Add thomas fermi ion

hack/Ionisation/Thomas_Fermi_ionisation.py

@@ -0,0 +1,43 @@
+import numpy as np
+import astropy.units as u
+from plasmapy.particles import Particle, particle_input
+from plasmapy.utils.decorators import validate_quantities
+
+@validate_quantities(density={"can_be_negative": False}, equivalencies=u.temperature_energy())
+@particle_input
+def Zav_TF(particle: Particle, rho: u.g/u.cm**-3 , T: u.eV=0) -> u.dimensionless_unscaled:
+    """
+    Finite Temperature Thomas Fermi Charge State using 
+    R.M. More (1985), "Pressure Ionization, Resonances, and the
+    Continuity of Bound and Free States", Adv. in Atomic 
+    Mol. Phys., Vol. 21, p. 332 (Table IV).
+
+    This is a light-weight fit of the Thomas-Fermi model, not the model itself.
+    """
+
+    Z = particle.atomic_number
+    A = particle.mass_number
+
+    alpha = 14.3139
+    beta = 0.6624
+    a1 = 0.003323
+    a2 = 0.9718
+    a3 = 9.26148e-5
+    a4 = 3.10165
+    b0 = -1.7630
+    b1 = 1.43175
+    b2 = 0.31546
+    c1 = -0.366667
+    c2 = 0.983333
+
+    rho1 = rho.value / A * Z
+    T1 = T.value / Z ** (4. / 3.)
+    Tf = T1 / (1 + T1)
+    Ac = a1 * T1 ** a2 + a3 * T1 ** a4
+    B = -np.exp(b0 + b1 * Tf + b2 * Tf ** 7)
+    C = c1 * Tf + c2
+    Q1 = Ac * rho1 ** B
+    Q = (rho1 ** C + Q1 ** C) ** (1 / C)
+    x = alpha * Q ** beta
+
+    return Z * x / (1 + x + np.sqrt(1 + 2. * x))