We describe modifications of a pulsed rotating supersonic beam source that improve performance, particularly increasing the beam density and sharpening the pulse profiles. As well as providing the familiar virtues of a supersonic molecular beam (high intensity, narrowed velocity distribution, and drastic cooling of rotation and vibration), the rotating source enables scanning the translational velocity over a wide range. Thereby, beams of any atom or molecule available as a gas can be slowed or speeded. Using Xe beams in the slowing mode, we have obtained lab speeds down to about 40 ± 5 m/s with density near 1011 cm−3 and in the speeding mode lab speeds up to about 660 m/s and density near 1014 cm−3. We discuss some congenial applications. Providing low lab speeds can markedly enhance experiments using electric or magnetic fields to deflect, steer, or further slow polar or paramagnetic molecules. The capability to scan molecular speeds facilitates merging velocities with a codirectional partner beam, enabling study of collisions at very low relative kinetic energies, without requiring either beam to be slow.

In exploring molecular interactions in the cold (<1 K) gas-phase realm,1–5 a chief aim is to gain access to dramatic quantum phenomena that become prominent at long deBroglie wavelengths. That requires molecules having very low translational velocities. Spectacular results have been obtained at temperatures below 1 μK with alkali dimer molecules formed from ultracold trapped alkali atoms by photoassociation or Feshbach resonances.5–9 Since such ultraprocesses are as yet limited to alkali dimers, much effort has been devoted to develop means to slow and cool preexisting molecules. More than a dozen innovative means have been pursued; compilations are given in Refs. 1–5 and Refs. 10–14. All have to contend with weakening of intensity as a cost of attaining slower molecules. Particularly for chemical reactions, it has not been feasible to obtain adequate yields at very low collision energies, by methods that require slowing both reactants. A redeeming strategy is to obtain low relative collision energy by merging codirectional molecular beams with closely matched speeds.14,15 Then high yields can be obtained because neither beam needs to be slow. Merged beams have long been used with ion beams at keV energies to perform collision experiments at relative energies below 1 eV.16 Recently, exemplary experiments by the Narevicius group at the Weizmann Institute employed merged supersonic beams to observe orbiting resonances down to 10 mK, in the Penning ionization reaction of metastable He with argon and with molecular hydrogen.17–19 Other low-energy merged beam experiments have been done by the Osterwalder group at Lausnne Polytechique, likewise on Penning ionization reactions.20–23 

At Texas A&M we are developing a pulsed rotating supersonic beam source,14 following prior work done at Harvard24,25 and Freiburg.26–28 The beam emerges from a nozzle near the tip of a rotor that can be spun with peripheral velocity up to hundreds of meters/s. As well as providing familiar properties of a supersonic molecular beam (high intensity, narrowed velocity distribution, and drastic cooling of rotation and vibration), the rotating source enables scanning the translational velocity over a wide range by adjusting the rotor speed and direction. Hence the rotating source can slow or speed any molecule that is available as a gas or can be entrained in a carrier gas. The apparatus required is relatively simple and compact. These features make the rotating source congenial for a broad variety of experiments, either by supplying preslowed molecules or as a partner in merged beams, to obtain low relative collision velocities by adjusting its beam speed up or down to match that from a stationary source.

A full description is given in Ref. 14 of the previous version of our apparatus, including details of the design, construction, operation, and performance of the pulsed rotating beam source and its gas input system. The current version29 attains a large reduction in background as well as markedly sharpening the shape and shortening the duration of the beam pulse profiles. These improvements come chiefly from two modifications. The gas input (“feeding system”) to the rotor was redesigned to avoid friction. A foil shield was installed to narrow the angular spread of molecules emitted from the spinning rotor that can enter the beam skimmer. Also, measurements of the beam intensity and pulse profiles were greatly improved by introducing a fast ionization gauge (FIG) as the detector, replacing a Residual Gas Analyzer (RGA) used previously.14 

Figures 1 and 2 exhibit basic features and new parts of the apparatus. The rotating source, in its original version24 and in that at Freiburg,26 emits the input gas in a continuous 360° spray, from which only a thin slice passes through a skimmer to become a collimated molecular beam. Such profligacy overburdens conventional pumping. As well as allowing deleteriously high background in the rotor and detector chambers, it lowers the tolerable level of input gas pressure and thereby the quality of the supersonic expansion. These handicaps were eliminated14 by introducing a pulsed feeding valve in the rotor gas inlet, retained in our current apparatus (3 in Figs. 1 and 2). The duration that the pulsed feeding valve is open can be adjusted, typically between 1 ms and 20 ms. Gas enters the rotor through the feeding system (4 in Figs. 1 and 2). The rotor position is monitored by an induction proximity sensor (5 in Fig. 2), responding to eddy currents to provide a time-zero for control of the pulsed feeding valve, as well as for time-of-flight (ToF) measurements. As the inlet gas pulses are much longer than the rotational period of the spinning source, the output that reaches the detector is a sequence of gas pulses spaced by the rotational period.

FIG. 1.

Sketch of the experimental configuration (top view, not to scale). (1) AC induction driving motor; (2) tubular rotor conducting input gas to exit nozzle near tip; (3) pulsed valve of the gas input system; (4) “feeding” system conducting gas into the rotor; (5) fast ion gauge; (6) adjustable foil shield; (7) beam skimmer; (8) cryo-pumping enclosure; and (9) beam propagation path. New components are indicated in italics. Rotor spins clockwise in the slowing mode and counter-clockwise in the speeding mode.

FIG. 1.

Sketch of the experimental configuration (top view, not to scale). (1) AC induction driving motor; (2) tubular rotor conducting input gas to exit nozzle near tip; (3) pulsed valve of the gas input system; (4) “feeding” system conducting gas into the rotor; (5) fast ion gauge; (6) adjustable foil shield; (7) beam skimmer; (8) cryo-pumping enclosure; and (9) beam propagation path. New components are indicated in italics. Rotor spins clockwise in the slowing mode and counter-clockwise in the speeding mode.

Close modal
FIG. 2.

View into the main chamber: (1) AC induction driving motor; (2) rotor; (3) pulsed valve of input system; (4) feeding system, shown in Fig. 3 ; (5) eddy current sensor; (6) adjustable foil shield; (7) beam skimmer; and (8) detector chamber containing fast ionization gauge. New components are indicated in italics.

FIG. 2.

View into the main chamber: (1) AC induction driving motor; (2) rotor; (3) pulsed valve of input system; (4) feeding system, shown in Fig. 3 ; (5) eddy current sensor; (6) adjustable foil shield; (7) beam skimmer; and (8) detector chamber containing fast ionization gauge. New components are indicated in italics.

Close modal

The feeding of gas into the rotor as done in our previous apparatus14 relied on a stationary tube made of PEEK (polyetheretherketone). The tube was inserted into a steel sting pressed into the rotor. However, the flexibility of the tube allowed contact with the rotating sting, resulting in friction heating. That resulted in charring the tube and also heating the beam. Figure 3 shows our current design, the simplest and most effective of several solutions tried. Contact was avoided by discarding the tube and instead enclosing the sting by a rigid cylinder of PEEK with I.D. = 0.257 in., slightly larger than the sting O.D. (0.250 in.). The slight gap (0.0035 in.) between the sting and the PEEK cylinder allowed some leakage of gas into the rotor chamber, but it proved insignificant as the pulsed input markedly reduced that leakage (relative to continuous flow).

FIG. 3.

Schematic (side view, not to scale) of means for inputting gas from the pulsed valve of the stationary supply chamber into the barrel of the rotor: (1) steel sting pressed into the rotor; (2) the stationary PEEK cylinder attached to (3) copper chamber mounted on a liquid nitrogen trap. (Compare Fig. 3 of Ref. 14.)

FIG. 3.

Schematic (side view, not to scale) of means for inputting gas from the pulsed valve of the stationary supply chamber into the barrel of the rotor: (1) steel sting pressed into the rotor; (2) the stationary PEEK cylinder attached to (3) copper chamber mounted on a liquid nitrogen trap. (Compare Fig. 3 of Ref. 14.)

