## Advanced Plasma Theory, Volume 25 |

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Page 78

The part perpendicular to n is

11) eq. (9) may be solved for /' but not uniquely; only up to a function of t, r, w and

...

The part perpendicular to n is

**zero**order which we use to find E±). To proceed to**zero**order in (16) we need / to**zero**order which by (18) involves /'. Because of (11) eq. (9) may be solved for /' but not uniquely; only up to a function of t, r, w and

...

Page 163

Expanding about this solution in powers of 8~\ one finds that when lm(p)^=0

either Re(p) = 0(l) (so that the growth rate is insignificant); or else the

current layer must have sharp resistivity gradients, which become increasingly so

as ...

Expanding about this solution in powers of 8~\ one finds that when lm(p)^=0

either Re(p) = 0(l) (so that the growth rate is insignificant); or else the

**zero**-ordercurrent layer must have sharp resistivity gradients, which become increasingly so

as ...

Page 206

Since there is no

theory. We consider a canonical transformation of the system to new variables Pr,

Qr and a new Hamiltonian H(Pr, Qr, t). We consider the transformation or ...

Since there is no

**zero**-order term, pr, qr are constants of the motion in**zero**- ordertheory. We consider a canonical transformation of the system to new variables Pr,

Qr and a new Hamiltonian H(Pr, Qr, t). We consider the transformation or ...

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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