Exact Expression for Radiation of an Accelerated Charge in Classical Electrodynamics

The present expression of radiation of an accelerated point charge is only approximately valid. The exact expression of radiation of an accelerated point charge is derived based on special relativity, and using the Larmor formulation for the radiation of an charged particle being accelerated, but instantaneously at rest. The totaled radiation power obtained by the exact expression is the same as Liénard’s generalization of the Larmor formula.     

The geometry of Larmor nutation

The nutation accompanying the well-known Larmor precession discussed with respect to an inertial frame in an earlier paper is now considered in the rotating Larmor frame where the precession is absent and the nutation is therefore fully emphasized. It is shown that, in this frame, the nutating vector generates, in general, what may be called interpenetrating partial cones, the two parts of which merge into a single cone traced twice over, when the orbit of the charged particle changes to a circle — giving an immediate explanation of the discontinuous jump in the nutation frequency to twice its value as the orbit changes continuously from an ellipse to a circle.     

Uncertainty principle in larmor clock

It is well known that the spin operators of a quantum particle must obey uncertainty relations. We use the uncertainty principle to study the Larmor clock. To avoid breaking the uncertainty principle, Larmor time can be defined as the ratio of the phase difference between a spin-up particle and a spin-down particle to the corresponding Larmor frequency. The connection between the dwell time and the Larmor time has also been confirmed. Moreover, the results show that the behavior of the Larmor time depends on the height and width of the barrier.     

Larmor time and proper time

The idea of a Larmor clock is reexamined in the relativistic regime. We propose a concept of proper time for quantum theoretical particles. The Larmor clock can measure, under some relevant conditions, the proper time that passes while the particle stays in a space region. Our approach to Larmor clock is different than those of other researchers in the following two aspects: our concept of Larmor clock does not distinguish whether the particle is transmitted or reflected at the end of its stay, and pointer of our Larmor clock is not the spin but the total angular momentum.     

Production of Fe clusters by collisions of metal vapour with supersonic argon beams

For a spin-polarized plane wave passing through a spin-rotator containing uniform magnetic field, we provide a detailed analysis for solving the appropriate Schrödinger equation. A modified expression for spin precession is obtained which reduces to the standard Larmor precession relation when kinetic energy is very large compared to the spin-magnetic field interaction. We show that there are experimentally verifiable regimes of departure from the standard Larmor precession formula. The treatment is then extended to the case of a spin-polarized wave packet passing through a uniform magnetic field. The results based on the standard expression for Larmor precession and that obtained from the modified formula are compared in various regimes of the experimental parameters.     

Potential of the test particle in the magnetic field II

The potential of the test particle in an external homogeneous magnetic field is studied for the collisionless magnetized plasma. It is shown for the case when the parallel velocity component of the test particle is greater than the thermal velocity of the background particles that the test particle potential has a Coulomb character. The test particle Larmor radius and the cyclotron and plasma frequencies of the background particles appear as additional parameters in this potential. When the parallel velocity component of the test particle is, on the contrary, small compared with the thermal velocity of the background particles, the potential has a rather complicated form. In the first approximation this potential is of a Debye character with the test particle Larmor radius as an additional parameter.     

Relativistic Neutrino Spin Precession in Magnetic Fields

The spin rotation formula of a relativistic neutrino propagating in a constant magnetic field is derived. Contrary to a recent assertion, we find that in the ultrarelativistic limit, the formula actually reduces to the standard Larmor result.     

