Conductance Peaks at the Cyclotron Harmonics in a Cylindric Plasma Capacitor

These waves are called cyclotron harmonic waves (CHW) because they propagate in passbands adjacent to the harmonics of the cyclotron frequency. Harmonic conductance is related to the loss component of the rf electric field. Therefore, a study of harmonic conduction peaks is directly related to plasma absorption and emission at cyclotron harmonics.

This suggested that the observed harmonic effects could be the result of collective behavior of the plasma electrons. COLD PLASMA THEORY OF THE ALLOWANCE OF A COAXIAL MAGNETO PLASMA CAPACITOR 2.1 The quasi-static approach. Harp, Kino and Pavkovich [20] and Gould (21) have also shown that electron transit time effects occur in the sheath. contribute to the dissipative component of the plasma access.

In Figure 2.4, the model of the plasma capacitor with a vacuum sheath around the center wire (radius= R.) is shown. Because the electric field in the capacitor is everywhere radial to the center wire, only the perpendicular component of the hot plasma dielectric constant is needed to describe the propagation of cyclotron harmonic waves. Mantei showed that the transmitted signal between two probes can be expressed in terms of the plasma admittance between the probes [3].

The primary hot plasma effect of a density profile on the access will be to offset some of the cyclotron harmonic interference effects that depend most.

ANODE

CATHODE

COILS

CAPACITOR

The plasma radial density profile largely depended on the uniformity of emission from the oxide cathode. A closely matched rf connector is connected to the semi-rigid coax 1/4~ inch tube assembly outside the plasma. The minimum transmission if the magnetic field (w /w) is swept marks the location of the upper hybrid fre-.

Langmuir probe measurements yielded similar results and showed that the electron temperature was essentially uniform up to the edge of the discharge. The absorption coefficient is defined as the ratio of the power absorbed in the plasma to the power incident on a matched load. The plasma density was again inferred from the location of the hybrid upper frequency in the transmission experiments.

In the theoretical sketches, the zero sensitivity closely follows the location of the upper hybrid. If a larger value for A were used in the theoretical low-density plots, the magnitude of Strong similarities are also apparent between the experimental conductance (admittance measurement) data in Figure 4.10 and the theoretical plots in Figure 4.11, both in the overall peak shape and peak amplitude as the density varies.

The experimental curves show less structure at the top of the peaks than the theoretical curves. This is attributed to a radial density profile and possibly a slight misalignment of the center wire. Comparison of the experimental values of the admittance measurement with theoretical values for harmonic conductivity peak height as density is varied.

In Figure 4.2, the theoretical peak height increases linearly with density above the minimum point at the upper hybrid frequency. In Figure 4-13 the overall fit of the theoretical curve to the experimental points is much better for the second harmonic than for the third harmonic peak. The theory also predicts the variation with density of the base edge location of the low w/w Hanonic peak.

Figure 4.2 Langmuir probe ion saturation current I+ for various magnet currents IB and discharge currents In

THEORY V/W=.009

2N°HARMONIC

PASS BAND EDGE

In Figure 4.15, the experimental height of the harmonic peak, normalized to the height of the second harmonic for the admittance measurement, is compared with the height variation for the two options. At very high densities, where the dispersion relation is insensitive to density, the spacing of the df fluctuations could be used to determine the electron temperature of the plasma. The theoretical model can explain the changes in the shape of the conductivity peaks as the density changes and can predict the change in peak height with density and harmonic number.

At both low and high density, the height of the conduction peaks varies linearly with the density. The base width of the conduction peaks provides an absolute method of measuring the peak plasma density in a region near the probe. To account for the intensity of the observed radiation, Tanaka et al [8] and Canobbio and Croci [9,24] proposed that fast electrons moving through a thermal plasma excite longitudinal waves (cyclotron 'harmonic waves'), which again coupling to the transverse EM waves observed outside the plasma.

Their results assume that only one value of the wavenumber k contributes to the observed radiation. As will be seen in Section 5.2, the noise output measured at the center wire of the capacitor is related to the conductance of the plasma capacitor in thermal equilibrium. An equivalent circuit for measuring noise on the center wire of a cylindrical capacitor is shown in Figure 5.1, where G.

This hybrid layer gives rise to a finite conductance which contributes to the total conductance of the plasma capacitor in equation 5. The input attenuation of the General Radio 1236 IF amplifier is carefully adjusted so that the output of. In the course of the noise measurements, a way was found both to calibrate the magnetic field axis of the XY recorder and to estimate the effective collision frequency.

The capacitor shields the plasma directly inside it from direct radiation (almost no signal is received when the plasma is turned off), but the rest of the plasma interacts. The density was measured using the location of the UHF in two probe transmission experiments, and using the base width3 · of the noise peaks. Because the center wire of the capacitor was supported by glass fibers with a diameter of 5 times the diameter of 0.005 cm.

Figure 5.1 Equivalent circuit for measuring the noise of the plasma capacitor

EXPER!MENT

Initially, the center wire of the condenser was connected to the radiometer by a semi-rigid coaxial cable 0.085 inch in diameter. Instabilities were found to play a significant role in the intensity of the noise peaks at low magnetic field and low discharge currents. In the following experiments, the effective radius of the probe sheath is reduced by applying a positive bias voltage to the center wire of the capacitor.

Sheath modulation of the noise on the center wire of the capacitor showed the same effects with respect to density and magnetic field. As the plasma density increased and the location of the higher hybrid frequency moved below a harmonic peak, the received noise decreased as the clad size decreased. In both experimental and theoretical results, the height of the conductance peak within a passband was found to be very sensitive to the size of the mantle.

Because the thickness of the sheath region along different parts of the center wire and capacitor wall changes in response to the. Specific attention was given to the behavior of the conductance peaks at the cyclotron harmonics. The difference between the experimental and theoretical spacing of the oscillations was caused by the radial density profile in the capacitor.

Noise oscillations in the center wire of the plasma capacitor were measured with a noise radiometer described in Chapter 5. The shape and height of the noise peaks were found to vary with density in the same way that the theoretical conductance peaks varied. Finally, the role of the wrap around the center wire of the capacitor was investigated.

CHW propagation near the passband edge is very sensitive to the size of the cloak. This modulation of the effective envelope size creates a more diffuse region for launching and detecting harmonic cyclotron waves than assumed in theory. The results of this research have been applied to an investigation of the longitudinal noise oscillations in the capacitor and the effects of shell size on the harmonic wave transmission of cyclotrons.

It is assumed that the motion of plasma electrons is described by the Vlasov equation. Pavkovich, "Numerical Computations Related to the RF Properties of the Plasma Sheath," Stanford University Microwave Laboratory Report no.