Contains reports on two research projects.Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E

Fulghum, S. F., Jr.

George, E. Victor

Pleasance, L. D.

Raff, G. J.

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VI. GASEOUS ELECTRONICSAcademic and Research StaffProf. G. Bekefi Prof. S. C. Brown J. J. McCarthyProf. W. P. Allis Prof. B. L. Wright W. J. MulliganDr. E. V. GeorgeGraduate StudentsS. F. Fulghym, Jr.L. D. PleasanceG. RaffA. TIME-DEPENDENT THRESHOLD CHARACTERISTICS OFPULSED NOBLE ION LASERSStudy of the time-dependent characteristics of the laser output from pulsed Xenonand Argon discharges continues. The 5145 A Ar II transition was found to exhibit laserpulse delay characteristics similar to those of the Xenon lines previously reported.1Figure VI-1 illustrates a delay time of 28 ps between the initiation of the excitation cur-rent pulse (upper trace) and the start of the laser pulse (lower trace) for the 5145 Aline. With increasing values of peak current, the time delay to onset of laser oscil-lation is observed to decrease, as is shown in Fig. VI-2 for two pressures of Argon,again at the 5145 A transition.Figure VI-3 shows the relevant energy levels in singly ionized Argon for both the5145 A and 4880 A lines. It is seen that the two lines share a common lower level which,in turn, depopulates via an extremely fast (T=0.4 ns) vacuum ultraviolet radiativetransition to the ion ground state. Under the assumption that this ultraviolet radiationis not significantly trapped, the time-dependent characteristics of the 5145 A line, to agood approximation, can be expected to involve only the population processes of itsupper level, principally the spontaneous decay rate and the electron-ion destructivecollision cross section. The lack of delay phenomena in the 4880 A transition throughoutthe ranges of pressure and current in which the 5145 A characteristics are exhibited,indicates that the assumption of negligible trapping is justified. To verify theseassumptions regarding the shared lower level, we plan to insert a Littrow prism inplace of one of the end reflectors so that the 4880 A laser line is suppressed. Furtherinformation will be obtained from planned measurements of the spontaneous emission ofthe Argon transitions that terminate on the 4s 2 P 3 / 2 level.Spontaneous emission measurements were taken of several ionized Xenon lines. Ingeneral, the time relationship between current pulse and laser seems to be upheld*This work was supported by the Joint Services Electronics Programs (U. S. Army,U. S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E).QPR No. 983020Fig. VI-I.The 5145 A laser line of Ar II;pressure = 30 mTorr. Uppertrace: current pulse, 10 A/div.Fig. VI-4. Upper trace:Lower, trace:4954 A Xe III10 mV/div.traces from bthe order of t]PRESSURE:O 30 TorrA 22 Torr, I , I , I I i8 10 12 14CURRENT PULSE (A)Fig. VI-2.Time delay T as a function ofpeak discharge current I forthecurrent pulses, 20 A/div.spontaneous emission of theline at 30 mTorr pressure,The order of the emissionottom to top corresponds tohe current traces.3/25/2 4p 2 D0S 3/23/2 4p 4D05/2 4 p7/24880A 5145 A4 2P 1/2------S 3/2731 AL7235 2p01/23p5 2 30 /2 ION GROUND STATEFig. VI-3.Partial energy level diagram for singlyionized Argon.(a) (b)Fig. VI-5. Upper trace: current pulse, 20 A/div. Lowertrace: spontaneous emission, of the 4954 AXe III line at 30 mTorr pressure, during laseroscillation. (b) Same as (a), except that laseroscillation is prevented.