# Alfven_speed

plasmapy.formulary.speeds.Alfven_speed(B: Quantity, density: (Unit('1 / m3'), Unit('kg / m3')), ion: = None, *, mass_numb: = None, Z: = None) [source]

Calculate the Alfvén speed.

The Alfvén speed $$V_A$$ is the typical propagation speed of magnetic disturbances in a quasineutral plasma, and is given by:

$V_A = \frac{B}{\sqrt{μ_0 ρ}}$

where $$B$$ is the magnetic field and $$ρ = n_i m_i + n_e m_e$$ is the total mass density ($$n_i$$ is the ion number density, $$n_e ≡ Z n_i$$ is the electron number density assuming quasineutrality, $$m_i$$ is the ion mass, and $$m_e$$ is the electron mass) .

Aliases: va_

Parameters:
• B (Quantity) – The magnetic field magnitude in units convertible to tesla.

• density (Quantity) – Either the ion number density $$n_i$$ in units convertible to m-3 or the total mass density $$ρ$$ in units convertible to kg m-3.

• ion (Particle, optional) – Representation of the ion species (e.g., 'p+' for protons, 'D+' for deuterium, 'He-4 1+' for singly ionized helium-4, etc.). If the density is an ion number density, then this parameter is required in order to convert to mass density.

• mass_numb (int, keyword-only, optional) – The mass number corresponding to ion.

• Z (float, keyword-only, optional) – The charge number corresponding to ion. Note that the value of Z does not impact the Alfvén speed.

Returns:

V_A – The Alfvén speed in units of m/s.

Return type:

Quantity

Raises:
Warns:

Notes

This expression does not account for relativistic effects, and loses validity when the resulting speed is a significant fraction of the speed of light.

Examples

>>> import astropy.units as u
>>> from astropy.constants.si import m_p, m_e
>>> B = 0.014 * u.T
>>> n = 5e19 * u.m**-3
>>> ion = "p+"
>>> rho = n * (m_p + m_e)
>>> Alfven_speed(B=B, density=n, ion=ion)
<Quantity 43173.870... m / s>
>>> Alfven_speed(B=B, density=rho)
<Quantity 43173.870... m / s>
>>> Alfven_speed(B=B, density=rho).to(u.cm / u.us)
<Quantity 4.317387 cm / us>
>>> Alfven_speed(B=B, density=n, ion="He-4 2+")
<Quantity 21664.18... m / s>
>>> Alfven_speed(B=B, density=n, ion="He", Z=1.8)
<Quantity 21664.18... m / s>