Abstract

Production of artificial gamma-ray source usually is a conception belonging to the category of experimental nuclear physics. Nuclear physicists achieve this goal through utilizing/manipulating nucleons, such as proton and neutron. Low-energy electrons are often taken as "by-products" when preparing these nucleons by ionizing atoms, molecules and solids, and high-energy electrons or β rays are taken as "wastage" generated in nuclear reaction. Utilization of those "by-products" has not won sufficient attention from the nuclear physics community. In this chapter, we point out a potential, valuable utilization of those "by-products." Based on a universal principle of achieving powerful mono-color radiation source, we propose how to set up an efficient powerful electron-based gamma-ray source through available solid-state components/elements. Larger charge-to-mass ratio of an electron warrants the advantage of electron-based gamma-ray source over its nucleonbased counterpart. Our technique offers a more efficient way of manipulating nuclear matter through its characteristic EM stimulus. It can warrant sufficient dose/brightness/intensity and hence an efficient manipulation of nuclear matter. Especially, the manipulation of a nucleus is not at the cost of destroying many nuclei to generate a desired tool, that is, gamma ray with sufficient intensity, for achieving this goal. This fundamentally warrants a practical manipulation of more nuclei at desirable number.

Keywords: gamma-ray source, electron oscillation, DC fields

## 1. Introduction

Powerful mono-color gamma-ray source is a very appealing, but also seemto-be-dream, topic in modern physics. This is because the gamma ray, an electromagnetic (EM) wave with sub-pm-level wavelength λ, is generated from quantum transition of nuclear matter in nuclear reaction. At present, using synthesized radioactive heavy elements, or radioisotope, is the main route for achieving a gamma-ray source [1–4]. Finite proton number in a radioactive heavy element is the bottleneck affecting the intensity and power of the gamma-ray output. Higher proton number is favorable not only to higher intensity and power but also faster decay or shorter life of the radioactive heavy element. For practical purposes, such a gamma-ray source should be of a stable output over a sufficiently long time duration. Piling large amount of radioactive heavy elements might be a solution to this requirement but its accompanied environment-protection cost might be overly high. Moreover, because a nucleon has smaller charge-to-mass ratio than an

electron, the accelerator cost and the reactor cost at the synthesis stage are also of considerable amount even though it is only aimed at low-energy nuclear physics applications rather than high-energy physics applications. To some extent, obtaining a powerful mono-color gamma-ray source corresponds to an artful skill of manipulating nuclear matter.

Moreover, Es and Bs are constant-valued electric and magnetic fields and meet Es ¼ ηcBs; λ ¼ c=ω and ω are reference wavelength and frequency, respectively; and

where the values of these constants, const, are determined from the initial con-

<sup>1</sup>þC<sup>2</sup> xþC<sup>2</sup> y <sup>p</sup> ; Cy ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ð Þ dsX <sup>2</sup> <sup>¼</sup> ½ � Cx � WB <sup>∗</sup> ð Þ <sup>η</sup><sup>s</sup> <sup>þ</sup> <sup>Y</sup> <sup>2</sup> <sup>∗</sup> <sup>1</sup> � ð Þ dsX <sup>2</sup> � ð Þ dsY <sup>2</sup> h i (9)

<sup>ω</sup> , where <sup>ω</sup><sup>B</sup> <sup>¼</sup> eBs

me is the cyclotron frequency.

:

dsZ � 0 (5)

<sup>1</sup>þC<sup>2</sup> xþC<sup>2</sup> y <sup>p</sup> ; <sup>0</sup>

<sup>∗</sup> <sup>1</sup> � ð Þ dsX <sup>2</sup> � ð Þ dsY <sup>2</sup> h i (8)

and, with the help of Eqs. (6) and

, (12)

(13)

ΓdsY � WBX ¼ const ¼ Cy; (6) ΓdsX þ WB½ �¼ ηs þ Y const ¼ Cx, (7)

!

<sup>1</sup> <sup>þ</sup> Cy <sup>þ</sup> WBX � �<sup>2</sup> <sup>þ</sup> ½ � Cx � WB <sup>∗</sup> ð Þ <sup>η</sup><sup>s</sup> <sup>þ</sup> <sup>Y</sup> <sup>2</sup> h i (10)

<sup>1</sup> <sup>þ</sup> Cy <sup>þ</sup> WBX � �<sup>2</sup> <sup>þ</sup> ½ � Cx � WB <sup>∗</sup> ð Þ <sup>η</sup><sup>s</sup> <sup>þ</sup> <sup>Y</sup> <sup>2</sup> h i : (11)

� WBη ∗X, which agrees with Takeuchi's theory [15], we can

<sup>¼</sup> <sup>1</sup> <sup>þ</sup> Cy <sup>þ</sup> WBX � �<sup>2</sup> <sup>þ</sup> ½ � Cx � WB <sup>∗</sup> ð Þ <sup>η</sup><sup>s</sup> <sup>þ</sup> <sup>Y</sup> <sup>2</sup>

þ ð Þ� Y þ ηs υ<sup>x</sup><sup>0</sup>

Γ0 .

