The experiments were performed in a molecular beam machine that is optimized for high-resolution crossed beam scattering experiments. It consists of a 2.6 meter-long Stark decelerator, two conventional molecular beams that are positioned at an angle of 90° and 180° with respect to the Stark decelerator’s axis, and a velocity map imaging (VMI) detector. This apparatus is schematically shown in Fig. 1, and has been described in detail elsewhere [33]. We here only describe the parts that are most relevant for the studies presented here.
The Stark decelerator is loaded with a molecular beam that is produced in a relatively large source chamber, that is pumped by a 1200 l/s turbo pump. The molecular beams formed are thus not limited by interactions with the vacuum chambers walls, or by limited pumping capacity. A 3 mm diameter commercially available skimmer (Beam Dynamics, model 2) is positioned between the source chamber and the Stark decelerator. A unique feature of our apparatus is that this skimmer is mounted on a movable gate valve [34], such that the source chamber can be vented without the need for breaking the vacuum in the remainder of the apparatus. This ensures the fast exchange of valves or adjustment of valve-to-skimmer distance.
Either a JV or a NPV is used to produce the molecular beam. Both valves are mounted in a cylindrical tube, which is inserted in a cylindrical donut-shaped bracket that is suspended inside the source chamber. This bracket is aligned with respect to the skimmer and axis of the Stark decelerator, and ensures that valves are positioned correctly and reproducibly. The distance between valve orifice and skimmer can be varied between 2 cm and 20 cm, and is adjusted by simply moving the tube inside the bracket.
In this work, mostly ND 3 molecules are used, as this molecule is amenable to the Stark deceleration technique, and is a stable gas. Molecular beams of ND 3 can thus be produced by simply seeding small amounts of ND 3 in a carrier gas, without the need for production methods that can disturb the beam such as photodissociation or dissociation in a discharge. In a limited number of experiments that involve VMI, NO radicals are used. The quantum state for ND 3 and NO that is selected by the Stark decelerator is the upper inversion level of the |J
K
〉=|11〉 state, and the upper Λ-doublet level of the X
2
Π
1/2,J=1/2 state, respectively.
The 2.6 meter-long Stark decelerator consists of 317 pairs of high-voltage electrodes that are placed horizontally and vertically in an alternating fashion [9]. The electrodes are spaced (center-to-center) 8.25 mm with respect to each other in the longitudinal direction, and they leave a 3 × 3 mm 2 opening for the beam to pass. All electrodes that are mounted in a certain direction are connected to each other such that the decelerator is operated with only four independent high voltage switches. The operation and characterization of a Stark decelerator has been described in detail before [35], and will not be repeated here. The Stark decelerator is operated in the s=3 mode [36] throughout, and a voltage difference of 30 kV is applied between opposing electrodes. A phase angle of ϕ
0=0° is used to guide the beam through the decelerator at constant speed; deceleration occurs for ϕ
0>0°.
The packet of molecules emerging from the decelerator is detected using Resonance Enhanced Multi Photon Ionization (REMPI) at a distance of 72 mm from the exit of the decelerator. For ND 3, we use a one-color (2+1) REMPI scheme at a wavelength around 317 nm. A commercially available dye laser is used to generate light at the appropriate wavelength. Typically, the dye laser produces an energy of around 15 mJ per pulse in a 4 mm diameter spot, while the laser is focussed into the interaction region by a spherical lens with a focal length of 43 cm. For NO, we use a two-color (1+1’) REMPI scheme that allows for the ionization of NO molecules at the energetic threshold. This is essential for high-resolution measurements of the beam velocity distribution using velocity map imaging [25, 33].
A set of ion optics consisting of a repeller, an extractor and a grounded plate is used to accelerate the ions towards a microchannel plate detector (MCP) connected to a phosphor screen. The ions can be detected in two different ways. In the first, the output of the MCP detector is directly connected to a digital oscilloscope to record the integral ion signal. In this mode of detection, the voltages on repeller and extractor plates are chosen such that the ion signal is dispersed over a large area on the MCP to reduce possible detector saturation effects. This method is most suited to compare signal intensities. In the second, the repeller and extractor voltages are tuned to velocity mapping conditions, and two-dimensional images of the ion arrival positions are recorded using the phosphor screen and a CCD camera. This VMI mode of detection allows for direct measurements of beam speeds and velocity distributions [33, 37].
Additional molecular beam sources are installed at crossing angles of 90° and 180°. At 90° a JV is mounted, whereas a NPV is used at 180°. Both beam sources are separated from the interaction region by 2 mm diameter skimmers (Beam Dynamics, model 2) that are mounted at a distance of 87 mm from the interaction region. This configuration allows a direct comparison between the conventional beam pulses and the pulses that emerge from the decelerator.
Procedures to optimally load the molecular beam into the decelerator
To appreciate the various aspects that play a role when coupling the beam into the decelerator, we first discuss the operation principles of the Stark decelerator using the schematic representation in Fig. 2. It is instructive to use phase-space coordinates in the discussion, i.e., the position (z) and velocity (v
z
) of particles in the longitudinal direction. A proper discussion on the operation principles of Stark decelerators, and an introduction to the relevant terminology such as phase angle ϕ
0 and synchronous molecule can be found elsewhere [28, 35]; we here restrict ourselves to the most basic concepts only.
