The wave equation of the electron, recently improved, allows physics to obtain all the quantum numbers and other results explaining the hydrogen spectrum. The Pauli exclusion principle then gives the description of el...The wave equation of the electron, recently improved, allows physics to obtain all the quantum numbers and other results explaining the hydrogen spectrum. The Pauli exclusion principle then gives the description of electron clouds used in chemistry. The relativistic wave equation is associated with a Lagrangian density, thus also with an energy-momentum tensorial density. The wave of an electron cloud adds these energy-momentum densities, while photons in light are precisely those differences between such energy-momentum densities.展开更多
Since the position of the electron in a hydrogen atom cannot be determined, the region in which it resides is said to be determined stochastically and forms an electron cloud. The probability density function of the s...Since the position of the electron in a hydrogen atom cannot be determined, the region in which it resides is said to be determined stochastically and forms an electron cloud. The probability density function of the single electron in 1s orbit is expressed as φ2, a function of distance from the nucleus. However, the probability of existence of the electron is expressed as a radial distribution function at an arbitrary distance from the nucleus, so it is estimated as the probability of the entire spherical shape of that radius. In this study, it has been found that the electron existence probability approximates the radial distribution function by assuming that the probability of existence of the electron being in the vicinity of the nucleus follows a normal distribution for arbitrary x-, y-, and z-axis directions. This implies that the probability of existence of the electron, which has been known only from the distance information, would follow a normal distribution independently in the three directions. When the electrons’ motion is extremely restricted in a certain direction by the magnetic field of both tokamak and helical fusion reactors, the probability of existence of the electron increases with proximity to the nucleus, and as a result, it is less likely to be liberated from the nucleus. Therefore, more and more energy is required to free the nucleus from the electron in order to generate plasma.展开更多
Electron cloud interaction with high energy positive beams are believed responsible for various undesirable effects such as vacuum degradation, collective beam instability and even beam loss in high power proton circu...Electron cloud interaction with high energy positive beams are believed responsible for various undesirable effects such as vacuum degradation, collective beam instability and even beam loss in high power proton circular accelerators. An important uncertainty in predicting electron cloud instability lies in the detailed processes of the generation and accumulation of the electron cloud. The simulation on the build-up of electron cloud is necessary to further studies on beam instability caused by electron clouds. The China Spallation Neutron Source （CSNS） is an intense proton accelerator facility now being built, whose accelerator complex includes two main parts： an H-linac and a rapid cycling synchrotron （RCS）. The RCS accumulates the 80 MeV proton beam and accelerates it to 1.6 GeV with a repetition rate of 25 Hz. During beam injection with lower energy, the emerging electron cloud may cause serious instability and beam loss on the vacuum pipe. A simulation code has been developed to simulate the build-up, distribution and density of electron cloud in CSNS/RCS.展开更多
Electron Cloud Instability has been studied in the operation of BEPC. The BEPCⅡ began the commissioning in November 2006 and the positron beam current has reached 500 mA. Because of such a high beam current, some ins...Electron Cloud Instability has been studied in the operation of BEPC. The BEPCⅡ began the commissioning in November 2006 and the positron beam current has reached 500 mA. Because of such a high beam current, some instabilities such as ECI, bunch lengthening et al, have appeared during the operation. The experimental investigation on ECI during the commissioning of BEPCⅡ will be reported in this paper.展开更多
In this paper we treat first some nonlinear beam dynamics problems in storage rings, such as beam dynamic apertures due to magnetic multipoles, wiggles, beam-beam effects, nonlinear space charge effect, and then nonli...In this paper we treat first some nonlinear beam dynamics problems in storage rings, such as beam dynamic apertures due to magnetic multipoles, wiggles, beam-beam effects, nonlinear space charge effect, and then nonlinear electron cloud effect combined with beam-beam and space charge effects, analytically. This analytical treatment is applied to BEPC II. The corresponding analytical expressions developed in this paper are useful both in understanding the physics behind these problems and also in making practical quick hand estimations.展开更多
文摘The wave equation of the electron, recently improved, allows physics to obtain all the quantum numbers and other results explaining the hydrogen spectrum. The Pauli exclusion principle then gives the description of electron clouds used in chemistry. The relativistic wave equation is associated with a Lagrangian density, thus also with an energy-momentum tensorial density. The wave of an electron cloud adds these energy-momentum densities, while photons in light are precisely those differences between such energy-momentum densities.
文摘Since the position of the electron in a hydrogen atom cannot be determined, the region in which it resides is said to be determined stochastically and forms an electron cloud. The probability density function of the single electron in 1s orbit is expressed as φ2, a function of distance from the nucleus. However, the probability of existence of the electron is expressed as a radial distribution function at an arbitrary distance from the nucleus, so it is estimated as the probability of the entire spherical shape of that radius. In this study, it has been found that the electron existence probability approximates the radial distribution function by assuming that the probability of existence of the electron being in the vicinity of the nucleus follows a normal distribution for arbitrary x-, y-, and z-axis directions. This implies that the probability of existence of the electron, which has been known only from the distance information, would follow a normal distribution independently in the three directions. When the electrons’ motion is extremely restricted in a certain direction by the magnetic field of both tokamak and helical fusion reactors, the probability of existence of the electron increases with proximity to the nucleus, and as a result, it is less likely to be liberated from the nucleus. Therefore, more and more energy is required to free the nucleus from the electron in order to generate plasma.
基金Supported by National Natural Science Foundation of China(11275221,11175193)
文摘Electron cloud interaction with high energy positive beams are believed responsible for various undesirable effects such as vacuum degradation, collective beam instability and even beam loss in high power proton circular accelerators. An important uncertainty in predicting electron cloud instability lies in the detailed processes of the generation and accumulation of the electron cloud. The simulation on the build-up of electron cloud is necessary to further studies on beam instability caused by electron clouds. The China Spallation Neutron Source （CSNS） is an intense proton accelerator facility now being built, whose accelerator complex includes two main parts： an H-linac and a rapid cycling synchrotron （RCS）. The RCS accumulates the 80 MeV proton beam and accelerates it to 1.6 GeV with a repetition rate of 25 Hz. During beam injection with lower energy, the emerging electron cloud may cause serious instability and beam loss on the vacuum pipe. A simulation code has been developed to simulate the build-up, distribution and density of electron cloud in CSNS/RCS.
基金Supported by National Natural Science Foundation of China (10605032)
文摘Electron Cloud Instability has been studied in the operation of BEPC. The BEPCⅡ began the commissioning in November 2006 and the positron beam current has reached 500 mA. Because of such a high beam current, some instabilities such as ECI, bunch lengthening et al, have appeared during the operation. The experimental investigation on ECI during the commissioning of BEPCⅡ will be reported in this paper.
文摘In this paper we treat first some nonlinear beam dynamics problems in storage rings, such as beam dynamic apertures due to magnetic multipoles, wiggles, beam-beam effects, nonlinear space charge effect, and then nonlinear electron cloud effect combined with beam-beam and space charge effects, analytically. This analytical treatment is applied to BEPC II. The corresponding analytical expressions developed in this paper are useful both in understanding the physics behind these problems and also in making practical quick hand estimations.
