calculated. Figure 5 shows the polar diagram of the angular distribution of the backscattering coefficient, when electrons with energies equal to 1 keV are incident on copper. From Fig. 5, it can be seen that for a normal incidence case, the angular distribution obtained by our simulation software agrees with the distribution obtained by the cosine distribution. For an oblique incidence case, the backscattering coefficients are larger in the opposite direction, as reported by others [24-26].

    4 Optimization of the collector

    The design of the HIAF electron cooler collector is shown in Fig. 6.It consists of a pre-deceleration electrode,suppressor electrode, and collector cup. The pre-deceleration electrode and collector cup are connected in series.The potential on the suppressor electrode is slightly lower than the potential on both the pre-deceleration electrode and the collector cup,resulting in an electric trap,as shown in Fig. 6. In this case, the primary electron beam can pass through the barrier to reach the collector cup;however,the secondary electrons whose energy is lower than the electric trap will be prevented from escaping.

    Fig. 6 (Color online) Collector layout. The blue lines are the trajectories of the primary electron beam, and the red lines are the trajectories for several secondary electrons

    In addition, a magnetic mirror was designed to further improve the collection efficiency of the collector. To form a magnetic mirror,the bottom of the collector is placed in a weak field Bc, and the exit of the collector is placed in a strong magnetic field B0. The magnetic field on the axis is shown in Fig. 6, and the typical primary electron beam trajectory (blue) and several secondary electrons (red) are also shown in Fig. 6.To optimize the collector,the effects of the magnetic mirror, collector structure, and electric potential barrier on the collection efficiency are simulated,and the results are summarized as follows.

    a. Magnetic mirror field

    One of the most fundamental tasks of a collector design is to ensure that the primary electron beam can be absorbed by the collector cup. Accordingly, the primary electron beam dimensions at the entrance should be smaller than the inner radius of the collector. In the HIAF electron cooler,the magnetic field B0at the entrance was designed to be equal to 0.220 T. In this case, the radius of the primary electron beam envelope is approximately 20.5 mm. The inner radius of the collector is designed to be 22.5 mm,larger than the beam dimensions. In this manner, the primary electron beam can enter the collector smoothly, as shown in Fig. 6.

    Owing to the magnetic mirror field in the collector, the collection efficiency is related to the value of Bc/B0[27].Any secondary electrons generated on the surface of the collector at an angle θ (the angle between its velocity and the field line on the collector surface) that are larger than the critical value θc will be reflected by the mirror field.θc is determined as follows:

    The effect of the magnetic mirror can be enhanced by reducing Bc/B0.The length of the collector was optimized by choosing a reasonable Bc/B0. In the simulation, the magnetic field at the entrance of collector B0and the distribution of the magnetic field along the longitudinal direction were not changed directly.The field at the surface of collector Bc was indirectly changed by increasing the length of the collector. When the length of the collector increases,Bc decreases,and Bc/B0also decreases.In these simulations, to exclude the effect of the electric potential,the voltage on the suppressor was equal to the voltage on the collector.It is worth mentioning that in the simulation,the collector entrance was placed at position 1.1 m.

    Figure 7 shows that the collection efficiency depends on where the bottom of the collector is placed.Figure 7 shows that with the increase in the position of the bottom of the collector,the escape rate of the secondary electrons and the field strength Bc decrease. When the position is greater than 1.4 m, the escape rate becomes almost constant.

    Fig. 7 (Color online) The collection efficiency and the field Bc depend on the position where the collector bottom is placed

    To gain a high collection efficiency, it is suggested that the position of the collector’s bottom should not be less than 1.4 m.For our collector,the position of the collector’s bottom is designed to be placed at 1.4 m, as Fig. 6 shows.In this case,Bc =0.002 T,and the length of the collector is 0.3 m. The collection efficiency can reach 2.22×10-2without the help of the electric barrier. In other words,when there is only a magnetic mirror field in the collector area and no electrical barrier, approximately 97.78% of primary electrons are collected by the collector.

    For a collector with a fixed critical angle θc,the escape rate of the electrons is affected by the angular distribution of the backscattered electrons, which is related to the magnetic field lines and the geometry of the collector [13,27].Two types of collector shapes were used in the simulations: cones (Fig. 8a) and inverted cones (Fig. 8b).

