jaxrts.ipd.ipd_ecker_kroell

jaxrts.ipd.ipd_ecker_kroell(Zi: float, ne: Quantity, ni: Quantity, Te: Quantity, Ti: Quantity, Z_max: Quantity, Zbar: float | None = None, arb_deg: bool = False, C: float | None = None) → Quantity[source]

The ionization potential for an atom with charge Zi in the Ecker-Kroell model. Defines a critical density under which the IPD is identical to ipd_debye_hueckel(). Above that value, the IPD is given by a Ecker Kröll length. If no value C is given, the latter value is scaled to have a continuous IPD. Some studies (e.g. [Preston et al., 2013] use a modified Ecker Kröll model, where a specific value of C (often 1) is set instead. For details see [Ecker and Kröll, 1963].

Parameters:

  • Zi – The charge state of the atom (note that this is the state before the ionization)

  • ne – Electron density. Units of 1/[length]**3.

  • ni – Ion density. Units of 1/[length]**3.

  • Te – The electron temperature.

  • Ti – The ion temperature.

  • Z_max (Quantity) – Array of maximal charges of the ions. Must be of the same shape as ni.

  • Zbar (float, optional) – The average ionization of the plasma. If not given, Zi is assumed to be the average ionization of the plasma.

  • arb_deg (bool, default false) – If True the Debye screening length is evaluated using inverse_screening_length_e(), which includes solving the Fermi integral, rather than the classical value.

  • C (float or None, default None) – Multiplicative factor for the high-density part of the EK model. If set to None, the factor is chosen to achieve a continuous IPD.

Returns:

Quantity – The ipd shift in units of electronvolt.