可靠的毫米波正交干涉仪（70GHz）（三）
3. INTERFEROMETER PERFORMANCE
Figure 3 above shows both interferometer outputs verses time, along with plasma discharge current on the LArge Plasma Device (LAPD) at UCLA [7]. Calibration by movement of the receiving horn, as discussed above, yielded A1 = 37 mV, A2 = 26 mV, VOFF1 = 135 mV, VOFF2 = -25 mV, and (theta)0 = 7 degrees. Using eq. (2) together with a normalized denisty profile measured by a scanned Langmuir probe, eq. (3) was integrated to give a density profile at time t = 4.5 ms as shown in figure 3(b) shown below
In addition the average electron density vs. time, n(t), could be computed. The frequency response of the instrument is limited only by the response of the quadrature mixer, which is DC - 100 MHz in our case.
Since the interferometer responds to phase shift, the accuracy of the instrument is limited by system phase noise. Total system phase noise is the sum of phase fluctuations from the Gunn oscillator and the nonlinear phase response of the quadrature mixer (variation of A1, A2, VOFF1, VOFF2, and (theta)0 with frequency and LO power). The maximum phase noise for the Epsilon-Lambda ELV173 oscillator is of order 0.1 degree. The ELMIX72 mixer is specified to have a phase quadrature error, (theta)0 of order 10 degrees. While (theta)0 can be determined for a given frequency and LO power as discussed above, its variation with frequency and power is not specified by the manufacturer. The user must therefore assume the maximum specified quadrature error in order to determine system accuracy. Taking the maximum error in theta as the difference between (theta)0 = 10 degrees and (theta)0 = 0, using eq. (2) yields a phase error of less than 0.1 degree.
The phase errors introduced by nonlinear changes in IF output amplitudes and offsets (A1, A2, VOFF1, VOFF2) of the mixer are more difficult to determine. No specifications for these variations are given by the manufacturer. However, RF to IF conversion loss is typically specified over the operating band. In the case of the ELMIX72, conversion power loss is given to vary less than 19%. Since P = V**2/R, the IF voltage variation into a constant impedance is therefore less than 9.1%. To determine the variations in IF offset voltages, VIF1 and VIF2 were measured in the 70 GHz ± 200 MHz band. It was found that VOFF1 and VOFF2 both had variations of approximately 5%. For phase error analysis, this was doubled to 10% to give a conservative estimate. Using these offset and amplitude variations in eq. (2), Monte Carlo analysis gives a phase error < ±1.8 degrees.
Summing the phase errors due to oscillator phase noise, mixer quadrature error, and IF voltage amplitude and offset variations gives a total system phase noise < ±0.1 degrees (oscillator) + ±0.1 degree (quadrature error) + ±1.8 degrees (nonlinear IF) < 2 degrees (total). This is a conservative estimate. In the case of the LAPD, with a plasma diameter of 0.50 m and nominal average ne = 1.0x1018 m -3, a two degree phase error corresponds to an error in average density of 0.6%.
The noise level of the LAPD interferometer has been measured to be PN <
-80 dBm, a typical level for laboratory plasma systems. The power at
the receiver horn can be estimated by the radar equation for identical
antennas [8] and including collisional damping by the plasma [9],
(4)
where
G is the antenna gain, c is the speed of light, l is the distance
between horns, f is the microwave frequency, and delta is the energy
damping length. This neglects the lenses which increase the received
power. The collisional damping length is given by
where fpe is the electron plasma frequency, and nei is the electron-ion collision frequency. nei = (2.91x10-12)Zneln LTev-3/2, where Z is the ion mass ratio, L = 12, pi*ne *lD3, and lD = (7.43x10-4)(Tev/ne)1/2 is the Debye length [9]. Using nominal LAPD plasma parameters, f = 70 GHz, ne = 1018 m-3, Tev = 10 eV, and Z = 4 (Helium plasma) gives delta = 7514 m, while for ne = 5x1018 m-3, Tev =
1 eV , delta = 13.6 m. With such a large values for delta, plasma
damping is obviously negligible for a laboratory-size plasma, and it is
reasonable to set e-l/d = 1. Further, taking G = 20 dB, l = 1m, and P0 = 0 dBm gives PR >
-30 dBm. The mixer power conversion loss is roughly 10 dB. The loss in
the receiver horn to mixer waveguide (V band, 3.4 m long) is < 10 dB
(8 dB measured). The mixer signal power, S, is therefore S = PR - 10 dBm - 10 dBm > -50 dBm. Thus the signal to noise ratio, S/N > -50 dBm/-80 dBm = 103.
