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Magnetized Plasmas

Amagnetized plasma is one in which the ambient magnetic field, ${\bf B}$ , is strong enough to significantly alter particletrajectories. In particular,magnetized plasmas are highly anisotropic, responding differently toforces that are parallel and perpendicular to the directionof ${\bf B}$ . Incidentally, a magnetized plasma moving withmean velocity ${\bf V}$ contains an electric field ${\bf E} = - {\bf V}\times {\bf B}$ that is not affected by Debye shielding. Of course, the electricfield is essentially zero in the rest frame of the plasma.

As is well known, charged particles respond to the Lorentz force,

$\displaystyle {\bf F} = q\,{\bf v}\times {\bf B},$

(1.28)

by freely streaming in the direction of ${\bf B}$ , while executingcircularLarmor orbits, orgyro-orbits, in the plane perpendicular to ${\bf B}$ (Fitzpatrick 2008). As the field-strength increases, the resulting helical orbits become moretightly wound, effectively tying particles to magnetic field-lines.

The typicalLarmor radius, orgyroradius, of a charged particle gyrating in amagnetic field is given by

$\displaystyle \rho\equiv \frac{v_t}{\mit\Omega},$

(1.29)

where

$\displaystyle {\mit\Omega} = \frac{e B}{m}$

(1.30)

is thecyclotron frequency, orgyrofrequency, associated with thegyration. As usual, there is a distinct gyroradius for each species.When species temperatures are comparable, the electron gyroradius isdistinctly smaller than the ion gyroradius:

$\displaystyle \rho_e \sim \left(\frac{m_e}{m_i}\right)^{1/2}\!\rho_i.$

(1.31)

A plasma system, or process, is said to be magnetized if itscharacteristic lengthscale, $L$ , is large compared to the gyroradius.In the opposite limit, $\rho\gg L$ , charged particles have essentiallystraight-line trajectories. Thus, the ability of the magnetic field tosignificantly affect particle trajectories is measured by themagnetization parameter,

$\displaystyle \delta \equiv \frac{\rho}{L}.$

(1.32)

There are some cases of interest in which the electrons are magnetized, but theions are not. However, a “magnetized” plasma conventionally refers toone in which both species are magnetized. This state is generally achievedwhen

$\displaystyle \delta_i \equiv \frac{\rho_i}{L} \ll 1.$

(1.33)

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