(VI. GASEOUS ELECTRONICS)between the current pulse and the spontaneous emission: that is, delays between currentpulse and emission occur for lines that show time-dependent laser characteristics, anddo not occur for lines showing no laser delays. Figure VI-4 illustrates the spontaneousemission of the 4950 A Xe III line as detected through the wall of the plasma tube, for3 values of discharge current. Figure VI-5 compares the emission of the same Xenonline when laser oscillation is allowed (a), and when it is prevented (b). These Xenondata are now being analyzed.G. Raff, S. F. Fulghum, Jr., E. V. GeorgeReferences1. E. V. George and S. F. Fulghum, Jr., "Time-Dependent Threshold Characteristicsof a Pulsed Xenon Laser," Quarterly Progress Report No. 96, Research Laboratoryof Electronics, M. I.T., January 15, 1970, pp. 113-115.B. MICROWAVE DIAGNOSTICS OF HIGH-DENSITYLASER PLASMASAn investigation of the properties of ion laser discharges by means of microwave13 -3cavity techniques has begun. Electron densities of 1013 cm or higher are requiredfor the operation of these lasers. The discharge current necessary to achieve thesehigh densities is held to a minimum by restricting the discharge to a column of a fewmillimeters diameter. Considerable experimental information is available on the rela-tionship of a laser output to gross discharge parameters, such as discharge current,voltage, and gas pressure. Much less information is available on its relationship tothe plasma parameters of such discharges. The predictions of various theoreticalmodels of the excitation mechanism for ion lasers are strongly dependent on theseplasma properties. In particular, the interpretation of power output saturation withincreasing current density depends critically on the assumed relationship between thecurrent density and electron density. It has been shown1 that the TE 0 1 1 mode may beused to probe high-density plasmas. The perturbation expansion used for calculatingthe expected frequency shift breaks down for 2 / ~ 10. The analysis described belowremoves this restriction by considering the detailed variation of the fields in the plasma.The electric field of the TE 0 1 1 mode is azimuthal and satisfies the equation18 8 2r - E + E- k E = 0, (1)rr r r 0 2 0where E = 1 - w/w 2 , and k = Tr/f is the axial wave number.pThe radial variation of E 6 is shown in Fig. VI-6. For wp/W > 1 the field decays intothe plasma with a characteristic length 6 = c/w . The resonant frequency, w, of thepQPR No. 98(VI. GASEOUS ELECTRONICS)CAVITY WALLFig. VI-6. Radial variation of the electric field of theTE 01l mode in the presence of a plasma.mode is determined by the boundary conditions at the cavity wall (E. = 0) and at the edgeof the plasma (continuity of E6 and its radial derivative). The resulting equation forw may be writtenf = g(w) - h(w, Op) = 0, (2)where h(w, w p) is a function of the fields in the plasma, and g(w) is a function of the fieldsbetween the plasma and the cavity wall. For a uniform plasmaI 1 (qb)p qI (qb)andJ) (pb) Y 1 (pa) - J 1 (pa)Yl(pb)g(w) = (4)p(Jo(pb)y (pa)+J (pa)Yo(pb))222 2  2 2 P 2 2where p c 2  and q =- + k >> 1. The resonant frequency calculated for thisc c cmodel is shown in Fig. VI-7 as a function of /w . The resonant frequency in the22 pabsence of plasma is w . As w p /0 increases, the fields are excluded from the plasmaand the resonant frequency approaches a limit, om, which corresponds to a metal postin the cavity.In principle the curve plotted in Fig. VI-7 could be used to convert measured fre-quency shifts into electron density. In practice, however, two further problems mustQPR No. 98(VI. GASEOUS ELECTRONICS)w, =5533 MHzRESONANT FREQUENCYTE011 MODEb = 0.03a= 5520 MHzI I I IFig. VI-7. Resonant frequency of the TE011 mode2 2p /w2 for a uniform plasma.pas a function ofbe considered. First, the fields used to generate Eq. 4 are modified by the presence ofthe discharge tube. Usually such effects are neglected, but in the experiments con-sidered here the volume of the cavity occupied by the cooling liquid and discharge tubeis much larger than that of the plasma. While it is possible to correct Eq. 4 rigorouslyfor the effect of the discharge tube, the following approximate approach is much sim-pler. The function f may be expanded in a Taylor series about the frequency Wm atwhich g(wO) = 0 to giveh(wm , Wp)(W-W M) = p(5)ag( m ) ah(w ,w)aw awFor (wm-Wo)/ m << I the derivative involving the fields outside the plasma may beag(om) -h(WO, 0)m o-h(wm' ph(wO 0) m p+m o -oam 0QPR No. 98I I I I ) I I I I Ii IW2x 10- 3(VI. GASEOUS