    In these simulations, the shape changes according to different angles θaand θb.To display the simulation results in one graph,θais defined as a negative angle varying from 0°to -70°, and θbis a positive angle varying from 0°to 80°. In these simulations, the magnetic field was fixed at B0=0.220 T and Bc=0.002 T, and the maximum current of the electron beam was 2 A.The collector cup voltage is 4 kV, and the suppressor voltage is set to 0.2 kV, 0.4 kV,0.6 kV, and 0.8 kV.

    Fig. 8 (Color online) Different inner collector surfaces used in simulations

    Fig. 9 (Color online) Collection efficiency ηcol, total backscattering yields Ns/Np, and rate (θc) Nθ<θc/Np for different collector shapes and suppressor voltages

    Figure 9 shows the dependence of the simulation results on the shape of the collector. The collecting efficiency ηcol =Ne/Np for different structures (θa,b) and voltages on the suppressor Us are shown in this figure. Ne is the number of electrons that escaped from the collector, and Np is the number of primary electrons used in the simulations. The generated electrons at the surface of the collector with an angle larger than the critical angle θ<θc are totaled and represented by Nθ<θc. The total generated electrons are represented by Ns. The rates Nθ<θc/Np and Ns/Np are also shown in Fig. 9.

    The collection efficiency ηcol is dependent on the collector shape. When θa,bis smaller than -50°or θa,bis larger than 40°, ηcol increases quickly; and when θa,bchanges from -50°to 40°, the change in ηcol is relatively stable. The minimum value of ηcol appears at approximately-50°.The trend of the curve Ne/Np is the same as the trend of the curve Nθ<θc/Np, but is different from the trend of the curve Ns/Np. This indicates that the angular distribution of the generated electrons has a greater correlation with ηcol, compared to the correlation with the scattering yield. The simulation results suggest that for the HIAF collector, the angle related to the interface shape should be selected in the range of-50°to 40°.Considering the difficulty of processing, a simpler collector with an angle equal to 0 was chosen for HIAF.

    c. Influence of the electric field

    The highest energy of the secondary electrons that can be reversed by the electric potential barrier of the collector depends on the electric potential at the collector surface and the potential at the entrance to the collector [27]. The electric potential at the collector surface is related to the voltage on the collector Uc.The potential at the entrance to the collector Um is related to the voltage on the suppressor Us, the space charge field of the primary electron beam,and Uc.

    Then the Prince seized the girl s hand and cried out, This is the Princess Hyacinthia! You re right again, said the Magician in amazement37; but I ve still another task for you to do

    To evaluate the influence of Uc and Us on the collection efficiency,the collection efficiency of the primary electron beam with a maximum of 2 A and a smaller current of 0.5 A were simulated. The results are shown in Figs. 10 and 11, respectively. The collection efficiency was simulated under different collector voltages (Uc) and suppressor voltages (Us). In these simulations, the typical magnetic field B0=0.220 T was chosen.

    The dependence of the collection efficiency ηcol on Us and Uc is shown in Figs. 10 and 11,respectively.It can be observed that for a certain collector voltage Uc, ηcol decreases with a decrease in Us. This is because when Us decreases, the potential barrier becomes larger, and electrons with higher energy can be stopped. However, when Us is too low,ηcol increases rapidly,owing to the refection of the primary electrons by the potential barrier.When Uc increases, the minimum value of ηcol obtained by decreasing Us decreases.

    Fig. 10 (Color online) Collection efficiency dependence on the voltages on the collector and suppressor for a 2-A electron beam

    Fig. 11 (Color online) Collection efficiency dependence on the voltages on the collector and suppressor for a 0.5-A electron beam

    For a large Uc, a negative voltage is required to obtain the minimum value of ηcol.It can be found that the escape rate can reach 2-3×10-4for both 2-A and 0.5-A primary electron beams when Us and Uc are chosen appropriately.The centrifugal drift in the toroid of the HIAF cooler is designed to be compensated by the electric field; in this case, the electrons escaping from the collector may travel through the cooler to the gun, fall into the collector again,and have the chance to be absorbed by the collector.

    Based on experiences with CSR electronic coolers and other coolers around the world [13, 28], the electrostatic compensation method can increase the efficiency of the collector by two orders of magnitude. Hence, it can be expected that for the HIAF cooler, the final recuperation efficiency can reach 10-5-10-6when the one-time collector efficiency is ηcol =2-3×10-4.This is within the design requirement of 5×10-4.

