## Advanced Plasma Theory, Volume 25 |

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Page 39

M. N. Rosenbluth. IV. - The Kinetic Equation in a

PIanck equation in a

possible to use the Liouville equation to describe the dynamics of a complete

system, and again one may integrate this to obtain the Boltzmann equation (IV.

1.1) %+vl/-+-\E + -xB\-^- + -~-{FviHvl,x1;v2,x2)^xi^vi, St ox m i c ] cv m cv J where

now the interaction forces F12 include, in general, terms of the form ...

M. N. Rosenbluth. IV. - The Kinetic Equation in a

**Magnetic Field**. 1. - Fokker-PIanck equation in a

**magnetic field**. As in the absence of a**magnetic field**, it ispossible to use the Liouville equation to describe the dynamics of a complete

system, and again one may integrate this to obtain the Boltzmann equation (IV.

1.1) %+vl/-+-\E + -xB\-^- + -~-{FviHvl,x1;v2,x2)^xi^vi, St ox m i c ] cv m cv J where

now the interaction forces F12 include, in general, terms of the form ...

Page 148

Q -f- kfu — w kzvth Insertion of (13) into the Poisson's equation finally allowes us

to examine the 2-stream instability in the presence of

also kept different T, and T± a similar form for the Harris instability could easily

have been found while the full 3x3 determinant would be necessary to study such

effects as the mii-ror and Alfven instabilities. 3. - We discuss next another version

of the two-stream instability appropriate to the

experiment, ...

Q -f- kfu — w kzvth Insertion of (13) into the Poisson's equation finally allowes us

to examine the 2-stream instability in the presence of

**magnetic field**. If we hadalso kept different T, and T± a similar form for the Harris instability could easily

have been found while the full 3x3 determinant would be necessary to study such

effects as the mii-ror and Alfven instabilities. 3. - We discuss next another version

of the two-stream instability appropriate to the

**magnetic field**. In a recentexperiment, ...

Page 254

For instance, in Fermi's theory [1] for the acceleration of cosmic rays, it is

assumed that the magnetic moment of a spiraling particle in a varying

one to show that a

magnetic moment of this patricle is not really a rigorous constant but is nearly so

if the relative space change in the

particle is small, ...

For instance, in Fermi's theory [1] for the acceleration of cosmic rays, it is

assumed that the magnetic moment of a spiraling particle in a varying

**magnetic****field**remains constant. Combined with the conservation of energy this enablesone to show that a

**magnetic field**can reflect such a spiraling particle. Themagnetic moment of this patricle is not really a rigorous constant but is nearly so

if the relative space change in the

**magnetic field**over the Larmor radius of theparticle is small, ...

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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