Meter water equivalent

In physics, the meter water equivalent (often m.w.e. or mwe) is a standard measure of cosmic ray attenuation in underground laboratories. A laboratory at a depth of 1000 m.w.e is shielded from cosmic rays equivalently to a lab 1,000 m (3,300 ft) below the surface of a body of water. Because laboratories at the same depth (in meters) can have greatly varied levels of cosmic ray penetration, the m.w.e. provides a convenient and consistent way of comparing cosmic ray levels in different underground locations.^[1]

Cosmic ray attenuation is dependent on the density of the material of the overburden, so the m.w.e. is defined as the product of depth and density (also known as an interaction depth). Because the density of water is 1 g/cm³, 1 m (100 cm) of water gives an interaction depth of 1 hectogram per square centimetre (100 g/cm²). Some publications use hg/cm² instead of m.w.e., although the two units are equivalent.^[2]

For example, the Waste Isolation Pilot Plant, located 660 m (2,170 ft) deep in a salt formation, achieves 1585 m.w.e. shielding. Soudan Mine, at 713 m (2,339 ft) depth is only 8% deeper, but because it is in denser iron-rich rock it achieves 2100 m.w.e. shielding, 32% more.

Another factor that must be accounted for is the shape of the overburden. While some laboratories are located beneath a flat ground surface, many are located in tunnels in mountains. Thus, the distance to the surface in directions other than straight up is less than it would be assuming a flat surface. This can increase the muon flux by a factor of 4±2.^[3]

The usual conversion between m.w.e. and total muon flux is given by Mei and Hime:^[4]

${\displaystyle I_{\mu }(h_{0})=67.97\times 10^{-6}e^{-h_{0}/285}+2.071\times 10^{-6}e^{-h_{0}/698}}$

where ${\displaystyle h_{0}}$ is the depth in m.w.e. and ${\displaystyle I_{\mu }}$ is the total muon flux per cm²⋅s. (The first term dominates for depths up to 1681.5 m.w.e.; below that, the second term dominates. Thus, for great depths, the factor of 4 mentioned above corresponds to a difference of 698 ln 4 ≈ 968 m.w.e.)

Standard rock

In addition to m.w.e., underground laboratory depth can also be measured in meters of standard rock. Standard rock is defined to have mass number A = 22, atomic number Z = 11, and density 2.65 g/cm³ (43.4 g/cu in).^[5] Because most laboratories are under earth and not underwater, the depth in standard rock is often closer to the actual underground depth of the laboratory.

Existing underground laboratories

Underground laboratories exist at depths ranging from just below ground level to approximately 6000 m.w.e. at SNOLAB^[4] and 6700 m.w.e. at the Jinping Underground Laboratory in China.^[6]

References

1. . National Science Foundation. Archived from the original on 2015-02-23. Retrieved 2014-10-03.
2. Grieder, Peter K. F. (2001). Cosmic Rays at Earth: Researcher's Reference Manual and Data Book. Gulf Professional Publishing. p. 482. ISBN 978-0-444-50710-5. Retrieved 2023-10-01 – via books.google.com.
3. Guo, Ziyi; et al. (JNE Collaboration) (2021). "Muon flux measurement at China Jinping Underground Laboratory". Chinese Physics C. 45 (2): 025001. arXiv:2007.15925. doi:10.1088/1674-1137/abccae. S2CID 244399721. A survey of muon fluxes at different laboratory locations situated under mountains and below mine shafts indicated that the former is generally a factor of (4±2) larger than the latter with the same vertical over-burden.
4. Mei, D.-M.; Hime, A. (6 March 2006). "Muon-induced background study for underground laboratories". Physical Review D. 73 (5): 053004. arXiv:astro-ph/0512125. Bibcode:2006PhRvD..73e3004M. doi:10.1103/PhysRevD.73.053004. S2CID 119446070.
5. K. A. Olive; et al. (Particle Data Group) (2014). "Review of Particle Physics". Chinese Physics C. 38 (9): 1–708. arXiv:1412.1408. Bibcode:2014ChPhC..38i0001O. doi:10.1088/1674-1137/38/9/090001. PMID 10020536.
6. Wu, Yu-Cheng; Hao, Xi-Qing; Yue, Qian; Li, Yuan-Jing; Cheng, Jian-Ping; Kang, Ke-Jun; Chen, Yun-Hua; Li, Jin; Li, Jian-Min; Li, Yu-Lan; Liu, Shu-Kui; Ma, Hao; Ren, Jin-Bao; Shen, Man-Bin; Wang, Ji-Min; Wu, Shi-Yong; Xue, Tao; Yi, Nan; Zeng, Xiong-Hui; Zeng, Zhi; Zhu, Zhong-Hua (August 2013). "Measurement of cosmic ray flux in the China JinPing underground laboratory". Chinese Physics C. 37 (8): 086001. arXiv:1305.0899. Bibcode:2013ChPhC..37h6001W. doi:10.1088/1674-1137/37/8/086001. S2CID 199686625.