    5 Experimental results

    The test setup was built at the Institute of Modern Physics (IMP). The main goal of the test setup is to evaluate the gun design proposed for HIAF and to test the collection efficiency of the collector.The layout of the test setup is shown in Fig. 12.The electron gun was installed at the bottom,and the collector was installed at the top.Three solenoids were used to guide the electron beam from the gun to the collector.

    Fig. 12 (Color online) Layout of the electron cooler test setup

    The collection efficiency was measured for different collector voltages(Uc)and suppressor voltages(Us)in the test setup. The results are shown in Fig. 13 by the lines with filled markers, and the results obtained by simulation are shown by the dashed lines with open markers.From the figure, it can be seen that the variation tendencies of the collecting efficiencies obtained from the experiment and simulation are the same. The phenomenon in which the escape rate rises rapidly when Us/Ucis small, for Uc=300 V and Uc=200 V was obtained both by experiments and simulations. This was caused by the reversal of the primary electrons.

    The collection efficiency obtained by the simulation is approximately two orders of magnitude greater than the efficiency obtained by the experiment.The main reason for this is that the electron flow in the test setup is completely reversible. The secondary electrons escaping from the collector can travel through the collector to the gun and then fall into the collector again.This situation is similar to the case in which an electric field is used to compensate for the electron centrifugal drift in the toroid of an electron cooler. In this case, the recovery efficiency can be two orders of magnitude higher than the single collection efficiency [13, 28].

    To further verify the reliability of our simulation software and to clarify the improvement effect of the collection efficiency by using the electrostatic compensation method in the toroids,the dependence of the single-time collection efficiency and total collection efficiency on voltages Uc and Us on the CSRm electron cooler is measured under two different conditions.

    The single-time collection efficiency is measured when the centrifugal drift in the toroids is compensated by the magnetic field. In this case, the electrons can only be collected once; the secondary electrons escaping from the collector will be lost in the cooler and cannot enter the collector and be collected again. The total collection efficiency is measured when the centrifugal drift in the toroids is compensated by the electric field; in this case, thesecondary electrons can be collected once again. For comparison, the single-time collection efficiency was also simulated for the CSRm cooler under the same conditions.

    Fig. 14 (Color online)Collection efficiency dependence on Us/Uc for the 50-mA electron beam. The dashed lines with open markers are experimental results for the electric-field compensation case, the dashed lines with closed markers are experimental results for the magnetic-field compensation case, and the solid lines with closed markers are simulated results

    Both the measured and simulation results are shown in Fig. 14.It can be observed that when the centrifugal drift in the toroids is compensated by the magnetic field, the measured results are near the simulation results. When an electric field is used to compensate for the draft, the recovery efficiency can be two orders of magnitude higher than the simulated single-time collection efficiency because the secondary electrons can be collected many times.

    The experimental results show that our simulation software can provide reliable results for single-time collection efficiency. Using electrostatic compensation in the toroids can significantly improve the total collection efficiency of the electron cooler.

    6 Summary

    A method based on the Monte Carlo method was used for collector efficiency simulations.Using this method,the collector for HIAF was simulated and optimized. The collecting capacities of the collector with different materials, structures, and electromagnetic fields were investigated. Based on these simulations, several conclusions were drawn:

    1. The backscattering yield and secondary electron yield were simulated by the Monte Carlo software for different materials; the results were in agreement with the experimental data published by other groups,which proves that the software is reliable.

    2. For a certain magnetic field, the magnetic mirror was optimized by optimizing the length of the collector.After optimization, when there was only a magnetic mirror without the help of a potential barrier, approximately 97.78% of the primary electrons were absorbed by the collector.

    3. For a certain magnetic field, the collector’s innersurface shape influences the collector’s efficiency,mainly because the angular distributions of the backscattering electrons are different for collectors with different shapes. For the HIAF electron cooler, a simpler columned collector with angle θa,b=0 was chosen.

    4. For the HIAF electron cooler collector, when the appropriate Us and Uc were chosen, the collection efficiency reached 2-3×10-4, which satisfies the design requirement ηcol<5×10-4. Based on experiences with coolers in the world and our experimental results, it can be predicted that for the HIAF cooler,using an electric field in the toroid to compensate for the centrifugal drift of the electron beam, the recuperation efficiency can reach 10-5-10-6.

