Buchsbaum_frequency

plasmapy.formulary.frequencies.Buchsbaum_frequency(B: Quantity, n1: Quantity, n2: Quantity, ion1: str | int | integer | Particle | CustomParticle | Quantity, ion2: str | int | integer | Particle | CustomParticle | Quantity, Z1: float | None = None, Z2: float | None = None, *, to_hz=False) → Quantity[source]

Return the Buchsbaum frequency for a two-ion-species plasma.

Parameters:

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

  • n1 (Quantity) – Particle number density of ion species #1 in units convertible to m-3.

  • n2 (Quantity) – Particle number density of ion species #2 in units convertible to m-3.

  • ion1 (Particle) – Representation of ion species #1 (e.g., ‘p+’ for protons, ‘D+’ for deuterium, or ‘He-4 +1’ for singly ionized helium-4). If no charge state information is provided, then species #1 is assumed to be singly charged.

  • ion2 (Particle) – Representation of ion species #2 (same behavior as for ion1).

  • Z1 (float or Quantity, optional) – The charge state for ion species #1. If not provided, it defaults to the charge number of ion1.

  • Z2 (float or Quantity, optional) – The charge state for ion species #2. If not provided, it defaults to the charge number of ion2.

Returns:

omega_BB – The Buchsbaum frequency of the plasma in units of radians per second. Setting keyword to_hz=True will apply the factor of \(1/2π\) and yield a value in Hz.

Return type:

Quantity

Raises:

  • TypeError – If the magnetic field is not a Quantity or particle is not of an appropriate type.

  • ValueError – If the magnetic field contains invalid values or particle cannot be used to identify a particle or isotope.

Warns:

UnitsWarning – If units are not provided, SI units are assumed.

Notes

In a magnetized plasma, the presence of two ion species allows the perpendicular component of the cold-plasma dielectric coefficient \(\epsilon_{\perp}\) to vanish at an angular frequency referred to as the Buchsbaum frequency [Buchsbaum, 1960], also called the bi-ion hybrid resonance frequency [Thompson et al., 1995], or ion-ion hybrid frequency [Vincena et al., 2013]. This frequency can be defined as:

\[ω_{BB} ≡ \sqrt{\frac{ω_{p1}^2 ω_{c2}^2 + ω_{p2}^2 ω_{c1}^2}{ω_{p2}^2 + ω_{p2}^2}}\]

Examples

>>> import astropy.units as u
>>> fbb = Buchsbaum_frequency(
...     0.1 * u.T, 1e18 * u.m**-3, 1e18 * u.m**-3, "proton", "He+", to_hz=True
... )
>>> fbb
<Quantity 764831.28372462 Hz>
>>> fc_helium = gyrofrequency(0.1 * u.T, "He+", to_hz=True)
>>> fc_proton = gyrofrequency(0.1 * u.T, "proton", to_hz=True)
>>> fbb / fc_helium
<Quantity 1.99327444>
>>> fbb / fc_proton
<Quantity 0.50168706>
Parameters:

to_hz (bool) – Set True to convert function output from angular frequency to Hz