rizer.transport.collision_frequency#

Define momentum transfer and energy collision frequency model used by [Mitchner1973].

Notes

  • \(\nu_{e h}^{(1)}\) is the momentum transfer collision frequency, in s^-1, between electrons and heavy particles (e.g. neutrals, ions), defined in equation (II 5.6) of [Mitchner1973].

  • \(\bar{\nu_{e h}}^{(1)}\) is the average momentum transfer collision frequency, in s^-1, between electrons and heavy particles (e.g. neutrals, ions), defined in equation (II 6.29) of [Mitchner1973].

  • \(\nu_{e h}^{E} = \frac{2 m_e}{m_h} \nu_{e h}^{(1)}\) is the energy exchange collision frequency, in s^-1, between electrons and heavy particles (e.g. neutrals, ions), defined in equation (II 7.6) of [Mitchner1973].

  • \(\bar{\nu_{e h}}^{E}\) is the average energy exchange collision frequency, in s^-1.

Attributes#

logger

Classes#

MomentumTransferCollisionFrequencyModel

IonMomentumTransferCollisionFrequencyModel

Module Contents#

rizer.transport.collision_frequency.logger#
class rizer.transport.collision_frequency.MomentumTransferCollisionFrequencyModel(name: str, cross_section_model: rizer.transport.cross_sections.MomentumTransferCrossSectionModel)#
name#
cross_section_model#
get_mean_momentum_transfer_collision_frequency(T: float, n_h: float, n_e: float | None = None) → float#

Get the mean momentum transfer collision frequency.

Parameters:

  • T (float) – Temperature in K.

  • n_h (float) – Heavy particle density in m^-3.

Returns:

Momentum transfer collision frequency in s^-1.

Return type:

float

Notes

The mean momentum transfer collision frequency is defined in equation (II 6.29) of [Mitchner1973] as:

\[\bar{\nu_{e h}}^{(1)} = n_h \bar{Q}_{12} v_{th}\]

where:

  • \(\bar{\nu_{e h}}^{(1)}\) is the average momentum transfer collision frequency,

  • \(n_h\) is the heavy particle density,

  • \(\bar{Q}_{12}\) is the mean momentum transfer cross section in m²,

  • \(v_{th}\) is the electron thermal velocity in m/s.

class rizer.transport.collision_frequency.IonMomentumTransferCollisionFrequencyModel(name: str, Z: int = 1)#

Bases: MomentumTransferCollisionFrequencyModel

name#
Z = 1#
cst#
get_mean_momentum_transfer_collision_frequency(T: float, n_h: float, n_e: float | None = None) → float#

Get the mean momentum transfer collision frequency.

It is defined in equation (II 8.10) of [Mitchner1973], and assumes that ions are only ionized once. For the case of multiply ionized ions, a factor of \(Z^2\) should be included in the collision frequency expression, where \(Z\) is the ion charge state. See eq. 3.33 in https://www-thphys.physics.ox.ac.uk/people/FelixParra/CollisionalPlasmaPhysics/notes/lecII_electronion.pdf

Parameters:

  • T (float) – Temperature in K.

  • n_h (float) – Ion density in m^-3.

  • m_h (float) – Heavy particle mass in kg.

  • n_e (float) – Electron density in m^-3.

  • model (str, optional) – Model to use for the collision frequency calculation. Default is “Mitchner”.

Notes

The mean momentum transfer collision frequency for collision between an electron and an ion is defined in equation (II 8.10) of [Mitchner1973] as:

\[\bar{v}_{e i} \equiv n_i \frac{4 \sqrt{2 \pi}}{3}\left(\frac{m_e}{k T}\right)^{3 / 2} \left(\frac{e^2}{4 \pi \epsilon_0 m_e}\right)^2 \ln \Lambda\]

where:

  • \(\bar{\nu_{e h}}^{(1)}\) is the average momentum transfer collision frequency,

  • \(n_h\) is the heavy particle density,

  • \(\bar{Q}_{12}\) is the mean momentum transfer cross section in m²,

  • \(v_{th}\) is the electron thermal velocity in m/s.