4. CONCLUSION
A
relatively inexpensive 70 GHz millimeter-wave interferometer has been
constructed and tested on a laboratory plasma. The hardware
configuration (Fig. 1) is textbook simple, and the output unambiguously
yields the phase shift due to plasma in the beam path. Since the
interferometer has a large bandwidth and small phase jitter, it can also
be used to measure line-averaged density perturbations from plasma
waves. The interferometer has been operated reliably on a daily basis,
with no tuning or attention, on the LAPD device for the past two years.
Acknowledgments
This work was supported by the Department of Energy, the Office of Naval Research, and the Cal. Space Institute.
REFERENCES
[1] C.B. Wharton, "Microwave Techniques" in Plasma Diagnostic Techniques (R.H. Huddlestone and S.L. Leonard eds.), Academic Press, New York (1965), pp. 500-502.
[2] C.W. Domier, W.A. Peebles, and N.C. Luhmann, Jr., "Millimeter-wave Interferometer for Measuring Plasma Electron Density", Rev. Sci. Instrum. Vol. 59, no. 8, pp 1588-1590, 1988.
[4] I. Iwasa, H. Koizumi, and T. Suzuki, "Automatic Ultrasonic Measuring System Using Phase-Sensitive Detection", Rev. Sci. Instrum. Vol. 59, no. 2, pp. 356-361, 1988.
[4] Frederick E. Coffield, "A High-Performance Digital Phase Comparator", IEEE Trans. on Instrum. and Meas. Vol. IM-36, no. 3, pp. 717-720, 1987.
[5] J. Brown, Microwave Lenses, John Wiley and Sons, New York (1953) pp. 31-37.
[6] T. Rikitake, Magnetic and Electromagnetic Shielding, D. Reidel Publishing, Tokyo (1987).
[7]
W. Gekelman, H. Pfister, Z. Lucky, J. Bamber, D. Leneman, and J. Maggs,
"Design, Construction, and Properties of the Large Plasma Research
Device - the LAPD at UCLA, Rev. Sci. Instrum., Vol. 62, no. 12, 2875 (1991) pp 2875-2883.
[8] J.L. Eaves and E.K. Ready, eds., Principles of Modern Radar, Van Nostrand Reinhold, New York (1987), p. 11.
[9] W.L. Kruer, The Physics of Laser Plasma Interactions, Addison-Wesley, New York (1987), pp 48-55.
BIOGRAPHIES
Mark Gilmore received
the B.S. degree from Boston University in 1986, and the M.S. degree
from Northeastern University in 1992, both in electrical engineering. He
is currently pursuing the Ph.D. degree in electrical engineering from
the University of California, Los Angeles. From 1986 to 1990 he was
employed by Delphax Systems in Canton, MA. where he worked on the
application of corona discharges to nonimpact printing. His research
interests include plasma diagnostics, plasma sources, and industrial
applications of low temperature plasmas. He enjoys rock climbing,
mountaineering, and music.
Walter Gekelman was
born in New York in 1944. In 1972 he received his doctorate in physics
from Stevens Institute of Technology. He then spent a year as a guest
Scientist at IEN, Torino Italy and has worked at UCLA ever since. He is
currently a Professor in Residence in the Physics Department. Over the
years his work has included development of plasma sources, and studies
of a variety of plasma phenomena (linear and nonlinear lower hybrid
waves, focused resonance cones, ion acoustic waves, whistler waves,
plasma turbulence and magnetic field line reconnection and Alfven
waves). His newest machine, constructed for space plasma related
experiments is ten meters in length and one meter in diameter with a 2.5
kG axial magnetic field. Other specialties include constructions and
programming of data acquisition systems and graphical data analysis. His
hobbies include travel, mountaineering, biking, swimming, and long
distance running.
Keith Kinkead Reiling,
born August 1973 in Fairfield,CA, and received the B.S. in physics with
honors from UCLA in 1995. Currently he is pusuing graduate studies in
biophysics at the University of California, San Francisco. He enjoys
rock climbing, skiing, and the outdoors.
FIGURE CAPTIONS
Fig. 1. Interferometer Circuit.
Fig.
2. Magnetic Shielding: 1) Iron tubing, 18 in. x 0.25 in. thick, 2
layers (innermost mu-metal layer not shown), 2) Gunn oscillator with
heat sink, 3) Directional coupler, 4) lens.
Fig. 3. (a) Interferometer outputs IF1 (Acos(theta)), IF2 (Asin(theta)), and plasma discharge current vs. time. The interferometer signal persists for about 100 ms after the discharge is terminated. The long decay time is due to the low electron temperature (Te < 1.5 eV) after the discharge, and the 10 m length of the device. (b) Interferometer phase vs. time, theta(t). The rapid change at t = 4.6 ms reflects the termination of the discharge.
