def beta(T: u.K, n: u.m**-3, B: u.T) -> u.dimensionless_unscaled:
"""
The ratio of thermal pressure to magnetic pressure.
Parameters
----------
T : ~astropy.units.Quantity
The temperature of the plasma.
n : ~astropy.units.Quantity
The particle density of the plasma.
B : ~astropy.units.Quantity
The magnetic field in the plasma.
Examples
--------
>>> import astropy.units as u
>>> beta(1*u.eV, 1e20*u.m**-3, 1*u.T)
<Quantity 4.02670904e-05>
>>> beta(8.8e3*u.eV, 1e20*u.m**-3, 5.3*u.T)
<Quantity 0.01261482>
Returns
-------
beta: ~astropy.units.Quantity
Dimensionless quantity.
"""
thermal_pressure = parameters.thermal_pressure(T, n)
magnetic_pressure = parameters.magnetic_pressure(B)
return thermal_pressure / magnetic_pressure
def test_magnetic_energy_density():
r"""Test the magnetic_energy_density function in parameters.py."""
assert magnetic_energy_density(B_arr).unit.is_equivalent(u.J / u.m ** 3)
assert magnetic_energy_density(B).unit.is_equivalent('J / m3')
assert magnetic_energy_density(B).value == magnetic_pressure(B).value
assert_quantity_allclose(magnetic_energy_density(2 * B), 4 * magnetic_energy_density(B))
assert_quantity_allclose(magnetic_energy_density(B).value, 397887.35772973835)
assert_quantity_allclose(magnetic_energy_density(B), magnetic_energy_density(B.to(u.G)))
assert isinstance(magnetic_energy_density(B_arr), u.Quantity)
with pytest.warns(u.UnitsWarning):
magnetic_energy_density(5)
with pytest.raises(u.UnitConversionError):
magnetic_energy_density(5 * u.m)
assert np.isnan(magnetic_energy_density(np.nan * u.T))
with pytest.raises(ValueError):
magnetic_energy_density(5j * u.T)
assert np.isnan(magnetic_energy_density(B_nanarr)[-1])
with pytest.warns(u.UnitsWarning):
assert magnetic_energy_density(22.2) == magnetic_energy_density(22.2 * u.T)
assert_can_handle_nparray(magnetic_energy_density)
def beta(T: u.K, n: u.m**-3, B: u.T) -> u.dimensionless_unscaled:
r"""
Compute the ratio of thermal pressure to magnetic pressure.
The beta (:math:`β`) of a plasma is defined by
.. math::
β = \frac{p_{th}}{p_{mag}}
where :math:`p_{th}` is the thermal pressure of the plasma
and :math:`p_{mag}` is the magnetic pressure of the plasma.
Parameters
----------
T : `~astropy.units.Quantity`
The temperature of the plasma.
n : `~astropy.units.Quantity`
The particle density of the plasma.
B : `~astropy.units.Quantity`
The magnetic field in the plasma.
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...>
Returns
-------
beta: `~astropy.units.Quantity`
Dimensionless quantity.
See Also
--------
~plasmapy.formulary.parameters.thermal_pressure
~plasmapy.formulary.parameters.magnetic_pressure
"""
thermal_pressure = parameters.thermal_pressure(T, n)
magnetic_pressure = parameters.magnetic_pressure(B)
return thermal_pressure / magnetic_pressure
def test_magnetic_pressure():
r"""Test the magnetic_pressure function in parameters.py."""
assert magnetic_pressure(B_arr).unit.is_equivalent(u.Pa)
assert magnetic_pressure(B).unit.is_equivalent(u.Pa)
assert magnetic_pressure(B).unit.name == "Pa"
assert magnetic_pressure(B).value == magnetic_energy_density(B).value
assert magnetic_pressure(B) == magnetic_energy_density(B.to(u.G))
assert np.isclose(magnetic_pressure(B).value, 397887.35772973835)
with pytest.warns(u.UnitsWarning):
magnetic_pressure(5)
with pytest.raises(u.UnitTypeError):
magnetic_pressure(5 * u.m)
assert np.isnan(magnetic_pressure(np.nan * u.T))
with pytest.raises(ValueError):
magnetic_pressure(5j * u.T)
assert np.isnan(magnetic_pressure(B_nanarr)[-1])
with pytest.warns(u.UnitsWarning):
assert magnetic_pressure(22.2) == magnetic_pressure(22.2 * u.T)
assert_can_handle_nparray(magnetic_pressure)
def time_magnetic_pressure(self):
magnetic_pressure(0.1 * u.T)