Close modal

As illustrated in Fig. 4, for molecular beams from a rotating source, the angular width of the emerging beam enables molecules to enter the skimmer that could not do so from a stationary source.14,24 An appreciable part of that “extra” flux comes when the rotor is approaching (ϕ2) or retreating (ϕ1) from the ideal “shooting position” (middle rotor position in Fig. 4; designated ϕ = 0). En route to the skimmer and detector, those molecules travel longer or shorter paths than the molecules emitted when the rotor is in the ideal position. Hence the time-of-flight of beam pulses is broadened. The ToF broadening imposed by the path length spread is much larger than that contributed from the velocity spread of the emitted supersonic beam. (We present simulations of ToF data in Sec. IV.) Another source of broadening associated with motion of the rotor arises from swatting background molecules. That can be reduced by installing a shutter in front of the skimmer, as done in Ref. 14. We found it is more practical, and less costly in beam intensity, simply to introduce a foil shield (6 in Figs. 1 and 2) that narrows the angular range accessible to the skimmer. The shield is mounted on a movable track that, by means of a rotatable feedthrough, is adjustable while the system is under vacuum. That allows the optimizing location of the shield to narrow the ToF pulse width without much loss of intensity.

FIG. 4.

Schematic (top view, not to scale) illustrating range of rotor positions (1) that permit molecules emitted from the rotating nozzle to pass through the skimmer (2) and reach the detector (3) if not intercepted by the foil shield (4). In the “ideal shooting position” (ϕ = 0°), the distance the emitted molecules travel to the detector is L = 120 mm, but in approaching and receding rotor orientations that distance ranges between L = 174 and 88 mm. The sketch is drawn for the slowing mode (clockwise rotation), but pertains as well to the speeding mode (counter-clockwise).

FIG. 4.

Schematic (top view, not to scale) illustrating range of rotor positions (1) that permit molecules emitted from the rotating nozzle to pass through the skimmer (2) and reach the detector (3) if not intercepted by the foil shield (4). In the “ideal shooting position” (ϕ = 0°), the distance the emitted molecules travel to the detector is L = 120 mm, but in approaching and receding rotor orientations that distance ranges between L = 174 and 88 mm. The sketch is drawn for the slowing mode (clockwise rotation), but pertains as well to the speeding mode (counter-clockwise).

Close modal

The FIG detector that we used29 was rebuilt from a venerable device (Beam Dynamics FIG-1, no longer manufactured). It is installed in a box ((8) in Fig. 1), attached to a liquid nitrogen trap, thereby substantially reducing background in the detector chamber. Defined by the entrance skimmer (I.D. 3 mm), the beam travels 120 mm to the FIG and passes through its open grid. The volume of the grid space is 320 mm3 and the fraction of incident molecules ionized is about 10−4. The response rise time of the FIG is less than 5 μs. Its useful DC pressure range is 10−8–10−2 Torr, sensitivity 105 V Torr−1 mA−1, and rms noise 20 mV. In the  Appendix, we describe our calibration procedure and list other specifications. The output voltage of the FIG is recorded using a 12 bit, 4-channel, 20 MHz data acquisition card (Measurements and Computing PCI-DAS4020/12) after passing through an analog isolation amplifier. Data from the FIG output and the proximeter are recorded simultaneously at a rate of 105 samples/s. Though the time of recording is dictated by the rotor speed, for most runs 16 384 data points are recorded from each channel.

In evaluating performance of the apparatus, we examined chiefly time-of-flight (ToF) profiles, particularly amplitude maxima and widths, and relation to beam density. The test runs used mostly Xe and less often Kr or Ar, the standard carrier gases for “inverse seeding” to slow molecules.14,24,26 Here we exhibit data, with brief commentary, and then in Sec. IV compare with simulations.

Figure 5 shows typical time-profile data for Xe beams, using the rotor in the slowing mode (upper panels) and speeding mode (lower panels). Results are compared that were obtained from our previous apparatus14 (designated I) and current apparatus (II), with the same operating conditions. The feeding valve, inputting gas at 900 Torr into the rotor, was opened at time zero and closed after 20 ms. The train of pulses that arrives at the FIG detector is spaced by the rotational period and persists much longer because once gas fills the rotor, it leaks out slowly from the nozzle orifice. Since the leading pulse emerges before gas has fully filled the rotor, that pulse is less intense than the next; likewise, trailing pulses become less intense as the rotor empties. As evident in the pulse trains, the gas surge on filling the rotor produces much less background at the detector in II than I, particularly in the slowing mode (cf. panels and (a) and (b)), an improvement attributed to the new version of the gas feeding system (Fig. 3). Also, the profile of individual pulses is narrower in II than I, particularly in the speeding mode (cf. panels (c) and (c′)). The narrowing of the time-profiles comes from installing in II the foil shield (Figs. 2 and 4).

FIG. 5.

Comparison of profiles for pulsed Xe beams obtained using the slowing mode ((a)–(c)) or speeding mode ((a′)–(c′)), from previous apparatus described in Ref. 14 (denoted I: (a) and (a′), dashed curves in (c) and (c′)), and from our current apparatus (denoted II: (b) and (b′), full curves in (c) and (c′)). Rotor spinning frequency was 225 Hz for both directions of rotation, giving peripheral rotor velocities of ±212 m/s. Corresponding lab velocities were 115 m/s and 539 m/s, respectively. Time was measured from opening of the gas feeding system valve. Panels (c) and (c′) compare typical single pulse profiles for slowing and speeding modes, normalized in order to contrast shapes obtained from I and II. The FIG detector was installed in both I and II; the new gas feeding system (Fig. 3) and foil shield (Figs. 2 and 4) were added only to II. Input pressure to the rotor was 900 Torr for both I and II.

FIG. 5.

Comparison of profiles for pulsed Xe beams obtained using the slowing mode ((a)–(c)) or speeding mode ((a′)–(c′)), from previous apparatus described in Ref. 14 (denoted I: (a) and (a′), dashed curves in (c) and (c′)), and from our current apparatus (denoted II: (b) and (b′), full curves in (c) and (c′)). Rotor spinning frequency was 225 Hz for both directions of rotation, giving peripheral rotor velocities of ±212 m/s. Corresponding lab velocities were 115 m/s and 539 m/s, respectively. Time was measured from opening of the gas feeding system valve. Panels (c) and (c′) compare typical single pulse profiles for slowing and speeding modes, normalized in order to contrast shapes obtained from I and II. The FIG detector was installed in both I and II; the new gas feeding system (Fig. 3) and foil shield (Figs. 2 and 4) were added only to II. Input pressure to the rotor was 900 Torr for both I and II.

Close modal

As described in Ref. 24, in the ancestral apparatus the rotor continually sprayed gas, thereby raising the background pressure in the main chamber which induced collisions that severely attenuated slow beams. Employing pulsed input, in I and II, allowed both use of higher input pressure and markedly reduced the background. Yet each pulse causes a pressure surge, typically up to 10−5 Torr. In II, as well as further reducing background, the path length to the skimmer was shortened. From model calculations (given in Ref. 24, Fig. 4) we estimate that even for our slowest beams (35 m/s) the attenuation is only about 15%.

Extensive runs were made to test the time-of-flight reproducibility of pulse profiles for a wide range of conditions. For fixed rotor speed and input pressure, the pulse shapes (normalized to the amplitude) do not change perceptibly over the major portion of a pulse train, wherein the pulse amplitudes are fairly constant (usually within 30%). Likewise highly consistent are the observed time intervals, both between successive members of the pulse trains, and the transit times to the FIG detector. Hence, we consider just single pulses. Unlike Figure 5, the time of flight is recorded as the difference, Δt = tD − t0, between the time of arrival of the pulse at the FIG detector and the eddy current signal that the rotor had reached the “ideal shooting position” (ϕ = 0 in Fig. 4), which has a direct line of sight through the skimmer to the FIG detector.

Figure 6 displays individual pulse profiles of Xe beams slowed or speeded using our current apparatus. With the high input pressure now feasible, the exit flow velocity, u, of the supersonic beam is very narrow (Δv ∼ 5 m/s or less). The peripheral velocity of the rotor, Vrot, proportional to the rotor frequency, ω (negative for slowing, positive for speeding), is accurately reproducible (better than 1 m/s). Accordingly, the lab speed, w = u + Vrot, has to good approximation the same narrow distribution as the flow velocity, merely shifted by the rotor speed. Figure 6(a) exhibits the lowest lab speeds attained by spinning the rotor contrary to the exit supersonic flow at frequencies of −300 Hz and −310 Hz. The corresponding lab speeds are about 44 and 35 m/s, with peak amplitudes of the pulse density of about 1011 cm−3 and half that, respectively. As indicated in the inset (for −300 Hz), at the high rotor spinning frequency required, successive pulses overlap appreciably. For the pulse chosen (marked by an asterisk) the profile curve displayed had overlap background subtracted, and noise at frequencies above 3 kHz filtered out, but raw data points are shown. Figure 6(b) exhibits the highest lab speed attained, about 657 m/s, with amplitude ∼1.6 × 1014 cm−3 and the rotor at 350 Hz.

FIG. 6.

