CHAPTER 4 RADIATION PASSIVE SHIELD ANALYSIS AND DESIGNS FOR ORBITAL SPACE STATIONS

An overview of this chapter

1. Introduction

· Rational;

· State of the art (current research status in literature);

· What we present;

· Our passive shield solutions;

2. Source classification (based on source geometry)

· Pointwise sources

- The Sun;

- Magnetars;

- Supernovae;

- Hypernovae and gamma ray bursts;

· Circular uniformly distributed source (approximation of the galactic cosmic radiation)

· General source case (uniform distributed source and pointwise sources)

3. Statement of the general shield model

Particularizations of the general shield model and of the sources – analysis cases:

4. Shield for pointwise sources

5. Shield for a single source (the Sun)

6. Semi-spherical, toroidal and cylindrical-shaped shields;

7. Determining the shield shape that guarantees a constant flux of radiation.

8. Shield for two pointwise sources

· Planar shield – 2 plates of variable lengths;

· Parabola shaped shield ( parabolic-type function, circle generating function);

· Simulation results.

9. Conclusions

10. ANNEX 1. Details upon types and sources of radiation in space

11. ANNEX 2. Calculus details

12. ANNEX 3. Axial and transversal sections

1. Introduction

Rational

We analyze passive shield designs and techniques for orbital space stations. The analysis is based on the shield geometry.

State of the art in literature

After extensive documentation, we have found that in literature there is a surprising lack of knowledge in designing of radiation passive shields. Lack of knowledge is found in determining outer space radiation sources’ position and their radiation flux output (e.g. at Magnetars). We also found a high degree of uncertainty in predicting bursts (e.g. gamma ray bursts or solar flares). This lack of knowledge combined with false hypotheses led to poor designs.

Due to lack of knowledge in the domain (like the position of hypernovae, Magnetars and even the distribution of the galactic cosmic radiation), we can only approximate the source distribution – by pointwise sources or circular distributed sources. Thus I considered as pointwise sources – the Sun, hypernovae and Magnetars and as a circularly distributed source the general galactic radiation. Of course, this is theoretically correct, yet it may be (from an engineering point of view) impractical.

General shield model conditions

The shield has to satisfy the following conditions:

1. The shield must protect in a specified area the people/equipment located in that area.

2. The shield’s geometry must correspond to the variation of the flux of radiation that enters the shield.

3. The shield has to ensure in the protected area a level of radiation below a given value (infinity of possible shield geometries result).

4. The shield must have a minimal mass, therefore a minimal volume (minimization problem).

What we present

The problems analyzed are: i) the efficiency of various shapes of shields; ii) the shield optimization, for several families of geometric shapes; iii) the distribution of radiation inside the shielded area (for one case). Notice that all the analysis is for primary radiation, not for the secondary generated radiation.

The later one will be analyzed in the future. Thus, recall that the secondary-radiation effect was not analyzed.

The following aspects have been treated:

1. A thorough analysis and synthesis of the knowledge on sources of radiation in outer space.

2. A thorough synthesis of the proposed passive shield designs.

3. A detailed analysis of rational, new shielding solutions that are based on the knowledge on the radiation source distribution in the outer space.

4. An optimization analysis of the shields, aiming at the insuring of a safe level of radiation while keeping the volume, hence the mass of the shield at the minimum.

Our passive shield designs:

· Planar shield, formed of two interconnected plates;

· Semi-spherical shield;

· Discoid shield;

· Parabolic shield;

· Cylindrical/toroidal shield;

· Optimized shield shapes.

Several cases are fully analyzed and come with simulation results. For the planar shield I have determined the best length ratio (for the two plates) such that the protected volume/shield volume is maximum. For the circularly distributed source case the solved problem was to determine the best-protected areas inside the station, if the station is a torus or a cylinder.

Each section or analysis case begins with a separate introduction briefly stating the problem and is ended with conclusions.

All simulations have been made for various coefficient values and were computed with Microsoft Excel and/or C programs.

Statement of the general problem

The shield has to satisfy the following conditions:

1. It has to protect in a given area the people/equipment located in that area.

2. The shield has to correspond to the irradiation geometry (so it has to correspond to the variation of the function ).

3. The shield has to ensure in the protected area a level of radiation below a given value[1]. This condition gives us infinity of possible shield geometries.

