The Alfvén Mach number (also known as the Alfvén number, Alfvénic Mach number, and magnetic Mach number; or ) is a
dimensionless quantity
Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into unit of measurement, units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that a ...
representing the ratio of the relative velocity of a fluid to the local
Alfvén speed. It is used in
plasma physics
Plasma () is a state of matter characterized by the presence of a significant portion of charged particles in any combination of ions or electrons. It is the most abundant form of ordinary matter in the universe, mostly in stars (including th ...
, where it is analogous to the
Mach number
The Mach number (M or Ma), often only Mach, (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.
It is named after the Austrian physicist and philosopher Erns ...
but based on
Alfvén wave
In plasma physics, an Alfvén wave, named after Hannes Alfvén, is a type of plasma wave in which ions oscillate in response to a restoring force provided by an Magnetic tension force, effective tension on the magnetic field lines.
Definition
...
s rather than sound waves.
Alfvén and
Mach
The Mach number (M or Ma), often only Mach, (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a Boundary (thermodynamic), boundary to the local speed of sound.
It is named after the Austrian physi ...
were physicists who studied
shock wave
In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a me ...
s.
Along with the
sonic Mach number, the Alfvén Mach number is frequently used to characterize
shock front
In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a me ...
s
and
turbulence
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to laminar flow, which occurs when a fluid flows in parallel layers with no disruption between ...
in magnetized plasmas.
where
* is the Alfvén Mach number,
* is the flow velocity, and
*
is the Alfvén speed.
When , the flow is referred to as ''sub-Alfvénic''; and when , the flow is referred to as ''super-Alfvénic''.
See also
*
Plasma parameters
Plasma parameters define various characteristics of a plasma, an electrically conductive collection of charged and neutral particles of various species (electrons and ions) that responds ''collectively'' to electromagnetic forces. Such particl ...
*
Magnetic Reynolds number
*
Lundquist number
In plasma physics, the Lundquist number (denoted by S) is a dimensionless ratio which compares the timescale of an Alfvén wave crossing to the timescale of resistive diffusion. It is a special case of the magnetic Reynolds number when the Alfv� ...
References
Dimensionless numbers of fluid mechanics
Plasma parameters
{{Plasma-stub