Pulse profiles for Xe beams slowed to lab speeds (a) of about 35 and 44 m/s and speeded (b) to 657 m/s. The corresponding rotor spinning frequencies and peripheral rotor velocities (ω and Vrot = 0.943ω) were (a) −300 Hz; −283; −310 Hz, −292 m/s and (b) 350 Hz, +330 m/s. The lab speeds, w = u + Vrot, are obtained with uncertainty of about ±5 m/s, as the sum of the calculated supersonic flow velocity (u = 327 m/s) and rotor speed (cf. Table I). Peak pulse profile amplitudes at the FIG detector were (a) 1 × 1011 and (b) 1.6 × 1014 atoms cm−3. Time-of-flight was measured (from eddy current signal when rotor reaches optimum alignment with skimmer (cf. Fig. 4)). Insets show portions of pulse trains (cf. Fig. 5); the profiles enlarged for (a) and (b) are marked with asterisks. The inset in (a) shows overlapping of pulses that occurs when the rotor spins at high speed contrary to the exit beam velocity, in order to get very low lab speed. Then the time between pulses becomes too short for tails of the slow pulses to travel outside the rotor orbit. Also, for (a) signal levels drop low, so ambient high frequency electrical noise becomes intrusive. Therefore the data were filtered to remove frequencies above 3 kHz. Signals were high enough for lab speeds above 50 or 60 m/s to make negligible the electrical noise.

FIG. 6.

Pulse profiles for Xe beams slowed to lab speeds (a) of about 35 and 44 m/s and speeded (b) to 657 m/s. The corresponding rotor spinning frequencies and peripheral rotor velocities (ω and Vrot = 0.943ω) were (a) −300 Hz; −283; −310 Hz, −292 m/s and (b) 350 Hz, +330 m/s. The lab speeds, w = u + Vrot, are obtained with uncertainty of about ±5 m/s, as the sum of the calculated supersonic flow velocity (u = 327 m/s) and rotor speed (cf. Table I). Peak pulse profile amplitudes at the FIG detector were (a) 1 × 1011 and (b) 1.6 × 1014 atoms cm−3. Time-of-flight was measured (from eddy current signal when rotor reaches optimum alignment with skimmer (cf. Fig. 4)). Insets show portions of pulse trains (cf. Fig. 5); the profiles enlarged for (a) and (b) are marked with asterisks. The inset in (a) shows overlapping of pulses that occurs when the rotor spins at high speed contrary to the exit beam velocity, in order to get very low lab speed. Then the time between pulses becomes too short for tails of the slow pulses to travel outside the rotor orbit. Also, for (a) signal levels drop low, so ambient high frequency electrical noise becomes intrusive. Therefore the data were filtered to remove frequencies above 3 kHz. Signals were high enough for lab speeds above 50 or 60 m/s to make negligible the electrical noise.

Close modal

Table I lists parameters for Xe beams for rotor peripheral speeds ranging between −292 and +330 m/s, together with corresponding lab speeds and the observed ToF at the peak amplitude of each pulse profile and its FWHM. The lab speeds, w = u + Vrot, are predicted from the peripheral rotor speed and direction plus the supersonic flow velocity, u = 327 ± 5 m/s, governed by the input pressure (900 Torr) and temperature (∼340 ± 10 K) of the rotor.

TABLE I.

Parameters for slowed and speeded beams.a

Rotor frequency ω, Hz Rotor speed Vrot, m/s Lab speed w, m/s ToF at Max Δtpk, ms FWHM ms
−310  −292  35  3.0  1.53 
−300  −283  44  2.6  1.52 
−275  −259  68  1.8  1.05 
−250  −235  91  1.2  0.73 
−225  −212  115  0.94  0.59 
−200  −188  139  0.74  0.51 
−175  −165  162  0.60  0.49 
−150  −141  185  0.50  0.48 
−125  −117  220  0.40  0.51 
−100  −94  233  0.32  0.54 
−75  −70  257  0.23  0.66 
−50  −47  280  0.07  0.89 
−25  −23  304  −0.30  1.62 
25  23  350  1.01  1.39 
50  47  374  0.62  0.67 
75  70  397  0.48  0.42 
100  94  421  0.41  0.30 
125  117  444  0.36  0.23 
150  141  468  0.32  0.18 
175  165  492  0.29  0.14 
200  188  525  0.28  0.12 
225  212  539  0.26  0.098 
250  235  562  0.26  0.088 
275  259  586  0.23  0.072 
300  282  609  0.22  0.071 
350  330  657  0.20  0.067 
Rotor frequency ω, Hz Rotor speed Vrot, m/s Lab speed w, m/s ToF at Max Δtpk, ms FWHM ms
−310  −292  35  3.0  1.53 
−300  −283  44  2.6  1.52 
−275  −259  68  1.8  1.05 
−250  −235  91  1.2  0.73 
−225  −212  115  0.94  0.59 
−200  −188  139  0.74  0.51 
−175  −165  162  0.60  0.49 
−150  −141  185  0.50  0.48 
−125  −117  220  0.40  0.51 
−100  −94  233  0.32  0.54 
−75  −70  257  0.23  0.66 
−50  −47  280  0.07  0.89 
−25  −23  304  −0.30  1.62 
25  23  350  1.01  1.39 
50  47  374  0.62  0.67 
75  70  397  0.48  0.42 
100  94  421  0.41  0.30 
125  117  444  0.36  0.23 
150  141  468  0.32  0.18 
175  165  492  0.29  0.14 
200  188  525  0.28  0.12 
225  212  539  0.26  0.098 
250  235  562  0.26  0.088 
275  259  586  0.23  0.072 
300  282  609  0.22  0.071 
350  330  657  0.20  0.067 
a

Profiles are displayed in Fig. 6 for ω = − 300 Hz and ω = 350 Hz; others in Fig. 9. Rotor speed Vrot = 2πωR0, with ω the rotor frequency and R0 the length of rotor from axis to nozzle exit (150 mm); ToF at max, denoted Δtpk, is time interval between rotor reaching “ideal shooting” position detected by eddy current sensor (cf. Fig. 4) and maximum of observed profile recorded at the detector; and FWHM is the full width at half-maximum. Lab speed, w = u + Vrot, is estimated from supersonic flow velocity (u = 327 m/s), with uncertainty of about ±5 m/s, as discussed in the footnote of Table II in Sec. IV.

Figure 7 plots the observed ToF (square points, denoted Δtpk in Table I) at the maximum amplitude of the pulse profile. At low rotor speeds, it is evident that the peaks of the profiles occur well removed from ToF locations (curve) expected for the “ideal” rotor orientation at ϕ = 0. Instead, the maximum of the profile detected at the FIG detector comes from gas emitted earlier or later than the rotor reaches ϕ = 0, depending on the rotation direction. The increment in time it takes the rotor spinning at frequency ω to travel from a nonideal orientation at angle ϕo to ϕ = 0 is given by Δtϕ = ± (ϕo/360)/ω, positive for slowing and negative for speeding. As seen in Fig. 7, adjusting the ToF to Δtpk + Δtϕ with an effective or averaged ϕ0 = 6° (circle points) closely accounts for the differences between the actual TOF locations of the profile peaks and the predicted ϕ = 0 locations.

FIG. 7.

Observed transit time ToF for Xe beams listed in Table I (square points), measured from rotor exit to FIG detector at peak of pulse profile, Δtpk, versus rotor speed Vrot. Estimate of what TOF would be (curve) if the rotor were fixed at the “ideal” orientation (ϕ = 0°, Fig. 4) is given by Δtpk(0) = L/(u + Vrot), with L = distance (120 mm) from nozzle exit to FIG detector and u the supersonic flow velocity (∼327 m/s) at the exit. The observed peaks of the profiles actually correspond to nominal rotor orientations at ϕo = ± 6°, as described in the text and demonstrated (circle points) by plotting Δtpko) = Δtpk(0) + Δtϕ.

FIG. 7.

Observed transit time ToF for Xe beams listed in Table I (square points), measured from rotor exit to FIG detector at peak of pulse profile, Δtpk, versus rotor speed Vrot. Estimate of what TOF would be (curve) if the rotor were fixed at the “ideal” orientation (ϕ = 0°, Fig. 4) is given by Δtpk(0) = L/(u + Vrot), with L = distance (120 mm) from nozzle exit to FIG detector and u the supersonic flow velocity (∼327 m/s) at the exit. The observed peaks of the profiles actually correspond to nominal rotor orientations at ϕo = ± 6°, as described in the text and demonstrated (circle points) by plotting Δtpko) = Δtpk(0) + Δtϕ.

