Shear Alfvén Wave Perpendicular Propagation from the Kinetic to the Inertial Regime

We report on observations of shear Alfvén waves radiated from a source of small transverse size, and the subsequent radial confinement of wave magnetic field energy within a cylindrical plasma. The radius of confinement lies between the kinetic regime of the bulk plasma and the inertial regime at the plasma edge; this radius is found to be a function of wave frequency. Numerical calculations using kinetic theory predict a zero in the perpendicular group velocity at a radius which varies in accord with the observations. An analytic expression for the perpendicular group velocity (valid for small perpendicular wave numbers) is given in the vicinity of the zero crossing.

Figure 1

Schematic of experimental setup.

Figure 2

(a) Measured radial profiles of electron density and temperature. (b) The resulting scaled electron plasma beta, ${\overline{\mathrm{\beta }}}_{\mathrm{e}}={\beta }_e{m}_i/m_e$, along with an analytic fit as described in the text.

Figure 3

Time evolution of the radial magnetic field energy density profiles (integrated over the azimuthal coordinate). Error bars (approximately 5% for each value) have been omitted for clarity. The wave frequency is one-half of the ion-cyclotron frequency.

Figure 4

Frequency variation of the radial magnetic field energy density profiles (integrated over the azimuthal coordinate). The two frequencies shown are (a) $\overline{\mathrm{\omega }}=0.5$ and (b) $\overline{\mathrm{\omega }}=0.9$. For both frequencies, a $1/r$ profile is fit to the data, subtracted, and that result is fit to a Gaussian, shown in curves (c) and (d). For small radii, the wave pattern does not behave as $1/r$ and the subtraction results in large negative numbers, which are not plotted.

Figure 5

Radial location of zero perpendicular group velocity as a function of frequency. Shown are (a) measured locations determined from Gaussian fits to the wave energy pileup, (b) predictions using the simplified expression of Eq. (6), (c) predictions of Eq. (3) [this nearly overlaps (b)], and (d) predictions using the theory of Streltsov et al. [11] with $T_i=0$.