Stationary flow conditions in pulsed supersonic beams Wolfgang Christen Citation: The Journal of Chemical Physics 139, 154202 (2013); doi: 10.1063/1.4824155 View online: http://dx.doi.org/10.1063/1.4824155 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/139/15?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Infrared absorption imaging of 2D supersonic jet expansions: Free expansion, cluster formation, and shock wave patterns J. Chem. Phys. 139, 024201 (2013); 10.1063/1.4812772 Role of coherent structures in supersonic impinging jetsa) Phys. Fluids 25, 076101 (2013); 10.1063/1.4811401 Flow structure and acoustics of supersonic jets from conical convergent-divergent nozzles Phys. Fluids 23, 116102 (2011); 10.1063/1.3657824 Shock-induced flow resonance in supersonic jets of complex geometry Phys. Fluids 11, 692 (1999); 10.1063/1.869940 Compressibility effects in supersonic transverse injection flowfields Phys. Fluids 9, 1448 (1997); 10.1063/1.869257
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THE JOURNAL OF CHEMICAL PHYSICS 139, 154202 (2013)
Stationary flow conditions in pulsed supersonic beams Wolfgang Christena) Institut für Chemie, Humboldt-Universität zu Berlin, Brook-Taylor-Straße 2, 12489 Berlin, Germany
(Received 15 August 2013; accepted 20 September 2013; published online 17 October 2013) We describe a generally applicable method for the experimental determination of stationary flow conditions in pulsed supersonic beams, utilizing time-resolved electron induced fluorescence measurements of high pressure jet expansions of helium. The detection of ultraviolet photons from electronically excited helium emitted very close to the nozzle exit images the valve opening behavior—with the decided advantage that a photon signal is not affected by beam-skimmer and beam-residual gas interactions; it thus allows to conclusively determine those operation parameters of a pulsed valve that yield complete opening. The studies reveal that a “flat-top” signal, indicating constant density and commonly considered as experimental criterion for continuous flow, is insufficient. Moreover, translational temperature and mean terminal flow velocity turn out to be significantly more sensitive in testing for the equivalent behavior of a continuous nozzle source. Based on the widely distributed Even-Lavie valve we demonstrate that, in principle, it is possible to achieve quasi-continuous flow conditions even with fast-acting valves; however, the two prerequisites are a minimum pulse duration that is much longer than standard practice and previous estimates, and a suitable tagging of the appropriate beam segment. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4824155] I. INTRODUCTION
In many research areas supersonic molecular beams are indispensable, including spectroscopy and cluster science. Owing to the decreased duty cycle, pulsed jet sources1–108 enable beam parameters that are difficult to achieve with a continuous expansion. In particular, they facilitate substantially increased source densities, allowing for the convenient generation of supersonic beams from compressed gases, supercritical fluids, and liquids. Besides accessible source pressure, pulsed supersonic beams are also advantageous in terms of sample consumption, signal intensity, cluster growth, and translational cooling. As a drawback, it is a good deal of work to characterize their properties: a pulsed valve does not only modulate the number density, it also affects beam temperature and the distributions of cluster size and velocity. Hence, at “short” durations of the jet pulse the issue of quasi-continuous, stationary flow conditions becomes increasingly important, because a “steady state” is mandatory every time that meaningful values of the beam temperature, mean cluster size, and flow velocity are required: owing to the complex collision dynamics, current model calculations are based on the assumption of a continuous, steady flow. Accordingly, the comparison of experimental results with theoretical models requires a sufficiently long and non-throttled opening of the valve. Too short pulse durations do not allow for the evolution of stationary flow and thus may lead to wrong estimates of beam properties. Because the large particle number in supercritical fluid jet expansions prohibits numerical simulations, the value of “sufficiently long” has to be determined experimentally for each particular case. Thus, the most relevant characteristic of a pulsed valve with respect to reliable and predictable beam properties is the a) Electronic mail: [email protected]
0021-9606/2013/139(15)/154202/11/$30.00
time required to reach stationary flow conditions; this time depends on the electrical and mechanical characteristics of the particular valve but also on the working fluid. Moreover, both the operation of the valve and the viscosity of the fluid are greatly influenced by source pressure and temperature. Because for many experiments the precise knowledge of energy and velocity of the particles under investigation is required, recognizing the relevant valve parameters and ensuring welldefined flow properties is of vital importance: calculations of the mean terminal flow velocity and estimates of the mean cluster size using scaling laws109–115 are based on continuous flow. Surprisingly, despite the wide-spread use of fast-acting valves with ultrashort pulse durations, see the comprehensive roundup in Table I, this issue is rarely addressed. Instead, all too often it is referred to two simple estimates resting on ideal gas and ideal valve behavior.116, 117 Supposing that for a specific combination of working fluid, source conditions, and operating parameters of the pulsed valve the essentially equivalent behavior of a continuous nozzle source can be achieved, these quasi-static properties prevail in a restricted section of the jet pulse only. In consequence, the characteristic properties of the hydrodynamic flow have to be determined all along the jet pulse in order to localize the appropriate segment of the beam. A technique suitable to cope with these challenges is presented. The article outline is as follows: After a concise review of the experimental configuration a versatile method for determining the actual opening behavior of pulsed supersonic jet sources is introduced (Sec. III). Extending this approach, electronic tagging of particle bunches is used as a powerful tool to analyze the beam properties (density, velocity distribution) with high spatio-temporal resolution. These timeresolved “beam scans” permit to localize that beam segment where quasi-static properties prevail (Sec. IV). Beam scans
139, 154202-1
© 2013 AIP Publishing LLC
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J. Chem. Phys. 139, 154202 (2013)
TABLE I. Compilation of fast-acting valves (pulse duration of δtv < 100 μs) for the generation of pulsed supersonic beams. Operation mechanism Cantilever piezo
Electromagnetic plunger
Lorentz force
Magnet plus Lorentz force
Pulse width δtv
Reference
>7 μs 12–40 μs 60 μs
98 96 100
>10 μs 10–100 μs 20 μs 20–30 μs 30–100 μs 30–150 μs 50–75 μs 70 μs 80 μs
76 18, 59 89 95 79 83 48 14, 60 34
>10 μs >20 μs 50 μs 55 μs
8 108 51, 69 26
17–45 μs
32
are also utilized for the systematic analysis of beam properties as a function of the opening time of the pulsed valve. This makes it possible to obtain the valve settings required for the essentially equivalent behavior of a continuous nozzle source (Sec. V).
FIG. 1. Timing scheme for the spatio-temporal characterization of pulsed supersonic beams. A digital delay/pulse generator provides a precisely timed series of control pulses, t0 and t1 ; t1 ≥ t0 . Electronically tagging the expanding jet provides a temporal resolution of few hundred nanoseconds and is realized by switching the voltage applied to the output lens of the electron source. Energetic photons and particles impacting on the detector surface generate stop events; these are counted in the exact relation to their arrival time using an ultrafast time digitizer.
uum chamber is always less than 1 × 10−4 Pa even for a source pressure of 10 MPa, in the second chamber below 1 × 10−6 Pa, and in the third chamber below 7 × 10−8 Pa.
