The information is prepared on the basis of data from the information-analytical system RSF, informative part is represented in the author's edition. All rights belong to the authors, the use or reprinting of materials is permitted only with the prior consent of the authors.

Research area 02 - PHYSICS AND SPACE SCIENCES, 02-602 - Quantum field theory, quantum mechanics

Keywordselectron, orbital angular momentum, particle accelerator, cathod, particle source, detector, laser, magnetic lens, scattering, radiation

Annotation
Theoretical prediction and experimental generation of quantum states of photons, electrons, neutrons, and atoms with orbital angular momentum (OAM) served as a trigger for the emergence of a new interdisciplinary field at the intersection of atomic physics, electron microscopy with subnanometer resolution, spin and hadron physics, quantum and neutron optics. However, the existing technologies for generating particles with OAM are limited to relatively low energies - no more than 300 keV in electron microscopes, which does not allow the use of such beams for applied and fundamental research on the subatomic scale. In this interdisciplinary Project, we propose to carry out a set of theoretical and engineering works to develop and create a unique source of relativistic "vortex" electrons based on the Linac-200 accelerator complex of the Joint Institute for Nuclear Research, with an energy of 5 MeV and the possibility of further increase to 200 MeV. The development and experimental implementation of such a source are at the intersection of the latest achievements of quantum mechanics, atomic physics, and quantum optics, on the one hand, and require the solutions of the non-standard engineering problems in the physics of accelerators, particle sources, and their detectors, on the other hand. The implementation of the Project will require the combined efforts of theoretical physicists in the field of quantum electrodynamics and high energy physics from ITMO University, as well as engineers and experimental physicists from JINR. The scientific novelty of the Project lies in the fact that relativistic electron beams with OAM can become a unique research tool not only in atomic and molecular physics, in the diagnostics of nanomaterials and surfaces, where the orbital momentum allows one to obtain new information about a sample, but also in nuclear physics, spin and hadron physics, where such electrons can be used to analyze the proton spin, study nuclear forces at low energies, instead of the spin-polarized beams, etc. The angular momentum of relativistic electrons can be transferred to other particles, which can also lead to the creation of a "factory" of X-ray and gamma-ray photons with angular momentum. The creation of such a factory based on Compton backscattering at the Large Hadron Collider is currently being actively discussed, however, it is unlikely to be implemented before 2030. To implement the Project, we plan to study theoretically and experimentally various schemes for the generation of vortex electrons, including field emission and photo-emission in a strong solenoid field, as well as with laser photons with OAM. A theoretical model of the photoelectric effect with twisted photons will be developed, as well as models for diagnosing the angular momentum of relativistic electrons. ITMO University will create an experimental setup to study the generation of twisted photons. At JINR, a setup will be created on the basis of the existing laser driver, an RF photogun and a 5 T solenoidal magnet, and a series of experiments will be carried out, as a result of which an electron source with an OAM will be made. For acceleration to an energy of 5 MeV with the possibility of subsequent increase to 200 MeV and the transport through a system of focusing lenses, a theoretical and experimental analysis of the conservation of angular momentum will be carried out, taking into account radiation and inhomogeneity of the lens fields. The interaction of electrons with OAM with various materials and properties of the electromagnetic radiation will be studied theoretically and experimentally in order to develop a scheme for detecting OAM of a relativistic electron. At the final stage of the 4-year Project, it is planned for the first time in the world to demonstrate the acceleration of electrons with an angular momentum up to an energy of about 5 MeV. Within the framework of the Project, the ITMO-JINR team will jointly solve advanced theoretical and engineering problems. The successful implementation of the Project is guaranteed by the rich experience of both teams in conducting relevant research and the complementarity of the necessary skills.

