ACOUSTIC RESONANCES IN HIGH FREQUENCY OPERATED LOW WATTAGE METAL HALIDE LAMPS

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1 Philips J. Res. 38, ,1983 R 1074 ACOUSTC RESONANCES N HGH FREQUENCY OPERATED LOW WATTAGE METAL HALDE LAMPS by J. W. DENNEMAN Philips Lighting Division, 5600 MD Eindhoven, The Netherlands Abstract The operation of high pressure gas discharge lamps at current frequencies higher than mains frequency can be complicated by acoustic resonance phenomena. n this paper an experimental set-up will be described for the determination of the resonance frequencies of small metal halide lamps. Experiments have been carried out in spherically shaped lamps. The influences of discharge bulb radius, mercury filling, metal halide addition and lamp power on resonance behaviour have been studied. A simplified calculation of the resonance frequencies, using a constant "effective velocity of sound" will be given. The calculated resonance frequencies are in good agreement with the experimentally measured values. 1. ntroduetion When high pressure gas discharge lamps are operated at current frequencies higher than mains frequency their operation can be complicated by standing pressure waves called acoustic resonances. These acoustic resonances can lead to changes in arc position, to colour changes or to unstable arcs, which sometimes causes the lamp to extinguish. Acoustic resonances occur when lamp power varies at specific frequencies or within specific frequency bands, corresponding to the acoustic resonance frequencies of the discharge envelope. The study of acoustic resonance phenomena is necessary when electronic ballasting systems are considered. Electronic control gears ar~ attractive, especially for small gas discharge lamps, because of their small size and weight and their good properties in stabilizing lamp power. These electronic ballasting systems are optimal at frequencies between 20 and about 1 MHz, a frequency range in which problems with acoustic resonances mayalso be expected. Electronic ballasts often deliver a non-sinusoidal lamp current, leading to higher-order harmonics in the lamp power, which can also cause instabilities. Philips Journalof Research Vol.38 Nos 4/

2 J. W. Denneman oj b) Fig. 1. Photographs of spherical mercury lamp in stable operation a) and with deformed are position b) due to acoustic resonances at 54.0 khz. (R = 3 mm; 1.9 mg Hg; P = 25 W.) n fig. la a spherical mercury lamp is shown with internal diameter of 6 mm, operating stable at a frequency of 50 Hz and a lamp power of 25 W. n fig. lb the same lamp is shown operated at a power frequency of 54 khz. n this case the are position is deformed, caused by acoustic resonances. n figs 2a and b the same is shown for a spherical metal halide lamp, containing sodium, scandium and thorium iodides. The lamp has also been operated at 25 W. The deformed are position due to acoustic resonances occurs in this case at a power frequency of 43.8 khz. Due to the deformed are position also the condensated iodide has been displaced on the inner bulb wall. t is the object of this paper to give some insight into the frequencies at which acoustic resonances occur in low wattage metal halide lamps, especially in spherically shaped discharge bulbs. Mercury discharges and low wattage metal halide lamps were studied. Some remarks will be made on the differences between acoustic resonance phenomena in high pressure sodium lamps and low wattage metal halide lamps as reported in literature. After that, an explanation will be given of our experimental set-up. A simplified calculation will be performed, in order to determine the resonance frequencies of spherical discharge envelopes. n this calculation the concept of "effective velocity of sound" will be introduced. A comparison between calculations and experiments will be given. t will be shown what effects a change in mercury pressure or discharge bulb radius has on resonance behaviour. 264 Phtlips Journalof Research Vol.38 Nos 4/5 1983

3 Acoustic resonances in highjrequency operated low wattage metal halide lamps aj b) Fig. 2. Photographs of spherical metal halide lamp in stable operation a) and with deformed arc position b) due to acoustic resonances at 43.8 khz. (R = 3 mm; 4.6 mg Hg; 2.2 mg Nal, Sela, Thl.; P = 25 W.) 2. Literature n 1978 Witting published data about acoustic resonances in cylindrical high pressure sodium discharges 1). He found relatively narrow specific frequency regions in which are instabilities occurred. These frequencies corresponded closely with the theoretical resonance frequencies for the standing pressure waves in a cylindrical geometry. n small metal-halide lamps, however, are instabilities occur in broad frequency bands, as has been reported by Davenport and Petti on the recent les conference in Atlanta 2). Because of the large width of the instability bands the resonance frequencies could not be determined. Thus it was not possible to compare calculated resonance frequencies with experimental results. 3. Experimental set-up With our experimental set-up it is possible to determine the resonance frequencies of low wattage metal halide lamps, even if the are instabilities normally occur in broad frequency bands. For that purpose the lamps are operated on direct current. A high frequency sinusoidal current is superimposed on this current. See fig. 3. n order to avoid cataphoretic effects in the lamps, the polarity of the direct current is reversed with a low frequency. This, however, has hardly any influence on the lamp power frequency spectrum. The resulting current wave form is illustrated in the diagram of fig. 3. The amplitude and Philips Juurnal of Research Vol. 38 Nos 4/

