## Advanced Plasma Theory, Volume 25 |

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Page 65

The matrix ^Vjcx^x, corresponds to our operator F and is obviously

since it is symmetric. Our theory corresponds to a continuum of dimensions but is

otherwise algebraically the same. The proof of d) follows the remarks in c) with ...

The matrix ^Vjcx^x, corresponds to our operator F and is obviously

**self**-**adjoint**,since it is symmetric. Our theory corresponds to a continuum of dimensions but is

otherwise algebraically the same. The proof of d) follows the remarks in c) with ...

Page 67

The theorem « SW< 0=> instability » relies on both completeness and

need not be a normal mode. Although temporarily the system gains kinetic

energy at ...

The theorem « SW< 0=> instability » relies on both completeness and

**self**-**adjointness**. If 811" < 0 for \ this need not imply instability in a general case since \need not be a normal mode. Although temporarily the system gains kinetic

energy at ...

Page 86

For this purpose it is necessary that F and J together satisfy a

This

proof of it. In these notes we follow the indirect method of the fluid theory in

finding ...

For this purpose it is necessary that F and J together satisfy a

**self**-**adjointness**.This

**self**-**adjointness**was first discovered by Newoomb [15] who gave a directproof of it. In these notes we follow the indirect method of the fluid theory in

finding ...

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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