# buchsbaum_frequency

hack.Buchsbaum_frequency.buchsbaum_frequency(B: Unit('T'), n1: Unit('1 / m3'), n2: Unit('1 / m3'), particle1: Particle, particle2: Particle, Z1=None, Z2=None, to_hz=False)

Calculate the Buchsbaum frequency in units of radians per second.

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

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

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

• particle1 (Particle) – Representation of the first particle species (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.

• particle2 (Particle) – Representation of the first particle species (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-2 is assumed to be singly charged.

• Z1 (float or Quantity, optional) – The charge state for ion species #1. If not provided, it defaults to the charge number of particle1.

• Z2 (float or Quantity, optional) – The charge state for ion species #2. If not provided, it defaults to the charge number of particle2.

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 , also called the bi-ion frequency or ion-ion hybrid frequency . This frequency can be defined as:

$\omega_{BB} \equiv \sqrt{\frac{\omega_{p1}^{2}\omega_{c2}^{2} + \omega_{p2}^{2}\omega_{c1}^{2}}{\omega_{p2}^{2}+\omega_{p2}^{2}}}$
Parameters

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