Specmchimica Acka, Vol. 49B, No. 7, pp. 691~7Ct2, 1994 Copyright @ 1994 Elswier S&me Ltd

Printed in Great Britain. Au rights reserved o%4-@47/94 $7.03 + .oo

On the possibility of direct evaluation of ionization rates induced by laser radiation in flames-I. Time-resolved ionization measurements

OLEG I. MAT~EEV* and NICOL~ OMENE~TO Commission of the European Communities, Joint Research Centre, Environment Institute,

21020 Ispra (VA), Italy

(Received 12 November 1993; accepted 28 February 1994)

Abstract-The possibility of direct experimental evaluation of the ionization rates pertinent to a given excitation scheme of atomic species in an air-acetylene flame is here reported for the first time. The method reties on the observation of the rise time of the current pulse induced on the electrode by the negative charge created in the ionization process. The signal collected on the burner, after amplification by a 300 MHz preamplifier, is analyzed by a fast digital storage scope. The resolution is limited on one side by the response time of the preamplifier used (-1.2 ns) and on the other side by the duration of the laser pulse (-15 ns), which then restricts the range of measurable rates to one order of magnitude. The method is applied to the determination of the “effective” ionization rate of the sodium 46 levels (Qn, s/2) reached in a two-step excitation scheme via the 3p levels (*Pin, &. Car e was taken to avoid space charge effects in the flame. Under saturation, the measured values vary from 0.27 to 3.4 GHz. To increase the versatility of the method, a ratioing procedure between two time-resolved ionization signals is also proposed.

1. INTRODUCTION

THE EFFECWE rate of laser enhanced ionization (LEI) or photoionization is an important parameter in the description of the excitation process of atoms in atmospheric- pressure flames and plasmas. Indeed, when atomic fluorescence is used as a means of evaluating the total number density of atomic species, it is essential to estimate the ionization losses occurring during the laser pulse: it is known that such losses can be considerable when the energy difference between the fluorescing level and the ionization continuum is small [l-7]. In the literature, both time-integrated ionization and fluorescence measurements under saturation conditions have been reported and used to obtain collisional and photoionization rates [4-81. However, these rates could not be evaluated directly but rather through the knowledge of other parameters, such as the ionization yield (i.e. the ratio between the ions formed and the atoms present in the interaction volume), the ionization efficiency (i.e. the ratio between the ions formed and the photons absorbed) and the decrease in the fluorescence signal (fluorescence dip). Moreover, in all cases, it is necessary to know the laser photon irradiance (photons per unit time per unit area).

Time-resolved measurements of the current pulse induced by the charges created in the flame and hollow cathode discharges were also both theoretically modeled and experimentally observed [g-14]. With the noticeable exception of ionization measurements of uranium atoms in a hollow cathode lamp [14], the aim of these studies, however, was to elucidate the process of defection of charges, with the assumption that their creation was instantaneous. The purpose of the present work, on the other hand, is to show that the rtie time of the ionization signal bears a direct relationship with the rate of ion production, which can then be evaluated. The application of this method is discussed in the case of sodium atoms in an air-acetylene flame, excited by two excimer laser-pumped dye lasers. The limitations of the proposed method are also discussed, together with a ratioing procedure, which would allow a considerable extension of its versatility.

* On leave from: “Mozaika II”, Moscow, Russia.

691

692 0. I. MAT~EEV and N. OMENE~O

2. THEORETICAL C~NSIDERA~ONS

The following theoretical considerations are not new: they can be found in several papers specifically dealing with LEI processes in flames [l, 9-131 or optogalvanic detection in hollow cathode lamps [14]. Furthermore, it is worth noting that concepts such as those of currents induced by electron motion have been thoroughly illustrated in older literature, especially in connection with ionization chambers and counters [15-181. Here, a simple effort is made to summarize a few relationships that constitute the background of the experiments reported.

2.1. Time behavior of the charge detection process The pictorial representation of the one-dimensional model is identical to that of

Ref. [lo]. The electrode, at potential -V,, is immersed in the flame, and the field, E(x), has its maximum value at the cathode and decreases linearly with distance, x, from it until it reaches a zero value at the edge of the space charge (x = x,). The laser position is indicated as x r. The following relations apply:

E(x) = 6(x, - x) (la)

E(x) = - 2$ 1 - t ( i

-5 I E(x)dx = - v, 0

v,(x) = % = L(eqxe - 4

xe(t)=x.-xsexp(-i) +%exP(-:)

(lb)

From Eqn (2b), the initial conditions are that x, = xL at t = 0. In Eqn (2), /A~ is the electron mobility (cm” V-l s-l), S is the slope of the field and is related to the mobility of the positive ions in the space charge, p+, to the volume ionization rate (cmm3 s-l) of th e fl ame, r,, and to the ratio between the electron charge, e (C), and the permittivity of free space, ec, (CV-l cm-l).