ELECTRONICS)Equation 6 expresses the frequency shift in terms of the fields in the plasma and a singlemeasurable parameter, wm - o , representing the fields outside the plasma. The fre-quency shift calculated with Eqs. 3 and 6 agrees with the exact solution shown inFig. VI-7, provided the calculated value of (w -m_) is used. Unfortunately, (6) cannotbe expressed as a universal curve and must be solved for each experimental geometry.A second consideration is the effect of radial density gradients on the fields insidethe plasma. Since the fields decay inward from the plasma edge with a characteristic2 2 2  22length 6 = c/p , deviations should be expected for /2 > c2/ 2b2. For the dimensionsin this experiment this gives w /W 20 ZOO. Rigorous calculations of h(w, u ) for a para-p pbolic density distribution shows, however, that for the condition given above the fre-quency shift differs by less than 10%o from the corresponding uniform density case at thesame central density. This is not unexpected, since the fields in the plasma are deter-mined mainly by the high-density regions. While additional calculations are being madeto confirm this result, it is felt that calculations using (3) and (6) can be used withreasonable accuracy up to w / ~ 1000.pPreliminary experimental measurements have been made on the Argon-ion lasershown schematically in Fig. VI-8. The demountable discharge tube is a 2 mm ID quartzcapillary with 12 mm OD cooling jacket. The tube is cooled by a liquid (Dow CorningTO VACUUMSYSTEMCOOLING IN TE011 COOLING OUT / PIRANICAVITY GAUGE+ DIRECTIONALQUARTZ COUPLERDISCHARGE TUBEDIODEISOLATER350 V10 AC- BANDFREQUENCYSWEEPERFig. VI-8. Experimental system.silicone fluid) having low losses at microwave frequencies. The active length of the dis-charge is 40 cm. The microwave cavity is 7. 8 cm in diameter and 5. 4 cm long. TheTE 0 1 1 mode is excited by a loop at a frequency of 5475 MHz with the discharge tube inthe cavity but without a plasma. The frequency shift associated with a metal post theQPR No. 98p = 3 . 9 Torrp = 1.70S p 0.94Fig. VI-9.Frequency shift as a function ofdischarge current in the Argonlaser.I I I I I I I I2 3 4 5 6 7 8DISCHARGE CURRENT (A)ELECTRON DENSITY x 10- 14 / c m3Fig. VI-10.Measured and predicted frequencyshift for a model based on electronneutral collisions.50 100I P (mmho - Torr)VQPR No. 9815 F10 -(VI. GASEOUS ELECTRONICS)size of the plasma is found to be 27. 5 MHz. This is accomplished by filling the dis-charge tube with mercury.The resonant frequency of the cavity was measured as a function of discharge currentfor several pressures. The voltage drop across the discharge tube was also recorded.Pressures were measured with a Pirani gauge. The measured frequency shifts areshown in Fig. VI-9. If the discharge is dominated by electron neutral collisions, theelectron density is related to the discharge parameters by the expression2 I= PP (7)where p is a constant determined by the geometry and electron temperature, and p isthe pressure. The electric field in the plasma has been taken to be proportional to thetotal voltage drop across the discharge. The data of Fig. VI-9, renormalized to testEq. 7 is shown in Fig. VI-10. Also shown is the calculated relationship between thefrequency shift and electron density. This curve was adjusted to fit a single point. Theadjustable parameter is the constant P in (7). The value of P taken from Fig. VI-10was found to be consistent with an electron temperature of a few electron volts. Thedisplacement of the curves probably results from inaccuracies in the measurements ofthe pressure.The main conclusion reached thus far is that it is possible to measure electron den-sities in the range found in ion lasers using microwave cavities. The preliminary datashow no gross deviation from the behavior expected for a discharge dominated by elec-tron neutral collisions.L. D. Pleasance, E. V. GeorgeReferences1. S. J. Buchsbaum and S. C. Brown, Phys. Rev. 106, 196 (1957).QPR No. 98

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