    Author ContributionsAll authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Mei-Tang Tang,Li-Jun Mao,and Jei Li.The first draft of the manuscript was written by Mei-Tang Tang,and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

    国产日韩欧美亚洲二区| 亚洲中文字幕日韩| 老司机深夜福利视频在线观看| 91九色精品人成在线观看| 午夜免费鲁丝| 精品国产乱子伦一区二区三区| 黄色成人免费大全| 国产淫语在线视频| 男女免费视频国产| 国产激情久久老熟女| 欧美人与性动交α欧美软件| 欧美精品高潮呻吟av久久| 亚洲av电影在线进入| 亚洲色图 男人天堂 中文字幕| 欧美另类亚洲清纯唯美| 国产精品98久久久久久宅男小说| 国产淫语在线视频| 又大又爽又粗| 久久人妻av系列| 一边摸一边抽搐一进一出视频| 亚洲美女黄片视频| 精品免费久久久久久久清纯 | 亚洲精品中文字幕在线视频| 啦啦啦 在线观看视频| 在线观看免费日韩欧美大片| 人人妻人人添人人爽欧美一区卜| 久久久久久久国产电影| 五月开心婷婷网| 久久久国产成人免费| 黄色丝袜av网址大全| 激情在线观看视频在线高清 | 精品第一国产精品| 国产亚洲av高清不卡| 成年动漫av网址| 性色av乱码一区二区三区2| 日本vs欧美在线观看视频| 国产1区2区3区精品| 悠悠久久av| www.999成人在线观看| 欧美日韩成人在线一区二区| 欧美精品av麻豆av| 少妇 在线观看| 精品人妻在线不人妻| 国产成人精品久久二区二区91| 少妇的丰满在线观看| 亚洲欧美一区二区三区久久| av线在线观看网站| 欧美日韩中文字幕国产精品一区二区三区 | 成人影院久久| 老汉色∧v一级毛片| 日韩欧美三级三区| 久久精品亚洲av国产电影网| 午夜免费鲁丝| 亚洲国产欧美日韩在线播放| 免费高清在线观看日韩| 久久久久视频综合| 女性被躁到高潮视频| 欧美在线黄色| 久久久久国内视频| 精品国产乱子伦一区二区三区| 国产一区二区三区视频了| 午夜福利,免费看| 亚洲av熟女| 中亚洲国语对白在线视频| 国产男女内射视频| 欧美日韩瑟瑟在线播放| 另类亚洲欧美激情| 久久国产精品大桥未久av| 亚洲一卡2卡3卡4卡5卡精品中文| 婷婷丁香在线五月| 在线国产一区二区在线| 91成人精品电影| 免费女性裸体啪啪无遮挡网站| 久久久国产成人精品二区 | 日韩成人在线观看一区二区三区| 高清黄色对白视频在线免费看| 精品久久蜜臀av无| 水蜜桃什么品种好| 国产一卡二卡三卡精品| 制服诱惑二区| 美女福利国产在线| videos熟女内射| 免费观看人在逋| 18禁裸乳无遮挡动漫免费视频| 亚洲一区二区三区不卡视频| 日韩精品免费视频一区二区三区| 免费看十八禁软件| 欧美最黄视频在线播放免费 | av欧美777| 99国产精品一区二区蜜桃av | 啦啦啦 在线观看视频| 久99久视频精品免费| 丁香六月欧美| www.