� �<sup>2</sup> <sup>þ</sup> <sup>1</sup> � <sup>η</sup><sup>2</sup> ð Þυ<sup>2</sup>

h i

1 � η<sup>2</sup>

<sup>Γ</sup><sup>0</sup> and <sup>υ</sup><sup>y</sup><sup>0</sup> <sup>¼</sup> Cy

There will be an elliptical trajectory for η , 1 and a hyperbolic one for η . 1 [15, 16]. The time cycle for an electron traveling through an elliptical trajectory can

h i<sup>2</sup>

x0

Γ0 WB

Γ0 WB � �<sup>2</sup>

¼

,

<sup>s</sup> <sup>¼</sup> <sup>ω</sup>t, Z <sup>¼</sup> <sup>z</sup>

<sup>λ</sup> , Y <sup>¼</sup> <sup>y</sup>

Eqs. (1)–(3) lead to

whose solution reads

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> <sup>þ</sup> <sup>C</sup><sup>2</sup>

<sup>y</sup> <sup>þ</sup> <sup>C</sup><sup>2</sup> x

Γ ¼

as Γ ¼

q

or

39

q

q

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> <sup>þ</sup> <sup>C</sup><sup>2</sup>

where Γ<sup>0</sup> ¼

<sup>y</sup> <sup>þ</sup> <sup>C</sup><sup>2</sup> x

h i<sup>2</sup>

q

<sup>λ</sup> , X <sup>¼</sup> <sup>x</sup>

Electron Oscillation-Based Mono-Color Gamma-Ray Source

DOI: http://dx.doi.org/10.5772/intechopen.82752

ditions <sup>ð</sup>X; <sup>Y</sup>; <sup>Z</sup>; dsX; dsY; dsZÞjs¼<sup>0</sup> <sup>¼</sup> <sup>0</sup>; <sup>0</sup>; <sup>0</sup>; Cx ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Eqs. (5)–(7) can yield an equation for dsX and dsY

ð Þ dsY <sup>2</sup> <sup>¼</sup> Cy <sup>þ</sup> WBX � �<sup>2</sup>

ð Þ dsX <sup>2</sup> <sup>¼</sup> ½ � Cx � WB <sup>∗</sup> ð Þ <sup>η</sup><sup>s</sup> <sup>þ</sup> <sup>Y</sup> <sup>2</sup>

(7), ds<sup>Γ</sup> ¼ �WB<sup>η</sup> <sup>∗</sup> dsX (i.e., mec<sup>2</sup>dt<sup>Γ</sup> <sup>¼</sup> eEdtX). Noting <sup>Γ</sup> can be formally expressed

ð Þ dsY <sup>2</sup> <sup>¼</sup> Cy <sup>þ</sup> WBX � �<sup>2</sup>

It is easy to verify that the solutions (10, 11) will lead to

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> <sup>þ</sup> Cy <sup>þ</sup> WBX � �<sup>2</sup> <sup>þ</sup> ½ � Cx � WB <sup>∗</sup> ð Þ <sup>η</sup><sup>s</sup> <sup>þ</sup> <sup>Y</sup> <sup>2</sup>

find that the electronic trajectory can be expressed as

<sup>1</sup> � <sup>η</sup><sup>2</sup> ð Þ <sup>X</sup> <sup>þ</sup> ð Þ <sup>η</sup>þυy<sup>0</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> <sup>þ</sup> <sup>C</sup><sup>2</sup>

<sup>y</sup> <sup>þ</sup> <sup>C</sup><sup>2</sup> x

be exactly calculated by re-writing Eq. (10) as [15]

1�η<sup>2</sup>

, <sup>υ</sup><sup>x</sup><sup>0</sup> <sup>¼</sup> Cx

� �<sup>2</sup>

Γ0 WB

η þ υ<sup>y</sup><sup>0</sup>

� WBη ∗X

<sup>λ</sup> ,WB <sup>¼</sup> <sup>ω</sup><sup>B</sup>

Therefore, new working principle of achieving radiation source with narrower output spectrum is of significant application value. Based on Takeuchi's theory [5], we proposed a universal principle of achieving mono-color radiation source at arbitrary wavelength [6, 7]. According to this principle, available parameter values can ensure a powerful mono-color gamma-ray source.

The core of this working principle can be summarized as "tailoring" Takeuchi orbit. Takeuchi's theory reveals that the orbit of a classical charged particle, such as electron, in a DC field configuration Es � Bs, where Es and Bs are constant, can be elliptical or parabolic according to values of Es and Bs and that of initial particle's velocity entering into this configuration [5, 8]. The time cycle of an elliptical orbit can be in principle an arbitrary value by choosing suitable values of these parameters. Thus, for a far-field observer on the normal direction of this 2-D orbit, electrons moving along the orbit will behave like a radiation source whose central frequency is the inverse of the time cycle of the orbit. But a realistic factor affecting its practicality is the geometric size of such an orbit. Overly large geometric size will hurt the practicality of such a radiation source. At present, for available values of Es and Bs, about MVolt=meter-level and Tesla-level, the size can be down to m-level for s-level time cycle or Hz-level frequency.

For warranting the practicality of such a radiation source, we propose a scheme for making it compact by "tailoring" Takeuchi orbit through targeted designed DC field configuration [6]. In this configuration, Bs is made space-varying along the direction normal to the unperturbed path of an electron bunch by not letting two Helmholtz coils be co-axial on purpose [6]. By choosing suitable values of related parameters, such as the relative distance between the bunch path and the Bs ¼ 0 contour, Es-values and the slope β ¼ dxBs, where Bs is along the y-direction, its magnitude ∣Bs∣ is a function of the coordinate x, and the unperturbed path is along the z-axis.
