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 nucleon-based 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 seem-to-be-dream, topic in modern physics. This is because the gamma ray, an electromagnetic (EM) wave with sub-
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
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,
2. Theory and method
2.1 Theoretical basis
For the convenience of readers, we paste related materials published elsewhere [7]. For a simple configuration containing merely static electric field (along
where
Moreover,
where the values of these constants,
Eqs. (5)–(7) can yield an equation for
whose solution reads
It is easy to verify that the solutions (10, 11) will lead to
or
where
There will be an elliptical trajectory for
where
where
we can find the time for an electron traveling through an elliptical trajectory to meet
The motion on an elliptical trajectory is very inhomogeneous. The time for finishing the
For convenience, our discussion is based on the parameterized ellipse. For the case
It is interesting to note that if there is
Clearly, the time cycle of such an oscillation, or that of a “tailored” Takeuchi orbit, is
Under fixed values of
This result implies a simple and universal method of setting up quasi-mono-color light source at any desirable center wavelength: by applying vertically static electric field
Of course, such a step-like magnetic field profile is overly idealized. Therefore, we propose using a more realistic magnetic slope to achieve such a tailored Takeuchi orbit [6].
2.2 Details on electron source
The above discussions have revealed theoretically the feasibility of an electron oscillation-based gamma-ray source. It is obvious that the electron oscillation-based radiation source is more advantageous than its proton oscillation-based counterpart because of larger oscillation magnitude, as well as power, available in the former. Utilization of electrons receives less attention than that of protons in experimental nuclear physics. It is really a pity if taking electrons as by-products of preparing protons. Reasonably utilizing those “by-products” is worthy of consideration.
Electron source can be designed to be compact and easily prepared. Among familiar electron sources, thermion-emission cathode is limited by its efficiency, and photocathode needs to be driven by high-intensity laser. The simplest method of achieving a high-efficiency electron source can share the same idea as that embodied in above sections, that is, using Hall effect by a magnetic slope in the above-mentioned discussion. Details are presented as follows.
Hall effect of a metal by a static (DC) magnetic field
Beside the strength of
If the strength
When studying applications such as probing and imagining local magnetic moment and magnetic microscopic structure [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], many authors have made in-depth investigation on the Hall effect of semiconductors in highly inhomogeneous magnetic field (HIMF). Because the purpose of these applications is detection or probing, the electric field or bias DC field is designed to avoid the breakdown of the semiconductor and hence its strength is usually not too strong. That is, in applications for detection purpose, Hall current is not required to be large enough.
It is worth noting the potential value of the extension of the same idea to a different case. The purpose of such an extension is aimed at a controllable “breakdown” of the metal. Therefore, higher DC field strength is chosen. Now that Hall effect implies that electrons have the potential to run along a direction normal to the applied electric field, it is natural for us to consider the feasibility of side escape of electrons from a conducting wire through Hall effect. This drives us to actively establish a HIMF and apply it to metal under a higher-strength DC electric field.
As shown in
Figure 1
, the solenoid is arranged on the demarcation line of two magnetic mediums. The end section of the solenoid is taken as the
Because the DC magnetic field can effectively penetrate into metal interior if its direction is normal to the surface of a metal (in normal state), it can affect bulk electron states of the metal. In contrast, the AC magnetic field, or a light beam, is limited to the skin layer of the metal [21, 22].
For
Emission is a many-body process because the sheath field, or space charge effect, left by emitted electrons in turn affects emission [23, 24, 25, 26]. This phenomenon can be reflected by following quantum theory (21, 23–26),
where
The equation of
where the space inhomogeneity of
Note that
Actively applying highly space-inhomogeneous external field, especially DC magnetic field, might be an effective way of enhancing the effect of the external field on the electrons. According to Hamiltonian formula or Eq. (22), there is always an operator
To warrant the technique route to be competitive in economics and efficiency among all candidates for a same goal, we avoid more intermediate conversion steps in EM energy utilization, and favor direct usage of EM energy in power frequency (PF), the most primitive EM energy form for all physics laboratories.
3. Conclusion
The application value of such an electron oscillation-based gamma-ray source is obvious. It offers a more efficient way of manipulating nuclear matter through its characteristic EM stimulus, that is, gamma ray. At present, the goal of manipulating nuclear matter is mainly achieved through: (1) using Bremsstrahlung by proton output from accelerators—this implies the application of an EM stimulus of a broad spectrum to the nucleus, and hence the efficiency of this route is poor because most photons are of low frequency relative to nuclear matter; (2) using EM radiations from heavier radioactive elements—the dose, or the brightness, or the intensity of gamma ray generated in this route is limited and hence the manipulation is also less efficient; (3) injecting protons into target nucleus. In contrast, the electron oscillation-based mono-color gamma-ray source proposed in this work 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.
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