beta

plasmapy.formulary.dimensionless.beta( T: Annotated[Quantity, Unit('K')], n: Annotated[Quantity, Unit('1 / m3')], B: Annotated[Quantity, Unit('T')], ) → Annotated[Quantity, Unit(dimensionless)][source]

Compute the ratio of thermal pressure to magnetic pressure.

The beta (\(β\)) of a plasma is defined by

\[β = \frac{p_{th}}{p_{mag}} = \frac{n k_B T}{B^2/2μ_0}\]

where \(p_{th}\) is the thermal_pressure of the plasma and \(p_{mag}\) is the magnetic_pressure of the plasma.

Parameters:

T (Quantity) – The temperature of the plasma.
n (Quantity) – The particle density of the plasma.
B (Quantity) – The magnetic field in the plasma.

Returns:

beta – Dimensionless quantity.

Return type:

Quantity

See also

thermal_pressure, magnetic_pressure

Examples

>>> import astropy.units as u
>>> beta(1 * u.eV, 1e20 * u.m**-3, 1 * u.T)
<Quantity 4.0267...e-05>
>>> beta(8.8e3 * u.eV, 1e20 * u.m**-3, 5.3 * u.T)
<Quantity 0.01261...>