II. EXPERIMENTAL CONFIGURATION
III. OPENING CHARACTERISTICS OF THE PULSED VALVE
Details of the experimental configuration have been described earlier.118–121 In short, it consists of a differentially pumped ultrahigh vacuum set-up with a customer-specific version of the Even-Lavie pulsed valve. The valve control122 provides two complementary means for adjusting the opening behavior, namely, the maximum solenoid current, Iv , and the pulse width of the valve control signal, δt0 . Directly attached to the valve body is a shielded electron source;118 its output electrode voltage is pulsed, allowing for a time-resolved tagging of the expanding He (purity of 99.9999%) few millimeters in front of the nozzle exit: electrons with a kinetic energy of approximately 120 eV are directed perpendicular to the propagation axis of the supersonic jet; the interaction region has been optimized by means of the electron source lens voltages. The nozzle in this study has a diameter of 0.1 mm and is of parabolic shape,121 providing an improved collimation of the expanding flow.96 The valve is mounted on a xyz precision translation stage and aligned to the beam axis, which is defined by two 50.8 mm long nickel skimmers with diameters of 3.0 mm (Beam Dynamics). The distance between valve and first skimmer is 233 mm, the skimmerskimmer distance amounts to 209 mm. After the flight distance of about 3.5 m an electrically shielded detector, comprising a multichannel plate-scintillator-photomultiplier assembly, registers energetic photons and particles with a time resolution of approximately 1 ns, see the schematic diagram of Fig. 1. Due to the deliberately low repetition frequency of the valve of fv = 2.0 Hz the working pressure in the first vac-
As illustrated schematically in Fig. 2, a control signal of rectangular pulse shape and pulse width of δt0 applied at the valve driver gives reason to expect the corresponding opening time of the valve, provided that this duration is defined via the full width at half maximum (FWHM) of the pulse. Caused by the finite speed of the mechanical movement of the plunger the period allowing for constant flow is shorter. In particular, it is obvious that this type of valve cannot achieve steady-state conditions for pulses that are shorter than the rise time of the valve opening, i.e., δtv ≤ 10 μs. Similar restrictions apply to all pulsed valves, especially at ultrashort opening times, cf. Table I. The actual opening characteristics of a valve can be investigated experimentally, making use of ultraviolet photons that are emitted from excited particles right in front of the valve and registered time-resolved by a suitable detector. For effective lifetimes of the electronically excited states of a few nanoseconds this photon signal represents the convolution of the opening function of the valve according to Fig. 2(b) with the local velocity distribution of the expanding particles. The velocity broadening is minimized for helium expanding from a high source pressure, and a short distance between nozzle exit and electronic excitation of a few millimeters only. As an example, the photon signals corresponding to control pulse durations of δt0 = 16 μs and of δt0 = 18 μs are depicted in Fig. 3. Both rise time and fall time are in accordance with the expected value of 10 μs, whereas the peak widths are considerably larger. This discrepancy is attributed to an effectively
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J. Chem. Phys. 139, 154202 (2013)
(a)
(a)
(b) (b)
FIG. 2. Illustration of the trapezoidal opening characteristics of the pulsed valve, resulting from a rectangular voltage pulse of the delay/pulse generator. (a) Valve control signal at the time of t0 , featuring a pulse width of δt0 = 16.0 μs. (b) After some intrinsic delay the plunger of the valve starts moving at the time of t0 . With an approximate speed of 10 ms−1 it reaches its full stroke of 0.1 mm after 10 μs. Although the FWHM of the valve opening, δtv , is supposed to match the pulse width of the control signal, δt0 , constant flow is possible for a maximum of δtv = 6 μs only.
longer opening time of the valve, δtv > δt0 ; δtv is also affected by the maximum solenoid current, Iv , set at the valve driver. Also note that the amplitude of the photon signal in Fig. 3(b) is significantly larger. Evidently, “constant flow” or constant density does not imply that the valve is fully open. The contribution of the velocity broadening of the expanding jet to the pulse width of the photon signal, δtp , can be judged by varying the distance between valve and electron source, lve , see Fig. 4(b): the variation in photon pulse width yields an estimated effective opening time of the valve of δtv ≈ 0.85 × δtp . Also, the systematic study of the dependence δtp (δt0 , Iv ) reveals the full opening of the valve; according to this analysis a valve opening time of δtv 40 μs is required for saturating the photon signal, see Fig. 4(d); for shorter times the flow is throttled. In conclusion, for short pulse durations the mechanical response of the valve is almost as expected, with one notable exception: the true opening time of the valve, δtv , may be appreciably longer than the control pulse applied at the valve
FIG. 3. Ultraviolet photons resulting from a pulsed, electronically excited He beam at a source pressure of P0 = 9.60 MPa and a source temperature of T0 = 319.0 K, providing an ultrafast in situ characterization of the jet. Operating conditions are a duration of the valve control signal of δt0 = 16.0 μs (a) and of δt0 = 18.0 μs (b), respectively. The distance between nozzle exit and electron source is lve ≈ 6 mm. The gate control pulses of the valve driver and of the electron source are switched on concurrently. The switch-on time of the electron beam is δt1 = 4 ms, resulting in a quasi-continuous excitation of the entire jet pulse. The estimated focal diameter of the electron beam of 0.5 mm contributes less than 0.3 μs to the photon pulse width (FWHM) of δtp = 30 μs (a) and 43 μs (b), respectively. The solid lines visualize the fit of an exponential power function, which is also known as generalized Gaussian distribution.
driver, δt0 ; for the most part this prolongation is attributed to the self-inductance of the solenoid. The collision-induced fluorescence signal permits to determine the operating parameters required for an entirely open valve, with the decided advantage that the detected photon signal is not affected by beam-skimmer and beam-residual gas interactions. Although a “flat-top” signal indicates constant particle density it is important to note that this does neither imply a fully open valve, cf. Fig. 3(a), nor stationary flow, see Sec. V. IV. VARIATION OF CHARACTERISTIC BEAM PROPERTIES WITHIN THE JET PULSE
In consequence of the finite opening time of the pulsed valve, the number density in the jet initially increases and
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J. Chem. Phys. 139, 154202 (2013)
(a)
(b)
(c)
(d)
FIG. 4. Opening period of the pulsed valve, investigated using the optical emission from electronically excited helium at source conditions of P0 = 9.60 MPa and T0 = 319.0 K. The photon peak width, δtp , is obtained as the FWHM of a fitted exponential power function, cf. Fig. 3. (a) Output current pulse of the valve driver, showing a delayed response with respect to the control pulse of the delay/pulse generator, see Fig. 2(a), with t0 − t0 < 2 μs. The maximum of the solenoid current, Iv , depends both on the setting of the current control knob of the valve driver and on the pulse duration of the valve control signal, δt0 . The reproducibility of δt0 is better than 100 ns and of Iv better than 1 A. (b) Influence of the duration of the valve control signal, δt0 , on the photon peak width, for distances between valve exit and electron source of lve ≈ 6 mm and of lve ≈ 11 mm, respectively: the velocity distribution of the jet results in an additional broadening of the photon pulse at longer distances. Extrapolation to zero distance yields an estimate for the “true” opening time of the valve. (c) Influence of the maximum valve current, Iv , on the photon peak width, for durations of the valve control signal of δt0 = 17.0 μs, δt0 = 21.0 μs, and δt0 = 25.0 μs, respectively, and a distance of lve ≈ 11 mm. The variation of both valve current and control pulse duration permits effective opening times in a large range, from 10 μs to 100 μs. (d) Standardization of the offset corrected photon signal to its FWHM clearly reveals “saturation,” i.e., above a δt0 -dependent threshold value higher valve currents increase the duration but not the overall intensity of the photon peak. This is interpreted as an indication of the full opening of the valve and is observed for photon peak widths of δtp 47 μs.
