New Plasma Diagnosis by Coherence Length Spectroscopy Nopporn Poolyarat a and Young W. Kim b a The Development and Promotion of Science and Technology (DPST), Thailand b Department of Physics, Lehigh University 16 Memorial Dr. East, Bethlehem, PA 18015, USA Abstract A new methodology and instrumentation have been developed for diagnosis of dense high temperature plasmas. In a plasma medium, collision processes shorten the optical coherence length at a given emission wavelength. By measuring the coherence length, the rate of collisions a radiating particle experiences can be determined. A map of the collision rates throughout the plasma can speak volumes about the atomic and thermal state of the plasma. Both the time-integrated and time-resolved interference fringes are obtained 2 5 2 o using emissions due to the transition between ( 32) 2 5 2 o ( 32) 3s 3p P 4p 3s 3p P 7d. We have observed that the coherence length indeed decreases with increasing collision rate, and in addition, as a function of time as a result of cumulative collisions. The coherence length was found to be 4200 ± 800 nm at 50 and torr where the collision frequency is 11-1 2.14 10 s, and 2400 ± 130 nm at 140 torr 11-1 where the collision frequency is 8.13 10 s. We have also discovered that the coherence length varies with the direction of the viewing line of sight into the discharge plasma. The anisotropy results from the non-uniform structure in the discharge current, and this is further investigated by
intentionally deforming the tip of the cathode. A photographic examination of both the cathode and the anode disc confirms the non-axis-symmetric structure of the plasma, which leads to the asymmetry in the plasma, in agreement with the angular dependence of the coherence length. Keywords: Plasma diagnosis; Coherence Length Spectroscopy; 1 Introduction In plasma medium, the collision process shortens the optical coherence length of plasma emission from radiating particles by broadening the emission lines (van Vleck 1945; Shore 1990; Sobel man 1995), thus decreases the coherence time which is conjugated to the spectral line width according to the uncertainty principle as (Hecht 1998) Δυ Δτ 1 (1) where Δυ and Δτ are spectral line width and the coherence time, respectively. The coherence length, l c, is a propagation distance over this coherence time as l c = c Δτ (2) Experimentally, it can be measured from the decay of the visibility of the interference fringes over the path difference of the two arms of the interferometer. 2 Instrumentation Our instrumentation consists of a modified Mach-Zehnder interferometer, a spectrometer, and an imaging camera. The modified Mach-Zehnder interferometer has been designed and constructed in such a way that it can determine the autocorrelation of plasma emission from a single point in plasma as well as the cross correlation from two difference points in plasma. Once the interference fringes are formed, they are
wavelength-resolved by the spectrometer. The wavelength-resolved interference fringes are then recorded by a CCD camera for the determination of coherence length. Figure 1 shows the arrangement of our instrumentation for coherence length spectroscopy. We have used a pulsed discharge plasma for our study. The discharge cell consists of an anode disc with a pinhole and a rod-shaped cathode with a rounded end facing the disc. The electrical breakdown is triggered in synchronization with measurement. The excitation is thus temporally and spatially localized. The plasma is characterized by first directly measuring the ablation loss of the cathode electrode and the energy input into the plasma when the gap is filled with argon. A full Saha calculation (Chen 1984; Chakraborty 1990) is then carried out for the mixture of argon and iron to find the plasma temperature. Table 1 shows the temperature of our plasma at different filled argon pressure. 3 Determination of Coherence Length and Results Both the time-integrated and time-resolved interference fringes are obtained 2 5 2 o using emissions due to the transition between ( 32) 3s 3p P 4p and 2 5 2 o ( 32) 3s 3p P 7d of neutral argon. The time-integrated interference fringes at different argon pressure are shown in Figure 2. The visibility of recorded interference fringes is then determined as a function of optical path difference between the two arms of the interferometer and the coherence length is determined from the exponential decay of the visibility as a function of path difference (Steel 1983) as follows, ( ) ( ) V Δ x = V exp 0 Δ x lc (3)
