## Proceedings of the International School of Physics "Enrico Fermi.", Volume 25 |

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Page 108

To find the particle density (n+)t and the average velocity (o+), it is necessary to

know the

turn requires the evaluation of the energy balance for the whole cathode region

of the arc. This is an extremely difficult problem, the details of which are given

elsewhere (>). We sketch here only the basic assumptions and equations. The

calculation of the contraction zone follows in principle the procedures of the

column theory ...

To find the particle density (n+)t and the average velocity (o+), it is necessary to

know the

**temperature**close to the boundary (s) of the contraction region. This inturn requires the evaluation of the energy balance for the whole cathode region

of the arc. This is an extremely difficult problem, the details of which are given

elsewhere (>). We sketch here only the basic assumptions and equations. The

calculation of the contraction zone follows in principle the procedures of the

column theory ...

Page 113

Cathode

end contraction B„IR. Te is the ga«

cathode outside the contact area. on the one hand the ion saturation current of

the gas, I+(R) (resp. I-(ir)), I+(R) (resp. /_ function of the con- and on the other the

defect current, J — J,(R) as traction parameter R. As was already stated we call

this whole arrangement the « diagram of existence », that is the « ^-diagram ».

Cathode

**temperature**, 7'c, of the representative Hg discharge as a function of theend contraction B„IR. Te is the ga«

**temperature**in the neighbourhood of thecathode outside the contact area. on the one hand the ion saturation current of

the gas, I+(R) (resp. I-(ir)), I+(R) (resp. /_ function of the con- and on the other the

defect current, J — J,(R) as traction parameter R. As was already stated we call

this whole arrangement the « diagram of existence », that is the « ^-diagram ».

Page 131

05 But now an additional difficulty arises, since in the case of the fully ionized

column with external particle production we can no longer introduce the

assumption of constant

governed by the energy gain in a homogeneous electrical field and an energy

loss due to collisions with uniformly distributed balance. We omit the details of

this calculation (:) which, starting from eq. (4.14), produces two simultaneous

equations for the ...

05 But now an additional difficulty arises, since in the case of the fully ionized

column with external particle production we can no longer introduce the

assumption of constant

**temperature**. Here the**temperature**of the particles is notgoverned by the energy gain in a homogeneous electrical field and an energy

loss due to collisions with uniformly distributed balance. We omit the details of

this calculation (:) which, starting from eq. (4.14), produces two simultaneous

equations for the ...

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### Contents

Lezioni | 1 |

carrier mass | 159 |

hydrodynamique an voisinage dun axe magnetique | 214 |

Copyright | |

2 other sections not shown

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### Common terms and phrases

adiabatic invariant amplitude approximation assumed Boltzmann equation boundary conditions boundary layer calculated cathode charge coefficient collision components consider const constant contraction corresponds courbe critère current density Debye length derived differential equations diffusion discharge dispersion relation distribution function double adiabatic theory eigenvalue electric field electromagnetic waves electrons and ions electrostatic energy principle equations of motion equilibrium expand experimental F(co finite fluid theory frequency given Hence inertia-limited instability integral interaction ionized Kruskal 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 quantities radial region satisfied saturation current self-adjointness solution solving stabilité stability surface temperature thermal tion transverse wave values vanish variables vector velocity Vlasov equation waves in plasmas zero zero-order