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Positron Bunch Radiation in the System of Tightly Packed Nanotubes

Hayk L. Gevorgyan, Koryun L. Gevorgyan, Lekdar A. Gevorgian

TL;DR

The paper addresses the generation of radiation from a relativistic positron bunch channeled in tightly packed carbon nanotubes, explicitly accounting for medium polarization. Using a harmonic nanotube potential $U(s)=U_0 s^2$, it derives the positron trajectory, the zero-angle radiation field, and the spectral line shapes for both single particles and bunches at the amplitude-dependent threshold energy, providing analytic expressions for the frequency distribution and photon yield. A key result is the identification of threshold energies $\gamma_{\text{th}}(s)$ that govern radiation formation and a delta-like line-shape behavior for large bunch lengths, complemented by a numerical example predicting ~3 keV photons with narrow line width. The findings suggest that nanotube-based undulators could produce intense, quasi-monochromatic, circularly polarized soft X-ray beams, with potential applications in spectroscopy and imaging, thereby offering a pathway to compact, directed X-ray sources that leverage medium polarization effects.

Abstract

Radiation emitted by a bunch of positrons channeled in nanotubes at zero emission angle is studied taking into account medium polarization. The formation of radiation is characterized by an energy threshold that depends on the oscillation amplitude of each positron. When the bunch energy reaches the maximum value of the threshold energy, radiation is produced by all positrons in the bunch. The nanotube potential barrier is described using a harmonic model. The spectral line shape of the radiation from the positron bunch, the fundamental radiation frequency, and the number of emitted photons are determined. It is shown that a system of tightly packed carbon nanotubes can generate an intense, quasi-monochromatic, and directed beam of circularly polarized soft X-ray photons with an energy of about $3$~\SI{}{\kilo\electronvolt} (wavelength $4.1$~\SI{}{\angstrom}).

Positron Bunch Radiation in the System of Tightly Packed Nanotubes

TL;DR

The paper addresses the generation of radiation from a relativistic positron bunch channeled in tightly packed carbon nanotubes, explicitly accounting for medium polarization. Using a harmonic nanotube potential , it derives the positron trajectory, the zero-angle radiation field, and the spectral line shapes for both single particles and bunches at the amplitude-dependent threshold energy, providing analytic expressions for the frequency distribution and photon yield. A key result is the identification of threshold energies that govern radiation formation and a delta-like line-shape behavior for large bunch lengths, complemented by a numerical example predicting ~3 keV photons with narrow line width. The findings suggest that nanotube-based undulators could produce intense, quasi-monochromatic, circularly polarized soft X-ray beams, with potential applications in spectroscopy and imaging, thereby offering a pathway to compact, directed X-ray sources that leverage medium polarization effects.

Abstract

Radiation emitted by a bunch of positrons channeled in nanotubes at zero emission angle is studied taking into account medium polarization. The formation of radiation is characterized by an energy threshold that depends on the oscillation amplitude of each positron. When the bunch energy reaches the maximum value of the threshold energy, radiation is produced by all positrons in the bunch. The nanotube potential barrier is described using a harmonic model. The spectral line shape of the radiation from the positron bunch, the fundamental radiation frequency, and the number of emitted photons are determined. It is shown that a system of tightly packed carbon nanotubes can generate an intense, quasi-monochromatic, and directed beam of circularly polarized soft X-ray photons with an energy of about ~\SI{}{\kilo\electronvolt} (wavelength ~\SI{}{\angstrom}).

Paper Structure

This paper contains 7 sections, 25 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The trajectory of a channeled positron in the nanotube potential barrier
  3. Radiation field of a positron at zero emission angle with initial radial coordinate $s$
  4. Spectral line shape of radiation from a positron channeled in a nanotube with oscillation amplitude $s$ ($0<s\leq 1$)
  5. Spectral line shape of a bunch at maximum threshold energy
  6. Example
  7. Conclusion

Figures (1)

  • Figure 1: Frequency distribution (spectral line shape) $\phi(x)$ of radiation from a bunch of positrons channeled in a nanotube, with the bunch energy equal to the maximum threshold energy.