Close modal

Figure 8 plots the observed FWHM of the ToF profiles versus the rotor speed (square points) compared with estimates from a model given in Sec. IV. At the lowest rotor frequency used, ±25 Hz, the FWHM is similar for both slowing and speeding modes. As the frequency is increased, for the slowing mode the FWHM first narrows until reaching a minimum near −150 Hz and then grows again. For the speeding mode, the FWHM decreases steadily as the frequency is increased.

FIG. 8.

Observed pulse profile widths, specified by FWHM, versus Vrot, for Xe beams listed in Table I (square points). Results predicted from model simulations described in Sec. IV (circle points). Curves drawn close to the observed points show fit obtained from the model by adjusting just one parameter that is the same for the slowing and speeding modes.

FIG. 8.

Observed pulse profile widths, specified by FWHM, versus Vrot, for Xe beams listed in Table I (square points). Results predicted from model simulations described in Sec. IV (circle points). Curves drawn close to the observed points show fit obtained from the model by adjusting just one parameter that is the same for the slowing and speeding modes.

Close modal

Figure 9 displays, in the order listed in Table I, the observed pulse profiles, with the peaks normalized to unity. The profiles are shown in four groups, ranging from (a) the most slowed beams to (b) more modestly slowed beams, to (c) modestly speeded beams and (d) the most speeded ones. Where necessary in (a), the portion of the FIG signal attributed to background has been removed (as in Figure 6(a)). As in Table I, the ToF to the detector was measured from the “ideal shooting position” of the rotor recorded by the eddy current sensor. At right, corresponding panels (a′)–(d′) compare the shapes of the profiles by means of a simple rescaling. The scaled versions are obtained by merely adjusting the observed maxima to coincide, designating that point as the zero for the scaled ToF, and replacing the observed FWHM by that for a chosen representative profile. Thereby, the shapes of the scaled versions are seen to be quite similar for the slowed beams (a′) and (b′): steep on the ToF < 0 side, less so on the ToF > 0 side. Moreover, the shape of the scaled version for the modestly speeded beams (c′) is similarly skewed, but with the signs of the ToF sides reversed. In contrast, the shape of the scaled version for the most speeded beams is close to symmetrical. These features will be discussed in Sec. IV.

FIG. 9.

Pulse profiles for the slowed (a) and (b) and speeded (c) and (d) beams that are listed in Table I. Peak amplitudes are normalized to unity. The time-of-flight, as in the table, is measured from the “ideal shooting position” (cf. Fig. 4) of the rotor. Successive profiles pertain to steps of 25 Hz in rotation frequency, negative for the slowing mode (−25 to −300 Hz) and positive for the speeding mode (25 to 350 Hz). At right, scaled versions of the profiles are shown in corresponding groups. The scaled versions have the profile peaks shifted to coincide at the scaled ToF zero, and the FWHMs are scaled linearly to a particular profile (in italics in Table I) in each group: −275 Hz for ((a) and (b)) and +275 Hz for ((c) and (d)). For example, for the profile at 200 Hz the scaled FWHM = 0.072/0.122.

FIG. 9.

Pulse profiles for the slowed (a) and (b) and speeded (c) and (d) beams that are listed in Table I. Peak amplitudes are normalized to unity. The time-of-flight, as in the table, is measured from the “ideal shooting position” (cf. Fig. 4) of the rotor. Successive profiles pertain to steps of 25 Hz in rotation frequency, negative for the slowing mode (−25 to −300 Hz) and positive for the speeding mode (25 to 350 Hz). At right, scaled versions of the profiles are shown in corresponding groups. The scaled versions have the profile peaks shifted to coincide at the scaled ToF zero, and the FWHMs are scaled linearly to a particular profile (in italics in Table I) in each group: −275 Hz for ((a) and (b)) and +275 Hz for ((c) and (d)). For example, for the profile at 200 Hz the scaled FWHM = 0.072/0.122.

Close modal

Figure 10 exhibits the variation with rotor speed of the beam density at the maximum of maximum of pulse profiles. The data for Xe beams pertain to the profiles listed in Table I and plotted in Figure 9. Results shown for Kr and Ar were obtained without changing the apparatus or operating conditions (except using somewhat higher input pressures). As found in previous work,14,24 for constant input pressures, the beam intensity varies strongly with the rotor speed. Over the range of rotor speeds used for the Xe and Kr beams, the density variation is quite similar when normalized to the supersonic flow velocity, Vrot/u. As compared with a stationary source, the Xe beam density drops about 10-fold when slowed down to Vrot/u = − 0.8 and drops 100-fold by −0.9, whereas the density climbs about 20 to 30-fold when speeded up to Vrot/u = + 0.8.

FIG. 10.

Beam density at maximum of pulse profiles, attained at the detector location, for beams of Xe (full circles), Kr (triangles) and Ar (squares) slowed or speeded by the rotating source. The normalized rotor speed, Vrot/u (bottom abscissa scale), is scaled to the calculated flow velocity within the supersonic nozzle, u = 327 m/s for Xe, 409 for Kr, and 592 for Ar (values specified in Table II, Sec. IV). Corresponding lab speed is w/u = 1 + Vrot/u (top abscissa scale). Input pressures were 900 Torr for Xe and 950 Torr for Kr and Ar.

FIG. 10.

Beam density at maximum of pulse profiles, attained at the detector location, for beams of Xe (full circles), Kr (triangles) and Ar (squares) slowed or speeded by the rotating source. The normalized rotor speed, Vrot/u (bottom abscissa scale), is scaled to the calculated flow velocity within the supersonic nozzle, u = 327 m/s for Xe, 409 for Kr, and 592 for Ar (values specified in Table II, Sec. IV). Corresponding lab speed is w/u = 1 + Vrot/u (top abscissa scale). Input pressures were 900 Torr for Xe and 950 Torr for Kr and Ar.

Close modal

As a prelude, we note standard approximate formulas for supersonic beams30 and kindred formulas pertaining to the rotating source.24,31 The velocity distribution of molecular flux obtained on transforming to the lab frame is given by

F(V ) = C N V 2 ( V V rot ) exp { [ ( V w ) / Δ v ] 2 } ,
(1)

with CN a normalization constant dependent on input pressure and apparatus parameters. Vrot is the peripheral velocity of the rotor, w = u + Vrot is the flow velocity along the centerline of the beam in the lab frame, and u the flow velocity relative to the rotating exit nozzle. In the slowing mode, the rotor spins contrary to the exiting gas flow (Vrot < 0), and in the speeding mode it spins (Vrot > 0) with the flow. The flow velocity and its spread are specified by

u = ( 2k B T 0 / m ) 1 / 2 [ γ / ( γ 1 ) ] 1 / 2 [ 1 ( T | | / T 0 ] 1 / 2 ,
(2)
Δ v = ( 2k B T | | / m ) 1 / 2 ,
(3)

with kB the Boltzmann constant and m the molecular mass. The parallel temperature, T|| (also designated longitudinal), pertains to the molecular translational motion relative to the flow velocity. According to the thermal conduction model,32 T||/T0 is proportional to (P0d)−β, with d the nozzle diameter and T0 and P0 the temperature and pressure within the source. The exponent β = 6(γ − 1)/(γ + 2), with γ = Cp/Cv the heat capacity ratio. The proportionality constant (with P0 in Torr, d in cm) is 0.0241, 0.0320, and 0.0412 for Xe, Kr, and Ar, respectively. Because the rotating source acts as a gas centrifuge,24,33 if the gas within the rotor remains at thermal equilibrium, the pressure behind the exit aperture, P0, is governed by

P 0 = P in exp [ mV rot 2 / ( 2k B T 0 ) ] ,
(4)

where Pin is the input pressure. Typically, |V rot| < u; hence, via Eq. (2), the maximum of P0/Pin ∼ exp[γ/(γ − 1)] = 12 for monoatomic gases. However, the pulsed input is nonstationary and brief, so the pressure distribution within the rotor may not conform to thermal equilibrium.14 We observed that as the rotor speed increased from 100 to 300 m/s, the drain time shortened from 85 to 50 ms. That trend is qualitatively consistent with a centrifugal enhancement of pressure. Yet the shorter drain time also renders uncertain the equilibrium presumed in Eq. (4). Criteria based on empirical results14,30 indicate that, if Eq. (4) is applicable, high rotor speeds of 300 m/s should produce several percent dimers in Xe beams (and likely some trimers too). Figure 9 offers evidence that centrifugal enhancement of clustering is not severe, since the ToF profiles for a wide range conform nicely when scaled to those for the highest speeds.