shortly afterwards decreases again. This yields a strong variation of the number of particle-particle collisions. As a result, also the velocity distribution changes, influencing, first and foremost, translational cooling and cluster formation. This time dependence of beam properties can be analyzed in detail by the systematic variation of the time delay between the gate control pulses of the electron source and of the valve driver, t1 − t0 , see Figs. 1 and 5(a). In this manner thin “slices” of the jet pulse can be electronically tagged,124 allowing to study the time evolution of characteristic beam properties with a temporal resolution of few hundred nanoseconds only, improving earlier work22, 125, 126 by orders of magnitude. For the supersonic expansion of He at P0 = 9.60 MPa and T0 = 319.0 K and a switch-on duration of the electron beam
of 0.3 μs FWHM, the estimated diameter of the electron beam of ≤0.5 mm contributes negligibly to the spatial extent of the excited jet, see Fig. 5(b). That matters because all recorded arrival time distributions are inherently broadened by this instrument function; its experimental determination is depicted in Fig. 5(c). By way of illustration Fig. 6 displays 46 arrival time spectra of an electronically tagged helium beam at source conditions of P0 = 9.60 MPa and T0 = 319.0 K as a function of the excitation delay, t1 − t0 ; all other parameters are kept constant. Accordingly, this method permits the spatio-temporal analysis of the beam profile; at short delay times the leading particles of the jet pulse are probed. The temporal variation of beam properties can be analyzed in terms of signal amplitude, intensity, mean arrival
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Wolfgang Christen
J. Chem. Phys. 139, 154202 (2013)
(a)
(b)
(c)
FIG. 5. (a) Illustration of the experimental approach of a time-resolved characterization of beam properties within a bunch of particles (blue area), using a pulsed electron beam for tagging a localized, specific portion of the jet at the time of t1 . The time resolution of a few hundred nanoseconds permits monitoring the time evolution of beam temperature and velocity within the jet pulse with unprecedented granularity. (b) Detail view of the instrument function of the electronic labeling, resulting from the convolution of a 0.5 mm long focal excitation region of the supersonic jet with the trapezoidal switching function of the electron beam. For the flow velocity of helium of 1.8 × 103 ms−1 the axial extent of the excited molecular beam slice corresponds to a pulse width of 280 ns. The voltage pulse applied at the output electrode of the electron source features a FWHM of 300 ns and a rise time of 100 ns. In consequence, for these parameters the excitation width, δt1 , is not affected by the focal spot size of the electron beam. The center position of this pulse defines the time origin of time-of-flight spectra123 with exceptional accuracy. (c) Detection of ultraviolet photons from a pulsed, electronically excited helium beam at a source pressure of P0 = 9.60 MPa and a source temperature of T0 = 319.0 K. Acquisition parameters are 54 000 sweeps and an interval width of 8 ns.
time, peak width, peak shape, etc., as is depicted in Fig. 7. Here, a robust and model-free statistical data evaluation127 is used deliberately, allowing to eliminate all possible artifacts from fitting procedures; accordingly, median and interquartile range (IQR) serve to characterize arrival time and peak width, respectively. Obviously, the depicted parameter values change substantially, and only a rather narrow region located close to the center of the jet pulse, at time delays of 51–54 μs, appears approximately uniform. However, even the observation of a trapezoidal, “flat-top” pulse shape does not guarantee continuous flow conditions; it may not even be indicative of a fully open valve. First, for such short opening times a “uniform” particle density is difficult to judge because this judgment is based on a few data points only. Second, besides density, other properties such as temperature and velocity of the particles in the beam are just as important and must be considered as well: for example, in the depicted spectra no region with constant flight times exists. But even if a portion of the jet features (approximately) uniform parameter values, as is indicated by the shaded areas of Figs. 7(a) and 7(d), this does not imply that these regions represent characteristics of the equivalent continuous beam: the opening time of the valve still may be too short to allow for steady hydrodynamic flow, see Sec. V. The difference in meaning of Figs. 7(a) and 7(b) is that the maximum signal amplitude of the spectra, (a), is affected by the velocity distribution of the beam. In comparison, the signal intensity, (b), i.e., the summation of all events within a certain region of interest, is expected to make up for the broadening of the jet pulse during its flight to the detector. Assuming an undisturbed and lossless propagation, this intensity distribution reflects the actual extent of the molecular beam pulse at the place of its electronic excitation, few millimeters in front of the nozzle.
The analysis of the peak width as a measure of translational temperature reveals the smallest values for time delays of 50–57 μs, see Fig. 7(d). In this central section of the beam translational cooling is most efficient. Fig. 7(c) confirms that at shorter delay times preferentially faster particles are excited and recorded at the time-of-flight detector, whereas predominantly slower particles are probed at longer delay times. V. STEADY-STATE FLOW CONDITIONS IN PULSED BEAMS
Addressing the pivotal issue of the minimum opening time required to achieve quasi-static conditions of supersonic flow raises the question how those parameter values that correspond to a continuous beam can be recognized in an experiment. Certainly, both a uniform density and velocity distribution within a section of the jet pulse are required for this, but also the peak widths of the arrival time spectra need to be minimized. This is because the velocity distribution of a pulsed jet is broader than that of a continuous expansion under equivalent conditions if the time of unrestricted flow is too short.8 Accordingly, a systematic variation of the pulse duration of the valve opening is essential. The results shown in Fig. 8 reveal that at the given setting of the maximum valve current the valve does not open at all for gate control pulses of δt0 < 12 μs. On the other hand, considering amplitude and rising edge of these distributions, the valve appears to be completely open for gate control pulses of δt0 ≥ 18 μs, corresponding to δtv 40 μs. This result is in good agreement with the analysis of the photon signal, cf. Fig. 4(d). Although the width of the jet density distributions depicted in Fig. 8 linearly increases with the pulse duration
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Wolfgang Christen
J. Chem. Phys. 139, 154202 (2013)
A suitable alternative is the analysis of the velocity distribution, see Fig. 9 for results of the peak width. The energy resolution of the TOF spectra corresponds to a relative kinetic energy of 5 × 10−7 eV, whereas the binding energy of helium dimers, 4 He2 , is only 1 × 10−7 eV.128–130 Thus the formation of small helium clusters, verified mass spectrometrically, should not have any effect on the peak widths observed. Interestingly, the examination of Fig. 9 shows that a fully open valve (at δt0 = 18 μs) does not yet yield the minimum peak width; for an optimized translational cooling even longer pulse durations are required. This extension of the beam analysis to other properties reveals that the definition of stationary flow is not unique but strongly depends on the chosen criterion. Obviously, density, translational temperature, and flow velocity provide rather different sensitivities, see Fig. 10: whereas a control pulse duration of δt0 ≥ 18 μs is sufficiently long to allow for a constant mean amplitude of the photon signal and also for the maximum amplitude of TOF spectra of metastable helium, the maximum intensity of the beam is reached only later. Likewise, the peak widths as the measure of parallel beam temperature attain their minimum value only for δt0 ≥ 21 μs; a beam segment with constant time-of-flight is found only for δt0 ≥ 23 μs. These control pulse widths correspond to opening times of the valve of δtv ≈ 58 μs, δtv ≈ 65 μs, and δtv ≈ 80 μs, respectively. Interestingly, the minimum opening time of the pulsed valve required to achieve a constant flow velocity is twice as large as the time needed for complete opening; phrased differently, after the valve is open it takes another 40 μs to reach uniform flow velocities within the central section of the jet pulse. Although the stated numeric values are specific for helium at these conditions of source pressure and temperature, two universal conclusions are possible: First, continuous flow should be linked to constant flow velocity rather than to constant density. Second, these opening times are much longer than is standard practice for fast acting valves.
