Upper Hybrid Resonance and Waves

The upper hybrid frequency is a resonance phenomenon for electromagnetic waves with E perpendicular to B, propagating across the static magnetic field B0. A resonance (infinite k) is a layer of strong wave absorption. Vice versa, it is a region of strong thermal emission. Furthermore, warm plasma modes play a role and there is the possibility of mode conversion when both modes have the same resonance. These phenomena have been studied experimentally. The findings offer interesting diagnostic applications for perturbation-free and sensitive density and temperature measurements.

Schematic

Fig. 1. Pictures and schematic drawing of the plasma device for studying upper hybrid wave phenomena. (a) A magnetized rf discharge plasma in a glass tube traverses an S-band waveguide. The absorption of incident em waves and the emission of thermal noise from the plasma are studied. (b) Schematic of the experiment. (c) Picture of the laboratory setup.

The experimental setup shown in Fig. 1 is relatively simple. A pulsed rf discharge is created in a glass tube aligned along an external magnetic field. it passes through the sides of a rectangular S-band waveguide so as to interact with electromagnetic waves with polarization of extraordinary modes. However, the plasma dimension is small compared to the electromagnetic wavelength, hence is nearly an interaction in a capacitor field. The measurement setup uses a radiometer, which contains a sensitive receiver and measures in alternating pulses the signal with and without plasma. The absorption of the plasma is found to be nearly total when the plasma provides an upper hybrid resonance at the test wave frequency.

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Fig. 2. Upper hybrid layer in a nonuniform plasma column. (a) The upper hybrid frequency (omegauh)2=(omegac)2+ (omegap)2 depends on density which has a parabolic profile in a discharge tube and decays in the afterglow. (b) The radial position of the upper hybrid layer varies with frequency and magnetic field.

Figure 2 shows the condition for the upper hybrid resonance in a nonuniform plasma column. The radial density profile is parabolic and decays in the afterglow of the pulsed discharge. The upper hybrid frequency is shown in a graph of density vs magnetic field for a constant signal frequency. At the highest density in the plasma center the upper hybrid resonance occurs at the lowest magnetic field. Vice versa, at the lowest density (column edge) the upper hybrid frequency coincides with the cyclotron resonance.

Schematic

Fig. 3. Absorption coefficient used for density diagnostics. (a) Absorption vs magnetic field, showing nearly total absorption in the range of upper hybrid frequencies. (b) The peak density is obtained from the onset magnetic field and plotted vs afterglow time. This perturbation-free diagnostic is useful for diffusion studies.

measurements of the absorption coefficient are shown in Fig. 3a. throughout the range of upper hybrid resonances there is strong absorption. The onset of absorption occurs at the highest density, hence yields the density in the column center. With increasing afterglow time the onset shifts from which one can obtain the peak density decay as shown in Fig. 3b.

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Fig. 4. Blackbody radiation measurements used for electron temperature diagnostics. (a) Experimental setup to obtain the electron temperature by comparison with a calibrated noise source, using a low-noise radiometer. (b) Noise emission from the plasma in the range of upper hybrid frequencies.

By Kirchhoff's law a medium with high absorption coefficient will also be a strong emitter of thermal radiation. This is verified with a sensitive radiometer, which compares the thermal emission from the plasma with a calibrated blackbody radiation source. Since an afterglow plasma has a Maxwellian distribution the radiation temperature is the electron temperature. In Fig. 4a the radiation temperature is plotted vs magnetic field for different afterglow times. For the lowest magnetic field the resonance lies in the column center, hence the temperature refers to r=0. Near cyclotron resonance the temperature is that at the column edge. In between the traces show the radial temperature profiles. The peak electron temperature decay is shown in Fig. 4b. Electron temperatures can almost be resolved to room temperature. This temperature diagnostics is both non-perturbing and very sensitive.

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Fig. 5. Space and time resolved electron temperature diagnostics. (a) Blackbody radiation temperature vs magnetic field or radius. The center temperature is given by the emission onset at low magnetic fields. The onset shifts as the density decays. At the cyclotron frequency the temperature is measured at the column radius. (b) Peak electron temperature vs afterglow time. This temperature diagnostics is non-perturbing and sensitive to almost room temperature.

So far the upper hybrid layer has been inferred externally. In the next experiment is made visible by electron heating with a strong "test" wave. Figure 6a shows electron temperature measurements made with the radiometer after the end of a short heating pulse. The electron temperature is locally raised, where the radial position is obtained from the magnetic field dependence (Fig. 5a). Further increase in rf power creates light emission at the upper hybrid layer (Fig. 5b). An axial view of the normally dark afterglow plasma shows a bright ring whose radius varies with frequency or magnetic field. It follows the position of the upper hybrid resonance layer measured without the heating pulse. It provides a visual confirmation that the upper hybrid layer is a localized region of strong absorption and emission.

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Fig. 6. Electron heating at the upper hybrid layer. (a) With a strong incident em wave the electron temperature increases locally at the upper hybrid layer. The heating is measured from the radiation temperature after the end of the heating pulse. (b) With further power increase the heating leads to excitation and ionization. Light emission is observed along the plasma column in the form of a hollow ring whose radius varies with magnetic field. This observation confirms the local absorption and heating at the upper hybrid layer.

It has been pointed out that the upper hybrid frequency is a resonance for both cold plasma waves (extraordinary em waves) and warm plasma modes (electron cyclotron harmonic waves). The latter form radial standing waves in the plasma interior which can be seen in absorption measurements shown in Fig. 7a. Resonant oscillations are seen as the density decays in the afterglow and the number of standing waves changes. The observed mode spacing in density for different magnetic fields has been compared with theory and shown good agreement (Fig. 7b).

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Fig. 7. The upper hybrid frequency is a cold plasma resonance for transverse electromagnetic waves. However, there are also warm plasma electron cyclotron waves which have a resonance at the upper hybrid frequency, thereby allowing mode coupling. These waves propagate radially inward from the resonance layer and form standing waves, known as Buchsbaum-Hasegawa modes. They form oscillations in the absorption coefficient vs afterglow time or density. (b) Dependence of the resonance lines vs density and magnetic field.

References