## Advanced Plasma Theory, Volume 25 |

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Page 64

For a simple example of an energy principle consider the one-dimensional

motion of a particle in a potential V: 3x ' is the condition for

motion about

is ...

For a simple example of an energy principle consider the one-dimensional

motion of a particle in a potential V: 3x ' is the condition for

**equilibrium**. A smallmotion about

**equilibrium**is given by 32 V If 32F/3.c2 is negative the**equilibrium**is ...

Page 83

replaced by integrals over e and v (and summed over ±) with the the

corresponding factor of p/q. 3'4. Static

a static

Section 3'3.

replaced by integrals over e and v (and summed over ±) with the the

corresponding factor of p/q. 3'4. Static

**equilibrium**. - We first consider the case ofa static

**equilibrium**satisfying the equations of the adiabatic theory given inSection 3'3.

Page 152

We also choose the simplest geometry: magnetic field in the z direction, and

plasma parameters and field strength varying with x- Thus, for the

field, we can take, locally, (4.1) B = B0(l + eX) and construct arbitrary

...

We also choose the simplest geometry: magnetic field in the z direction, and

plasma parameters and field strength varying with x- Thus, for the

**equilibrium**field, we can take, locally, (4.1) B = B0(l + eX) and construct arbitrary

**equilibrium**...

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adiabatic invariant amplitude approximation assumed Boltzmann equation boundary conditions boundary layer calculated cathode charge coefficient collision column components consider const constant contraction corresponds courbe current density Debye length derived differential equations diffusion discharge dispersion relation distribution function double adiabatic theory effect eigenvalue electric field electromagnetic waves electrostatic energy principle equations of motion equilibrium expand experimental finite fluid theory frequency given Hence hydromagnetic inertia-limited instability integral interaction ionized Kruskal Kulsrud l'axe magnétique lignes limit linear theory lowest order magnetic field Maxwell's equations mode negative ions nonlinear obtain Ohm's law parameter particle perturbation Phys plasma oscillations plasma physics Poisson's equation potential pressure problem produced quantities radial region satisfied saturation current self-adjointness solution solving stability surface temperature thermal tion transverse wave values vanish variables vector velocity Vlasov equation waves in plasmas zero zero-order