where V is initial visibility, and Δx is the optical path difference between the two 0 arms of the interferometer. We have observed that the coherence length indeed decreases with increasing collision rate. The coherence length was found to be 4200 ± 800 nm at 50 torr where the collision frequency is 11-1 2.14 10 s, and 2400 ± 130 nm at 140 torr where the 11-1 collision frequency is 8.13 10 s as shown in Figure 3. In addition, the coherence length also decreases as a function of time as a result of cumulative collisions as shown in Figure 4. 4 Anisotropic Distribution of Coherence Length in Discharge Plasma We have also discovered that the coherence length varies with the direction of the viewing line of sight into the discharge plasma. The anisotropy results from the non-uniform structure in the discharge current because the ignition of discharge is done by free electrons which are created by cosmic ray (Hippler 2001). This anisotropic distribution of coherence length is further investigated by intentionally deforming the tip of the cathode. On top of electrode modification, the orientation of the discharge cell has changed by rotating 45 around the discharge axis in both clockwise and counter-clockwise direction for a comparison. The coherence length from both normal cathode and deformed cathode at three different orientations is shown in Figure 5, suggesting that the anisotropic distribution of coherence length from plasma emission is further amplified in case of the deformed cathode. Photos of both the cathode and the anode disc after discharge has been triggered, as shown in Figure 6, have been examined. The results show the evidence of the non-axissymmetric structure of the plasma, which leads to the asymmetry in the plasma. 5 Conclusions
We have developed a new plasma diagnosis by means of coherence length spectroscopy. By measuring the coherence length at a given wavelength of plasma emission, a collision rate, which is related to atomic and thermal state of plasma, can be determined. We have also discovered that the coherence length varies with the direction of the viewing line of sight into the discharge plasma. The anisotropy results from the non-uniform structure in the discharge current, which leads to the asymmetry in the plasma. A photographic examination of both the cathode and the anode disc confirms the non-axis-symmetric structure of the plasma and in agreement with the angular dependence of the coherence length. 5 Acknowledgements The author would like to thank the Development and Promotion of Science and Technology (DPST), Thailand and Department of Physics, Lehigh University for all supports due this work. 6 References Chakraborty, B. (1990). Principles of Plasma Mechanics, 2 nd ed. John-Wiley. New York. Chen, F., (1984). Introduction to plasma physics and controlled fusion. Plenum Press: New York. Hecht, E.(1998). Optics, 3 rd ed. Addison Wesley. Hippler, R., eds. (2001). Low Temperature Plasma Physics: Fundamental Aspects and Applications. Wiley-VCH. Berlin. Kazantsev, S.A. et. al., (1995). Spectropolarmetric Effects Induced by Ion Drift in Plasma. Phys. Scr. 52:572-578
Shore, B.W., (1990). The Theory of Coherent Atomic Excitation. Vol 2, John-Wiley &Sons. Inc.: New York. Sobel man, I.I., L.A. Vainshtein, and E.A. Yukov. (1995). Excitation of Atoms and Broadening of Spectral lines. 2 nd ed. Springer-Verlag: Germany. Steel, W.H. (1983), Interferometry. 2 nd ed. Cambridge University Press. van Vleck, J. H. and Weisskopf, V.F.(1945). Rev. mod. Phys. 17, 227
Figure 1: The arrangement of our instrumentation for coherence length spectroscopy, consists of the modified Mach-Zehnder interferometer, a spectrometer, and a CCD camera. The discharge cell shown in the figure was used as a plasma light source. Discharge and Trigger circuit M6 M5 L3 Discharge Cell L1 Pinhole M3 L2 M4 M7 M2 M1 L4 Vacuum pump and Gas supply Interferometer L5 Spectrometer M8 CCD camera Table 1: Argon pressure, temperature of from Saha calculation, and collision frequency among plasma species. Argon Pressure Collision T (ev) (torr) Frequency ( /s ) 50 1.58 2.74E+11 70 1.49 3.95E+11 90 1.48 5.10E+11 110 1.45 6.30E+11 140 1.41 8.13E+11
Figure 2: Time-integrated interference fringes from plasma emission due to the 2 5 2 o 2 5 2 o transition between 3s 3p ( P 32) 4p and ( 32) difference filled argon pressure. 3s 3p P 7d of neutral argon at Shot#1 Shot#2 Shot#3 Shot#4 50 torr 70 torr 90 torr 110 torr 140 torr
Figure 3: Plot of Coherence Lengths for plasma emission due to the transition 2 5 2 o 2 5 2 o between 3s 3p ( P 32) 4p and ( 32) 3s 3p P 7d of collision frequency among plasma species. of neutral argon as a function 6000 5000 Coherence Length (nm) 4000 3000 2000 1000 0 0 1E+11 2E+11 3E+11 4E+11 5E+11 6E+11 7E+11 8E+11 9E+11 Collision frequency ( /s )
Figure 4: Plot of Time-resolved Coherence Lengths for plasma emission due to the 2 5 2 o 2 5 2 o transition between 3s 3p ( P 32) 4p and ( 32) 140 torr and 300 torr argon. 3s 3p P 7d of neutral argon at 4000 3500 3000 Coherence Length (nm) 2500 2000 1500 1000 140 torr 300 torr 500 0 0 0.5 1 1.5 2 2.5 3 3.5 ( μs) Time delay (us)
Figure 5: Coherence length distribution from discharge plasma emission as function of angle from normal electrode and electrode with indentation; a) when the discharge cell is in its normal orientation, b) when the discharge cell is rotated,and c) when the discharge cell is rotated 45 o counter-clockwise. 45 o clockwise a) b) c) h (nm) Coherence lengt Coherence length (nm) e length (nm) Coherenc 10000 5000 Normal position 0-60 -50-40 -30-20 -10 0 10 20 30 Rotate Right 10000 5000 0-60 -50-40 -30-20 -10 0 10 20 30 Rotate Left 10000 5000 Normal electrode Electrode with 3/16" indentation 0-60 -50-40 -30-20 -10 0 10 20 30 Angle (degree)
Figure 6: Wear pattern on the tip of normal cathode electrode, a), and cathode electrode with indentation, b) after 5 shots with identical condition in argon at 140 torr. Wear pattern on anode disc with normal cathode electrode, c), and cathode electrode with indentation, d), after 5 shots with identical condition in argon at 140 torr. a) b) c) d)