The solid lines indicate the trajectories in phase-space that molecules will follow if the decelerator is operated using ϕ
0=0° (left panel) or ϕ
0=70° (right panel). Closed curves in the phase-space diagram correspond to bound orbits, i.e., molecules within the ’bucket’ or ’phase fish’ bound by the thick contour (called ’separatrix’) will oscillate around the synchronous molecule and are kept together [38]. These molecules are selected by the decelerator from the molecular beam pulse, and transferred to the final velocity at the end of the decelerator. This process occurs without losing any molecules in this bucket, and without the usual spreading of the molecules during the time they spend inside the decelerator. Note that since in a Stark decelerator all electrodes are coupled to each other, there is a series of buckets spaced by twice the distance between adjacent electrodes. For the decelerator used in this work, this distance is 16.5 mm.
The beam of molecules exiting the valve and passing the skimmer will occupy a certain area in phase-space. This area is schematically illustrated in Fig. 2 by the red ellipsoid. We here only discuss the situation in which the molecule of interest is a stable gas, i.e., the molecules are not produced at a well-defined time by a laser or discharge pulse. The exact shape of this area then strongly depends on the valve used: in the z direction, the width of the area is roughly determined by the opening time τ of the valve multiplied by the mean speed v
0 of the beam. The longer the valve emits molecules, the wider the distribution will be. In the v
z
direction, the width is determined by the velocity distribution of the molecules. Note that the ellipsoid is drawn slightly tilted to represent the evolution of the phase-space distribution in the free flight region between valve orifice and entrance of the Stark decelerator [35].
Optimal loading of the beam pulse into the decelerator is achieved if (i) the mean speed v
0 of the beam coincides with the central speed of the first bucket, and (ii) the decelerator is switched on when the most intense part of the beam has reached the center position z
0 of the first bucket. To experimentally find both parameters, and to select the appropriate timings and trigger pulses in the experiment, can be less straightforward than one may think. The largest uncertainty originates from the beam source itself. It is usually unknown at which time with respect to the valve trigger pulse the molecules are emitted from the valve. In addition, the final mean velocity of the beam is usually only reached at a significant distance from the nozzle (often only even after passage through the skimmer). In addition, the valve may produce a gradient in beam speeds over the valve temporal opening profile.
We therefore here describe a protocol to experimentally determine the correct timings, such that the pulse of molecules is optimally loaded into the first bucket. This protocol will also serve as an excellent proxy for the characteristics of the molecular beam pulse emitted from the valve. The protocol is further illustrated by experimental data on the guiding (ϕ
0=0°) and deceleration (ϕ
0=50°) of ND 3 molecules seeded in Kr using an NPV. For this, the decelerator is programmed to select a packet of molecules with an initial velocity of 435 m/s, whereas the molecules emerge from the decelerator with a final velocity of 435 m/s and 313 m/s, respectively.
The relevant distances in the experiment are defined in Fig. 3
a, together with a schematic representation of the trigger scheme in the experiment in panel b. The distance between valve orifice and Stark decelerator is denoted by L
1, the decelerator itself has length L
2, and the distance between exit of the decelerator and interaction region is given by L
3. In the most basic trigger scheme, the experiment only involves three timings. We define the trigger pulse to open the valve as t=T
0. The first high voltage pulse to the Stark decelerator is then applied at t=T
inc
. It is convenient to apply the burst sequence at the time when the synchronous molecule has reached the center of the first electrode pair. We refer to this time as the incoupling time. The Stark decelerator itself is operated by applying a burst of high voltage pulses to the electrodes through a programmable pulse generator. The burst itself is pre-calculated, and cannot (and should not!) be optimized during the experiment. Finally, the laser is fired at time t=T
detect
, leaving a time difference Δ
T
ff
between the laser trigger pulse and the time T
off
at which the last high voltage pulse of the decelerator is switched off. During this time, the molecules propagate in free flight with the final velocity that was obtained in the last stage of the decelerator.
The first task is to obtain a rough estimate of the mean beam speed v
0. This is most easily determined by measuring the arrival time distribution of the beam in free flight, i.e., no voltages are applied to the decelerator, and the signal on the detector is recorded as a function of T
detect
. This ensures that the beam is measured with no distortions originating from the switched electric fields. It is noted that if the length of the decelerator does not allow for such free flight measurements, a DC voltage of a few kV can be applied to the decelerator to raise signal levels. A time-of-flight (TOF) profile for ND 3 seeded in Kr is shown in panel c. The beam arrives about 6.6 ms after T
0, and the arrival time distribution has a width (FWHM) of about 12 %. From the mean arrival time, and the known dimensions of the experiment, a first rough estimate of the mean beam speed v
0 is obtained.