Rather than flux, the FIG detector measures ambient pressure, hence records the beam density distribution, D(V ) = F(V )/V . Since t = L/V , with L the flight distance from the exit aperture of the source to the detector, the corresponding time-of-flight distribution is

D(t) = ( C N / t ) ( L/t ) 2 ( L/t V rot ) exp { [ ( L/t w ) / Δ v ] 2 } .
(5)

Table II lists the supersonic flow velocity and its spread obtained from Eqs. (2) and (3). As the input pressure is much higher than that used in previous rotary sources,14,24–27 the parallel temperature and hence the spread of the flow velocity are much smaller. The spread in the predicted lab speed, w, thus is for Xe beams only about ±5 m/s. Rotating the supersonic source merely shifts the exit flow velocity distribution up or down by ±Vrot, but could narrow somewhat the velocity spread Δv because of the (possibly partially) centrifugal effect of Eq. (4).

TABLE II.

Supersonic beam parameters.a

Gas u, m/s Δv, m/s T||, K
Xe  327  4.6  0.16 
Kr  409  6.8  0.21 
Ar  592  11.2  0.27 
Gas u, m/s Δv, m/s T||, K
Xe  327  4.6  0.16 
Kr  409  6.8  0.21 
Ar  592  11.2  0.27 
a

For P0 = 900 Torr; d = 0.04 cm; T0 = 340 K, γ = 5/3. Here, Δv and T||, calculated from Eqs. (2) and (3), represent upper limits, as the centrifugal enhancement available by Eq. (4) is neglected. The value assigned to T0 is an estimate taking account of typical heating by the rotor driving motor. The uncertainty in To is about ±10 K; that imposes uncertainty of ∼1.6% on the calculated flow velocity. Thus, for Xe beams the uncertainty in u is ±5 m/s and about the same in values derived for the lab speed w, as the uncertainty in Vrot is well below ±1 m/s.

For beams with such narrow velocity distributions and short distances to the detector, ToF data cannot provide resolution adequate to extract realistic values of the speed and spread. Instead, the ToF profiles arise mostly from the wide spread in path lengths to the detector resulting from the range of rotor orientations that contribute signal. The conformity of the ToF profiles for a wide range of rotor speeds, as displayed at the rightside of Fig. 9, is consistent with near constancy of the shape of the velocity distributions.

Figure 11 exhibits the geometry that governs a simple model for the ToF profiles. The line-of-sight (LoS) paths from the rotor exit to the detector are specified by intersections with the rotor orbit and by the locations and widths of the skimmer and detector orifice. Hence, with notation defined in the caption, the LoS paths obey

y = mx + b and x 2 + ( y r ) 2 = r 2
(6)

and strike the detector at x = LD with y = d in the range d_ < d < d+, thereby delivering intensity proportional to I(d) = (d + d+)/(d+ − d_). Of prime interest are paths grazing the top edge of the skimmer (y = s+) and reaching the bottom or top edge of the detector orifice (y = d±) for which I(d_) = 0 and I(d+) = 1. The paths at or between those limits are given by

m = ( d ± s + ) / ( L D L S ) and b = ( s + L D d ± L S ) / ( L D L S ) ,
(7)

with

x = [ B ± ( B 2 4AC ) 1 / 2 ] / 2A ,
(8)

where A = 1 + m2, B = 2m(b − r), and C = b(b − 2r). The distances from the rotor exit to the detector are

L ± ( d ) = [ ( x ± L D ) 2 + ( y ± d ) 2 ] 1 / 2 .
(9)

These define the upper and lower limits: L_(d_) > L(d) > L+(d+), for the range emitted beams to reach the detector. The corresponding angular orientations of the rotor ϕ+(d+) and ϕ_(d_) are obtained from

2 r sin ( ϕ ± / 2 ) = ( x ± 2 + y ± 2 ) 1 / 2
(10)

and are well approximated by ϕ± = 2 arcsin[(LD − L)2/2r].

FIG. 11.

Schematic displaying geometry that defines the range of orientations of the spinning rotor from which exiting beams can reach some portion of the FIG detector. Drawn in (x, y) plane. Dashed arc is orbit of rotor exit aperture; point (0, 0) is “ideal shooting position” (cf. Fig. 4). Horizontal straight line indicates beam path from (0, 0) through midpoints of the skimmer at (LS, 0) and the detector orifice at (LD, 0). Slanted straight line intersecting rotor orbit at points (x±, y±) represents beam path that traverses the upper edge of the skimmer at (LS, s+) and lower edge of the detector orifice at (LD, d_ ). That path defines the limiting orientation angles ϕ+ and ϕ_ of the rotor between which emitted beams can reach the detector. Dimensions, in units of mm, are LD = 120 and LS = 60; s± = ± 1.5, d± = ± 3, and r = R0 = 150, the length of the rotor from its rotation axis to exit aperture.

FIG. 11.

Schematic displaying geometry that defines the range of orientations of the spinning rotor from which exiting beams can reach some portion of the FIG detector. Drawn in (x, y) plane. Dashed arc is orbit of rotor exit aperture; point (0, 0) is “ideal shooting position” (cf. Fig. 4). Horizontal straight line indicates beam path from (0, 0) through midpoints of the skimmer at (LS, 0) and the detector orifice at (LD, 0). Slanted straight line intersecting rotor orbit at points (x±, y±) represents beam path that traverses the upper edge of the skimmer at (LS, s+) and lower edge of the detector orifice at (LD, d_ ). That path defines the limiting orientation angles ϕ+ and ϕ_ of the rotor between which emitted beams can reach the detector. Dimensions, in units of mm, are LD = 120 and LS = 60; s± = ± 1.5, d± = ± 3, and r = R0 = 150, the length of the rotor from its rotation axis to exit aperture.

Close modal

We obtain an explicit formula for the ToF profile shapes in three steps: (1) relates the location d(L) where a beam hits the detector to the distance L traveled from the rotor exit; (2) transforms I(d), the fraction of the intensity at the detector location, into I(L); and (3) then L is specified in terms of the rotor peripheral speed, Vrot, and beam lab speed, w = u + Vrot. For step (1) we take advantage of the smallness of the y-coordinate, as seen in Fig. 11, by neglecting y2 in the second part of Eq. (6) and by using the approximation x = LD − L. Then, using Eq. (7) we obtain x2 = 2r(mx + b) and

( L D L ) 2 = 2r [ d ( 1 L/L 0 ) + s + ( L/L 0 ) ] ,
(11)

where L0 = LD − LS. Thus,

d(L) = [ ( L D L ) 2 / 2r s + ( L/L 0 ) ] / [ ( 1 L/L 0 ) ] .
(12)

In step (2) we include a factor of L−2 to account for the drop in beam intensity with distance from the nozzle exit, so we obtain

I ( L ) / L 2 = [ ( d(L) + d + ) / ( d + d _ ) ] / L 2 ,
(13)

aside from a normalization factor. For step (3), transforming from L to time differs somewhat for the slowing and speeding modes, since the rotor moves in opposite directions. As depicted in Fig. 11, the initial transmission to the detector occurs at different rotor orientations, ϕ±, with corresponding pathlengths, L±, to the detector. The time required to reach intermediate points (ϕ, L) is proportional to r(ϕ − φ±), the arc length along the rotor orbit, which is well approximated by (L± − L). The travel time from points (ϕ, L) to the detector is closely approximated as L/w, since spread of the lab speed is quite small. For either mode, if we set a stopwatch to start from the initial point (ϕ±, L±), the total time of flight is given by

t(L) = ( L ± L ) / V rot + L/w .
(14)

However, to compare with the observed profiles, as in Fig. 9, where the time scale has its zero when the rotor reaches point (0,0), the watch needs to be reset as

Δ t(L) = t(L) t ( L D ) = ± ( L L D ) ( u/w | V rot | ) ,
(15)

where (+) pertains to slowing (as Vrot < 0) and (−) for speeding (as Vrot > 0).

