Equations of motion of particle in circular accelerator with general field

Lagrange equations of motion are derived for a particle in a circular accelerator with arbitrarily spatially variable guiding magnetic field describing the motion of a particle by means of dimensionless deviations of the particle from a circle as the reference curve. The author also derives linearized equations of motion (so-called equations of perturbations used in stability investigations according to the Ljapunov method of the 1st approximation). The equations are given in the closed form and are thus quite exact.     

Canonical algorithms for numerical integration of charged particle motion equations

A technique for numerically integrating the equation of charged particle motion in a magnetic field is considered. It is based on the canonical transformations of the phase space in Hamiltonian mechanics. The canonical transformations make the integration process stable against counting error accumulation. The integration algorithms contain a minimum possible amount of arithmetics and can be used to design accelerators and devices of electron and ion optics.     

Symmetry of equations of motion for a free particle in riemann space

Spaces are classified in which the equations of motion of a free test particle admit a partial separation of variables aided by a set of first integrals of the second order.     

Neutron dosimetry in the particle accelerator environment

Radiological safety aspects in general and neutron dosimetry in particular, around medium and high-energy particle accelerators pose some unique challenges to the practitioners of radiation protection. This is mainly because the source of radiations are directional, dynamic, pulsed and a mixture of different types. In conventional dosimetry, measurements are done in the units of the quantities in which the radiological protection limits are expressed. In the accelerator environment, measurement of energy and angular distribution of radiations is preferred instead. Research activities being carried out (particularly in India) in the field of neutron dosimetry are discussed. Measurements of neutron ambient dose equivalent directly using conventional rem-meters as well as neutron energy distributions using the time-of-flight technique employing proton recoil scintillators have been done at different directions with respect to light and heavy ion projectiles incident on various thick elemental targets. The observations and conclusions are summarized. Finally, a discussion on the concept of dose and radiological protection and operational quantities is done along with the recommendation of using Evidence theory instead of Bayesian probability in assessing radiological risk.     

Operator method of integration of the equations of motion of a particle in an external field

A method is proposed for the determination of the laws of motion of a particle in an external field. Solutions are found for the equations of motion of a charged particle in the field of an undulator, and of the Dirac-Lorentz equation in a magnetic field. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 72–75, February, 1993.     

Metrical form of the equations of motion of a specimen point particle in a potential field

It is shown in the present work that the three-dimensional trajectories of a specimen point charged particle in potential fields may be regarded as geodesic lines lying on isotropic surfaces of some four-dimensional configurational space, the connectedness of which has distortion, while the transference is nonmetric.     

The equations of motion for green's functions and superconductivity solutions in particle physics

Three quantum field models are treated in a unified manner by using the method familiar from statistical many-body theory of solving the equations of motion for the Green functions in a particle number representation, with the following results: While the Nambu model does undergo dynamical symmetry breaking in its (1 + 1) dimensional version, it fails to do so in the original (3 + 1) dimensional case. For spinor QED, we get a critical value of the coupling parameter $\text{α}{}_{\mathrm{<mtext>c</mtext>}}\text{≡}\text{e}{}_{\mathrm{<mtext>c</mtext>}}{}^2\text{4π}\text{= 2π}$, above which the model becomes unstable.     

近景摄影测量技术在粒子加速器准直中的应用

第一次提出将近景摄影测量技术应用于国内粒子加速器隧道的控制点和设备测量,制定详细测量方案以适应加速器隧道狭窄空间环境,设计满足加速器隧道环境的半球目标、五面体目标,提出了编码立体化的方法,并在普通标准杆的短基线基准的基础上,增加跟踪仪测量的长基线基准进行约束。最后在中国散裂中子源的RCS环隧道中选取70 m长隧道进行测量实验,成功获取加速器控制网和设备的三维坐标,与激光跟踪仪结果对比,精度0.5 mm,显著提高测量效率,达到良好预期效果。     

The classical equations of motion for a spinning point particle with charge and magnetic moment

The classical, special relativistic equations of motion are derived for a spinning point particle interacting with the electromagnetic field through its charge and magnetic moment. Radiation reaction is included. The energy tensors for the particle and for the field are developed as well-defined distributions; consequently no infinities appear. The magnitude of spin and the rest mass are conserved.     

Concerning the full integrability of hamiltonian equations of charged particle motion in a weakly inhomogeneous magnetic field

The Hamiltonian of a charged particle in a weakly inhomogeneous magnetic field is calculated up to terms on the order of a small parameter. Fast phase-averaged equations of motion are derived. It is shown that these equations are intergrable in quadratures. Thus, the problem of particle motion in a weakly inhomogeneous field is solved in the first-order approximation. To calculate the Hamiltonian, the coordinates related to the field are used. Then, the canonical change of variables is done with the help of the generating function; in the case of a homogeneous field, this results in the action-angle variables. Such a procedure has been already used in [1]. However, the small parameter was not explicitly introduced and final expressions for small and large parts of the Hamiltonian were not calculated in that paper. It is shown that the small part of the Hamiltonian is a trigonometric polynomial of the fast phase (this can be important when analyzing the influence of additional perturbations). Besides, the averaged equations appear to be treatable and can be integrated in quadratures.     

Simulation on buildup of electron cloud in a proton circular accelerator

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 Me V proton beam and accelerates it to 1.6 Ge V 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.     

Quantum theory of electron motion in a cyclic resonant accelerator

The motion of a relativistic electron in a constant focusing magnetic field and a high-frequency rotational electromagnetic field, used to offset the radiative energy loss, is studied on the basis of the Klein-Gordon equation. The solutions found may be used to construct a theory for electron storage rings, in which quantum fluctuations are particularly important.Translated from Izvestiya VUZ. Fizika, No. 4, pp. 12–22, April, 1970.     

Conservation equations and equations of motion in the null formalism

The object of this paper is to relate three equations in the Newman-Penrose system of equations to the conservation laws and, hence, to the equations of motion. To do so, the corresponding result is first obtained using the Einstein equations in a null coordinate system. The Newman-Penrose equations are then analyzed. They are separated into hypersurface, propagation, supplementary, and conservation equations. When all field equations except the three conservation equations have been appropriately satisfied, the desired result follows.Research supported by the National Science Foundation under Grant GP-34641X.