The protocol starts with applying a time sequence to the decelerator based on v
0 and ϕ
0=0°, and by configuring the trigger scheme such that the laser trigger pulse is defined with respect to T
inc
, rather than T
0 or T
off
. In the remainder of this paper, we therefore refer to TOF as the time difference between T
detect
and T
inc
, i.e, the TOF is the time needed to propagate from the entrance of the Stark decelerator to the interaction region, independent of the time spent in the source region. The value for Δ
T
ff
is calculated from the final velocity of the packet – which is again v
0 for ϕ
0=0° – and the known distance L
3
1. The advantage of linking the laser trigger to T
inc
is that now T
inc
can be scanned with respect to T
0. Referring back to Fig. 2, such a scan effectively moves the buckets along the z-axis. Since the laser trigger pulse was already synchronized to the burst sequence (and thus final velocity of the packet), a large signal should appear on the detector whenever the beam overlaps with the first bucket. We refer to such a scan as incouple time scan (ITS). Such an ITS for a time sequence with v
0=435 m/s and ϕ
0=0° is shown in the inset to panel d. The distribution is symmetric, and has a width (FWHM) of 33 μs. This width results from a convolution of bucket size and the spatial extent of the beam at the entrance of the decelerator (see also Fig. 2). From this, we can estimate τ∼15−20μs for the NPV.
The second step of the protocol is to select the optimal value of T
inc
from the ITS, and to record a TOF as is shown in panel d by scanning T
detect
with respect to T
inc
. If the rough estimate of v
0 indeed represents the mean velocity of the beam, a symmetric TOF should result, featuring a central intense peak and a series of small wiggles on either side of the central peak. A detailed interpretation of this structure is given elsewhere [35]. If the TOF is not symmetric, i.e., there is substantially more signal intensity on one side of the central peak, the protocol must be repeated using a new value of v
0 until a symmetric TOF is obtained. This procedure will result in the optimal selection of v
0 and T
inc
.
In the third step of the protocol the molecules are decelerated by simply applying a burst sequence pertaining to v
0 and ϕ
0>0° to the decelerator. Again, Δ
T
ff
is calculated from the exit velocity and L
3. To record an ITS, T
detect
is fixed based on the calculated time the molecules spend inside the decelerator, and the calculated value for Δ
T
ff
; to record a TOF, T
detect
is scanned with respect to T
inc
. The resulting ITS and TOF for ϕ
0=50° are shown in panel e. Clearly, a packet of molecules is selected from the molecular beam pulse, is decelerated, and arrives in the interaction region at later times. The ITS is slightly asymmetric and has a width of only 25 μs, reflecting the asymmetry and reduced size of the bucket compared to ϕ
0=0°. Note that the maximum in the ITS for ϕ
0=0° and ϕ
0=50° is found at almost the same time. This is the consequence of our choice to define T
inc
as the time when the synchronous molecule has reached the first electrode pair. The different center positions z
0 for buckets pertaining to different values of ϕ
0 are thus incorporated in the decelerator burst sequence, and for a given value for v
0 identical values for T
inc
are used throughout.
Influence of opening time on time-of-flight profiles
In the experimental TOF profiles as presented in panels d and e, the selected packet of molecules is well separated from the remainder of the molecular beam. This is even the case for the guiding sequence in panel d (ϕ
0=0°), where the final velocity of the packet is identical to the mean velocity of the molecular beam pulse. This ’contrast’ is the result of the relatively small value for τ of the NPV.
Indeed, an important criterium for the use of Stark-decelerated beams in crossed beam scattering experiments is the ability to produce a wide range of velocities with a TOF contrast that is similar to the ones presented in Fig. 3. Let’s therefore have a closer look at the influence of the valve opening time τ on the quality of the TOF profiles. Figure 4 shows TOF profiles that result from numerical trajectory simulations of different deceleration processes. These simulations pertain to the experimental conditions as present in the TOFs of Fig. 3, i.e., v
0=435 m/s and ϕ
0 is either 0° (left column) or 50° (right column). Three different valve opening times are used in the simulations: τ= 20 μs (panels a and b), τ= 50 μs (panels c and d), and τ= 100 μs (panels e and f). These are representative values for τ for an NPV, JV, and GV, respectively.
Clearly, the best contrast in the TOFs is obtained for valves with the shortest opening times. For large values of τ, the spatial extent of the beam at the entrance of the Stark decelerator exceeds the size of the first bucket. Multiple buckets can be filled, resulting in multiple peaks in the TOF. The spatial extent of the beam scales with v
0
τ, such that for v
0= 435 m/s one expects to start filling the second bucket when τ>35μs. This is indeed seen for τ= 50 μs in Fig. 4, where the signature of the second bucket can be identified.
For τ= 100 μs, multiple buckets are filled and the TOFs become progressively more congested. This has indeed been observed in Stark deceleration experiments that use a GV as beam source [39, 40]. Whereas for trapping experiments such a TOF does not necessarily impose a problem (as only a single bucket will be loaded into a trap), crossed beam scattering experiments may suffer significantly from the reduced contrast.
Based on these considerations, we consider the opening time of a GV too large for scattering experiments, and the use of this valve as a source for Stark deceleration experiments should be carefully considered. In addition, from extensive experience with various types of valves, the GV produces beams with rather low peak intensity. In the remainder of this paper, we therefore focus exclusively on the differences between the JV and NPV.