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Critical Hall Parameter s parameter Formulae and Calculator

Instrumentation, Electronics and Control Sensors

Critical Hall "s" parameter Equations and Calculator

The electrothermal instability (also known as the ionization instability) is a magnetohydrodynamic ( MHD ) instability appearing in magnetized non-thermal plasmas used in MHD converters. This instability is a turbulence of the electron gas in a non-equilibrium plasma (i.e. where the electron temperature Te is greatly higher than the overall gas temperature Tg). It arises when a magnetic field powerful enough is applied in such a plasma, reaching a critical Hall parameter βcr.

This formula calculates the 's' parameter of the Critical Hall parameter.

Use this formula in combination with the other available “Critical Hall parameter” formulas.

Eq. 1
s = ( 2 · k · T_e² ) / ( E_i · ( T_e - T_g )· 1 / [ 1 + ( 3 k T_e ) / ( 2 E_i ) ]

Where :

s = 's' parameter (see : "Critical Hall parameter" formulas) (dimensionless)
k = Boltzmann constant ( 1.3806488 x 10^-23 J/K)
T_e = The electron temperature (K)
E_i = The ionization energy (1.609 x 10^-19 J) (J)
T_g = The overall gas temperature (K)

Reference:

Wikipedia, "Critical Hall parameter"

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