自偷自拍.com| 亚洲国产精品一区二区三区在线| 国产片内射在线| 亚洲精品成人av观看孕妇| 久久精品国产清高在天天线| 国产精品成人在线| 91九色精品人成在线观看| 天天影视国产精品| 最新的欧美精品一区二区| 久久久久久久久免费视频了| 人人妻,人人澡人人爽秒播| 精品国产一区二区三区久久久樱花| 亚洲成a人片在线一区二区| 国产在视频线精品| 国产淫语在线视频| 天堂中文最新版在线下载| 一进一出抽搐动态| 一级片'在线观看视频| 久久青草综合色| 欧美乱码精品一区二区三区| 午夜激情av网站| 一级a爱视频在线免费观看| 老汉色∧v一级毛片| 日韩成人在线观看一区二区三区| 精品国产美女av久久久久小说| 欧美日韩乱码在线| 1024视频免费在线观看| 国产成人一区二区三区免费视频网站| 国产精品 欧美亚洲| 亚洲成人手机| 下体分泌物呈黄色| 婷婷成人精品国产| av视频免费观看在线观看| 国产精品成人在线| 无限看片的www在线观看| 成年动漫av网址| 超色免费av| 国精品久久久久久国模美| 久久精品国产a三级三级三级| 香蕉丝袜av| 国产激情久久老熟女| 日本黄色视频三级网站网址 | 热99国产精品久久久久久7| 久久精品熟女亚洲av麻豆精品| 午夜福利在线观看吧| 最新美女视频免费是黄的| 精品一区二区三区视频在线观看免费 | av欧美777| 久久精品亚洲av国产电影网| 久久国产亚洲av麻豆专区| 精品人妻1区二区| 国产成人精品无人区| 制服人妻中文乱码| 老司机靠b影院| 久久中文字幕人妻熟女| 欧美久久黑人一区二区| 国产日韩欧美亚洲二区| 91国产中文字幕| 亚洲成人手机| 宅男免费午夜| 国产精品美女特级片免费视频播放器 | 中文字幕色久视频| 国产精品98久久久久久宅男小说| 久久久国产精品麻豆| 自拍欧美九色日韩亚洲蝌蚪91| 成年版毛片免费区| 男女床上黄色一级片免费看| 亚洲一区高清亚洲精品| 超碰97精品在线观看| 亚洲性夜色夜夜综合| www.精华液| 久久久精品区二区三区| 免费女性裸体啪啪无遮挡网站| 国产片内射在线| 十八禁人妻一区二区| 一区二区三区国产精品乱码| 久久精品国产亚洲av香蕉五月 | 国产日韩欧美亚洲二区| 成年人黄色毛片网站| 99国产精品99久久久久| 亚洲第一av免费看| a在线观看视频网站| 精品少妇久久久久久888优播| 人人妻,人人澡人人爽秒播| 天天操日日干夜夜撸| 两个人看的免费小视频| 亚洲av成人不卡在线观看播放网| 十八禁人妻一区二区| 午夜日韩欧美国产| 亚洲第一青青草原| 欧美一级毛片孕妇| 亚洲自偷自拍图片 自拍| 久久天堂一区二区三区四区| 国产成人av教育| 亚洲一区中文字幕在线| 五月开心婷婷网| 高清av免费在线| 超碰97精品在线观看| 丝袜美腿诱惑在线| 午夜免费鲁丝| 久久精品熟女亚洲av麻豆精品| 麻豆国产av国片精品| 香蕉久久夜色| 人人妻人人爽人人添夜夜欢视频| 亚洲成a人片在线一区二区| 9热在线视频观看99| 捣出白浆h1v1| 亚洲成a人片在线一区二区| 黄色a级毛片大全视频| tube8黄色片| 成年人黄色毛片网站| 国产精品久久久久成人av| 欧美黄色片欧美黄色片| 熟女少妇亚洲综合色aaa.| 悠悠久久av| 男女下面插进去视频免费观看| 国产99久久九九免费精品| tube8黄色片| 久久午夜亚洲精品久久| 亚洲欧美精品综合一区二区三区| 午夜亚洲福利在线播放| 怎么达到女性高潮| 国产不卡av网站在线观看| 无人区码免费观看不卡| 女同久久另类99精品国产91| 黄频高清免费视频| 99精品在免费线老司机午夜| 宅男免费午夜| 法律面前人人平等表现在哪些方面| 欧美 日韩 精品 国产| 高清黄色对白视频在线免费看| 国产精品电影一区二区三区 | 淫妇啪啪啪对白视频| 午夜福利视频在线观看免费| av福利片在线| 久久国产精品影院| 老司机影院毛片| 丰满迷人的少妇在线观看| 中文字幕制服av| 91成年电影在线观看| 国产精品永久免费网站| 丝瓜视频免费看黄片| 18禁裸乳无遮挡免费网站照片 | 91成年电影在线观看| 