Figure 12 illustrates results for slowing and speeding modes, as obtained from Eq. (13) with the geometric parameters listed in the caption of Fig. 11. The top pair of panels (a) and (a′) plot I(L)/L2 versus L, over the range specified by Eq. (9), which extends between the limits L+ = 88 mm and L_ = 174 mm. Pathlengths marked L1 and L2 define the FWHM and L3 designates the maximum intensity. Thus, Eq. (15) specifies the ToF width as

FWHM = ± ( L 1 L 2 ) ( u/w | V rot | ) .
(16)

For both the slowing and speeding modes, the model finds (L1 − L2) = 47 mm. Since the beam flow velocity is also the same, the model predicts that the FWHM is merely inversely proportional to the product of the beam lab velocity and the rotor speed. That accounts fairly well for the striking variation of the observed FWHM seen in Fig. 8. A modest adjustment, (L1 − L2) = 39 mm, gives close agreement (curve plotted in Fig. 8) with most of the data, except for slowing below about −200 m/s. Similarly, the ToF for the peak intensity (denoted Δtpk) may be obtained from Eq. (16) with ±(L1 − L2) replaced by ±(L3 − LD), which is 16 mm for the slowing mode and 36 mm for the speeding mode. The results for Δtpk given by the model compare much less well with the observed values listed in Table I than for the FWHM. However, the model nicely simulates asymmetric aspects of the profiles. The nominal ϕo = 6°, inferred in Fig. 7, represents a rough average between the limiting rotor orientations (ϕ+ = 12.5° and ϕ_ = 21.7°). The skewed shape of profiles and its variation with rotor speed and direction, prominent in Fig. 9, reflect the denominator of Eq. (12) in the model. These aspects are illustrated in the lower pair of panels (b) and (b′) in Fig. 12, which exhibit ToF profiles obtained from Eq. (15) for ±25 Hz and ±275 Hz. The ToF profiles for the ±25 Hz cases closely resemble the (a) and (a′) pathlength distributions. That occurs because the sedate rotor speed (|Vrot| = 23 m/s) is much lower than the lab speed (w = 303 m/s for slowing, 350 m/s for speeding). Hence the emitted beam in effect takes snapshots that map onto the detector the slow motion of the rotor. For ±275 Hz, the profile shapes change substantially. In the slowing case, the rotor speed (|Vrot| = 259 m/s) is much higher than the lab speed (w = 68 m/s), and thereby spreads out the mapping to the detector. In the speeding case, the rotor speed (again Vrot = 259 m/s) is comparable to but below the lab speed (w = 586 m/s), so the spreading is less pronounced.

FIG. 12.

Shapes of ToF profiles, left panels for the slowing mode and right panels for the speeding mode. (a) and (a′) Beam intensity at the detector as function of pathlength L from rotor exit aperture, obtained from model of Eq. (13), using the geometric quantities specified in the caption of Fig. 11. Dashed lines designate pathlengths L1 and L2 that define FWHM, and L3 marks intensity peak. (b) and (b′) Simulated time-of-flight profiles obtained from Eq. (15), which relates travel time to path lengths. Examples shown are for rotor frequencies ±25 Hz and ±275 Hz; the ToF scales are adjusted to match Fig. 9. Short spikes represent very narrow hypothetical profiles obtained from Eq. (5) by presuming that beams are emitted only when the rotor was oriented at ϕ = 0°, so with flight time to the detector ToF = LD/w. The spikes (red) labeled SS pertain to a stationary source (w = u = 327 m/s; ToF = 0.37 ms). The shorter dashed spikes pertain to ±25 Hz (w = 303 and 350 m/s; ToF = 0.40 and 0.34 ms, respectively) and shorter dotted ones to ±275 Hz (w = 68 and 586 m/s; ToF = 1.96 and 0.20 ms).

FIG. 12.

Shapes of ToF profiles, left panels for the slowing mode and right panels for the speeding mode. (a) and (a′) Beam intensity at the detector as function of pathlength L from rotor exit aperture, obtained from model of Eq. (13), using the geometric quantities specified in the caption of Fig. 11. Dashed lines designate pathlengths L1 and L2 that define FWHM, and L3 marks intensity peak. (b) and (b′) Simulated time-of-flight profiles obtained from Eq. (15), which relates travel time to path lengths. Examples shown are for rotor frequencies ±25 Hz and ±275 Hz; the ToF scales are adjusted to match Fig. 9. Short spikes represent very narrow hypothetical profiles obtained from Eq. (5) by presuming that beams are emitted only when the rotor was oriented at ϕ = 0°, so with flight time to the detector ToF = LD/w. The spikes (red) labeled SS pertain to a stationary source (w = u = 327 m/s; ToF = 0.37 ms). The shorter dashed spikes pertain to ±25 Hz (w = 303 and 350 m/s; ToF = 0.40 and 0.34 ms, respectively) and shorter dotted ones to ±275 Hz (w = 68 and 586 m/s; ToF = 1.96 and 0.20 ms).

Close modal

For contrast, Fig. 12 panels (b) and (b′) each include trios of short spikes. These represent very narrow hypothetical profiles obtained from Eq. (5) by supposing that beams were emitted only when the rotor was in the “ideal shooting” position at ϕ = 0°, for which the travel time to the detector is ToF = LD/w. The spike labeled SS pertains to a stationary source (w = u), the others to the ±25 Hz and ±275 Hz rotor frequencies.

In summary, using a pulsed supersonic source makes feasible a high input gas pressure that produces high beam density and a very narrow velocity width (Table II). Rotating the source spreads out pathlengths to the detector, which dominate ToF profiles, but simply shift up or down the velocity distribution without altering its width.

The rotating source usefully enlarges the scope of supersonic beams. Here we comment on aspects pertaining to applications facilitated by or requiring slow beams or merged beams.

The use of magnetic or electric field gradients to deflect or state-select beams of neutral gas-phase atoms or molecules is a venerable and versatile technique. The deflections attained for any given interaction and field configuration are proportional to the square of the transit time through the gradient and thus inversely proportional to the translational kinetic energy. As discussed extensively elsewhere,34 a rotating source can supply beams slow enough to enhance the deflection sensitivity and resolution, typically a hundredfold or more (despite the spreading limitation). Thereby, the chemical scope becomes much broader since feeble but ubiquitous interactions can be utilized, especially the induced electric dipole due to the molecular polarizability and magnetic moments resulting from molecular rotation or nuclear spins.

Particularly striking is enhanced sensitivity gained by the E-H balance, introduced by Bederson 50 yr ago.35 It employs congruent electric and magnetic deflecting fields that ensure that the gradient-to-field ratio and other factors are the same for both fields. When the field strengths are adjusted to attain a balance condition, molecules for which the electric and magnetic interactions have the same magnitude but opposite directions experience no net deflection. At the balanced condition, the dependence on kinetic energy cancels out. In an experiment with slow molecules the sensitivity in attaining the balance is much enhanced, providing high resolution in sorting states whose electric or magnetic effective dipole moments differ only modestly. Some prospective applications are detailed in Ref. 34. Often “inverse seeding” is used in supersonic beams, to slow a light molecule in a large excess of a heavy carrier gas (e.g., O2 in Xe). The E-H balance provides a means to efficiently filter the seeded molecule from the carrier gas. The high sensitivity of the balance also makes feasible microwave spectroscopy of nonpolar molecules. An example of current interest is Na2, among alkali dimer molecules populating ultracold traps.36 The alkali dimers are especially amenable for the E-H balance by virtue of having unusually large molecular polarizabilities and nuclear spin magnetic moments. For Na2, both the E and H field strengths are required and microwave frequencies for the lowest few JJ + 2 transitions fall in convenient ranges. The rotating source can produce a slow, intense beam with large dimer content.

When employed in the slowing mode, the rotating source can augment the operation of multistage Stark10 or Zeeman decelerators,12,13 by feeding preslowed molecules into the initial stage. A decelerator then needs fewer stages and can deal better with molecules that interact only weakly with the electric and/or magnetic fields. Clustering of the carrier gas would not be a handicap since the decelerator fields will select the unattached seed species. As yet, we have not had the opportunity to team up with a decelerator. However, comparison can be made with Zeeman deceleration of O2, a strongly paramagnetic molecule. The 64-stage decelerator developed by the Raizen group at Austin36 used input from a pulsed supersonic beam, with O2 seeded in Kr at flow velocity of about 389 m/s. The decelerator selects only low-field seeking molecules; for O2 nearly all of those were in a single quantum state (K = 1, J = 2, MJ = 2). At each stage, the decelerator removed from the selected molecules about 1.5% of their initial kinetic energy, in all ∼95%, thereby slowing them to 83 ± 3 m/s.37 The original rotating source at Harvard, using Xe as the carrier gas, slowed O2 to 67 m/s24 and our previous pulsed rotating source, using Kr as the carrier, slowed O2 to 126 m/s.38 Hence, the counter-rotating source removed more than 95% of the initial kinetic energy of O2 seeded in Xe and about 90% for O2 seeded in Kr. If the rotating source were coupled with the Austin decelerator, removing the remaining kinetic energy of O2 would require only a few stages, 3 or 4 if seeded in Xe and 7 or 8 in Kr.

