By W. B. Thompson (Auth.)

ISBN-10: 0080111807

ISBN-13: 9780080111803

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**Extra resources for An Introduction to Plasma Physics**

**Example text**

Vp = 0 and j . Vp = 0, the magnetic field lines and the currents must lie in surfaces of constant pressure and the magnetic field must form a set of magnetic surfaces. ) = - c u r l I —V J52 ( B . V)B L87T 4π J 47Γ The complete properties of the solutions to this complex non-linear partial differential equation are not known, however some simple systems have been studied. If field lines are straight then equilibrium requires p + (Β2/8π) = constant, and in particular there exist equilibria in which a fluid is confined to a cylindrical region by a magnetic field parallel to the axis and azimuthal currents about the axis.

Structure of the positive column. Measured and theoretical values of the potential as a function of radius for short mean free path, where ions diffuse. and the plasma is held positive with respect to the wall by the sheath poten tial. If the potential of a small section of the wall is made less negative with respect to the plasma then an excess of electrons will reach the wall, while the ion current is only slightly altered. The electron current will be ~ ^(kT) exp(eF/&T); hence by plotting the log of the current against V, the probe potential, a straight line of slope (e/JcT_) should be obtained.

The theory of PETSCHEK was used to calculate both the density p and conductivity σ behind the shock, as well as the time τ needed to reach thermal equilibrium. Since the length of the ionized column was short, only if τ < 10~5 sec could an inter action be expected. From the calculated values of p and σ and the known values of the magnetic field and tube radius, the magnetic Reynold's num ber M could be calculated. It was found that interactions occurred only in the expected region. Subsequent experiments on the distortion of the magnetic field verified the calculated value of σ.

### An Introduction to Plasma Physics by W. B. Thompson (Auth.)

by William

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