The Application of Curved Crystals for the Control of Particle Beam Report

Introduction

Modern particle accelerators like LHC tend to provide efficient platforms for exploring the nature of vital interactions of particles. In most cases, they give high energy beam particle achievable through an exceptional intensity. The ability to extracting a multi-TeV beam for certain targeted experiments is increasingly becoming fascinating in the high-energy physics world. The intensity and energy frontiers require unique technologies in regards to the control and manipulation of the particle beam. A non-resonant scheme is an integral process that aids in providing a solution towards the extraction of the heavy-ion or multi-TeV proton beams of the LHC. In order to facilitate this approach, an electromagnetic noise in the machine is introduced, considering that the beam halo is congested. On the same note, the use of an asynchronous electromagnetic noise injection can be integral in enhancing lateral diffusion of the particle beam (Biryukov et al., 2013). Subsequently, the beam particle’s deflection is achieved by incorporating curved crystals on the kicker magnet’s same path¹.

It is possible to achieve the entire process since the highly accelerating particles tend to assume the electric field of the crystal, which sets efficient deflection angles on the lattice planes.

Consequently, the beam particle will shift through the channeling effect to the curved crystal, thereby exiting from the central deflection plane if its surface is curved. The curvature has the potential of producing a much better beam deflection huge than 103 Tesla. In this sense, for a fixed static procedure, a 109 p/s extraction rate for the halo would be integral, especially for a 7 TeV protons signifying increased performance of approximately 50 percent crystal extraction (Biryukov et al., 2013). The utilization of curved crystals plays a crucial role in facilitating the collimations, deformation, and control of particle beam to achieve various high physics community applications².

Impact and Uses

The possibility of extracting the energy frontiers in the form of a multi-TeV hadron beam from the LHC for specific target experiments can be fundamental to research within the physics environment. For example, this application can create an opportunity for investigating stronger interactions within the negative rapidity level, thereby opening a practical domain for testing quantum chromo-dynamics. For instance, this also includes providing a platform to facilitate exploring cross-section of TeV-hadrons with the use of light elements, which is a significant part of understanding Ultra High Energy Cosmic Rays’ showers. Additionally, Biryukov et al. (2013) assert that the resulting LHC beam has a crucial function of determining dipole values of minimum heavy-quark baryons thereby examining the progress of the deflecting particle. Precisely, the knowledge can be utilized in the process of determining electric dipole moments of charm and strange baryons, hence establishing an innovative platform for new investigations in physics³.

Charged particles connecting with a twisted crystal can be caught in directing states and redirected by the nuclear planes of the crystal lattice. The utilization of curved crystals for particle beam control in high energy particle accelerators is a very much evaluated idea quickly developing into useful applications. Over the most recent thirty years, an enormous number of research outcomes have been added to explain our insight and improve our control of crystal–particle connections. Curved crystals can confer precise avoidances to the approaching particles through volume or diverting reflection mechanisms (Biryukov et al., 2013). The proficiency of the last component has been discovered to be characteristically fundamental, while the controlling productivity has been improved by the expanded innovative aptitude in crystal cutting and bowing⁴.

Operation

The first process in the control of the particle beam by curved crystals is beam extraction. This step is commonly facilitated using magnetic devices and crystals, where intensified experimental procedure utilizing U-70 contributes towards the deflection process from a highly charged accelerating particle using a curved crystal (Biryukov et al., 2013). Nevertheless, with a wide curvature of curved crystals that creates inhomogeneity, it is possible to dechannel the particle beam. In most cases, simulations reveal that the crystal lengths utilized at Tevatron and SPS provide effective extraction efficiencies of 99 percent, especially for a 270 GeV proton extraction. However, simulation models tend to be ineffective in designing crystal deflectors and have opened ways for developing subsequent types of curved crystal schemes (Biryukov et al., 2013). The new generation has played a crucial role in revolutionizing the control of particle beam because they have facilitated an increase in extraction capacities with 85 percent efficiency levels⁵.

The successful implementation of the new models has resulted in the use of SPS. Notably, they play integral roles towards the creation of essential platforms for the use of technological advances necessary for facilitating LHC deflection (Biryukov et al., 2013). In this regard, it has enabled the installation of curved crystals within the LHC, thereby allowing the observation of coherent interactions even at 6.5 TeV. Towards that end, the new technology has created the opportunity for the high energy community to achieve collimation of the LHC particle beam through the aid of curved crystals. Notably, the radius and shape of the curvature of the LHC crystals need to undergo perfect modification to achieve a successful dechanelling operation of a beam⁶.

Silicon is commonly used to make the crystals used for the collimation tests at LHC. In order to facilitate the deflection and control of highly charged particle beams, quasi-mosaic or anticlastic deformations can be utilized (Biryukov et al., 2013). However, the former cannot allow operations with a thickness of 100 mm crystal, making it hard to create efficient curvature of the crystals. On that note, the anticlastic deformation is often prioritized due to its ability to facilitate the creation of crystals whose thickness along the particle beam can be varied to achieve the desired length, as shown in figure 1⁷.

