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Spherical Coordinates01:23

Spherical Coordinates

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Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
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Most bones contain compact and spongy osseous tissue, but their distribution and concentration vary based on the bone's overall function.
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The compacting factor test is a method used to assess the workability of concrete. It is  especially suitable for concrete mixes containing aggregates up to one and a half inches in size. This test involves specialized equipment consisting of two truncated cone-shaped hoppers and a cylinder, all with polished interior surfaces to minimize friction.
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A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have  equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
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Newton's law of gravitation describes the gravitational force between any two point masses. However, for extended spherical objects like the Earth, the Moon, and other planets, the law holds with an assumption that masses of spherical objects are concentrated at their respective centers.
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Construction of a Compact Low-Cost Radiation Shield for Air-Temperature Sensors in Ecological Field Studies
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Shielding materials in the compact spherical tokamak.

Samuel A Humphry-Baker1, George D W Smith2,3

  • 11 Centre for Nuclear Engineering, Imperial College London , London SW7 2BP , UK.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|April 11, 2019
PubMed
Summary

Tungsten carbide composites show promise as neutron shielding materials for compact fusion tokamaks. These materials offer improved properties over traditional tungsten, addressing space constraints and magnet protection needs.

Keywords:
central columncompact spherical tokamaksneutron shieldingnuclear fusionplasma-facing materialstungsten carbide

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Area of Science:

  • Materials Science
  • Nuclear Engineering
  • Plasma Physics

Background:

  • Neutron shielding is crucial for nuclear fusion technology, especially in compact spherical tokamaks with limited space.
  • The central column shield must protect superconducting magnets from radiation damage and heating, impacting cryogenic system energy consumption.

Purpose of the Study:

  • To assess structure-property relationships of tungsten carbide (WC) and its composites for neutron shielding in fusion devices.
  • To evaluate WC and a new WC-FeCr cermet as potential materials for central column shielding.

Main Methods:

  • Review of fundamental material properties of monolithic tungsten carbide (thermal transport, mechanical properties, plasma interaction).
  • Presentation of recent results on accident safety, thermo-mechanical properties, and irradiation behavior of WC-FeCr cermet.
  • Assessment of structure-property relationships relevant to plasma-facing materials challenges.

Main Results:

  • Monolithic tungsten carbide (WC) exhibits favorable properties compared to metallic tungsten for shielding applications.
  • The WC-FeCr cermet demonstrates promising accident safety, thermo-mechanical, and irradiation behavior.
  • Key structure-property relationships for WC-based materials in fusion environments were identified.

Conclusions:

  • Tungsten carbide and its composites are attractive neutron-attenuating materials for compact tokamak central column shielding.
  • Further research is needed on irradiation damage and hydrogen trapping in these advanced shielding materials.
  • WC-based materials offer a viable solution for enhancing shielding efficiency under severe space constraints in fusion reactors.