欧美精品av麻豆av| 亚洲片人在线观看| 久久久久久亚洲精品国产蜜桃av| 三上悠亚av全集在线观看| 欧美精品人与动牲交sv欧美| 99国产精品一区二区三区| 91精品三级在线观看| 欧美中文综合在线视频| 久久国产乱子伦精品免费另类| 大香蕉久久成人网| 国产乱人伦免费视频| 成人亚洲精品一区在线观看| 在线播放国产精品三级| 丰满饥渴人妻一区二区三| 宅男免费午夜| a级毛片在线看网站| 少妇的丰满在线观看| 久久久久久免费高清国产稀缺| 黄频高清免费视频| netflix在线观看网站| 欧美黄色片欧美黄色片| 亚洲欧洲精品一区二区精品久久久| av天堂在线播放| 久久性视频一级片| 亚洲五月色婷婷综合| 国产精品av久久久久免费| 黄片播放在线免费| 日韩欧美一区二区三区在线观看 | 国产成人欧美| 亚洲人成电影观看| 一级黄色大片毛片| 99国产精品一区二区蜜桃av | 1024视频免费在线观看| 欧美日韩av久久| 成在线人永久免费视频| 啦啦啦在线免费观看视频4| 80岁老熟妇乱子伦牲交| 成人三级做爰电影| 91成人精品电影| av福利片在线| 欧美 日韩 精品 国产| 久久精品成人免费网站| 国产精品免费视频内射| 电影成人av| 一本大道久久a久久精品| 国产三级黄色录像| 精品一区二区三区av网在线观看| 国产在线观看jvid| 国产成人免费观看mmmm| 十八禁高潮呻吟视频| 制服诱惑二区| 999久久久精品免费观看国产| 久久久久久久精品吃奶| 热99国产精品久久久久久7| 亚洲人成77777在线视频| 人人妻人人添人人爽欧美一区卜| 日韩欧美三级三区| 久久人妻av系列| 久久精品aⅴ一区二区三区四区| 国产成人免费观看mmmm| 免费看a级黄色片| 欧美日韩视频精品一区| 午夜两性在线视频| 超色免费av| av免费在线观看网站| 少妇裸体淫交视频免费看高清 | 侵犯人妻中文字幕一二三四区| 亚洲九九香蕉| 黑人操中国人逼视频| 亚洲熟妇熟女久久| 怎么达到女性高潮| 欧美日本中文国产一区发布| 黄色怎么调成土黄色| 国产一卡二卡三卡精品| 国产高清videossex| 国产在线观看jvid| 777米奇影视久久| videos熟女内射| 99久久国产精品久久久| 自线自在国产av| 欧美成狂野欧美在线观看| 又紧又爽又黄一区二区| 亚洲五月天丁香| 老司机亚洲免费影院| 天天添夜夜摸| 美国免费a级毛片| 91成年电影在线观看| 国产激情欧美一区二区| 捣出白浆h1v1| 窝窝影院91人妻| 18禁国产床啪视频网站| 国产aⅴ精品一区二区三区波| 久久久精品区二区三区| 1024视频免费在线观看| 国产精品亚洲一级av第二区| 中国美女看黄片| 国产精品一区二区精品视频观看| 天天操日日干夜夜撸| 亚洲va日本ⅴa欧美va伊人久久| 丝袜美腿诱惑在线| 又黄又粗又硬又大视频| 亚洲七黄色美女视频| 欧美乱色亚洲激情| 中文字幕另类日韩欧美亚洲嫩草| 黑人操中国人逼视频| 久久精品人人爽人人爽视色| 亚洲av成人一区二区三| 国产一区二区三区在线臀色熟女 | 乱人伦中国视频| 99久久国产精品久久久| 精品人妻1区二区| 久久这里只有精品19| 久久人人97超碰香蕉20202| 亚洲人成电影免费在线| 三上悠亚av全集在线观看| 国产熟女午夜一区二区三区| 久久久久久久国产电影| 无人区码免费观看不卡| 亚洲 国产 在线| av福利片在线| av线在线观看网站| 十分钟在线观看高清视频www| 女人高潮潮喷娇喘18禁视频| 日本vs欧美在线观看视频| 乱人伦中国视频| 很黄的视频免费| 乱人伦中国视频| 精品无人区乱码1区二区| 韩国精品一区二区三区| 国产成人免费观看mmmm| 久久国产精品男人的天堂亚洲| 国产97色在线日韩免费| 啦啦啦免费观看视频1| 久久精品国产99精品国产亚洲性色 | 大陆偷拍与自拍| 午夜成年电影在线免费观看| 一区福利在线观看| 成人18禁在线播放| 久久久精品免费免费高清| 一进一出抽搐动态| 黄网站色视频无遮挡免费观看| 91av网站免费观看| 亚洲色图综合在线观看| 免费少妇av软件| 久久香蕉激情| 一边摸一边抽搐一进一出视频| 国产精品.