Channeling in Bent Crystallites: A New Method to Enhance the Radiation Shielding Efficiency*

A new method is proposed here aiming at designing a shielding wall with the efficiency significantly higher than that of traditional designs. This new design arises from the idea of using channeling in multilayered shielding wall structure, each layer composed of bent crystallites distributed in a way that each layer covers a small section of 2π angular range of which wall is exposed. Part of the incident charged particles will get channeled in bent crystallites in each layer. Bending of channeled particles in bent crystallites will change their directions in the wall increasing their path lengths in the wall which would enhance its shielding efficiency for charged particle radiations. Proposed design is useful for radiation shielding in fission power plants, future fusion reactors and air travel.


Introduction
Radiation shielding is a great concern in environments of nuclear technology and air travel [1] [2]. These environments include various radiation fields with a considerable component of charged particle rays. Charged particle rays include fission fragments, heavy and light ions and nuclei, and electrons. A major fraction of these particles from nuclear/thermonuclear reactors and cosmic rays has high energy loss rate in tissue and other materials. Shielding of human beings and material devices against their radiation is highly desirable. There are several radiation shielding designs using numerous materials of special characteristics, *  Details of the method and its implementation are given below. Section 2 describes channeling condition in bent crystals whereas proposed method for enhancement of shielding efficiency is given in Section 3. Section 4 includes conclusion of the study. Steering of channelled particles in a crystal continues even if the crystal is slightly bent deviating from their original direction as in strong magnetic fields of strength several thousand tesla. This fact provides us with the possibility of designing a "crystalline kicker" (Uggerhøj, 2005) [3]. This crystalline kicker for charged particles is shown in Figure 1.

Channeling in Bent Crystals
Lindhard [16] has shown that incident angle ( i θ ) of the particle trapped in transverse field of the crystalline channel must not exceed the limiting angle, called Lindhard angle ( L θ ), as given below, where T U is the transverse potential of the channel and || ε is longitudinal kinetic energy of the particle in the channel and is given by, where γ is the well known Lorentz factor. Under the condition given in Equation (1), transverse kinetic energy of the channeled particle will remain below the transverse potential T U . Let SO θ is the angle of the curvature in the bent crystal subtended on length of one transverse oscillation of the planar channeled , where r is radius of curvature of the bent crystal. Channeling in the bent crystal will persist if, Maximum bending angle of the channeled particle ( max θ ) in the bent crystal is given by the following condition [17], where Osc N is the number of transverse oscillations made by the channeled particle in the bent channel of the crystal. Above Equations (1)-(4) describe completely the condition of channeling in the bent crystal for the purpose being served in this paper.

Proposed Method for Enhancement of Shielding Efficiency
It is shown in Section 2 that charged particles entering channels of a bent crystal under certain conditions would bend by an angle up to max θ (Equation (4) ing angle ( max T θ ) of a charged particle in the above mentioned bent crystal piece is given by, where labels "T" and "SO" refer to test crystal piece and single transverse oscillation of the channeled particle, respectively.  shielding wall, wall surface will be divided in 2D grid with each grid element having a multilayered bent crystal structures. Alignment of crystal pieces will be arranged according to the range of incidence angles of charged particle rays.
These bent crystal pieces will have length from fraction of a millimeter to tens of a millimeter depending upon charge and energy of radiations. Cross-sectional dimension of these elements will have inverse relationship with bending efficiency. This shield design will show efficiency better than the traditional shield wall. High efficiency amorphous material layers can also be joined behind this new multilayered structure for better shielding.

Conclusion
A new charged particle radiation shield design is proposed here. This design will have a higher shielding efficiency than the tradition designs. In the new design, multilayered wall structure with each wall composed of bent crystal pieces is proposed. Each layer will bent a part of charged particle rays entering in bent crystals under channeling condition increasing path lengths of radiations in the shield. If a sufficient number of layers are used, major fraction of charged particles will be bent in the shield travelling longer distance in the shield compared with the traditional design, hence enhancing shielding efficiency. This shielding design can be employed in a number of radiation environments with situations comparable to that described in Figure 3. It may be noticed that the present design is different but has some similarity with a proposal by Breese [18]. This design will consume shielding materials in a smaller quantity compared to the tra-