Expected results
Within the Project, a set of theoretical and engineering tasks is proposed to develop and create a unique source of relativistic electrons with quantized angular momentum that has no analogs in the world. Tasks include the development and implementation of a scheme for detecting the angular momentum of electrons with an energy of about 5 MeV with the possibility of increasing to 200 MeV. Tasks are split between the ITMO and JINR groups and read: 1. Development of quantum-electrodynamic models of electron generation with quantized angular momentum during field and photo-emission in a strong magnetic field of a solenoid (from 1 T and above), including processes induced by "twisted" laser photons. Generalization of previously known models with "plane-wave" photons and without a magnetic field. An essential step forward in the development of theoretical models will be the analysis of the role of quantum entanglement of finite particles and methods for detecting particles with angular momentum. 2. Theoretical analysis of the conservation of angular momentum of twisted electrons in realistic fields of a linear accelerator, taking into account the focusing of the beam by electromagnetic lenses and the spatial inhomogeneity of the field. Evaluation of the spontaneous radiation and possible loss of angular momentum during acceleration. 3. Development of methods for detecting angular momentum electrons based on the basic scattering processes on atomic targets of various widths and electromagnetic radiation in the fields of lenses and undulators, accounting for the possible spatial inhomogeneity of the fields. Development of methods for restoring (quantum tomography) the state of an electron from the measured angular and spectral characteristics of scattered/radiated particles. 4. Development of an experimental test stand at ITMO University to study the conversion of plane-wave laser photons into Twisted ones. This stand will also be used in further research. 5. Creation of an experimental test stand at JINR for the study and selection of optimal methods for generating twisted electrons in a magnetic field using the available laser driver, RF photo gun, and a 5 T solenoid magnet. Investigation of the possibility of using schemes with auto-emission in a magnetic field and photo-emission with twisted photons in the field and without the field, selection of the optimal generation method and parameters: field strength, angular momentum, laser spot size on the cathode, laser pulse duration, etc. Creation of a prototype of the source of relativistic electrons with angular momentum and energy of about 5 MeV. 6. Development and testing at JINR of detection schemes for relativistic electrons with angular momentum and energy from 5 MeV and higher based on scattering processes in solid-state targets and electromagnetic radiation, taking into account models developed at ITMO University and realistic parameters of the generated electron beam. Measurement of the beam emittance, analysis of the influence of spatial charge on the quality of the beam with angular momentum, selection of the optimal current, and analysis of the possibility of increasing the angular momentum. 7. Preparation for the creation within 2-3 years after the completion of the 4-year Project of a setup for the generation of relativistic electrons with angular momentum and their acceleration to an energy of 200 MeV on the basis of the Linak-200 linear electron accelerator at JINR. Analysis of the conservation of angular momentum of electrons during transport and acceleration on a traveling wave and the possibility of a significant increase in energy without significant loss of beam quality. The theoretical tasks of the Project (paragraphs 1-3) will be solved mainly by the ITMO team. Experimental and engineering tasks (paragraphs 4-7) will be solved by the JINR team with the participation of the ITMO group, for which mutual trips of participants during the experiments are assumed. The ITMO team has extensive experience in theoretical studies of angular momentum electron generation processes, including in collaboration with leading scientists from accelerator physics. The quantum generalization of Bush's theorem developed in the works of ITMO researchers demonstrates the fundamental possibility of generating twisted electrons in strong magnetic fields (~1 T and higher), but accessible in laboratories. Researchers from ITMO also have experience in experimental work in leading accelerator centers in the USA. JINR researchers have many years of experience in the development of accelerator technology for Linak-200 installations (https://accelconf.web.cern.ch/ipac2021/doi/JACoW-IPAC2021-WEPAB042.html ), IRENE (https://iopscience.iop.org/article/10.1088/1748-0221/15/11/T11006 ), the accelerator complex of the JINR LFVE (https://link.springer.com/article/10.1134/S1547477120040081 ), as well as photo-injection systems (https://ufn.ru/ru/articles/2017/10/i /). The principal innovation of the proposed Project is the development of non-standard engineering solutions for the generation of quantum relativistic beams, previously studied only on electron microscopes with relatively low energies and small currents, whereas the physics of accelerator beams have always been successfully described by classical electrodynamics. As a result of the implementation of this interdisciplinary project, the efforts of both teams will develop new models and create codes to describe the processes of generation of twisted electrons, taking into account the effects of quantum entanglement and the detection process. Techniques for detecting such states of relativistic particles and measuring the emittance of a twisted beam, taking into account the possible influence of space charge, will also be developed and experimentally implemented for the first time. The developed models can also be used to analyze the processes of particle generation in strong magnetic fields of astrophysical sources (e.g., neutron stars). The developed generation and detection technologies are of particular value for the development of particle sources and accelerator technology and can be implemented at other accelerators, including the Large Hadron Collider and next-generation accelerators (ILC, CLIC, etc.). The created source of relativistic twisted electrons can be used for advanced fundamental and applied studies of nanostructures and surfaces with the subnanometer resolution, including studies of fast-flowing processes based on electron diffraction, for the development of methods of weakly perturbing diagnostics using so-called "measurements without interaction", as well as for atomic and nuclear physics, including studies of elastic and inelastic electron scattering on atoms, light, and heavy nuclei, where the use of twisted electrons allows testing phenomenological models of strong interactions outside the field of applicability of perturbative quantum chromodynamics. In turn, the study of the quantum properties of relativistic beams, the development of emittance manipulation methods, and their application can become a separate interdisciplinary direction at the intersection of accelerator and detector physics, quantum optics, and particle physics. Finally, relativistic electron beams with angular momentum accelerated to an energy of ~200 MeV can be used to generate twisted photons of the hard X-ray and gamma ranges for the purposes of nuclear physics and high-energy physics, where the processes of interaction of such photons with nuclei have different selection rules. A similar project of such a photonic "factory" based on reverse Compton scattering is now being actively discussed in the context of the upgrade of the Large Hadron Collider, however, it is unlikely to be implemented before 2030. In Russia, there is a factory of such photons only in the THz range based on a free electron laser in Novosibirsk.