久久久| 国产精品永久免费网站| 国产日韩欧美亚洲二区| 欧美成狂野欧美在线观看| 下体分泌物呈黄色| 俄罗斯特黄特色一大片| 精品国内亚洲2022精品成人 | 国产色视频综合| 国产精品1区2区在线观看. | 欧美国产精品va在线观看不卡| 免费女性裸体啪啪无遮挡网站| 国产精品乱码一区二三区的特点 | 黑丝袜美女国产一区| 9191精品国产免费久久| 免费观看人在逋| 欧美日韩瑟瑟在线播放| 一边摸一边抽搐一进一小说 | 亚洲欧美激情综合另类| 一级a爱片免费观看的视频| 亚洲第一欧美日韩一区二区三区| 久久久精品免费免费高清| 搡老乐熟女国产| 在线免费观看的www视频| 50天的宝宝边吃奶边哭怎么回事| 黄色视频不卡| 亚洲欧美一区二区三区久久| 高清黄色对白视频在线免费看| 亚洲色图av天堂| 中国美女看黄片| 日本黄色视频三级网站网址 | 一级a爱片免费观看的视频| 一级片'在线观看视频| 日韩欧美一区视频在线观看| 两个人看的免费小视频| 久久久久久久午夜电影 | 亚洲国产毛片av蜜桃av| 国产男女内射视频| 亚洲男人天堂网一区| 日日夜夜操网爽| 老司机影院毛片| 老司机深夜福利视频在线观看| 一个人免费在线观看的高清视频| 精品久久久久久久久久免费视频 | 欧美乱色亚洲激情| 国产伦人伦偷精品视频| 国产精品1区2区在线观看. | 女同久久另类99精品国产91| 亚洲一卡2卡3卡4卡5卡精品中文| 国产日韩欧美亚洲二区| 法律面前人人平等表现在哪些方面| 一区福利在线观看| 中出人妻视频一区二区| 脱女人内裤的视频| 国产精品98久久久久久宅男小说| 99精国产麻豆久久婷婷| 日日摸夜夜添夜夜添小说| 久久天堂一区二区三区四区| 精品久久蜜臀av无| 午夜视频精品福利| 国产av又大| 麻豆成人av在线观看| 亚洲欧美一区二区三区黑人| 91精品国产国语对白视频| 精品人妻熟女毛片av久久网站| 欧美日韩亚洲国产一区二区在线观看 | 伊人久久大香线蕉亚洲五| 久99久视频精品免费| 亚洲 国产 在线| av福利片在线| 国产精品99久久99久久久不卡| 中文字幕另类日韩欧美亚洲嫩草| 97人妻天天添夜夜摸| 国产精品成人在线| av天堂在线播放| 久久久国产一区二区| 精品乱码久久久久久99久播| 在线观看免费高清a一片| 久久中文字幕人妻熟女| 一级a爱视频在线免费观看| 如日韩欧美国产精品一区二区三区| 丝瓜视频免费看黄片| 777米奇影视久久| 国产一卡二卡三卡精品| 看黄色毛片网站| 男女之事视频高清在线观看| 亚洲成人免费av在线播放| 久久精品国产99精品国产亚洲性色 | av一本久久久久| 国产一区二区三区综合在线观看| 国产成+人综合+亚洲专区| 欧美在线一区亚洲| 老汉色∧v一级毛片| av片东京热男人的天堂| 日韩欧美一区二区三区在线观看 | 黄片小视频在线播放| 国产成人免费无遮挡视频| 香蕉丝袜av| 在线观看66精品国产| 久9热在线精品视频| 国产在线一区二区三区精| 熟女少妇亚洲综合色aaa.