FIG. 6. Arrival time distributions of an electronically tagged He beam as a function of the time delay between the valve trigger at the time of t0 and the gate control pulse of the electron source at the time of t1 . The electron beam is switched on for the term of δt1 = 300 ns. For each spectrum 600 sweeps are acquired; interval width is 128 ns.
of the valve control signal, as is expected, their symmetry is increasingly distorted for pulse durations exceeding δt0 = 16 μs. For gate control signals with δt0 ≥ 19 μs the distortions result both in a diminished amplitude and an apparently reduced FWHM of these distributions. At still longer opening times of the valve, not shown here, a shoulder emerges at the large delay time side of the distributions. A detailed peak shape analysis reveals that at elevated source densities neither amplitude nor intensity of time-of-flight (TOF) spectra are a reliable measure of beam density, for they are easily distorted by beam scattering, cluster formation, and throttled flow. Hence, they are unsuitable for determining continuous hydrodynamic flow conditions.
VI. APPLICATIONS AND SIDE EFFECTS
Because the effective opening times of the Even-Lavie valve comprise a broad range, from δtv = 10 μs to 100 μs, the expansion can last long enough to yield pulsed beams with characteristics matching those of continuous beams. One fundamental application where quasi-static flow conditions are mandatory is the experimental determination of the mean terminal flow velocity120, 121, 131 of supersonic beams and its comparison with model calculations.132–135 By way of illustration Fig. 11 presents the mean time-of-flight of tagged helium in a wide range of source temperatures, from T0 = 228.0 K to 410.0 K. Pulse durations of the control signal reach from δt0 = 23 μs to 26 μs and are long enough to ascertain an extended section of the beam with uniform flight times. In the highlighted region TOF spectra feature the narrowest peak widths, thus providing both constant velocity and maximized cooling. Accordingly, the observed temperature dependence agrees fairly good with the theoretical expectation.
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Wolfgang Christen
J. Chem. Phys. 139, 154202 (2013)
(a)
(b)
(c)
(d)
FIG. 7. Robust and model-free statistical evaluation of the unprocessed arrival time spectra of Fig. 6. (a) Spectrum amplitude, expressed as the maximum number of registered events per acquisition interval, and standardized to the number of sweeps. (b) Overall signal intensity, representing all counts of a spectrum within a given time range (from 1.3 ms to 2.0 ms, compare Fig. 6), standardized to the number of sweeps. (c) Median of arrival times. For electronically tagged particles the arrival time, t2 , differs from the time-of-flight, t = t2 − t1 . (d) Interquartile range (IQR) of arrival times as a measure of peak width. The shaded areas indicate regions of approximately constant density (a) and translational temperature (d), respectively.
Because source temperature affects the spring constant of the valve and thus the effective opening time, δtv , the pulse width of the valve control signal, δt0 , is adjusted to provide comparable expansion conditions. In the experiments of Fig. 11 a photon signal of δtp = 100 μs FWHM is used as
a reference; a variation in source temperature of ±100 K requires a change in δt0 of approximately ∓1.9 μs. Unfortunately, pulsed valves tend to bounce the larger the valve current and the longer the pulse duration. This characteristic is illustrated in Fig. 12 for different control signals,
FIG. 8. Amplitudes of tagged helium spectra as a function of the pulse width of the valve control signal, δt0 , and of the time delay between triggering the gate control signals of the electron source and of the valve driver, t1 − t0 . Source conditions are P0 = 9.60 MPa and T0 = 319.0 K.
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J. Chem. Phys. 139, 154202 (2013)
FIG. 9. Interquartile ranges of the arrival time spectra of electronically tagged helium as robust measures of their peak widths, plotted as a function of the pulse width of the valve control signal, δt0 , and of the time delay between triggering the gate control signals of the electron source and of the valve driver, t1 − t0 .
(a)
(b)
(c)
FIG. 10. Performance of the pulsed valve in terms of (a) maximum intensity, (b) minimum width of the arrival-time distribution, and (c) constancy of the mean TOF as a function of the control pulse width of the valve, δt0 . For these graphs the temporal evolution of TOF spectra of an electronically tagged helium beam at source conditions of P0 = 9.60 MPa and T0 = 319.0 K has been analyzed in analogy to Fig. 7; here, however, the properties refer to the entire jet pulse. For steady state conditions the change of the time-of-flight with the time delay between the gate control pulses of the valve driver and of the electron source, t1 − t0 , should be zero. The arrows indicate the minimum control pulse width needed for achieving steady-state conditions with respect to the particular parameter: for constant density, δtv ≥ 58 μs, for minimum peak width, δtv ≥ 65 μs, and for constant time-of-flight, δtv ≥ 80 μs.
(a)
(b)
FIG. 11. Temperature dependence of the mean flight time of electronically tagged helium at a source pressure of P0 = 9.60 MPa. (a) “Beam scan” for source temperatures from T0 = 228.0 K to T0 = 410.0 K. Quasi-static flow with respect to constant time-of-flight and minimum spread is observed for a time delay between the gate control pulses of the valve driver and of the electron source of t1 − t0 = 90–110 μs (shaded area). (b) Mean time-of-flight of particles in the quasi-static flow regime as a function of the source temperature.
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J. Chem. Phys. 139, 154202 (2013)
FIG. 12. Illustration of valve bouncing, observed for a pulsed beam of metastable helium via the emission of ultraviolet photons. For this analysis the gate control pulses of the valve driver and of the electron source are switched on simultaneously, with a quasi-continuous switch-on time of the electron beam of 4 ms. Source conditions are a pressure of P0 = 9.60 MPa and a temperature of T0 = 319.0 K. The number of repeated openings increases with the opening time of the valve.
making use of a long lasting electronic excitation. For short gate control signals of the valve of 12–14 μs individual jet pulses, i.e., without bouncing, can be generated. However, for these valve parameters no stationary flow is possible; also, adiabatic cooling is very inefficient. On the other hand, “long” pulse durations involve multiple valve bounces and require some kind of tagging, be it by electronic, optical, or mechanical means, in order to select the appropriate beam segment.136 VII. SUMMARY
Two complementary experimental methods for the detailed in situ analysis of the opening and closing behavior of pulsed supersonic jet sources are introduced. In particular, they permit to determine those operating conditions that yield a jet with properties equivalent to a continuous expansion. This accomplishment is of major importance because quasi-stationary flow is mandatory whenever the mean terminal flow velocity or the mean cluster size shall be calculated. The first diagnostic tool is the detection of the electroninduced fluorescence of a high-pressure helium expansion. Because the electron beam excitation is quasi-continuous and in close vicinity to the pulsed valve the photon signal reflects the opening properties of the valve. A decided advantage of this technique is that photons are not affected by beamskimmer and beam-residual gas interactions. The second method rests on the analysis of arrival time distributions of tagged particles. In this case the electron beam is pulsed and features an ultrashort switch-on time, exciting a very narrow segment of the expanding jet. This permits characterizing the evolution of beam properties, i.e., particle density, translational temperature, and mean flow velocity with a time resolution that is better by two orders of magnitude as compared to the fastest ionization gauges. Performing this beam scan analysis as a function of the pulse duration of the valve allows to identify quasi-continuous flow conditions. Actually one of the most important results of this work is that it is feasible to achieve quasi-continuous flow using fast-
acting jet sources—even though eligible operating parameters are rather different from “standard” settings. It is also learned that constant density is reached much faster than maximized cooling and constant velocity. In addition, the photoemission of excited particles close to the valve reveals that “flat-top” signals neither signify a fully open valve nor stationary flow conditions. It also turns out that the true opening time of fast-acting valves may be significantly longer than the control pulse applied to the valve driver. For the Even-Lavie valve studied this prolongation is attributed to the mechanical response of the plunger and the self-inductance of the solenoid. This shows that even for a very advanced valve the assumption of ideal valve behavior116, 117 is not justified—for He at P0 = 9.60 MPa and T0 = 319.0 K it may take about 40 μs to reach complete opening. At long opening times the valve may bounce and nozzle flow is throttled; the latter results in an effectively smaller nozzle diameter, a fact that has to be considered if scaling laws for determining the mean cluster size are used.