The fraction of total charge induced at the anode by the electron motion depends on the position of the electron, i.e.

qa= :4 0 and the current induced in the circuit will then be given by

(3)

or, by using Eqn 2(c)

i,(t) = ie(t = 0) exp i )

- t (54

Evaluation of ionization rates-1 693

ie(t = 0) = (ie),, = q x+ $ . s

As can be seen from Eqn 5(a), the time behavior of the current induced at the electrode by the moving negative charge, once this charge is created, has essentially no build-up time, i.e. for t = 0, i(t) = i,,. For increasing values of t, the current pulse decays exponentially with a time constant given by 7,. By inserting typical values of the parameters in Eqns (2d) and (2e) (CL+ = 25 cm2 s-l V-l; (e/6) = 1.807 X lob6 V cm; we = 5 X 103 cm2 V-i s-l; and r, = 2 x 1013 cmm3 s-l), T, can be calculated to be 166 ns.

The above derivation has been made under the assumption of an instantaneous establishment of the induced current due to the electron motion. In fact, the electric field drives the laser-produced charges to the respective electrodes according to the well-known equation

dv,(f)= dt

- ; E - &v,(t) .

Here, m is the electron mass and & its collision frequency. Equation (6) can be solved to obtain the following expression for the electron drift velocity:

eE v,(t) = - ~

mj3 [’ - exp(-Pet)1 e

where

or

(74

By using in Eqn (7~) the numerical values for cue (0.5 m2 V-l s-l), m (9.1 X 10m3’ kg) and e (1.6 x lo-l9 C), the time constant for the establishment of the velocity of the charged particle, as given by v, = peE, is only a few picoseconds [9]. r+ can be identified with the “transient response time” of the development of an induced circuit current.

The above considerations are only valid if the Coulombic forces between the separating ions and electrons produced by the laser are much less than those acting on the same charges by the applied electric field. If this is not the case, the pulse shape can be severely distorted by space charge effects [9-131. These are due to the fact that the Coulombic attraction between the ions and electrons produced by the laser retard the separation of the charges owing to the applied field. The typical double structure of the induced anodic current can therefore be explained. In conclusion, given for granted that the above expressions are only applicable to that particular geometry and assumed field distribution, the time behavior of the induced current at the anode is represented by Eqns (5a) and (5b).

The experimentally observed time behavior of the ionization signal will be given by the convolution integral

T(t) = Jf(t - t’) I#‘) dt . (8)

Here, f(t) is the transient response function of the current induction in the

694 0. I. MATVEEV and N. OYENETNJ

(a) Ionization Limit ---________

5s- 5p===zE 4d *D

3/z, 5/L?

(b)

4p-- ?JQ

/

3d= 4s-

Fig. 1. (a) Simplified energy level diagram of sodium showing the transitions used: A1 = 588.995 nm; 1\2 = 568.822 nm. The energy difference between the 4d level and the ionization continuum is 0.85 eV. (b) Oversimplified model of the interaction: Rm and Rm indicate the simulated absorption and emission rates, while A, and Q, are the overall rates due to

spontaneous emission and quenching collisions. Rzi represents the effective ionization rate.

flame-electrode system and $(r) is the response time behavior of the amplifier. Assuming that Ni(t = 0) ion pairs are created at f = 0, the voltage developed in the measuring device will be given by:

V(t) = KNi(t = 0) Kf) * (9)

Clearly, in the preceding discussion, only the detection process was considered, irrespective of how the charges were produced. In a continuously variable ionization process, the number of ion pairs produced and the output voltage will be related to each other by the convolution integral

V(t) = K J Ni(t - t’) 5(t’) dt’ e 00)

In Eqns (9) and (lo), K is an instrumental constant, and Ni(t) represents the ion production rate. If s(t) can be described by a 6 function in comparison with N,(t), the output signal will then accurately describe N,(t).