GaAs光电导天线辐射太赫兹波功率的计算

在Larmor公式的基础上建立了适合计算光电导天线辐射太赫兹波功率的数学模型,利用此数学模型通过蒙特卡罗方法分别计算了不同实验条件下GaAs光电导天线辐射太赫兹电磁波功率.计算结果表明,增加光电导天线的偏置电场或触发光能量,都能够提高天线辐射太赫兹波功率,大孔径光电导天线能够承载更多的光生载流子,因而可以产生比小孔径光电导天线功率更高的太赫兹波. 关键词： 光电导天线 Larmor公式 太赫兹波功率     

Self-Diffusion Imaging by Spin Echo in Earth's Magnetic Field

The NMR of the Earth's magnetic field is used for diffusion-weighted imaging of phantoms. Due to a weak Larmor field, care needs to be taken regarding the use of the usual high field assumption in calculating the effect of the applied inhomogeneous magnetic field. The usual definition of the magnetic field gradient must be replaced by a generalized formula valid when the strength of a nonuniform magnetic field and a Larmor field are comparable (J. Stepišnik,Z. Phys. Chem.190, 51–62 (1995)). It turns out that the expression for spin echo attenuation is identical to the well-known Torrey formula only when the applied nonuniform field has a proper symmetry. This kind of problem may occur in a strong Larmor field as well as when the slow diffusion rate of particles needs an extremely strong gradient to be applied. The measurements of the geomagnetic field NMR demonstrate the usefulness of the method for diffusion and flow-weighted imaging.     

The Larmor nutation

The classical non-relativistic problem of the motion of a charged particle in an external central force field and a weak uniform magnetic field is revisited to show that the motion of the kinetic angular momentumL = r × p of the particle, in the so-called Larmor approximation, is not a simple precession but is actually a composite motion involving precession as well as a high frequency nutation. The precession-nutation motion ofL is discussed in the Larmor approximation when the Larmor-frame-orbit of the charged particle is an ellipse (or a circle) for the case of the two central forces namely the Coulomb and the Hooke-law-force, which are the only two central forces known to permit closed orbits.     

Force approach to radiation reaction

The difficulty of the usual approach to deal with the radiation reaction is pointed out, and under the condition that the radiation force must be a function of the external force and is zero whenever the external force be zero, a new and straightforward approach to radiation reaction force and damping is proposed. Starting from the Larmor formula for the power radiated by an accelerated charged particle, written in terms of the applied force instead of the acceleration, an expression for the radiation force is established in general, and applied to the examples for the linear and circular motion of a charged particle. This expression is quadratic in the magnitude of the applied force, inversely proportional to the speed of the charged particle, and directed opposite to the velocity vector. This force approach may contribute to the solution of the very old problem of incorporating the radiation reaction to the motion of the charged particles, and future experiments may tell us whether or not this approach point is in the right direction.     

New approach to the quantum tunneling process: Characteristic times for transmission and reflection

In [1] we have demonstrated that scattering of a quantum particle on a one-dimensional potential barrier should be considered as a combined process involving two alternative elementary transmission and reflection processes. For symmetric potential barriers, we have found solutions of the Schrödinger equation which describe the transmission and reflection processes in all stages of scattering. The present work studies time aspects of both processes. The local and asymptotic group tunneling times, dwell time, and Larmor tunneling time are determined for each process. Among these time characteristics, the group tunneling times should be considered as auxiliary. As to the dwell and Larmor tunneling times, they are the best estimates (of the expected values) of times the quantum particle in stationary and localized nonstationary states dwells in the barrier region. Moreover, the Larmor time is simply the dwell time averaged over the corresponding ensemble of particles. This characteristic can be measured experimentally and hence the suggested model of scattering can be verified.     

空心锥状双高斯光束传输特性研究

建立了空心锥状双高斯光束的模型.在空心高斯光束模型的基础上,由初始光场的光强分布,利用柱坐标下的柯林斯公式,导出了空心锥状双高斯光束经过傍轴光学系统的解析传输变换式由传输变换式计算分析了空心锥状双高斯光束在自由空问的可控传输特性,及在1,10和60 m的截面光环的光强分布.用KNbO3双轴晶体进行实验,获得了空心锥状双高斯光束,外锥折射的锥角等于入射光会聚角.实验表明,当空心光束处于锥状发射状态时,空心光束的光环内黑斑面积随传输距离的增加而增加,实验结果与模型吻合较好.该研究为进一步设计制备基于空心锥状舣高斯光束的新型激光元件提供了理论依据和设计参量.     

