Density Gradient Effects on Alfvén Wave Propagation in a Cylindrical Plasma

Abstract

The propagation of nonaxisymmetric Alfvén waves in a linear discharge tube filled with a nonuniform plasma under a 30-kG axial field has been investigated theoretically and experimentally in the frequency range 1–5 Mc/sec. Typical plasma densities were 3–4 × 1015 ions/cm3 near the center of the tube and fell to low values at the wall. It was found that the density gradient introduces a frequency dependent coupling between the torsional and compressional waves of the uniform plasma. As a result, an axial component of the magnetic field perturbation, which is normally associated only with the compressional wave, is now carried by the torsional wave as well, and was in fact detected at frequencies well below the lowest waveguide cutoff of the compressional wave. At still lower frequencies, this component disappeared, and the remaining transverse field components were found to propagate at a radially varying speed which agreed well with the local Alfvén speed deduced from the measured ion density profile. A theoretical analysis is presented, and its predictions are compared with experimental measurements of signal amplitudes, wave speeds, attenuation rates, and density profiles.

Theory of plasma heating by low frequency waves: Magnetic pumping and Alfvén resonance heating

“…If A ? * 0 for the parameters of interest, Eqs (7.58) and (7.59) still possess discrete spectra associated with the eigenmodes of the fast magnetoacoustic wave and the global eigenmodes of the Alfve"n wave [54,57,63,67,106,113,122,129,132,141,183]. These spectra are not much different from those presented in Section 7.2 (see below).…”

“…( 7.64) can be written in the form (see Ref. [54]) E r = E r 5 ( r -r s ) (7.65) where E r is an arbitrary constant. The associated frequency is given by (see Ref.…”

Decay of MHD waves by phase mixing

“…The existence of a continuous spectrum in problems describing MHD waves has been oberved often in the past [1][2][3]. The influence of the continuous spectrum on unstable plasma configurations has also received attention [4].…”

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It is well known, [1][2][3][4][5][6], that the linearized equations of motion of ideal MHD possess a continuous spectrum which leads to damping of propagating waves through phase mixing. We show how this arises by examining the dispersion relation for plasmas with non-uniform profiles and comparing the results with those of a sharp boundary model.

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Overstable Modes Due to Resistivity Gradients in a Current-Carrying Plasma Column

“…The apparatus is described in detail in Ref. 10. Characteristic plasma parameters are 10 16 -cm~" 3 H-ion density and 5-eV temperature.…”