2.2. Time behavior of the charge production process Two-step LEI of sodium atoms in an air-acetylene flame was chosen as the test

model for the proposed method. A simplified energy level diagram is shown in Fig. 1. Ground state atoms are excited into a 3p state by one dye laser tuned at 588.995 nm, and subsequently into a 4d state by another dye laser, tuned at 568.822 nm. The duration of the interaction was 15 ns for the first step and 20 ns for the second one. A rate equation analysis, based upon unit step excitation function for A1 and AZ, allows one to derive the following relationship [2] (see Fig. l(b)):

Ni(t) ~ G Y,(t) = 1 - exp Rm &i - NT R~+&o+A~+Q20+R2if 014

or, if saturation is reached in both excitation steps

Evaluation of ionization rates-1 695

Yi(t) = 1 - exp (- g Rzi t) (lib)

where g indicates the ratio of the statistical weights of the levels involved and is given by the relation

g= g2

go + g1+ g2 * 014

In the above equations, Yi(t) is the time-dependent ion yield, and an experimental time-resolved ionization waveform would then be described by Eqn (llb). The ion yield then grows with a time constant, 9, given by the reciprocal of the product (g Rzi). If one defines now, for our purposes, the “rise time”, t,, of the signal as the time taken to reach 90% of its final value, it is easy to see that this time is related to the time constant Ti by the relation

t, = 2.37, = 2.3 1 gR2i *

(124

By substituting the values of the statistical weights in Eqn (llc), g is equal to 0.56, and the effective ionization rate, Rzi, can therefore be calculated from the expression

Rzi = ‘+ . r

W)

Clearly, the laser pulses cannot be identified with unit-step and rectangular excitation functions, with zero rise and decay times. However, if both excitation steps are saturated for most of the interaction time, the approximation of a rectangular excitation is closely justified, especially considering that one is interested here only in the rising part of the waveform. On the other hand, it is clear that the interaction (and therefore the ionization process) will stop with the ending of the laser pulses, and with the depopulation of the excited level, which then implies that no information whatsoever will be obtained if the rise time of the ionization waveform equals the duration of the interaction. Conversely, when the rise time is less than the interaction time, it is possible to conclude that a unity ion yield LY effectively achieved.

The above considerations suggest a natural extension of the method to the measurements of ionization rates smaller than the reciprocal of the duration of the laser pulse, T,. The procedure consists of ratioing two ionization signals measured at a time tm (f,,, < T,) for two waveforms (here labelled 1 and 2). Let this ratio be denoted by

VlW -- Wm) = V,&) (13)

where V,(a) and V,(t,) are the voltages observed on the oscilloscope at time t,,, for the two waveforms. Assume now that waveform 1 is obtained under conditions of unity ion yield, so that its ionization rate, ‘Rzi, can be directfy evaluated from Eqn (12a). In this case, it is easy to see from Eqn (llb) that the ionization rate for the second waveform will be given by the expression

2& = + exp(-&Rzi tm

I V(a) * (14)

Since lRzi and V(a) are known, ‘Rzi, can be calculated. It is clear that the same conditions under which Eqn (llb) was derived must still hold here for both waveforms.

6% 0. I. MATWJEV and N. OMENETID

LEI-chamber \

0.7 MR 0.7 M$2 \ 21 kV@-w+pA& ::

1~0.01 pF

DIGITAL SCOPE

I

PRE-AMP

/ 50 I2 i

Fig. 2. Experimental scheme for monitored at the burner with a

the measurement of the LEI signal. The induced current is fast preamplifier and a digital scope. C, indicates the stray capacitance of the circuit.

3. EXPERIMENTAL

The experimental set-up used in the present work has been described in detail in previous publications [2, 4] (see Fig. 2). Briefly, two dye lasers are simultaneously pumped by an excimer laser (XeCl). The output beams are directed into an air-acetylene flame, supported by a 10 cm slot burner, in which a sodium solution is aspirated. An electrode immersed in the flame is negatively biased up to -2 kV. The distance between the laser beams and the electrode is kept constant at 1.5 cm. The.signal induced at the burner was measured with a 50 fl load and a fast preamplifier (300 MHz bandwidth, Model SR 445, Stanford Res. Corp., Sunnyvale, U.S.A.). The amplified LEI waveform was displayed on a fast digitizer (Model 602A, Tektronix, Beaverton, U.S.A.) with a 2 GHz bandwidth. The overall response time of the detection circuit was 1.2 ns and was limited by preamplifier response time. Special care was devoted to minimize radio frequency interferences. Both laser pulses were observed with a Microchannel Plate Photomultiplier: the duration of the first excitation pulse (hi) was 15 ns while the second (A*) was 20 ns. Both pulses were characterized by a rise time of about 3 ns and by an energy of l-4 mJ/pulse.