The intensity of the 83 m/s packet of O2 obtained with the 64-state decelerator, recorded as the average of 200 pulses, was estimated to be in the range ∼108 cm−3.39 The intensity delivered by the rotating source, in a single pulse, was estimated to exceed ∼109 cm−3. Moreover, the pulses emerging from a decelerator are restricted in volume (typically to ∼0.03 cm3), whereas those from the rotating source are ∼50-fold larger. The correspondingly larger flux of molecules adds to the advantage of markedly reducing the number of stages by coupling the rotating source to a decelerator. The coupling may be particularly congenial to use in a new method proposed by Raizen and colleagues for slowing atoms.40 Termed “magneto-optical cooling” (MOP), it promises to surpass laser cooling by providing much wider chemical scope and far higher flux of ultracold atoms. The method exploits internal-state optical pumping and velocity-sensitive stimulated rapid adiabatic passage (STIRAP),41 preceded by Zeeman deceleration.

Obtaining very low relative collision energies via merged beams has the great advantage that both beams can be operated in the usual “warm” range or not far below it.14–23 As well as the major benefit in intensity, many molecular species not amenable for slowing techniques become available as reactants. For a stationary supersonic source, to adjust the flow velocity requires changing the temperature or, if the beam species of interest is seeded in a carrier gas, changing the seed ratio. That is awkward and often imprecise. With a rotating source, the lab speed can be scanned easily and precisely to better than 1 m/s by merely changing the rotor speed. The velocity width for a beam from the rotating source is likely to be wider (especially in the slowing mode). It will often be desirable to further narrow the velocity spreads in both beams by means of electric or magnetic fields or a mechanical chopper. Such narrowing operations can benefit from having the peak intensities of both beams preselected to occur near the desired relative velocity.

The recent use of merged beams for collisions of neutral molecules, emulating a technique long used with ions, may seem belated. That perhaps was due to concern about resolution. For keV ions, the velocity spreads in the parent beams can readily be made quite small, typically ∼0.1% or less. For thermal molecular beams, however, the velocity spreads are usually ∼10% or more. For merged beams, the high intensity makes feasible reducing the velocity spreads in various ways, but at best cannot narrow them below ∼1%. Even then, the merged energy resolution would be inadequate for experiments in the subkelvin range, according to customary calculations.14,15 This dire prospect was banished by the Weizmann Institute experiments.17 The customary calculations indicated that the lowest relative collision energy attainable would not have reached below 350 mK and the energy resolution would have been much too poor to resolve the orbiting resonances. Yet the experiments attained collision energy more than two orders of magnitude lower, along with one order of magnitude improvement in resolution. This revealed a dramatic, overlooked advantage of pulsed supersonic nozzles. If the pulse duration is short compared to the time-of-flight, a correlation in velocity-position space develops such that the local velocity standard deviation decreases. This effect and its consequences are modeled in a lucid paper by Shagam and Narevicius,18 who also analyze possible further improvements in resolution by varying the detection time duration.

Our current rotating beam source is still an exploratory prototype. It is relatively simple and robust, yet adequate to enhance substantially many varieties of experiments that deal with control of translational motion of molecules. Prospects are encouraging for three important improvements.

  1. Shortening the pulse durations would provide better resolution for merged beams and also reduce the overlap of pulses that occurs at high rotor frequencies in the slowing mode. Magnetic or electrically activated valves of several kinds can provide pulse durations near 20 μs,42 and comparably short pulses have been obtained using a high-speed mechanical chopper wheel, especially suited to deal with corrosive gases.43 The shortening device need not be connected with the rotor but can sit ahead of the skimmer.

  2. Increasing the peripheral velocity of the rotor would, in the counter-rotating mode, enable offsetting much more of the supersonic flow velocity or, in the speeding mode, augment the flow velocity much further. Increasing Vrot = 2πωR0 can be done either by increasing the rotor frequency or lengthening the rotor. Our current rotor has been operated up to Vrot ∼ 500 m/s, but not routinely because lower speeds suffice to match the flow velocity of Xe or Kr employed as carrier gas to slow lighter passengers such as O2 via “inverse seeding.” We expect to attain Vrot > 600 m/s or higher by extending the length (to 20 cm) and optimizing the taper of the rotor25,31 and also by upping the spinning frequency to at least 700 Hz. At such speeds, vibrations can become limiting.26 However, we use the same driving motor and mounting as our Harvard precursor,24 which ran serenely at 650 Hz, albeit with a shorter rotor (10 cm). Magnetically levitated carbon fiber rotors offer an elegant option; such rotors (solid rather than hollow) have been operated up to Vrot ∼ 1500 m/s.31 By attaining Vrot > 600 m/s, molecules such as O2 could be slowed to lab speeds of ∼100 m/s without use of inverse seeding. That would be a great advantage, because inverse seeding reduces the centerline intensity of the seed species both by its small mole fraction and by another a factor of about mseed/mcarrier due to mass defocusing. Also, the centrifugal fractionation disfavors the lighter seed species. Escaping those effects by feeding a decelerator with a pure beam would gain more than 100-fold in intensity.

  3. Lowering the temperature of the input gas and rotor would reduce the flow velocity, so in the counter-rotating mode a given Vrot could obtain a corresponding reduction in the lab speed. Stationary supersonic sources are typically operated at T0 ∼ 300 K, but sometimes have been cooled to ∼150 K, thereby, as expected, lowering by 2−1/2 the flow velocity.36,44 For the rotary source, the input gas could readily be cooled, but both the rotor and its driving motor, which generate appreciable heat, would in effect have to be enclosed within a refrigerator. That might entail more engineering than the mechanical options mentioned above.

Our chief focus has been on slowing molecules, to obtain longer deBroglie wavelengths. However, spinning in the opposite direction, the rotary supersonic source in its speeding mode can increase kinetic energy of beam collisions enough to overcome potential barriers for a host of chemical reactions. Sixty years ago, Philip Moon was a pioneering apostle for rotor accelerated molecular beams.31,45–49 He considered trying effusion from a hollow rotor, but opted to use a solid rotor. Using it to sweep up molecules from a gas at low pressure or evaporating substances deposited on the tip of the rotor, Moon generated very fast beams. Ultimately, with carbon fiber rotors and magnetic levitation, he developed a crossed-beam system employing two synchronous, phase-locked rotors, which attained relative velocities up to 3.5 km/s. He remarked: “Rotor-impelled beams remain to be exploited further…”

We are grateful for support of this work by the National Science Foundation (under Grant No. CHE-1309961) and by the TAMU Institute for Quantum Science and Engineering. We also thank Don Naugle for advice and Simon North for discussions of several experimental aspects.

Our rebuilt FIG was calibrated against a standard ionization gauge (Granville Phiollips 355 Micro-Ion Gauge, GP-355), using static pressures of Xe in the detector chamber. The pressure readings obtained with GP-355 were cross-checked with another gauge (Vacuum Generators nude gauge). The FIG voltage readings were recorded for a wide range of emission currents (0.02–2.0 mA). Figure 13 displays typical calibration results, plotting the GP-355 pressure readings vs. the FIG voltage readings and exhibiting the strong dependence on emission current. Figure 14 plots the coefficients C, L, and Q for a quadratic fit to the calibration data, specifying the dependence on emission current. The nonlinearity can be attributed to space charge effects that occur at high pressures. The calibration data are essential both for determining beam densities and avoiding use of currents that would burn out the FIG filaments.

FIG. 13.

Calibration curves of the FIG for different emission currents (in mA). The inset shows the region of small pressures, which corresponds to the slowing mode. There the FIG output is nearly linear up to 10−4 Torr pressure.

FIG. 13.

Calibration curves of the FIG for different emission currents (in mA). The inset shows the region of small pressures, which corresponds to the slowing mode. There the FIG output is nearly linear up to 10−4 Torr pressure.

Close modal
FIG. 14.

Dependence on emission current of coefficients C (circles), L (squares), and Q (triangles) of quadratic fit, P = C + LV + QV 2, made to the FIG calibration curves of Fig. 13.

FIG. 14.

Dependence on emission current of coefficients C (circles), L (squares), and Q (triangles) of quadratic fit, P = C + LV + QV 2, made to the FIG calibration curves of Fig. 13.

Close modal

Other properties of the FIG, in addition to those mentioned in the text, are DC voltage output: 4 mV to −10 V; emission current: 5 μA to 3 mA, 7 ranges; filament current: 2 A; filament voltage: up to 5 V; grid potential: 160 V; collector potential: 0 V; and power requirement: 40 W, 115 V/60 Hz. A photo of a FIG similar to ours is shown in Ref. 50.