4 J. W. Denneman 10ms Fig. 3. Lamp current wave form with superimposed HF sinusoidal current. frequency of the superimposed current can be varied. The amplitude will be expressed as a power modulation depth, varying between 0 and Total lamp power, however, is kept constant, in order to make sure that vapour pressures and gas temperatures do not vary during the experiments. n fig. 4 experimental results are shown for a spherical Na, Se, Th-iodide discharge (94.5 molojona, 4.4 molojoscls, 1.1 molojoth 4 ). Lamp power was 25 W. The frequencies at which instabilities occur are given for various values of the modulation depth of the superimposed high frequency power. When modulation depth is zero, no instabilities occur at all of course. At a low modulation depth, the resonance frequencies can be determined. When modulation depth increases, the instabilities take place in broader frequency bands, until a large overlap of resonance modes manifests itself. These wide instability bands cojrespond very well to the measurements of Davenport and Petti 2) ~ ;S 40 á},! : : ' "0, c, h 1 ' 1, 1 :g : 1 / A /,.g 20 ' ~ ", r/ ", 1'. 1 " ~ t ~ f, J ::J, " 11. '',, V,, ': ", 1,,,,' ' 11 " Ol ool_ lo ro~0-----k---5~ ~20~0~-----2~50 - power frequency (khz) Fig. 4. Are instabilities at different frequencies as a function of modulation depth. Spherical metal halide lamp. (R = 3 mm; 2.2 mg Na, Scls, Th4; 4.6 mg Hg.) The are instabilities occur between the broken lines. 266 Phillps Journal ot Research Vol.38 Nos 4/5 1983

5 Acoustic resonances in highfrequency operated low wattage metal halide lamps 4. Theory A simplified theory will be used for the calculation of the acoustic resonance frequencies of spherical geometries:' A periodic fluctuation of the lamp power results in a gas pressure fluctuation of the same frequency. f this frequency corresponds with the acoustic resonance frequency belonging to the discharge envelope, standing pressure waves can be built up. The standing pressure waves inside the discharge envelope are usually assumed to'be the cause of the are instabilities. n order to calculate the resonance frequencies, the pressure-wave eq. (1) has to be solved, (1) n this equation p is gas pressure which depends on radial coordinate r and on time t. The velocity of sound c, which in fact is the propagation velocity of the pressure wave, can be expressed as a function of gas temperature T. This is shown in eq. (2) V = C Cp RgasT Cv M. (2) This equation is true for the case that the buffer gas mercury can be treated as an ideal gas. t is seen that c is proportional to the square root of T, which in turn is a function of the sphere radius. n our calculation, an :'effective velocity of sound" ë will be used, which is constant across the lamp volume. Equation (1) can now be solved analytically, because c is taken constant. The solution is shown in eq. (3), expressed in spherical coordinates 3) p = cos (m rp) P::'(cos f))jn C ;f r) exp (- 2n ift), (3) P::' is the associated Legendre function of the mth kind and of order n; i; is the spherical Bessel function of the first kind and of order n. n order to find the resonance frequencies, the boundary condition implying that particle velocity near and perpendicular to the wall is zero must be used. This condition is mathematically expressed in eq. (4) ap = 0 f R ar or r =. (4) Phllips Journalof Research Vol. 38 Nos 4/

6 J. W. Denneman The resulting resonance frequencies ins are given in formula (5) ans ë 1, ns = 2nR' (5) where ë is the effective velocity of sound, R the sphere radius and ans the Slh zero of ajn/ar, the first derivative of the spherical Bessel function, of the first kind and of order n. n table the first twenty values of a ns are listed. 5. Determination of the effective velocity of sound c n table can be seen that the lowest resonance frequency unequal zero belongs to the au-mode. ans is the Slh zero of ajn/ar, TABLE the first derivative of the spherical Bessel function of the first kind and of order n. ns ans Phillps Journalof Research Vol.38 Nos 4/5 1983

7 Acoustic resonances in highjrequency operated low wattage metal halide lamps n relation (6) the theoretical expression for the lowest resonance frequency is given ë f11-2nr' (6) By substituting the experimentally found lowest resonance frequency in this equation we can find a value for the effective velocity of sound ê. f, for example, in the Na, Sc, Th-odide discharge lamp, shown in figs 2 and 4 the lamp power is 25 W, the lowest resonance frequency has been measured to be 43.8 khz. Together with R = 3 mm and formula (6), this results in an effective velocity of sound of 398 ms". Together with eq. (2) an effective "acoustic" gas temperature of 2300 K is obtained. See table l. 6. Comparison of theory with experiments Once knowing the effective velocity of sound, the higher-order resonance frequencies can be calculated by means of eq. (5). n fig. 5 the resonance frequencies of the spherical metal halide lamp are shown once more. The calculated frequencies for the higher-order resonance modes are indicated in the diagram. t may be concluded that there is a fairly close correspondence between measured and calculated frequencies; especially for the lowest frequencies, because these can be classified rather accurately. Some higher-order resonance modes, however, have not been found experimentally. They are indicated below the diagram. --. ~ ~ '"0 c 11 1 e t ', ' ~ ~ 21, '' " ',' ),: V, 02 12~ 31 1," 1 " h,/,, ~ 1 1: A,~",, 11 ", 'T,, 4 03,f' 71 / 1 / ~ 04 V (411 (511 (611 (131 (231 - power frequency (khz) 42 Fig. 5. Arc instabilities at different frequencies as a function of modulation depth together with calculated resonance frequencies. Spherical metal halide lamp. (R = 3 mm; 2.2 mg Na, Scls, Th.; 4.6 mg Hg.) Philips Journal of Research Vol. 38 Nos 4/