ACKNOWLEDGMENTS
The author is much obliged to Professor Klaus Rademann for his support and Bo-Gaun Chen for lab assistance. This work has been generously supported by a grant of the Deutsche Forschungsgemeinschaft (CH262/5). 1 O.
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THE JOURNAL OF CHEMICAL PHYSICS 139, 154202 (2013)
Stationary flow conditions in pulsed supersonic beams Wolfgang Christena) Institut für Chemie, Humboldt-Universität zu Berlin, Brook-Taylor-Straße 2, 12489 Berlin, Germany
(Received 15 August 2013; accepted 20 September 2013; published online 17 October 2013) We describe a generally applicable method for the experimental determination of stationary flow conditions in pulsed supersonic beams, utilizing time-resolved electron induced fluorescence measurements of high pressure jet expansions of helium. The detection of ultraviolet photons from electronically excited helium emitted very close to the nozzle exit images the valve opening behavior—with the decided advantage that a photon signal is not affected by beam-skimmer and beam-residual gas interactions; it thus allows to conclusively determine those operation parameters of a pulsed valve that yield complete opening. The studies reveal that a “flat-top” signal, indicating constant density and commonly considered as experimental criterion for continuous flow, is insufficient. Moreover, translational temperature and mean terminal flow velocity turn out to be significantly more sensitive in testing for the equivalent behavior of a continuous nozzle source. Based on the widely distributed Even-Lavie valve we demonstrate that, in principle, it is possible to achieve quasi-continuous flow conditions even with fast-acting valves; however, the two prerequisites are a minimum pulse duration that is much longer than standard practice and previous estimates, and a suitable tagging of the appropriate beam segment. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4824155] I. INTRODUCTION
In many research areas supersonic molecular beams are indispensable, including spectroscopy and cluster science. Owing to the decreased duty cycle, pulsed jet sources1–108 enable beam parameters that are difficult to achieve with a continuous expansion. In particular, they facilitate substantially increased source densities, allowing for the convenient generation of supersonic beams from compressed gases, supercritical fluids, and liquids. Besides accessible source pressure, pulsed supersonic beams are also advantageous in terms of sample consumption, signal intensity, cluster growth, and translational cooling. As a drawback, it is a good deal of work to characterize their properties: a pulsed valve does not only modulate the number density, it also affects beam temperature and the distributions of cluster size and velocity. Hence, at “short” durations of the jet pulse the issue of quasi-continuous, stationary flow conditions becomes increasingly important, because a “steady state” is mandatory every time that meaningful values of the beam temperature, mean cluster size, and flow velocity are required: owing to the complex collision dynamics, current model calculations are based on the assumption of a continuous, steady flow. Accordingly, the comparison of experimental results with theoretical models requires a sufficiently long and non-throttled opening of the valve. Too short pulse durations do not allow for the evolution of stationary flow and thus may lead to wrong estimates of beam properties. Because the large particle number in supercritical fluid jet expansions prohibits numerical simulations, the value of “sufficiently long” has to be determined experimentally for each particular case. Thus, the most relevant characteristic of a pulsed valve with respect to reliable and predictable beam properties is the a) Electronic mail: [email protected]
0021-9606/2013/139(15)/154202/11/$30.00
time required to reach stationary flow conditions; this time depends on the electrical and mechanical characteristics of the particular valve but also on the working fluid. Moreover, both the operation of the valve and the viscosity of the fluid are greatly influenced by source pressure and temperature. Because for many experiments the precise knowledge of energy and velocity of the particles under investigation is required, recognizing the relevant valve parameters and ensuring welldefined flow properties is of vital importance: calculations of the mean terminal flow velocity and estimates of the mean cluster size using scaling laws109–115 are based on continuous flow. Surprisingly, despite the wide-spread use of fast-acting valves with ultrashort pulse durations, see the comprehensive roundup in Table I, this issue is rarely addressed. Instead, all too often it is referred to two simple estimates resting on ideal gas and ideal valve behavior.116, 117 Supposing that for a specific combination of working fluid, source conditions, and operating parameters of the pulsed valve the essentially equivalent behavior of a continuous nozzle source can be achieved, these quasi-static properties prevail in a restricted section of the jet pulse only. In consequence, the characteristic properties of the hydrodynamic flow have to be determined all along the jet pulse in order to localize the appropriate segment of the beam. A technique suitable to cope with these challenges is presented. The article outline is as follows: After a concise review of the experimental configuration a versatile method for determining the actual opening behavior of pulsed supersonic jet sources is introduced (Sec. III). Extending this approach, electronic tagging of particle bunches is used as a powerful tool to analyze the beam properties (density, velocity distribution) with high spatio-temporal resolution. These timeresolved “beam scans” permit to localize that beam segment where quasi-static properties prevail (Sec. IV). Beam scans
139, 154202-1
© 2013 AIP Publishing LLC
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154202-2
Wolfgang Christen
J. Chem. Phys. 139, 154202 (2013)
TABLE I. Compilation of fast-acting valves (pulse duration of δtv < 100 μs) for the generation of pulsed supersonic beams. Operation mechanism Cantilever piezo
Electromagnetic plunger
Lorentz force
Magnet plus Lorentz force
Pulse width δtv
Reference
>7 μs 12–40 μs 60 μs
98 96 100
>10 μs 10–100 μs 20 μs 20–30 μs 30–100 μs 30–150 μs 50–75 μs 70 μs 80 μs
76 18, 59 89 95 79 83 48 14, 60 34
>10 μs >20 μs 50 μs 55 μs
8 108 51, 69 26
17–45 μs
32
are also utilized for the systematic analysis of beam properties as a function of the opening time of the pulsed valve. This makes it possible to obtain the valve settings required for the essentially equivalent behavior of a continuous nozzle source (Sec. V).
FIG. 1. Timing scheme for the spatio-temporal characterization of pulsed supersonic beams. A digital delay/pulse generator provides a precisely timed series of control pulses, t0 and t1 ; t1 ≥ t0 . Electronically tagging the expanding jet provides a temporal resolution of few hundred nanoseconds and is realized by switching the voltage applied to the output lens of the electron source. Energetic photons and particles impacting on the detector surface generate stop events; these are counted in the exact relation to their arrival time using an ultrafast time digitizer.
uum chamber is always less than 1 × 10−4 Pa even for a source pressure of 10 MPa, in the second chamber below 1 × 10−6 Pa, and in the third chamber below 7 × 10−8 Pa.
