Meter water equivalent explained

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 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, of water gives an interaction depth of 1hg/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 deep in a salt formation, achieves 1585 m.w.e. shielding. Soudan Mine, at 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 .[3]

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

I\mu(h0)=67.97 x 10-6

-h0/285
e

+2.071 x 10-6

-h0/698
e

where

h0

is the depth in m.w.e. and

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 .[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 and 6700 m.w.e. at the Jinping Underground Laboratory in China.[6]

References

  1. Web site: Deep Science . . 2014-10-03 . dead . https://web.archive.org/web/20150223150019/http://www.deepscience.org/contents/underground_universe.shtml . 2015-02-23.
  2. Book: Grieder, Peter K. F. . Cosmic Rays at Earth: Researcher's Reference Manual and Data Book . books.google.com . 2001 . Gulf Professional Publishing . 978-0-444-50710-5 . 482 . 2023-10-01.
  3. 2007.15925 . Muon flux measurement at China Jinping Underground Laboratory . Ziyi . Guo . Chinese Physics C . 2021 . 45 . 2 . 025001 . 10.1088/1674-1137/abccae . 244399721 . etal . JNE Collaboration . 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. Muon-induced background study for underground laboratories . D.-M. . Mei . A. . Hime . Physical Review D . 73 . 5 . 053004 . 6 March 2006 . 10.1103/PhysRevD.73.053004 . astro-ph/0512125 . 2006PhRvD..73e3004M . 119446070 .
  5. 10.1088/1674-1137/38/9/090001. Review of Particle Physics. Chinese Physics C. 38. 9. 1–708. 2014. K. A. Olive . 10020536. etal . Particle Data Group . 2014ChPhC..38i0001O . 1412.1408.
  6. 10.1088/1674-1137/37/8/086001 . 1305.0899 . 2013ChPhC..37h6001W . Measurement of cosmic ray flux in the China JinPing underground laboratory . Chinese Physics C . 37 . 8 . 086001 . August 2013 . 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 . 199686625 .