Finite radius models¶

Finite radius models relax the restriction on the OML theory that the radius should be small, and may be accessed through the following function:

finite_radius_current(geometry, species, V=None, eta=None, table='laframboise-darian-marholm', normalization=None)

Example of use:

from langmuir import *
import numpy as np
import matplotlib.pyplot as plt

plasma = Electron(n=1e11, T=1000)
geometry = Sphere(r=5*debye(plasma))

V = np.linspace(0, 2, 100)

I_OML = OML_current(geometry, plasma, V)
I_FR = finite_radius_current(geometry, plasma, V)

plt.plot(V, -I_OML*1e6, label='OML')
plt.plot(V, -I_FR*1e6, label='FR')
plt.xlabel('V [V]')
plt.ylabel('I [uA]')
plt.legend()
plt.show()

The model is built from two sets of tabulated numerical results, which can be found in [Laframboise] and [Darian]. The former is more accurate but covers only Maxwellian plasmas, whereas the latter covers the more general Kappa-Cairns distributions. By default interpolation between tabulated values will use the most accurate values. The model is valid for $0\leq\eta\leq 25$ , $\kappa\geq 4$ and $\alpha\leq 0.2$ . Probe radii extends up to 10 Debye lengths, or even 100 Debye lengths as the distribution approaches Maxwellian.