In order to test the time-resolving capabilities of our system, the ionization signal was recorded while varying the time coincidence of the two beams. This was accomplished by sliding the mirror used for directing AZ in the flame along an optical rail, thus allowing a time displacement of 3.1 and 2.1 ns, respectively. As can be seen in Fig. 3, the difference in the rise time of the three waveforms is clearly evident. From an expanded view of the waveforms (lower part of the figure) it can be concluded that differences of about 100 ps in the rise times could’ still be detected, assuming the same signal-to-noise ratio.

4. RESULTS AND DISCUSSION

As discussed in the theoretical section, the derivation of Eqn (5) was made under the assumption of negligible space charge effects in the flame. In fact, their presence would distort not only the .decay time of the induced current pulse but also its build- up time, which is just what is needed for the proposed method. In order to evaluate the importance of such effects, several ionization waveforms were recorded at different sodium concentrations and at variable laser irradiances. In the last case, the output power of the first laser (A,) was kept constant while the second beam (A,) was attenuated with neutral density filters. The results are summarized in Figs 4-7.

The retarding effect caused by the mutual influence of the excess ions and electrons created by the laser is clearly evident in the shapes shown in Fig. 4. Here, the sodium concentration was kept constant (0.5 &ml) and the laser power (AZ) was decreased up to 2000 times. These shapes conform (apart from the much better signal-to-noise ratio obtained here) to those experimentally observed in previous studies [9] and theoretically predicted [lo], even though it would be impossible to claim a quantitative agreement, owing to the unknown distribution of the electric field in the flame. It is clear, however, that the rise time. becomes an ill-defined quantity here, since one cannot identify the true maximum value of the signal with that experimentally observed.

Evaluation of ionization rates-1 697

Time, 5 ns/div

Time, 1 ns/div

Fig. 3. Oscilloscope tracings showing the build-up time of three ionization waveforms (negative pulse) when the time coincidence between the two laser pulses is varied. (a) Af = +2.1 ns; (b) At = 0; (c) At = -3.1 ns. The time scale in the lower part of the figure has been expanded

5 times.

Time, 50 ns/div

Fig. 4. Ionization waveforms obtained at different laser irradiances. Na concentration = 0.5 llg/ ml. (a) & at full power: 63 kW/cm*; (b) & + ND 0.6; (c) A2 + ND 1.3; (d) & + ND 2.3; (e) A, + ND 3.3. The voltage was set at -1500 V. The distance between the electrode and the burner was 15 mm and that between the electrode and the lasers was 5 mm. Both lasers

had a diameter of 5 mm.

698 0. I. MMVEEV and N. OYENETKJ

v t Time, 50 ns/div

Fig. 5. Ionization waveforms obtained at different concentrations of sodium and full laser irradiance (63 kW/cm2): (a) unseeded flame; (b) distilled water; (c) Na = 0.1 pghnl; (d) Na

= 0.5 &ml.

Time, 50 ns/div

Fig. 6. Ionization waveforms obtained at different concentrations of sodium and at a laser irradiance decreased 2ooO times (32 W/c@: (a) Na = 0.1 &ml; (b) Na =I 0.5 @ml; (c) Na

= 3 &ml.

Similar results were obtained by keeping the laser irradiance constant while varying the sodium concentration (Figs 5-7).

From an inspection of the waveforms reported in Figs 5 and 6, one can derive the following conclusions:

(i) because of the high sensitivity of the LEI technique for sodium, a signal is easily observed when only distilled water is nebulized into the flame and even for an unseeded flame; and

(ii) when the ionization rate is low (i.e. when the irradiance of the second laser is decreased 2000 times) the signal waveform does not seem to be affected by space charge even from a sodium concentration of 3 CLg/ml.

Evaluation of ionization rates-1 699

t

Time, 10 ns/div

Fig. 7. Rise times of the ionization waveforms obtained at different sodium concentrations and laser irradiances: (a) Na = 0.1 &ml; A2 = full power: 63 kW/cm2; (b) Na = 3 &ml, A2 + ND 3.3. The slight difference in the decaying part of the signal is believed to be due to different electrical field distributions in the two cases. The rise time of both signals is 14 ns.