II. EXPERIMENTAL CONFIGURATION
III. OPENING CHARACTERISTICS OF THE PULSED VALVE
Details of the experimental configuration have been described earlier.118–121 In short, it consists of a differentially pumped ultrahigh vacuum set-up with a customer-specific version of the Even-Lavie pulsed valve. The valve control122 provides two complementary means for adjusting the opening behavior, namely, the maximum solenoid current, Iv , and the pulse width of the valve control signal, δt0 . Directly attached to the valve body is a shielded electron source;118 its output electrode voltage is pulsed, allowing for a time-resolved tagging of the expanding He (purity of 99.9999%) few millimeters in front of the nozzle exit: electrons with a kinetic energy of approximately 120 eV are directed perpendicular to the propagation axis of the supersonic jet; the interaction region has been optimized by means of the electron source lens voltages. The nozzle in this study has a diameter of 0.1 mm and is of parabolic shape,121 providing an improved collimation of the expanding flow.96 The valve is mounted on a xyz precision translation stage and aligned to the beam axis, which is defined by two 50.8 mm long nickel skimmers with diameters of 3.0 mm (Beam Dynamics). The distance between valve and first skimmer is 233 mm, the skimmerskimmer distance amounts to 209 mm. After the flight distance of about 3.5 m an electrically shielded detector, comprising a multichannel plate-scintillator-photomultiplier assembly, registers energetic photons and particles with a time resolution of approximately 1 ns, see the schematic diagram of Fig. 1. Due to the deliberately low repetition frequency of the valve of fv = 2.0 Hz the working pressure in the first vac-
As illustrated schematically in Fig. 2, a control signal of rectangular pulse shape and pulse width of δt0 applied at the valve driver gives reason to expect the corresponding opening time of the valve, provided that this duration is defined via the full width at half maximum (FWHM) of the pulse. Caused by the finite speed of the mechanical movement of the plunger the period allowing for constant flow is shorter. In particular, it is obvious that this type of valve cannot achieve steady-state conditions for pulses that are shorter than the rise time of the valve opening, i.e., δtv ≤ 10 μs. Similar restrictions apply to all pulsed valves, especially at ultrashort opening times, cf. Table I. The actual opening characteristics of a valve can be investigated experimentally, making use of ultraviolet photons that are emitted from excited particles right in front of the valve and registered time-resolved by a suitable detector. For effective lifetimes of the electronically excited states of a few nanoseconds this photon signal represents the convolution of the opening function of the valve according to Fig. 2(b) with the local velocity distribution of the expanding particles. The velocity broadening is minimized for helium expanding from a high source pressure, and a short distance between nozzle exit and electronic excitation of a few millimeters only. As an example, the photon signals corresponding to control pulse durations of δt0 = 16 μs and of δt0 = 18 μs are depicted in Fig. 3. Both rise time and fall time are in accordance with the expected value of 10 μs, whereas the peak widths are considerably larger. This discrepancy is attributed to an effectively
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154202-3
Wolfgang Christen
J. Chem. Phys. 139, 154202 (2013)
(a)
(a)
(b) (b)
FIG. 2. Illustration of the trapezoidal opening characteristics of the pulsed valve, resulting from a rectangular voltage pulse of the delay/pulse generator. (a) Valve control signal at the time of t0 , featuring a pulse width of δt0 = 16.0 μs. (b) After some intrinsic delay the plunger of the valve starts moving at the time of t0 . With an approximate speed of 10 ms−1 it reaches its full stroke of 0.1 mm after 10 μs. Although the FWHM of the valve opening, δtv , is supposed to match the pulse width of the control signal, δt0 , constant flow is possible for a maximum of δtv = 6 μs only.
longer opening time of the valve, δtv > δt0 ; δtv is also affected by the maximum solenoid current, Iv , set at the valve driver. Also note that the amplitude of the photon signal in Fig. 3(b) is significantly larger. Evidently, “constant flow” or constant density does not imply that the valve is fully open. The contribution of the velocity broadening of the expanding jet to the pulse width of the photon signal, δtp , can be judged by varying the distance between valve and electron source, lve , see Fig. 4(b): the variation in photon pulse width yields an estimated effective opening time of the valve of δtv ≈ 0.85 × δtp . Also, the systematic study of the dependence δtp (δt0 , Iv ) reveals the full opening of the valve; according to this analysis a valve opening time of δtv 40 μs is required for saturating the photon signal, see Fig. 4(d); for shorter times the flow is throttled. In conclusion, for short pulse durations the mechanical response of the valve is almost as expected, with one notable exception: the true opening time of the valve, δtv , may be appreciably longer than the control pulse applied at the valve
FIG. 3. Ultraviolet photons resulting from a pulsed, electronically excited He beam at a source pressure of P0 = 9.60 MPa and a source temperature of T0 = 319.0 K, providing an ultrafast in situ characterization of the jet. Operating conditions are a duration of the valve control signal of δt0 = 16.0 μs (a) and of δt0 = 18.0 μs (b), respectively. The distance between nozzle exit and electron source is lve ≈ 6 mm. The gate control pulses of the valve driver and of the electron source are switched on concurrently. The switch-on time of the electron beam is δt1 = 4 ms, resulting in a quasi-continuous excitation of the entire jet pulse. The estimated focal diameter of the electron beam of 0.5 mm contributes less than 0.3 μs to the photon pulse width (FWHM) of δtp = 30 μs (a) and 43 μs (b), respectively. The solid lines visualize the fit of an exponential power function, which is also known as generalized Gaussian distribution.
driver, δt0 ; for the most part this prolongation is attributed to the self-inductance of the solenoid. The collision-induced fluorescence signal permits to determine the operating parameters required for an entirely open valve, with the decided advantage that the detected photon signal is not affected by beam-skimmer and beam-residual gas interactions. Although a “flat-top” signal indicates constant particle density it is important to note that this does neither imply a fully open valve, cf. Fig. 3(a), nor stationary flow, see Sec. V. IV. VARIATION OF CHARACTERISTIC BEAM PROPERTIES WITHIN THE JET PULSE
In consequence of the finite opening time of the pulsed valve, the number density in the jet initially increases and
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154202-4
Wolfgang Christen
J. Chem. Phys. 139, 154202 (2013)
(a)
(b)
(c)
(d)
FIG. 4. Opening period of the pulsed valve, investigated using the optical emission from electronically excited helium at source conditions of P0 = 9.60 MPa and T0 = 319.0 K. The photon peak width, δtp , is obtained as the FWHM of a fitted exponential power function, cf. Fig. 3. (a) Output current pulse of the valve driver, showing a delayed response with respect to the control pulse of the delay/pulse generator, see Fig. 2(a), with t0 − t0 < 2 μs. The maximum of the solenoid current, Iv , depends both on the setting of the current control knob of the valve driver and on the pulse duration of the valve control signal, δt0 . The reproducibility of δt0 is better than 100 ns and of Iv better than 1 A. (b) Influence of the duration of the valve control signal, δt0 , on the photon peak width, for distances between valve exit and electron source of lve ≈ 6 mm and of lve ≈ 11 mm, respectively: the velocity distribution of the jet results in an additional broadening of the photon pulse at longer distances. Extrapolation to zero distance yields an estimate for the “true” opening time of the valve. (c) Influence of the maximum valve current, Iv , on the photon peak width, for durations of the valve control signal of δt0 = 17.0 μs, δt0 = 21.0 μs, and δt0 = 25.0 μs, respectively, and a distance of lve ≈ 11 mm. The variation of both valve current and control pulse duration permits effective opening times in a large range, from 10 μs to 100 μs. (d) Standardization of the offset corrected photon signal to its FWHM clearly reveals “saturation,” i.e., above a δt0 -dependent threshold value higher valve currents increase the duration but not the overall intensity of the photon peak. This is interpreted as an indication of the full opening of the valve and is observed for photon peak widths of δtp 47 μs.