Annotation of the results obtained in 2023
1. A theoretical model has been developed to describe the evolution of a quantum packet of a charged particle in the accelerating field of an RF gun. Within the framework of quantum electrodynamics, a corresponding solution to the Klein-Gordon equation is constructed and general expressions are obtained to estimate the total probability of photon emission by a spinless electron with angular momentum per unit time. It was found that for laboratory values of the accelerating field strength, the lifetime of the twisted state, as a rule, significantly exceeds the time of flight in a linear accelerator. 2. As a result of experimental work, photon beams with the non-zero orbital angular momentum at the light wavelength of 532 nm were obtained. Diffraction schemes for the generation of twisted photons in the UV range were developed. Preparations were made to obtain twisted photons at the light wavelength of 266 nm. 3. The solenoid magnetic field measurements of the photo-gun were performed: the field along the solenoid axis was measured and dependence of the field value on the solenoid coil current was obtained. Measurements have shown that with the ~1 kA power supply unit and the cooling system (or pulsed power supply unit without the cooling system) the magnetic field of 1 T and more can be obtained. 4. The vector network analyzer measurements have shown that the RF gun cavity can be used for the generation of a 5 MeV electron beam. The photoinjector test-bench was assembled: the laser driver (including a thermo-stabilization system), an accelerating structure (including an RF system and a gun cooling system), a vacuum system, a control and diagnostics system (including a synchronization system). The coordination of the project documentation for safety elements is ongoing. After the documentation is approved and permits are issued, the test-bench will be fully operational. 5. We have carried on a study of the possibility of using information on the scattering of relativistic and ultrarelativistic beams of twisted electrons on atomic targets to learn about the properties of these beams. It has been established that conducting scattering experiments on mesoscopic atomic targets of different sizes makes it possible to effectively determine the orbital angular momentum of an incident electron beam. Varying target sizes, one can in principle distinguish orbital angular momenta values as high as 1000 ћ.

Publications

1. Ivanov V. K., Chaikovskaia A.D., Karlovets D.V. Studying highly relativistic vortex-electron beams by atomic scattering PHYSICAL REVIEW A, 108, 062803 (year - 2023) https://doi.org/10.1103/PhysRevA.108.062803