4. The shield must have a minimal mass, therefore a minimal volume.

The second and third conditions give an expression through integral.

The fourth condition states a minimization problem.

Note: The secondary radiation produced by the decomposition of primary radiation when passing through the shield is neglected throughout the analysis. The shield solutions are analyzed only for primary radiation.

The variation of the flux of radiation is considered known and therefore, the radiation geometry. As an example, the radiation geometrical distribution is considered as in figure 1. An example is given for a corresponding shield shape to the given irradiation geometry.

Figure 1. An example of the incoming radiation geometrical distribution. This is the variation of the flux of radiation with the angle formed by the rays with the Ox axis. A polar angle-axis coordinate system is considered.

For the general case analysis, the variation of the flux of incoming radiation with the angle is considered known. Therefore, it is possible to determine the total flux of radiation that enters the shield:

(1)

The third condition states that:

, (2)

where is the maximum admitted total flux of radiation inside the protected area.

From the attenuation law the expression of is derived:

, (3)

where the following notations have been used:

· the flux of radiation that passes through the shield and enters the protected area for a given angle ;

· the flux of radiation that enters the shield for a given angle ;

· is the attenuation coefficient specific to a given material;[2]

· is the thickness of the shield for a given angle (please see Figure 2);

Figure 2. Example of a representation (transversal section) of a possible shield shape for the example of irradiation geometrical distribution given in Figure 1.

In the precedent figure a possible shield shape for a given irradiation geometrical distribution has been shown. The representation is in a polar (angle-axis) coordinate system. The contour of the transversal section of the shield is given by two functions, (for the interior) and (for the exterior).

The functions , and the function are defined below:

(4)

From (2), (3) and (4) we obtain:

(5)

Supposing that a function was found – satisfying all four conditions, then the volume of the shield will be in dependence with[3]:

(6)

By applying the fourth condition, we will obtain an optimization problem regarding the mass of the shield. Therefore, the volume of the shield will have to be minimal.

The family of functions is infinite for this general case. Unfortunately, mathematics at its present state of knowledge does not permit us to optimize such a family of functions, given by (4), (5) and (6). We cannot solve the problem in the general case.

The function has to be particularized for different shield shapes and structures to partly solve this problem. Starting from the statement of the general problem, first specific geometries of the radiation sources are considered. Namely, we consider pointwise sources, then a uniform circularly distributed source, and then mixed sources. The next step is to particularize the functions and to determine . These cases determine specific shield shapes.

Pointwise sources

A. A single source (the Sun)

In this case, the mass shield is designed for protecting an orbital space station against a single pointwise source (the Sun). The shield is designed such that it offers a best mass versus attenuation ratio. We present first a solution given in many past designs – semi-spherical or cylindrical shields. The transversal section of the shield is in this case delimited by two circle-generating functions. This also covers the case of a toroidal-shaped shield (shield designed at protecting a toroidal space settlement; the toroidal shield rotates separately and covers the station).

1. Semispherical shield

The problem in this case is to determine the attenuation function. For this, determining the apparent thickness of the shield in different points is important. The shield’s transversal section is considered as being delimited by two circle-generating functions and defined below:

, (1)

where the following notations have been used:

· the radius of the internal semicircle (the semicircle of radius is the internal contour of the shield);

· is the radius of the second semicircle (the semicircle of radius is the external contour of the shield);

· x is the point of reference; We consider for our analysis that

Note: The numbering of the formulas is reiterated at the beginning of each section.

Figure 3. Transversal section of a cylindrical mass shield.

In Figure 3 the transversal section of a semispherical shield is represented. The flux of radiation that comes from the Sun is and is considered constant in this case. The flux that comes out of the shield is variable with the position of the observer in reference with the shield (the observer being in any point on the horizontal axis between ).

The apparent thickness of the shield is defined as:

(2)

I recall that the apparent thickness is the thickness that a ray from source S would experience passing through the shield.

For reference a point on the Ox axis was considered. The flux of radiation that passes through the shield in the point is . Notice that as the point of reference varies in the interval , so does the apparent thickness of the shield in that point. This implies that the attenuation varies with .