1.
Cold Molecules: Theory, Experiment, Applications
, edited by
R. V.
Krems
,
W. C.
Stwalley
, and
B.
Friedrich
(
CRC Press
,
New York
,
2009
).
2.
L.
Carr
and
J.
Ye
, “
Focus on cold and ultracold molecules
,”
New J. Phys.
11
,
055009
055048
(
2009
).
3.
Cold and ultracold molecules, Faraday Discuss.142, 5–488 (
2009
).
4.
O.
Dulieu
,
R. V.
Krems
,
M.
Weidemuller
, and
S.
Willitsch
, “
Physics and chemistry of cold molecules
,”
Phys. Chem. Chem. Phys.
42
,
18703
19174
(
2011
).
5.
B. K.
Stuhl
,
M. T.
Hummon
, and
J.
Ye
,
Annu. Rev. Phys. Chem.
65
,
501
518
(
2014
).
6.
K.-K.
Ni
,
S.
Ospelkaus
,
D.
Wang
,
G.
Quemener
,
B.
Neyenhuis
,
M. H. G.
de Miranda
,
J. L.
Bohn
,
J.
Ye
, and
D. S.
Jin
,
Nature
464
,
1324
(
2010
).
7.
S.
Koop
,
H. F.
Ferlaino
,
M.
Berningr
,
M.
Mark
,
H. C.
Naegerl
,
R.
Grimm
,
J. P.
D’incao
, and
B. D.
Esry
,
Phys. Rev. Lett.
104
,
053201
(
2010
).
8.
M. H. G.
de Miranda
,
A.
Chotia
,
B.
Neyenhuis
,
D.
Wang
,
G.
Quemener
,
S.
Ospelkaus
,
J. L.
Bohn
,
J.
Ye
, and
D. S.
Jin
,
Nat. Phys.
7
,
502
(
2011
), and work cited therein.
9.
C.-H.
Wu
,
J. W.
Park
,
P.
Ahmadi
,
S.
Will
, and
M.
Zwierlein
,
Phys. Rev. Lett.
109
,
085301
(
2012
).
10.
S. Y. T.
van de Meerakker
,
H. L.
Bethlem
, and
G.
Meijer
,
Nat. Phys.
4
,
595
(
2008
).
11.
M. T.
Bell
and
T. P.
Softley
,
Mol. Phys.
107
,
99
(
2009
).
12.
S. D.
Hogan
,
M.
Motsch
, and
F.
Merkt
,
Phys. Chem. Chem. Phys.
13
,
18705
(
2011
).
14.
L.
Sheffield
,
M.
Hickey
,
V.
Krasovitsky
,
K. D. D.
Rathnayaka
,
I. F.
Lyuksyutov
, and
D. R.
Herschbach
,
Rev. Sci. Instrum.
83
,
064102
(
2012
).
15.
Q.
Wei
,
I.
Lyuksyutov
, and
D.
Herschbach
,
J. Chem. Phys.
137
,
054202
(
2012
).
16.
R. A.
Phaneuf
,
C. C.
Havener
,
G. H.
Dunn
, and
A.
Muller
,
Rep. Prog. Phys.
62
,
1143
1180
(
1999
), and work cited therein.
17.
A. B.
Henson
,
S.
Gersten
,
Y.
Shagam
,
J.
Narevicius
, and
E.
Narevicius
,
Science
338
,
234
(
2012
).
18.
Y.
Shagam
and
E.
Narevicius
,
J. Phys. Chem. C
117
,
22454
(
2013
).
19.
E.
Lavert-Ofir
,
Y.
Shagam
,
A. B.
Henson
,
S.
Gersten
,
J.
Klos
,
P.
Zuchowski
,
J.
Narevicius
, and
E.
Narevicius
,
Nat. Chem.
6
,
332
(
2014
).
20.
J.
Jankunas
,
B.
Bertsche
,
K.
Jachymski
,
M.
Hapka
, and
A.
Osterwalder
,
J. Chem. Phys.
140
,
244302
(
2014
).
21.
J.
Jankunas
,
B.
Bertsche
, and
A.
Osterwalder
,
J. Phys. Chem. A
118
,
3875
(
2014
).
22.
J.
Jankunas
,
K.
Jachymski
,
M.
Hapka
, and
A.
Osterwalder
,
J. Chem. Phys.
142
,
164305
(
2015
).
24.
M.
Gupta
and
D.
Herschbach
,
J. Phys. Chem. A
103
,
10670
(
1999
);
M.
Gupta
and
D.
Herschbach
,
J. Phys. Chem. A
105
,
1626
(
2001
).
25.
M.
Gupta
, “
A mechanical means of producing cold, slow beams of molecules
,” Ph.D. thesis,
Harvard University
,
2000
.
26.
M.
Strebel
,
F.
Stienkemeier
, and
M.
Mudrich
,
Phys. Rev. A
81
,
033409
(
2010
).
27.
M.
Strebel
,
S.
Spieler
,
F.
Stienkemeier
, and
M.
Mudrich
,
Phys. Rev. A
84
,
053430
(
2011
).
28.
M.
Strebel
,
T.-O.
Muller
,
B.
Ruff
,
F.
Stienkemeier
, and
M.
Mudrich
,
Phys. Rev. A
86
,
062711
(
2012
).
29.
L. S.
Sheffield
, “
Velocity augmentation of a supersonic source and the production of slow, cold molecular beams
,” Ph.D. thesis,
Texas A&M University
,
2014
.
30.
D. R.
Miller
, in
Atomic and Molecular Beam Methods
, edited by
G.
Scoles
(
Oxford University Press
,
New York
,
1988
), Vol.
1
, p.
14
.
31.
P. B.
Moon
,
C. T.
Rettner
, and
J. P.
Simons
,
J. Chem. Soc., Faraday Trans. 2
74
,
630
(
1978
).
32.
C.
Klots
,
J. Chem. Phys.
72
,
192
(
1980
).
33.
J. W.
Beams
,
Rev. Mod. Phys.
10
,
245
(
1938
).
34.
T. J.
McCarthy
,
M. T.
Timko
, and
D. R.
Herschbach
,
J. Chem. Phys.
125
,
133501
(
2006
).
35.
V.
Taarnovsky
,
M.
Bunimovicz
,
B.
Stumpf
, and
B.
Bederson
,
J. Chem. Phys.
98
,
3894
(
1993
), and references cited therein.
36.
D. R.
Herschbach
, in Ref. 3, pp. 9–23.
37.
E.
Narevicius
,
A.
Libson
,
C. G.
Parthey
,
I.
Chavez
,
J.
Narevicius
,
U.
Even
, and
M. G.
Raizen
,
Phys. Rev. A
77
,
051401
(
2008
).
38.
V.
Krasovitskiy
, unpublished experiment done in 2012, using apparatus of Ref. 14.
39.
E.
Narevicius
and
M. G.
Raizen
,
Chem. Rev.
112
,
4879
(
2012
).
40.
M. G.
Raizen
,
D.
Budker
,
S. M.
Rochester
,
J.
Narevicius
, and
E.
Narevicius
,
Opt. Lett.
39
,
4502
(
2014
).
41.
K.
Bergmann
,
N. V.
Vitanov
, and
B. W.
Shore
,
J. Chem. Phys.
142
,
170901
(
2015
).
42.
B.
Yan
,
P. F. Y.
Claus
,
B. G. M.
van Oorschot
,
L.
Gerritsen
,
A. T. J.
Eppink
,
S. Y. T.
van de Meerakker
, and
D. H.
Parker
,
Rev. Sci. Insrum.
84
,
023102
(
2013
).
43.
J.
Lam
,
C.
Rennick
, and
T.
Softley
,
Phys. Rev. A
90
,
063413
(
2014
).
44.
H. L.
Bethlem
and
G.
Meijer
,
Int. Rev. Phys. Chem.
22
,
73
(
2003
).
45.
T. H.
Bull
and
P. B.
Moon
,
Discuss. Faraday Soc.
17
,
54
(
1954
).
46.
P. B.
Moon
,
Proc. R. Soc. A
360
,
303
(
1978
).
47.
P. B.
Moon
and
M. P.
Rawls
,
Proc. R. Soc. A
423
,
361
(
1989
).
48.
P. B.
Moon
,
Proc. R. Soc. A
423
,
373
(
1989
);
P. B.
Moon
,
Proc. R. Soc. A
435
,
445
(
1991
).
49.
W. E.
Burcham
and
G. R.
Isaak
,
Biogr. Mem. Fellows R. Soc.
42
,
248
(
1996
).
50.
W. R.
Gentry
, in
Atomic and Molecular Beam Methods
, edited by
G.
Scoles
(
Oxford University Press
,
New York
,
1988
), Vol.
1
, p.
72
.