Furthermore, it is necessary to conduct two significant characterization for measuring and controlling the deflected beam particle. The morphologic examination of its curvature at both the start and end of curving process, which facilitates the achievement of high degree of precision is the first step. In this sense, it becomes easier to determine the beam’s crystal curvature or rather stimulated disarticulation. The second one is interferometric measurements aimed at characterizing the deformation of the curved planes through a high-resolution diffractometer within a monochromatic beam (Biryukov et al., 2013). Only the anticlastic deformations are often analyzed in the second measurement⁸.

Types

The dechanneling of curved crystals to facilitate the control of the particle beam is categorized into two major types, namely the diffusion theory and single electronic scattering. The diffusion theory reveals that the evolution of the particle beam within a curved crystal can be defined through the kinetic approach framework. For example, in distribution with only 30 mm at a 100 GeV proton in silicon, the length of the crystal plan tends to be smaller in one oscillation channeled towards the crystal plane. It is possible to control such a beam with a channeling mode of 1000 times larger for a typical length with a GeV particle. The diffusion theory ensures that the state of a particle (E_T) can change progressively, and thus the concept of transverse energy can be vital in the process of channeling (Biryukov et al., 2013). Based on the diffusion theory, the E_T can hardly change through an oscillation as all the functions the position of the particle beam X an average along its trajectory to reduce the dependence of E_T on that of X⁹.

On the other hand, single electronic scattering facilitates curved crystal beam steering and control through the trapping of some particles in a unique well that ensures that they follow the direction of the curved planes. In this sense, the particle achieves a free state of dechanneling or channeled state or trapped state. This type of dechanneling ensures that the physics of the particle scattering is considered in more detail within an aligned crystal. On that note, the trapped particle beam transitions further from the stable channeled states through electronic scattering. The energy lost by the particles can be related to the angular dispersion within the electronic collision. This process implies that during beam disarticulation, the position X function represents the lost energy (Biryukov et al., 2013). The projections can be utilized for modification of the angular displacement and energy lost in the crystal¹⁰.

Application

The use of curved crystals provides a platform for increasing their application in the high energy physics environment. The curved planes facilitate their use through extensions of both their angular range and volume of reflection angle through which the multiple or single crystal or volume reflection channeling occurs. One of the most significant applications of the curved crystals in relation to control of the particle beam is the provision of an alternative strategy in designing radiation and space shield protection at high energy accelerators. Additionally, curved crystals can achieve high efficiency in the deflection of electronic beams compared to magnets. In this sense, they can play a crucial role in the application of particle accelerator, such as in the development of next-generation X-ray lasers (Biryukov et al., 2013). This application can be vital for scientific discoveries, for instance, the unraveling of atomic motions and structures in unmatched detail¹¹.

Additionally, the curved crystal can be applied in the deflection of undesired electrons within the outer regions of an electronic beam. On that note, they can effectively deflect them away using high energy electrons accelerators, leaving the desired core of the particle beam on the path. Notably, the process of deflecting the unwanted particle beam is often referred to as collimation and is integral towards preventing damage to magnets within X-ray lasers. The permanent magnets are often damaged by extreme irradiation, thereby tampering with the quality of X-ray light produced if not well shielded. Moreover, the crystals can also facilitate the emission of intense lights from the deflected beam of electrons, which can be potentially utilized to generate intense gamma and X-rays¹².

Furthermore, the volume reflection and channeling through a large range of energy also holds a special role in the high energy physics community. Precisely, it can allow scientists to efficiently predict how curved planes can be employed in the next generation of high energy electron-positron colliders. Towards that end, this process can be useful in facilitating a better understanding of significant particles in the universe, such as the Higgs boson¹³.

Conclusion

The control of particle beams through the curved crystal is a fundamental concept within the high energy physic community. The deflection and control of the high accelerating beam particles are now practical due to the utilization of curved crystals in fixed targeted experiments. In this sense, a unique generation of specific length crystals is essential in order to effectively steer charged particle beams through the channeling process. The absence of crystalline errors and desirable choice of a curving radius are notable elements for the creation of an appropriate curved crystal with the ability to enhance efficient deflection of a multi-TeV LHC and multi-GeV SPS beam. Importantly, it is essential to ensure that the crystals are free from dislocation, especially in the case of LHC, because dislocated one tends to result in less dechanneling effect. The high physics community has been thriving at accomplishing the development of compact crystal control deflectors integral in FCC and LHC crystal-based extraction.

Reference

Biryukov, V. M., Chesnokov, Y. A., & Kotov, V. I. (2013). Crystal channeling and its application at high-energy accelerators. Springer Science & Business Media.

Footnotes

1. Chapter 1: Channeling phenomenon.
2. Chapter 1: Channeling phenomenon.
3. Chapter 5: The use of crystal deflectors in beam lines.
4. Chapter 5: The use of crystal deflectors in beam lines.
5. Chapter 3: Experimental Studies of High-Energy Channeling and Bending Phenomena in Crystals.
6. Chapter 3: Experimental Studies of High-Energy Channeling and Bending Phenomena in Crystals.
7. Ibid^6.
8. Ibid^7.
9. Chapter 4: Crystal Extraction.
10. Chapter 4: Crystal Extraction.
11. Chapter 6: Application of Crystal Channeling to Particle Physics Experiments.
12. Chapter 6: Application of Crystal Channeling to Particle Physics Experiments.
13. Ibid^12.