shortly afterwards decreases again. This yields a strong variation of the number of particle-particle collisions. As a result, also the velocity distribution changes, influencing, first and foremost, translational cooling and cluster formation. This time dependence of beam properties can be analyzed in detail by the systematic variation of the time delay between the gate control pulses of the electron source and of the valve driver, t1 − t0 , see Figs. 1 and 5(a). In this manner thin “slices” of the jet pulse can be electronically tagged,124 allowing to study the time evolution of characteristic beam properties with a temporal resolution of few hundred nanoseconds only, improving earlier work22, 125, 126 by orders of magnitude. For the supersonic expansion of He at P0 = 9.60 MPa and T0 = 319.0 K and a switch-on duration of the electron beam
of 0.3 μs FWHM, the estimated diameter of the electron beam of ≤0.5 mm contributes negligibly to the spatial extent of the excited jet, see Fig. 5(b). That matters because all recorded arrival time distributions are inherently broadened by this instrument function; its experimental determination is depicted in Fig. 5(c). By way of illustration Fig. 6 displays 46 arrival time spectra of an electronically tagged helium beam at source conditions of P0 = 9.60 MPa and T0 = 319.0 K as a function of the excitation delay, t1 − t0 ; all other parameters are kept constant. Accordingly, this method permits the spatio-temporal analysis of the beam profile; at short delay times the leading particles of the jet pulse are probed. The temporal variation of beam properties can be analyzed in terms of signal amplitude, intensity, mean arrival
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154202-5
Wolfgang Christen
J. Chem. Phys. 139, 154202 (2013)
(a)
(b)
(c)
FIG. 5. (a) Illustration of the experimental approach of a time-resolved characterization of beam properties within a bunch of particles (blue area), using a pulsed electron beam for tagging a localized, specific portion of the jet at the time of t1 . The time resolution of a few hundred nanoseconds permits monitoring the time evolution of beam temperature and velocity within the jet pulse with unprecedented granularity. (b) Detail view of the instrument function of the electronic labeling, resulting from the convolution of a 0.5 mm long focal excitation region of the supersonic jet with the trapezoidal switching function of the electron beam. For the flow velocity of helium of 1.8 × 103 ms−1 the axial extent of the excited molecular beam slice corresponds to a pulse width of 280 ns. The voltage pulse applied at the output electrode of the electron source features a FWHM of 300 ns and a rise time of 100 ns. In consequence, for these parameters the excitation width, δt1 , is not affected by the focal spot size of the electron beam. The center position of this pulse defines the time origin of time-of-flight spectra123 with exceptional accuracy. (c) Detection of ultraviolet photons from a pulsed, electronically excited helium beam at a source pressure of P0 = 9.60 MPa and a source temperature of T0 = 319.0 K. Acquisition parameters are 54 000 sweeps and an interval width of 8 ns.
time, peak width, peak shape, etc., as is depicted in Fig. 7. Here, a robust and model-free statistical data evaluation127 is used deliberately, allowing to eliminate all possible artifacts from fitting procedures; accordingly, median and interquartile range (IQR) serve to characterize arrival time and peak width, respectively. Obviously, the depicted parameter values change substantially, and only a rather narrow region located close to the center of the jet pulse, at time delays of 51–54 μs, appears approximately uniform. However, even the observation of a trapezoidal, “flat-top” pulse shape does not guarantee continuous flow conditions; it may not even be indicative of a fully open valve. First, for such short opening times a “uniform” particle density is difficult to judge because this judgment is based on a few data points only. Second, besides density, other properties such as temperature and velocity of the particles in the beam are just as important and must be considered as well: for example, in the depicted spectra no region with constant flight times exists. But even if a portion of the jet features (approximately) uniform parameter values, as is indicated by the shaded areas of Figs. 7(a) and 7(d), this does not imply that these regions represent characteristics of the equivalent continuous beam: the opening time of the valve still may be too short to allow for steady hydrodynamic flow, see Sec. V. The difference in meaning of Figs. 7(a) and 7(b) is that the maximum signal amplitude of the spectra, (a), is affected by the velocity distribution of the beam. In comparison, the signal intensity, (b), i.e., the summation of all events within a certain region of interest, is expected to make up for the broadening of the jet pulse during its flight to the detector. Assuming an undisturbed and lossless propagation, this intensity distribution reflects the actual extent of the molecular beam pulse at the place of its electronic excitation, few millimeters in front of the nozzle.
The analysis of the peak width as a measure of translational temperature reveals the smallest values for time delays of 50–57 μs, see Fig. 7(d). In this central section of the beam translational cooling is most efficient. Fig. 7(c) confirms that at shorter delay times preferentially faster particles are excited and recorded at the time-of-flight detector, whereas predominantly slower particles are probed at longer delay times. V. STEADY-STATE FLOW CONDITIONS IN PULSED BEAMS
Addressing the pivotal issue of the minimum opening time required to achieve quasi-static conditions of supersonic flow raises the question how those parameter values that correspond to a continuous beam can be recognized in an experiment. Certainly, both a uniform density and velocity distribution within a section of the jet pulse are required for this, but also the peak widths of the arrival time spectra need to be minimized. This is because the velocity distribution of a pulsed jet is broader than that of a continuous expansion under equivalent conditions if the time of unrestricted flow is too short.8 Accordingly, a systematic variation of the pulse duration of the valve opening is essential. The results shown in Fig. 8 reveal that at the given setting of the maximum valve current the valve does not open at all for gate control pulses of δt0 < 12 μs. On the other hand, considering amplitude and rising edge of these distributions, the valve appears to be completely open for gate control pulses of δt0 ≥ 18 μs, corresponding to δtv 40 μs. This result is in good agreement with the analysis of the photon signal, cf. Fig. 4(d). Although the width of the jet density distributions depicted in Fig. 8 linearly increases with the pulse duration
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154202-6
Wolfgang Christen
J. Chem. Phys. 139, 154202 (2013)
A suitable alternative is the analysis of the velocity distribution, see Fig. 9 for results of the peak width. The energy resolution of the TOF spectra corresponds to a relative kinetic energy of 5 × 10−7 eV, whereas the binding energy of helium dimers, 4 He2 , is only 1 × 10−7 eV.128–130 Thus the formation of small helium clusters, verified mass spectrometrically, should not have any effect on the peak widths observed. Interestingly, the examination of Fig. 9 shows that a fully open valve (at δt0 = 18 μs) does not yet yield the minimum peak width; for an optimized translational cooling even longer pulse durations are required. This extension of the beam analysis to other properties reveals that the definition of stationary flow is not unique but strongly depends on the chosen criterion. Obviously, density, translational temperature, and flow velocity provide rather different sensitivities, see Fig. 10: whereas a control pulse duration of δt0 ≥ 18 μs is sufficiently long to allow for a constant mean amplitude of the photon signal and also for the maximum amplitude of TOF spectra of metastable helium, the maximum intensity of the beam is reached only later. Likewise, the peak widths as the measure of parallel beam temperature attain their minimum value only for δt0 ≥ 21 μs; a beam segment with constant time-of-flight is found only for δt0 ≥ 23 μs. These control pulse widths correspond to opening times of the valve of δtv ≈ 58 μs, δtv ≈ 65 μs, and δtv ≈ 80 μs, respectively. Interestingly, the minimum opening time of the pulsed valve required to achieve a constant flow velocity is twice as large as the time needed for complete opening; phrased differently, after the valve is open it takes another 40 μs to reach uniform flow velocities within the central section of the jet pulse. Although the stated numeric values are specific for helium at these conditions of source pressure and temperature, two universal conclusions are possible: First, continuous flow should be linked to constant flow velocity rather than to constant density. Second, these opening times are much longer than is standard practice for fast acting valves.
FIG. 6. Arrival time distributions of an electronically tagged He beam as a function of the time delay between the valve trigger at the time of t0 and the gate control pulse of the electron source at the time of t1 . The electron beam is switched on for the term of δt1 = 300 ns. For each spectrum 600 sweeps are acquired; interval width is 128 ns.
of the valve control signal, as is expected, their symmetry is increasingly distorted for pulse durations exceeding δt0 = 16 μs. For gate control signals with δt0 ≥ 19 μs the distortions result both in a diminished amplitude and an apparently reduced FWHM of these distributions. At still longer opening times of the valve, not shown here, a shoulder emerges at the large delay time side of the distributions. A detailed peak shape analysis reveals that at elevated source densities neither amplitude nor intensity of time-of-flight (TOF) spectra are a reliable measure of beam density, for they are easily distorted by beam scattering, cluster formation, and throttled flow. Hence, they are unsuitable for determining continuous hydrodynamic flow conditions.