Figure 7 summarizes the above finding, by showing the rise time of two undistorted ionization waveforms obtained at different sodium concentrations and at different laser irradiances. Here, the rise time of 14 ns indicates clearly that the rate of ionization is close to the reciprocal of the duration of the laser pulse. As a consequence, the calculated rate (3 X lo8 s-l) is close to the lower limit of the method (2.7 X 108 s-l). It is interesting to note that, if Eqn (llb) is satisfied, the above rate would correspond to an ion yield of 92%.

It is clear that there is a conflicting requirement between the necessity of avoiding space charge effects and still having a high ionization rate, which must exceed the reciprocal of the duration of the laser pulse in order to be directly observed. Therefore, it was decided to work with higher laser n-radiances and without sodium, i.e. either by nebulizing distilled water or with the unseeded flame. Moreover, the irradiance of the second laser was increased to 1.6 MW/cnS by focusing the beam in the middle of the flame to a 2 mm diameter. The signal waveforms obtained in these conditions are shown in the upper part of Fig. 8, where one can see that, despite the presence of radio frequency noise, the signal-to-noise ratio is still remarkably good. Figure 8 (lower part) shows that the rise time of both waveforms is identical and equal to 6.8 ns, which corresponds to an ionization rate of 6 x lo8 s-l. This rate ensures that a 100% ion yield is reached during an interaction time of 15 ns: this important result indicates that one single time-resolved measurement of the rise time of the ionization signal can provide the most important parameter of the process. This evaluation procedure is certainly more direct than those described in the literature [4, 7, 191.

In addition, it is important to stress that in this case the photon irradiance of the second laser (1.9 x 1P5 crnm2 s-l) is such that direct photoionization of the sodium atoms excited in the 4d 2D3n, 5,2 level is significant if the magnitude of the ionization cross section is of the order of lo-r7 cm2. Indeed, assuming that photoionization dominates over collisional ionization of the D level, the cross section calculated from the rise time of Fig. 8 is 3 x lo-l7 cm2. This value is in good agreement with previously published data [13].

Finally, Fig. 9 collects three different signals illustrating the capabilities and the limitations of the proposed method. In fact, it can be seen that the dynamic range of our direct ionization rate measurements is restricted to about one order of magnitude

700 0. I. MATVEEV and N. OMENETKJ

Time, 50 ns/div

Time, 5 ns/div

Fig. 8. The upper part shows ionization waveforms obtained with the laser irradiance (AZ) increased to 1.6 MW/cmZ. The voltage at the electrode was set here at -2000 V: (a) unseeded flame; (b) distilled water. The lower part shows rise times of the two waveforms. The time

axis has been expanded 10 times.

(curves a and c). The limiting factors are on one side the response time of the preamplifier and on the other side the duration of the laser pulse. The precision of the measurement is limited by the radio frequency noise generated by the excimer laser firing.

5. CONCLUSIONS

It has been shown that the use of fast electronics allows one to resolve, with sufficient signal-to-noise ratio, the onset of the ionization process of sodium atoms in an air-acetylene flame. In this way, the rise time of the waveform is directly related (via the ionization time constant) to the effective rate of ionization of the final level reached by laser excitation. This only holds if space charge effects in the flame are absent, since their presence will cause a distortion not only in the decaying part of the signal, but also in its build-up.

Evaluation of ionization rates-1 701

Time, 5 ns/div

Fig. 9. Signal rise times observed for three limiting ionization rates: (a) Na = 0.5 cLg/ml, laser unfocused, AZ + ND 3.3; (b) water, laser unfocused, laser irradiance (hz) = 0.4 MW/cm2; (c)

water, laser focused, laser irradiance (a) = 1.6 MW/cm*.

The proposed approach has the advantage of providing directly, in one single measurement, the effective rate of ionization and therefore the ion yield of the process. On the other hand, however, if short-pulse lasers are used, the range of measurable rates is rather restricted. Of course, the simplified model assumed for sodium, with both transitions saturated, must retain its validity also if other elements are considered.

As a final consideration, another attractive possibility of the proposed approach seems worthy of being stressed. In fact, if (i) the duration of the laser pulse is shorter than the average time taken in the collkional ionization process, and (ii) the distance between the electrode and the laser is less than the average distance travelled by the electron as a result of its drift velocity in the flame, then the photoionization process would be distinguishable from the collisional process in one single, time-resolved ionization waveform. This possibility would be of particular usefulness in evaluating the background signal, due to either the matrix or the flame, and caused by non- selective multiphoton ionization. It is important to emphasize, however, that this is valid only if the presence of the matrix does not substantially modify the electrical field distribution between the electrodes: this simple approach would then fail in the presence of an alkaline matrix.

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