Measuring Alfvén waves: The left shows the set-up
used for the measurements. To the right is the magnetic B-dot
coil used to both excite and detect Alfvén waves.
Alfvén waves, low frequency magnetohydrodynamic plasma oscillations, are of fundamental importance in the behavior of many laboratory and space plasmas. Yet, despite the importance of Alfvén waves in all of magnetized plasma physics, comparatively few basic laboratory experiments have been done on these modes. The primary reason for this is that the study of Alfvén waves requires either a very large or very dense plasma. These requirements constrain the range of studies that can be performed. This is the reason for using a helicon source on ALESPI and HelCat, which efficiently creates a high-density plasma.
Initial investigations demonstrate the propagation of shear Alfvén waves within the plasma through the localization of the oscillations along the magnetic field lines and the expected phase velocity of the waves. More recent studies detail the propagation of shear waves in the presence of neutral atoms, and may be relevant to Alfvén wave propagation in Earth’s upper ionosphere and in the solar chromosphere.
To study Alfvén waves in we use two magnetic coils, B-dot loops. Shear Alfvén waves are produced in this discharge by means of an inductive coil positioned to oscillate the magnetic field perpendicular to the background field lines. This consists of several (100-200) turns of wire around a small spool, about 5 mm in diameter.To excite the waves, a function generator is used to supply a sine wave to the emitter coil with a 20 V peak-to-peak amplitude.This creates an oscillating magnetic field perpendicular to the background field, exciting the shear Alfvén mode. The waves are detected by means of a second inductive coil positioned down the plasma column located 20-60 cm away. This configuration means that non-axisymmetric Alfvén waves are excited.
The emitted and detected signals are digitized and cross-correlated to obtain phase information. The probes and detection method are calibrated in vacuum to account for any phase shift due to the electronics. For this series of studies the emitter was placed at fixed radial location. The detector is positioned downstream where it is stepped in radial position in 5 mm increments. At each radial location the emitted frequency is scanned in 10 kHz increments from 10 kHz to 400 kHz. For ALESPI parameters the ion cyclotron frequency is fci = 320 kHz.
Measuring Alfvén waves: The left shows the set-up used for the measurements. To the right is the magnetic B-dot coil used to both excite and detect Alfvén waves.
Plotted in figure below on the left is the amplitude of the detected signal as a function of radial location of the detector probe. The exciter is located at mid radius, 2.5 cm. Notice how the amplitude of the signal is strongly peaked at about 2.5 cm, which demonstrates that the waves are strongly guided by magnetic field lines. Shear waves tend to propagate only along field lines. In the graph on the right is the wave number as the exciting frequency is changed. As the frequency is increase the Alfvén wavelength decreases, causing the phase shift we detect. This is known as a dispersion relation. Near the ion cyclotron frequency the dispersion relation reaches a resonance where the wavelength of the wave approaches zero. There is a steep increase in wavenumber. The red squares are measured data, while the line is the best fit to the theoretical model.
Detection of shear Alfvén waves: To the left is shown the peaking of the signal when both the emitter and detector are on the same field line. The right plot shows the data fit to the theoretical dispersion relation.
For these studies we use a helium helicon discharge at a base initial fill pressure of 9 mTorr, with 900W of RF power at 10MHz. The neutral edge pressure drops to less than 1 mtorr during the discharge, and a chord-averaged density of 5.5x1018 m-3 is found using a 65 GHz microwave interferometer. Density and temperature measurements using Langmuir probes give a peak density of about 1.2x1019 m-3, with an electron temperature ranging from 3-10 eV. The cord-averaged density of the probe data agrees with the interferometer data to within a few percent.
Depending on the tuning of the matching circuit several different “modes” of the helicon discharge can be obtained in helium. These modes can be identified by a visual change in the pink core of the helium discharge. Depicted in the figure below are the density and pressure profiles for two of the modes used in this study. Above we discussed Alfvén wave measurements in what appears to be the most efficient mode, where the gas is nearly completely ionized. A high neutral fraction mode can also be obtained under similar conditions. In this case the electron density and temperature are significantly lower. As seen in the pressure profile, the edge neutral pressure is a sizable fraction of the central plasma pressure. Thus, the neutral penetration depth and hence the neutral fraction, though not directly measurable, is inferred to be significantly greater for this mode.
Plasma density and pressure profiles for the two helicon modes.
Data are plotted on the left in the figure below for the measured wavenumber vs. frequency with both the emitter and detector at the same radius (2.5 cm) for the “efficient” low neutral fraction mode. The data are the same as those shown above. The plot on the right shows similar data at two different radii, with both the emitter and detector at the same radius, for a plasma discharge with a high neutral fraction. Near the ion cyclotron frequency in both cases the dispersion relation changes abruptly, as expected. However, the data are poorly fitted by the usual Alfvén dispersion relation due to ion-neutral collision effects.
Measured Alfvén wave dispersion curve and fit to theory for (left) “efficient” low neutral fraction helicon mode and (right) a high neutral fraction mode. Error bars are of the order of the symbol size.
As a first attempt at modeling the data we use a theory for Alfvén wave propagation by Woods that accounts for neutral damping effects. We ignore the density gradient and treat the plasma as homogeneous with the local plasma parameters at the given radius. As discussed in Cross, the density gradient has a negligible effect on Alfvén wave propagation, and for emitter and detector at the same radius we can treat this as a ducted waveguide mode. For detector and emitter at different radii a more complete theory is required. We also ignore the non-axisymmetric nature of the wave.
The data at r = 3.0 cm are fit using the measured local plasma parameters: Te = 5 eV, Ti = 1 eV, ne = 3.5x1018 m-3 and B0 = 0.080 T. The neutral fraction is adjusted to provide the best fit. In this case, the neutral fraction is 15 x1018 m-3or nn/ne = 4.3, a reasonable value based on Figure 2. For data at r = 2.0 cm a good fit can only be obtained with ne = 9.0x1018 m-3, significantly higher than the measured electron density. We suspect that during this measurement scan the helicon discharge changed to a different mode from that used when measuring the density profile. In this case we found nn/ne = 3.1.
From these studies is clear that neutrals can play a significant role in Alfvén wave dynamics, which are well modeled by theory. Both Earth’s upper ionosphere and the solar photosphere have significant neutral populations. It has been suggested that the damping of Alfvén waves may play a role in heating these regions.
To learn more about our research on Alfvén waves, see our recent papers and conference presentations in the publications page.
 Return
to Plasma & Fusion Sciences main page |
Return
to Plasma Sciences Laboratory |
