The Spitzer resistivity (or plasma resistivity) is an expression describing the

electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallels ...

in a

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, which was first formulated by Lyman Spitzer in 1950. The Spitzer resistivity of a plasma decreases in proportion to the electron temperature as

T_e^

. The inverse of the Spitzer resistivity

\eta_

is known as the Spitzer conductivity

\sigma_=1/\eta_

Formulation

The Spitzer resistivity is classical model of electrical resistivity based upon electron-ion

collisions In physics, a collision is any event in which two or more bodies exert forces on each other in a relatively short time. Although the most common use of the word ''collision'' refers to incidents in which two or more objects collide with great f ...

and it is commonly used in plasma physics. The transverse Spitzer resistivity is given by: :

\eta_\perp = \frac\frac ,

and the parallel Spitzer resistivity by: :

\eta_\parallel = \eta_\perp/1.96 \qquad (\text Z=1),

where

Z

is the ionization of nuclei,

e

is the electron charge,

m_e

is the electron mass,

\ln\Lambda

is the Coulomb logarithm,

\varepsilon_0

is the electric permittivity of free space,

k_\text

is Boltzmann's constant, and

T_e

is the electron temperature in

kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phys ...

s. The two resistivities correspond to current perpendicular and parallel to a strong magnetic field (the collision rate is small compared to the gyrofrequency). In an unmagnetized case the resistivity is

\eta_\parallel

. In CGS units, the expression is given by: :

\eta_\perp = \frac\frac.

For arbitrary

Z

, :

\eta_\parallel = \eta_\perp F(Z),

where :

F(Z) =\frac

Disagreements with observation

Measurements in laboratory experiments and

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have shown that under certain conditions, the resistivity of a plasma tends to be much higher than the Spitzer resistivity. This effect is sometimes known as ''anomalous resistivity'' or ''neoclassical resistivity.'' It has been observed in space and effects of anomalous resistivity have been postulated to be associated with particle acceleration during magnetic reconnection. There are various theories and models that attempt to describe anomalous resistivity and they are frequently compared to the Spitzer resistivity.

References

Electrical resistance and conductance Plasma physics {{plasma-stub