plasmapy.formulary.braginskii.resistivity(T_e, n_e, T_i, n_i, ion, m_i=None, Z=None, B: ~astropy.units.quantity.Quantity = <Quantity 0. T>, model='Braginskii', field_orientation='parallel', mu=None, theta: float | None = None, coulomb_log_method='classical') Quantity[source]

Calculate the resistivity.

The resistivity (\(α\)) of a plasma is defined by

\[α = \frac{\hat{α}}{n_e e^2 \frac{τ_e}{m_e}}\]

where \(\hat{α}\) is the non-dimensional resistivity of the plasma, \(n_e\) is the electron number density of the plasma, \(e\) is Euler’s number, \(τ_e\) is the fundamental electron collision period of the plasma, and \(m_e\) is the mass of an electron.


The resistivity here is defined similarly to solid conductors, and thus represents the classical plasmas’ property to resist the flow of electrical current. The result is in units of ohm meters, so if you assume where the current is flowing in the plasma (length and cross-sectional area), you could calculate a DC resistance of the plasma in ohms as resistivity × length / cross-sectional area.

Experimentalists with plasma discharges may observe different \(V = IR\) Ohm’s law behavior than suggested by the resistance calculated here, for reasons such as the occurrence of plasma sheath layers at the electrodes or the plasma not satisfying the classical assumptions.

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