VI. APPLICATIONS AND SIDE EFFECTS
Because the effective opening times of the Even-Lavie valve comprise a broad range, from δtv = 10 μs to 100 μs, the expansion can last long enough to yield pulsed beams with characteristics matching those of continuous beams. One fundamental application where quasi-static flow conditions are mandatory is the experimental determination of the mean terminal flow velocity120, 121, 131 of supersonic beams and its comparison with model calculations.132–135 By way of illustration Fig. 11 presents the mean time-of-flight of tagged helium in a wide range of source temperatures, from T0 = 228.0 K to 410.0 K. Pulse durations of the control signal reach from δt0 = 23 μs to 26 μs and are long enough to ascertain an extended section of the beam with uniform flight times. In the highlighted region TOF spectra feature the narrowest peak widths, thus providing both constant velocity and maximized cooling. Accordingly, the observed temperature dependence agrees fairly good with the theoretical expectation.
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154202-7
Wolfgang Christen
J. Chem. Phys. 139, 154202 (2013)
(a)
(b)
(c)
(d)
FIG. 7. Robust and model-free statistical evaluation of the unprocessed arrival time spectra of Fig. 6. (a) Spectrum amplitude, expressed as the maximum number of registered events per acquisition interval, and standardized to the number of sweeps. (b) Overall signal intensity, representing all counts of a spectrum within a given time range (from 1.3 ms to 2.0 ms, compare Fig. 6), standardized to the number of sweeps. (c) Median of arrival times. For electronically tagged particles the arrival time, t2 , differs from the time-of-flight, t = t2 − t1 . (d) Interquartile range (IQR) of arrival times as a measure of peak width. The shaded areas indicate regions of approximately constant density (a) and translational temperature (d), respectively.
Because source temperature affects the spring constant of the valve and thus the effective opening time, δtv , the pulse width of the valve control signal, δt0 , is adjusted to provide comparable expansion conditions. In the experiments of Fig. 11 a photon signal of δtp = 100 μs FWHM is used as
a reference; a variation in source temperature of ±100 K requires a change in δt0 of approximately ∓1.9 μs. Unfortunately, pulsed valves tend to bounce the larger the valve current and the longer the pulse duration. This characteristic is illustrated in Fig. 12 for different control signals,
FIG. 8. Amplitudes of tagged helium spectra as a function of the pulse width of the valve control signal, δt0 , and of the time delay between triggering the gate control signals of the electron source and of the valve driver, t1 − t0 . Source conditions are P0 = 9.60 MPa and T0 = 319.0 K.
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154202-8
Wolfgang Christen
J. Chem. Phys. 139, 154202 (2013)
FIG. 9. Interquartile ranges of the arrival time spectra of electronically tagged helium as robust measures of their peak widths, plotted as a function of the pulse width of the valve control signal, δt0 , and of the time delay between triggering the gate control signals of the electron source and of the valve driver, t1 − t0 .
(a)
(b)
(c)
FIG. 10. Performance of the pulsed valve in terms of (a) maximum intensity, (b) minimum width of the arrival-time distribution, and (c) constancy of the mean TOF as a function of the control pulse width of the valve, δt0 . For these graphs the temporal evolution of TOF spectra of an electronically tagged helium beam at source conditions of P0 = 9.60 MPa and T0 = 319.0 K has been analyzed in analogy to Fig. 7; here, however, the properties refer to the entire jet pulse. For steady state conditions the change of the time-of-flight with the time delay between the gate control pulses of the valve driver and of the electron source, t1 − t0 , should be zero. The arrows indicate the minimum control pulse width needed for achieving steady-state conditions with respect to the particular parameter: for constant density, δtv ≥ 58 μs, for minimum peak width, δtv ≥ 65 μs, and for constant time-of-flight, δtv ≥ 80 μs.
(a)
(b)
FIG. 11. Temperature dependence of the mean flight time of electronically tagged helium at a source pressure of P0 = 9.60 MPa. (a) “Beam scan” for source temperatures from T0 = 228.0 K to T0 = 410.0 K. Quasi-static flow with respect to constant time-of-flight and minimum spread is observed for a time delay between the gate control pulses of the valve driver and of the electron source of t1 − t0 = 90–110 μs (shaded area). (b) Mean time-of-flight of particles in the quasi-static flow regime as a function of the source temperature.
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154202-9
Wolfgang Christen
J. Chem. Phys. 139, 154202 (2013)
FIG. 12. Illustration of valve bouncing, observed for a pulsed beam of metastable helium via the emission of ultraviolet photons. For this analysis the gate control pulses of the valve driver and of the electron source are switched on simultaneously, with a quasi-continuous switch-on time of the electron beam of 4 ms. Source conditions are a pressure of P0 = 9.60 MPa and a temperature of T0 = 319.0 K. The number of repeated openings increases with the opening time of the valve.
making use of a long lasting electronic excitation. For short gate control signals of the valve of 12–14 μs individual jet pulses, i.e., without bouncing, can be generated. However, for these valve parameters no stationary flow is possible; also, adiabatic cooling is very inefficient. On the other hand, “long” pulse durations involve multiple valve bounces and require some kind of tagging, be it by electronic, optical, or mechanical means, in order to select the appropriate beam segment.136 VII. SUMMARY
Two complementary experimental methods for the detailed in situ analysis of the opening and closing behavior of pulsed supersonic jet sources are introduced. In particular, they permit to determine those operating conditions that yield a jet with properties equivalent to a continuous expansion. This accomplishment is of major importance because quasi-stationary flow is mandatory whenever the mean terminal flow velocity or the mean cluster size shall be calculated. The first diagnostic tool is the detection of the electroninduced fluorescence of a high-pressure helium expansion. Because the electron beam excitation is quasi-continuous and in close vicinity to the pulsed valve the photon signal reflects the opening properties of the valve. A decided advantage of this technique is that photons are not affected by beamskimmer and beam-residual gas interactions. The second method rests on the analysis of arrival time distributions of tagged particles. In this case the electron beam is pulsed and features an ultrashort switch-on time, exciting a very narrow segment of the expanding jet. This permits characterizing the evolution of beam properties, i.e., particle density, translational temperature, and mean flow velocity with a time resolution that is better by two orders of magnitude as compared to the fastest ionization gauges. Performing this beam scan analysis as a function of the pulse duration of the valve allows to identify quasi-continuous flow conditions. Actually one of the most important results of this work is that it is feasible to achieve quasi-continuous flow using fast-
acting jet sources—even though eligible operating parameters are rather different from “standard” settings. It is also learned that constant density is reached much faster than maximized cooling and constant velocity. In addition, the photoemission of excited particles close to the valve reveals that “flat-top” signals neither signify a fully open valve nor stationary flow conditions. It also turns out that the true opening time of fast-acting valves may be significantly longer than the control pulse applied to the valve driver. For the Even-Lavie valve studied this prolongation is attributed to the mechanical response of the plunger and the self-inductance of the solenoid. This shows that even for a very advanced valve the assumption of ideal valve behavior116, 117 is not justified—for He at P0 = 9.60 MPa and T0 = 319.0 K it may take about 40 μs to reach complete opening. At long opening times the valve may bounce and nozzle flow is throttled; the latter results in an effectively smaller nozzle diameter, a fact that has to be considered if scaling laws for determining the mean cluster size are used.
ACKNOWLEDGMENTS
The author is much obliged to Professor Klaus Rademann for his support and Bo-Gaun Chen for lab assistance. This work has been generously supported by a grant of the Deutsche Forschungsgemeinschaft (CH262/5). 1 O.
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154202-10 11 S.
Wolfgang Christen
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