Promises and challenges of high-energy vortex states collisions

The semiclassical general formula for the probability of radiation of twisted photons by ultrarelativistic scalar and Dirac particles moving in the electromagnetic field of a general form is derived. This formula is the analog of the Baier-Katkov formula for the probability of radiation of one plane wave photon with the quantum recoil taken into account. The derived formula is used to describe the radiation of twisted photons by charged particles in undulators and laser waves. Thus, the general theory of undulator radiation of twisted photons and radiation of twisted photons in the nonlinear Compton process is developed with account for the quantum recoil. The explicit formulas for the probability to record a twisted photon are obtained in these cases. In particular, we found that the quantum recoil and spin degrees of freedom increase the radiation probability of twisted photons in comparison with the formula for scalar particles without recoil. In the range of applicability of the semiclassical formula, the selection rules for undulator radiation established in the purely classical framework are not violated. The manifestation of the blossoming out rose effect in the nonlinear Compton process in a strong laser wave with circular polarization and in the wiggler radiation is revealed. Several examples are studied: the radiation of MeV twisted photons by $180$ GeV electrons in the wiggler; the radiation of twisted photons by $256$ MeV electrons in strong electromagnetic waves produced by the CO$_2$ and Ti:Sa lasers; and the radiation of MeV twisted photons by $51.1$ MeV electrons in the electromagnetic wave generated by the FEL with photon energy $1$ keV.

/pdf/semiclassical-probability-of-radiation-of-twisted-photons-in-2gly4op8re.pdf

Semiclassical probability of radiation of twisted photons in the ultrarelativistic limit

In most cases, the twisted photons generated directly by charged particles in undulators and laser waves are produced by bunches of particles and not by one charged particle. However, up to now, the theoretical studies of such a radiation were mainly based on description of radiation produced by one charged particle. In the present paper, we investigate the effect of a finite width of a particle bunch on radiation of twisted photons. The general formulas connecting the radiation probability distribution of twisted photons produced by bunches of identical particles with the radiation probability distribution of twisted photons generated by one particle are obtained for axially symmetric bunches. The bunch is called axially symmetric if it is axially symmetric with respect to the detector axis at some instant of time and all the particles in the bunch move along parallel trajectories. The general sum rules for the probability of radiation of twisted photons by axially symmetric bunches are established. In particular, we prove that the projection of the average total angular momentum of radiated twisted photons per particle in the bunch does not depend on the radial profile of the bunch. The uniform, Gaussian, and exponential radial bunch profiles are considered in detail. The radiation of axially symmetric bunches in ordinary and crystalline undulators is investigated. The selection rules for radiation of twisted photons by one particle in undulators are violated when the finite width of the particle bunch is taken into account. We find the condition when this violation is marginal. The form of the radiation probability distribution of twisted photons becomes universal for wide incoherent axially symmetric particle bunches. We completely describe these universal distributions.

Probability of radiation of twisted photons by axially symmetric bunches of particles

The general formula for probability to record a twisted photon produced by a charged particle moving in an inhomogeneous isotropic dispersive medium is derived. The explicit formulas for probability to record a twisted photon are obtained for the radiation of a charged particle traversing a dielectric plate or an ideally conducting foil. It is shown that, in the case when the charged particle moves along the detector axis, all the radiated twisted photons possess a zero projection of the total angular momentum and the probability of their radiation is independent of the photon helicity. The radiation produced by helically microbunched beams of charged particles is also considered. The fulfillment of the strong addition rule for the projection of the total angular momentum of radiated twisted photons is demonstrated. Thus the helical beams allow one to generate coherent transitions and Vavilov-Cherenkov radiation with large projections of the total angular momentum. The radiation produced by charged particles in a helical medium is studied. Typical examples of such a medium are metallic spirals and cholesteric liquid crystals. It is shown that the radiation of a charged particle moving along the helical axis of such a medium is a pure source of twisted photons.

