Monocolor Radiation Source Based on Low-Energy Electron Beam and Dc Fields With High Gradient of Electromagnetic Energy Density

Copyright: © 2017 Lin H. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. A new route of monocolor radiation generation, which is based on the interaction of a low-energy electron with targeted designed driving DC fields, is proposed. It does not require the driving fields to be of high electromagnetic energy density. Instead, it relies on a high gradient of the electromagnetic energy density which can be achieved through reasonablly arranging components generating DC fields.

A new route of monocolor radiation generation, which is based on the interaction of a low-energy electron with targeted designed driving DC fields, is proposed. It does not require the driving fields to be of high electromagnetic energy density. Instead, it relies on a high gradient of the electromagnetic energy density which can be achieved through reasonablly arranging components generating DC fields.
The frequency spectrum has a closed relation with the properties of the field that the beam interact with. The properties include strength and space-time shape. Moreover, people are familiar with the radiation generation from transition among quantum states. In this quantum route, the energy of an electron should be high enough to afford that of photons generated. This viewpoint often drives people to pursue high energy electron beam whose kinetic energy can afford that of photons generated. Therefore, many beam-based routes emphasize the usage of accelerator. Emphasis on high strength of driving field and accelerator will affect economy of these routes. It is worthy to study how to ensure a radiation source, when technique targets are satisfied, to be as low cost as possible. Here, we present a new route of radiation generation based on low-energy electron beam.
The essence of this route is to use "defected" driving field to interact with the beam. The phrase "defected" means that the EM energy density has a large gradient. The driving field is static or DC. For example, we can put a solenoid, as shown in Figure 1, on the boundary region of two materials whose magnetic permeability are µ 1 and -µ 2 . The difference |µ 1 -µ 2 | will lead to contours of DC magnetic field B S to be bent. It is well-known that if |µ 1 -µ 2 |=0, B S contours will be planes normal to the axis of the solenoid, denoted as z-axis in Figure 1 |µ 1 -µ 2 |≠0, will mean a gradient ∂ x |B S | 2 . The larger |µ 1 -µ 2 | is, the larger ∂ x |B S | 2 . If a DC electric field E s is applied along the x-direction and a low-energy electron beam is injected into such a configuration along y-direction, it is feasible to achieve the generation of a quasi-monocolor radiation if the initial position of the beam on the x-z plane is appropriate. Detailed analysis is presented as below.
The DC fields that interact with the beam are: Namely, B S drops from B 0 at x=w to-B 0 at X=-w. Single-body dynamics of electron in such a field figuration can be strictly analyzed from 3D relativistic Newton equation set [14].
where constants C y is initial momentum component.
is the initial value of and Finally, we obtain a conservation law ( ) ( ) which suggests a time-periodic behavior of X. It is easy to find, from this conservation law, that when 0 X H is at a given value <1 and other parameters are same, smaller H will lead to smaller time cycle of X.
In principle arbitrary value of the time cycle of X can be achieved by choosing appropriate and feasible parameter-values. For example, B 0 is around 1T, E 0 is around 1V/cm, and H is around 1 µm. In such a case, EM energy density of the driving field |E 0 | 2 +|B 0 | 2 is not too high, but it has a great gradient nearby x=0. Namely, around x=0, there is a narrow but steep valley of the EM energy density profile. In ref. [14], we have pointed out that an extreme case in which w=0 and B s =B 0 if x<0 and Bs=0 elsewhere, can effectively generate quasi-monocolor radiations whose wavelength is determined by incident position and values of E 0 and B 0 and in principle can be at any desirable value by choosing appropriate parameter-values. Such a step-like B s -profile is too ideal, in contrast, slope-like B s -profile is more realistic.