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 calculate_thermal_pressure(form):
r''' Returns
--------
Quantity
Thermal pressure in Pascal (Pa)
Parameters
----------
`form`: The calculator form from the HTML page where the user enters data for calculation.
'''
num1 = form['temp'] # Get temperature
num2 = form['density'] # Get density
u1 = form['unitsT']
u2 = form['unitsN']
if num1 == "" or num2 == "" or u1 == 'select' or u2 == 'select':
return -1
# Convert units of temperature and density into Unit objects, and use them to make Quantity objects
unit1 = u.Unit(u1)
q1 = u.Quantity(num1, unit1)
unit2 = u.Unit(u2)
q2 = u.Quantity(num2, unit2)
sum = pfp.thermal_pressure(q1, q2)
return sum
def calculate_thermal_pressure(form):
num1 = form['temp']
num2 = form['density']
unit1 = u.Unit(form['unitsT'])
q1 = u.Quantity(num1, unit1)
unit2 = u.Unit(form['unitsN'])
q2 = u.Quantity(num2, unit2)
sum = pfp.thermal_pressure(q1, q2)
return sum
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_thermal_pressure():
assert thermal_pressure(T_e, n_i).unit.is_equivalent(u.Pa)
# TODO: may be array issues with arg "mass"
assert_can_handle_nparray(thermal_pressure)
def time_thermal_pressure(self):
thermal_pressure(1 * u.eV, 1e20 / u.m**3)
