Alfvén Mach number

The Alfvén Mach number (also known as the Alfvén number, Alfvénic Mach number, and magnetic Mach number; M_A or M_M) is a dimensionless quantity representing the ratio of the relative velocity of a fluid to the local Alfvén speed. It is used in plasma physics, where it is analogous to the Mach number but based on Alfvén waves rather than sound waves. Alfvén and Mach were physicists who studied shock waves.

Along with the sonic Mach number, the Alfvén Mach number is frequently used to characterize shock fronts^[1]^[2]^[3] and turbulence^[4]^[5] in magnetized plasmas.^[6]^[7] $\mathrm {M_{A}} ={\frac {u}{u_{\mathrm {A} }}}$ where

M_A is the Alfvén Mach number,
$u$ is the flow velocity, and
$u$ _A is the Alfvén speed.^[8]

When $u < M A$ , the flow is referred to as sub-Alfvénic; and when $u > M A$ , the flow is referred to as super-Alfvénic.^[2]

References

^ Droege, W.; Schlickeiser, R. (1986). "Particle Acceleration in Solar Flares". The Astrophysical Journal. 305: 909. Bibcode:1986ApJ...305..909D. doi:10.1086/164305.
^ ^a ^b Treumann, R. A. (2009). "Fundamentals of Collisionless Shocks for Astrophysical Application, 1. Non-Relativistic Shocks". The Astronomy and Astrophysics Review. 17 (4): 409–535. Bibcode:2009A&ARv..17..409T. doi:10.1007/s00159-009-0024-2.
^ Kang, Hyesung; Ryu, Dongsu (2013). "Diffusive Shock Acceleration at Cosmological Shock Waves". The Astrophysical Journal. 764 (1): 95. arXiv:1212.3246. Bibcode:2013ApJ...764...95K. doi:10.1088/0004-637X/764/1/95.
^ Cho, Jungyeon; Lazarian, A. (October 2003). "Compressible Magnetohydrodynamic Turbulence: Mode Coupling, Scaling Relations, Anisotropy, Viscosity-Damped Regime and Astrophysical Implications". Monthly Notices of the Royal Astronomical Society. 345 (1): 325–339. arXiv:astro-ph/0301062. Bibcode:2003MNRAS.345..325C. doi:10.1046/j.1365-8711.2003.06941.x.
^ Padoan, Paolo; Jimenez, Raul; Juvela, Mika; Nordlund, Åke (2004). "The Average Magnetic Field Strength in Molecular Clouds: New Evidence of Super-Alfvénic Turbulence". The Astrophysical Journal. 604 (1): L49 – L52. arXiv:astro-ph/0311349. Bibcode:2004ApJ...604L..49P. doi:10.1086/383308.
^ De Keyser, Johan; Roth, Michel; De Sterck, Hans; Poedts, Stefaan (2001). "A Survey of Field-Aligned Mach Number and Plasma Beta in the Solar Wind". The 3-D Heliosphere at Solar Maximum. Vol. 97. pp. 201–204. Bibcode:2001SSRv...97..201D. doi:10.1007/978-94-017-3230-7_31. ISBN 978-90-481-5723-5.
^ Tofflemire, Benjamin M.; Burkhart, Blakesley; Lazarian, A. (2011). "INTERSTELLAR SONIC AND ALFVÉNIC MACH NUMBERS AND THE TSALLIS DISTRIBUTION". The Astrophysical Journal. 736 (1): 60. arXiv:1103.3299. Bibcode:2011ApJ...736...60T. doi:10.1088/0004-637X/736/1/60.
^ Beresnyak, A. (October 2023). 2023 NRL Plasma Formulary. Washington, DC: Naval Research Laboratory.

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[1] Droege, W.; Schlickeiser, R. (1986). "Particle Acceleration in Solar Flares". The Astrophysical Journal. 305: 909. Bibcode:1986ApJ...305..909D. doi:10.1086/164305.

[treumann09-2] Treumann, R. A. (2009). "Fundamentals of Collisionless Shocks for Astrophysical Application, 1. Non-Relativistic Shocks". The Astronomy and Astrophysics Review. 17 (4): 409–535. Bibcode:2009A&ARv..17..409T. doi:10.1007/s00159-009-0024-2.

[3] Kang, Hyesung; Ryu, Dongsu (2013). "Diffusive Shock Acceleration at Cosmological Shock Waves". The Astrophysical Journal. 764 (1): 95. arXiv:1212.3246. Bibcode:2013ApJ...764...95K. doi:10.1088/0004-637X/764/1/95.

[4] Cho, Jungyeon; Lazarian, A. (October 2003). "Compressible Magnetohydrodynamic Turbulence: Mode Coupling, Scaling Relations, Anisotropy, Viscosity-Damped Regime and Astrophysical Implications". Monthly Notices of the Royal Astronomical Society. 345 (1): 325–339. arXiv:astro-ph/0301062. Bibcode:2003MNRAS.345..325C. doi:10.1046/j.1365-8711.2003.06941.x.

[5] Padoan, Paolo; Jimenez, Raul; Juvela, Mika; Nordlund, Åke (2004). "The Average Magnetic Field Strength in Molecular Clouds: New Evidence of Super-Alfvénic Turbulence". The Astrophysical Journal. 604 (1): L49 – L52. arXiv:astro-ph/0311349. Bibcode:2004ApJ...604L..49P. doi:10.1086/383308.

[6] De Keyser, Johan; Roth, Michel; De Sterck, Hans; Poedts, Stefaan (2001). "A Survey of Field-Aligned Mach Number and Plasma Beta in the Solar Wind". The 3-D Heliosphere at Solar Maximum. Vol. 97. pp. 201–204. Bibcode:2001SSRv...97..201D. doi:10.1007/978-94-017-3230-7_31. ISBN 978-90-481-5723-5.

[7] Tofflemire, Benjamin M.; Burkhart, Blakesley; Lazarian, A. (2011). "INTERSTELLAR SONIC AND ALFVÉNIC MACH NUMBERS AND THE TSALLIS DISTRIBUTION". The Astrophysical Journal. 736 (1): 60. arXiv:1103.3299. Bibcode:2011ApJ...736...60T. doi:10.1088/0004-637X/736/1/60.

[8] Beresnyak, A. (October 2023). 2023 NRL Plasma Formulary. Washington, DC: Naval Research Laboratory.

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Alfvén Mach number

See also

References

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