8 J. W. Denneman n the theory presented here a constant effective velocity of sound has been used. n fact, however, ë is a function of gas temperature, which varies across the lamp volume. t is hardly possible to take into account the variation of gas temperature as a function of bulb radius, because the temperature profiles are not known for most lamps. Furthermore, it has been shown that a good agreement between calculated and experimentally determined resonance frequencies is obtained, provided that a correct value for ë was used. 7. n8uence of sphere radius, mercury pressure and lamp power n fig. 6 the effective velocity of sound is given as a function of the mercury mass density in the lamps for three different bulb radius values. A higher mercury density results in a higher mercury pressure inside the lamp. t is seen that an increased mercury charge or bulb radius results in a lower effective velocity of sound and consequently in lower resonance frequencies. ë (ms") 500.~2mm 450,,, 3mm ~ mm 4mm 3500~---lLO----2~ ~0----4~0--~50-9 (pg mm- 3 ) Fig. 6. Effective velocity of sound if as a function of mercury mass density {! and sphere radius R (P = 25 W). pure Hg; Na, Seis, Th Phlllps Journolof Researcf Vol.38 Nos 4/5 1983

9 Acoustic resonances in highjrequency operated low wattage metal halide lamps The decrease of the effective velocity of sound is caused by a reduction of the effective gas temperature. When a metal halide is added to the mercury discharge, indicated by the square mark in the diagram, the effective velocity of sound is decreased as compared with the pure mercury discharge. This is caused by a decrease of the effective gas temperature. By the use of these values for the effective velocity of sound, the higher-order resonance frequencies can be calculated for these lamps, which again results in a good agreement with experiments. n the table l, the lowest resonance frequency, the effective velocity of sound and the effective gas temperature are given for three lamp power values for a Na, Sc, Th-iodide discharge. The table shows an increase of ë and of r as a function of lamp power, as may be expected. TABLE l nfluence of lamp power P on effective velocity of sound ë and effective temperature r pew) jn (khz) ë (ms ") rek) Spherical Na. Sela. Th4 lamp; R = 3 mm. n fig. 7 the resonance frequencies and the minimum modulation depths needed to cause the instabilities are given for two mercury lamps with effective pressures of 10 and 25 at. The lamp with the higher mercury pressure already shows instabilities at lower values of the modulation depth, which means that the instabilities can be excited more easily. The violence of the instabilities also increases when higher gas pressures are used. Another effect of higher gas pressure is that more acoustic resonance modes can be found. Modes that could not experimentally be found in lamps with lower gas pressures can be detected in lamps with higher gas pressures. Thesé extra modes have been indicated in fig. 7, namely the 51, 03, 71, 41 and 14 modes. When the sphere radius is increased, while lamp power is kept constant, experiments also show that acoustic resonances are excited at lower values of the modulation depth. Consequently, it is easier to cause are instabilities in wider than in narrower discharge bulbs. n wider bulbs, more resonance modes can also be found compared with narrower discharge bulbs. The addition of Na, Sc, Th-iodide to the mercury discharge also has the effect that instabilities are excited more easily. Phillps Journal of Research Vol. 38 Nos 4/

10 J. W. Denneman 8o ~ 20 PHg """OAt ~ ",,, /, / / ', /, / "/ / ---" '", / v / O~------~5~ ~m~0~ ~0~ ~0~----~250 - power frequency (khz) Fig. 7. Minimum modulation depth needed to excite an acoustic instability for two mercury pressures 10 resp. 25 at (R = 4 mm). 8; Conclusions We can wind up with the following conclusions. 1. The resonance frequencies can be determined by high frequency modulation ofthe lamp power. This is also possible for lamps which show a large overlap of resonance modes, when they are operated at a high frequency AC-current. 2. Resonance frequencies in sphericallamps calculated with the aid of a constant effective velocity of sound value correspond satisfactorily to those found in experiments. 3. The value for the effective velocity of sound can be determined from the lowest resonance frequency. 4. ncreasing the mercury pressure or increasing the bulb radius decreases the resonance frequencies. The instabilities can be excited more easily and more resonance modes have been.found. The addition of Na, Sc, Th-iodide to the pure mercury discharge also decreases the resonance frequencies and intensifies the instabilities. REFERENCES 1) H. L. Witting; J. Appl. Phys, 49, 2680 (1978). 2) J. M. Davenport and R. J. Petti; les conference Atlanta (1982).. 3) P. M. Morse and H. Feshbach; Methods of Theoretical Physics, Chapter 11, Mcöraw Hill, New York (1953). 272 Phillps Journol of Research Vol.38 Nos 4/5 1983