Probability of radiation of twisted photons in an inhomogeneous isotropic dispersive medium

The hard X-ray twisted photons and relativistic massive particles with orbital angular momentum -- vortex electrons, muons, protons, etc. -- have many potential applications in high-energy and nuclear physics. However, such states can be obtained so far mainly via diffraction techniques, not applicable for relativistic energies. Here we show that the vortex states of different particles, including hadrons, ions, and nuclei, can be generated in a large class of processes with two final particles simply by altering a postselection protocol. Thanks to entanglement and to the uncertainty relations, an evolved state of a final particle becomes twisted if the momentum azimuthal angle of the other particle is measured with a large uncertainty. We give several examples, including Cherenkov and undulator radiation, particle collisions with intense laser beams, $e\mu \to e\mu, ep \to ep$. This technique can be adapted for ultrarelativistic lepton and hadron beams of linear colliders, and it can also facilitate the development of sources of X-ray and $\gamma$-range twisted photons at storage rings and free-electron lasers. 

/pdf/generation-of-vortex-particles-via-generalized-measurements-19wcd4fq.pdf

Generation of vortex particles via generalized measurements

We study theoretically the angular momentum of radiation emitted at axial channeling of the fast particles in a crystal or in a bunch of micro- or nanotubes placed in strong magnetic field. It is shown that high energy particles channeled in the presence of magnetic field are effective source of vortex radiation in the X-ray and gamma-range of photons energies. We show that there are two factors that increase the angular momentum of emitted radiation in the presence of magnetic field. First, the magnetic field favours additional “twisting” of the channeled particles in a certain direction and, secondly, the particles that have the corresponding initial angular momentum are predominantly captured into the channeling mode. Dependence of the angular momentum of radiation on the value of magnetic field and on the incident angle is studied.

Angular momentum of radiation at axial channeling

The angular momentum of radiation related to the passage of relativistic particles in a cylindrical channel is studied theoretically. To enhance the angular momentum of radiation, it is proposed to place the channel in a strong magnetic field parallel to the channel axis. The trajectories of the particles in the channel, the conditions for trapping particles in the channeling mode are investigated and equations for calculating the orbital angular momentum of radiation are obtained. It is shown that the angular momentum of radiation of a uniform beam of particles in the channel is not equal to zero only if the particles enter the channel at an angle greater than the critical angle. A significant difference between vortex radiation from a bunch of cylindrical channels (for example bunch of carbon nanotubes) from laser or undulator radiation is that the radiation beam of the latter has only one vortex axis. While the radiation from the beam of cylindrical channels has one vortex axis per each channel. Dependence of the angular momentum of radiation on the value of magnetic field and on the incident angle is studied.

Angular momentum of radiation from a charge drifting along a cylindrical channel in a magnetic field

A new mechanism of radiation emitted at channeling of a relativistic charged particle in a crystal is studied The superposition of coherent radiation from atoms, which are excited to vibrate in the crystal lattice by a channeled charged particle, with the ordinary channeling radiation is considered It is shown that the coherent radiation from a chain of oscillating atoms forms a resonance peak on the tail of radiation emitted by the channeled particle

Coherent radiation from atoms and a channeled particle

Basic properties of radiation of the atomic chains excited by a channeled particle are considered. Using a very simple two-dimensional model of a crystal lattice we have shown that the main part of this radiation is generated on the frequency of oscillations of a channeled particle between the crystal planes, shifted by the Doppler effect. Spectral and angular distribution and spectral distribution of the radiation of the atomic chain excited by channeled particle were calculated. Emission spectrum of the atomic chain excited by channeled particle was plotted.

Emission spectrum of the atomic chain excited by channeled particle

The flux of angular momentum of electromagnetic field of an arbitrarily moving point charge is investigated. General equations are obtained for the transfer of angular momentum at arbitrary distance from the charge, and corresponding equations in the far-field approximation. An explicit expression is obtained for the flux of angular momentum in the wave zone in terms of coordinates, velocity, and acceleration of the charge. The torque is calculated, that would act on an object if it absorbed all the radiation incident on it. It is shown that this torque is proportional to the curl of the stress tensor of the electromagnetic field; in the far field approximation the torque is proportional to the curl of the Poynting vector.

Angular momentum transfered by the field of a moving point charge

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