| 国产精品二区激情视频| 成人永久免费在线观看视频| 亚洲精华国产精华精| 老司机靠b影院| 18禁裸乳无遮挡动漫免费视频| 热99久久久久精品小说推荐| 在线观看免费高清a一片| 久久99一区二区三区| 中文亚洲av片在线观看爽 | avwww免费| 黄色怎么调成土黄色| 日韩欧美免费精品| 一区二区三区激情视频| 操美女的视频在线观看| 他把我摸到了高潮在线观看| 国产成人精品久久二区二区免费| 夜夜爽天天搞| 亚洲精品中文字幕一二三四区| 精品少妇一区二区三区视频日本电影| 精品熟女少妇八av免费久了| 午夜福利欧美成人| 国产成人av激情在线播放| 久久人妻福利社区极品人妻图片| 中文亚洲av片在线观看爽 | 国产蜜桃级精品一区二区三区 | 亚洲aⅴ乱码一区二区在线播放 | 亚洲av日韩精品久久久久久密| 成年人午夜在线观看视频| 欧美日韩视频精品一区| 亚洲第一av免费看| xxxhd国产人妻xxx| а√天堂www在线а√下载 | 大码成人一级视频| 捣出白浆h1v1| 色老头精品视频在线观看| 国产欧美日韩一区二区精品| 天天影视国产精品| 高潮久久久久久久久久久不卡| 亚洲九九香蕉| 激情视频va一区二区三区| 操美女的视频在线观看| a级片在线免费高清观看视频| 色播在线永久视频| 亚洲一区二区三区欧美精品| 人人妻,人人澡人人爽秒播| 在线播放国产精品三级| 日韩视频一区二区在线观看| 亚洲精品成人av观看孕妇| 日韩一卡2卡3卡4卡2021年| 热99久久久久精品小说推荐| 欧美日韩国产mv在线观看视频| 久久久久国内视频| videos熟女内射| 久久热在线av| 狠狠婷婷综合久久久久久88av| 黄网站色视频无遮挡免费观看| e午夜精品久久久久久久| 欧美老熟妇乱子伦牲交| 一本大道久久a久久精品| 欧美成狂野欧美在线观看| 国产成人系列免费观看| 脱女人内裤的视频| 国产精品久久久久久人妻精品电影| 纯流量卡能插随身wifi吗| 欧美中文综合在线视频| 一个人免费在线观看的高清视频| 国产精品亚洲一级av第二区| 十分钟在线观看高清视频www| 99热只有精品国产| 久久精品亚洲熟妇少妇任你| tocl精华| 国产淫语在线视频| 亚洲成人手机| 桃红色精品国产亚洲av| 在线观看一区二区三区激情| 午夜免费鲁丝| 交换朋友夫妻互换小说| 丝瓜视频免费看黄片| 搡老乐熟女国产| 少妇裸体淫交视频免费看高清 | 一a级毛片在线观看| 国产1区2区3区精品| 亚洲精品自拍成人| 亚洲美女黄片视频| 午夜免费鲁丝| 夜夜爽天天搞| 亚洲少妇的诱惑av| 夜夜躁狠狠躁天天躁| 在线看a的网站| 亚洲全国av大片| 正在播放国产对白刺激| 91av网站免费观看| 欧美日韩亚洲高清精品| 国产精品免费大片| 黑丝袜美女国产一区| 国产99白浆流出| 欧美另类亚洲清纯唯美| 午夜福利在线免费观看网站| 国产亚洲一区二区精品| 老司机福利观看| 国产精品九九99| 欧美成人午夜精品| 在线av久久热| 黄色视频不卡| 女同久久另类99精品国产91| 成年女人毛片免费观看观看9 | 亚洲欧洲精品一区二区精品久久久| 叶爱在线成人免费视频播放| 黄色 视频免费看| 成人18禁在线播放| 中文字幕另类日韩欧美亚洲嫩草| 12—13女人毛片做爰片一| 免费av中文字幕在线| 91av网站免费观看| 日韩免费av在线播放| 制服人妻中文乱码| 国产精品自产拍在线观看55亚洲 | 久久天躁狠狠躁夜夜2o2o| 热re99久久精品国产66热6| 视频区图区小说| 国产在线观看jvid| 91大片在线观看| 久久99一区二区三区| 动漫黄色视频在线观看| aaaaa片日本免费| 一a级毛片在线观看| 久久久久久久久免费视频了| 日本a在线网址| 好男人电影高清在线观看| 搡老乐熟女国产| 国产成人精品无人区|