Spontaneous noise spectroscopy of an atomic magnetic resonance

We have experimentally demonstrated a new type of noise spectroscopy, which requires neither amplitude nor frequency noise of the light source. A highly stabilized diode laser provides low-noise light for the optical magnetic resonance of Rb atoms. The laser light transmitted through the Rb vapor contains significant intensity fluctuations whose power spectrum has a distinct peak at the Larmor frequency. The fluctuations are spontaneously generated by the atoms and are attributed to the stochastic properties of the photon scattering which randomly interrupts the Larmor precession of the atomic magnetic moment.     

Tempered wave functions: Schrödinger's equation within the light cone

The standard derivation of Schrödinger's equation from a Lorentz-invariant Feynman path integral consists in taking first the limit of infinite speed of light and then the limit of short time slice. In this order of limits the light cone of the path integral disappears, giving rise to an instantaneous spread of the wave function to the entire space. We ascribe the failure of the propagation in time according to Schrödinger's equation to retain the light cone of the path integral to the very nature of the limiting process: it is a regular expansion of a singular approximation problem, because the time-dependent boundary conditions of the path integral on the light cone are lost in this limit. We propose a distinguished limit of the time-sliced relativistic path integral, which produces Schrödinger's equation and preserves the zero boundary conditions on and outside the original light cone of the path integral. This produces an intermediate model between non-relativistic and relativistic mechanics of a single particle quantum particle. These boundary conditions relieve the solutions of Schrödinger's equation in the entire space of several annoying, seemingly unrelated unphysical artifacts, including non-analytic wave functions, spontaneous appearance of discontinuities, non-existence of moments when the initial wave function has a jump discontinuity (e.g., a collapsed wave function after a measurement), and so on. The practical implications of the present formulation are yet to be seen.     

LARMOR PRECESSION AND THE BARRIER INTERACTION TIME

The Larmor precession of a spinning particle in a magnetic field confined in the region of one dimensional-rectangular barrier is investigated with the spin coherent state of incoming particle, which has advantage to recognize the equation of the spin precession. Our new observation is that the precession time of spin is uniquely determined and is seen to be equal to the dwell time.     

Electron-ion collision integral in a strong magnetic field

Boltzmann’s collision integral is extended to the case of helical (Larmor) particle trajectories in a magnetic field of arbitrary strength. The main characteristics of collisions of electrons with positively charged ions in strong magnetic fields, where the Larmor radius of electrons becomes less than the characteristic impact parameter of close collisions in the absence of a magnetic field (Landau’s parameter), are investigated. The differential scattering cross section and the corresponding electron-ion collision integral in strong fields are found. The transport collision frequencies are calculated, and the results are compared with the similar quantities for weaker magnetic fields.     

Larmor precession and dwell time of a particle scattered by a quantum well

The Larmor precession of a neutral spin- particle in a uniform constant magnetic field confined to the region of a one-dimensional rectangular potential well is investigated. The spin precession serves as a clock to measure the time spent by a quantum particle dwelling at a potential well. With the help of a general spin coherent state it is explicitly shown that the spin precession time is equal to the dwell time. The comparison of the time in a potential well with that in free space shows apparent superluminality.     

The extended classical charged particle

A theory of the extended classical charged particle is presented. The theory assumes extension along the forward light cone of the particle instead of the usual now-plane. Solutions are given for many of the traditional problems including 4/3, instability, infinite self-energy, and runaway velocity. The Lorentz and Lorentz-Dirac equations are derived from a more general equation of motion.     

Potential of the test particle in the magnetic field I

The problem of the test particle potential in the external homogeneous magnetic field is solved in the unmagnetized plasma. It is shown that for the case when the parallel component velocity of the test particle is greater than the thermal velocity of the background particles, the potential has the Coulomb character while for the case where the parallel component velocity is less than the thermal velocity the potential is of Debye character. The Larmor radius of the test particle appears as a additional parameter in these potentials.