Download Double-arm three-dimensional ion imaging apparatus for the study

REVIEW OF SCIENTIFIC INSTRUMENTS 87, 023107 (2016)
Double-arm three-dimensional ion imaging apparatus for the study of ion
pair channels in resonance enhanced multiphoton ionization
M. S. Poretskiy,1,a) A. I. Chichinin,2 C. Maul,1 and K.-H. Gericke1
1
Institut für Physikalische und Theoretische Chemie, Technische Universität Braunschweig,
38106 Braunschweig, Germany
2
Institute of Chemical Kinetics and Combustion and Novosibirsk State University, 630090 Novosibirsk, Russia
(Received 1 October 2015; accepted 21 November 2015; published online 18 February 2016)
We present a novel experimental configuration for the full quantitative characterization of the
multichannel resonance enhanced multiphoton ionization (REMPI) of small molecules in cases
when the ion-pair dissociation channel is important. For this purpose, a double-arm time-of-flight
mass spectrometer with three-dimensional (3D) ion imaging detectors at both arms is constructed.
The REMPI of HCl molecules is used to examine the constructed setup. The apparatus allows
us to perform simultaneous measurements of the 3D velocity vector distributions of positive (H+,
HCl+, and Cl+) and negative (Cl−) photoions. The characterization consists of the determination of
“two-photon absorption cross sections” for the process HCl(X)+2hν → HCl∗, one-photon absorption
cross sections for subsequent processes HCl∗ + hν → HCl∗∗, and the probability of the subsequent
non-adiabatic transition HCl∗∗ → HCl(B) → H+ + Cl−, which leads to ionic pairs. All these data
should be obtained from the analysis of the dependencies of the number of ions on the laser energy.
The full characterization of the laser beam and the knowledge of the ion detection probability
are necessary parts of the analysis. Detailed knowledge of losses of produced ions in the mass
spectrometer before detection requires understanding and characterization of such processes like
electron emission from metallic grids under ion bombardment or charge transfer between positive
ions and the metal surface of the grids, like Cl+ + (grid) → Cl−. These important phenomena from
surface science are rarely discussed in the imaging literature, and here, we try to compensate for this
shortcoming. C 2016 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4936984]
I. INTRODUCTION
The resonance enhanced multiphoton excitation of molecules with subsequent fragmentation, photodissociation, or
photoionization has for decades been in the focus of interest of many laboratories as an effective method for studying
high-lying excited states and for monitoring chemical reaction products. The resonance enhanced multiphoton ionization
(REMPI) of diatomic molecules, HCl, for example, may occur
in several ways, see Refs. 1–4 and references therein,
nhν
hν
HCl(X) −−−→ HCl∗(IS1) −−→ HCl+ + e−,
+ hν
HCl −−→ Cl + H+ + e−,
hν
(2)
∗ hν
HCl∗(IS1) −−→ HCl∗∗(IS2) → H + Cl −−→ Cl+ + H + e−,
hν
→ H∗ + Cl −−→ Cl + H+ + e−,
+
HCl(B) → Cl + H .
−
(1)
(3)
(4)
(5)
Here, the non-radiative transition between different electronic
states is shown by a wave arrow, and the decays within a
single electronic state are shown by simple arrows. In the
simplest case, the molecule absorbs two photons (n = 2),
reaches an excited intermediate state IS1, and is then photoionized, see channel (1). In more complicated cases, there
are photoinduced transitions to superexcited states IS2 with
a)Electronic mail: [email protected]
subsequent decay into channels with excited atoms (3) and (4)
or into anion–cation pairs, also called “ion-pair” channel (5).
Hereafter, the initial intermediate states IS1 are referred to as
“excited states,” and the states IS2 are called “superexcited
states.” Sometimes the latter are also called “gateway” states
which are normally unknown. In the HCl molecule, the excited
state IS1 accessed in the first excitation step is frequently the
electronic B state having a double-minimum potential energy
curve, being a mixture of the Rydberg E1Σ+ state and the
valence V1Σ+ ion-pair state.
The general objective of our research in the recent years
has been to determine all IS2 states and quantitatively characterize all radiative and non-radiative transitions (1)–(5). In H2,
HX (X=F,Cl,Br), CH3Br, and several other molecules, an ionpair state has a double-well term with two minima at internuclear distances r 1 and r 2, where r 1 ≈ r e and r 2 ≫ r e , where r e
is the ground state internuclear distance. We use multiphoton
excitation, which opens the door for photoabsorption from the
ion-pair B state at large distances ∼r 2, which may be a new
kind of dynamics and/or spectroscopy, because the internuclear distances near r 2 are unavailable to one-photon excitation
from the ground state normally used in ion-pair studies. Thus,
the present study was partly stimulated by the interest in the
absorption dynamics at large internuclear distances and partly,
it is an attempt to characterize processes (1)–(5) quantitatively.
In this study, we focus on channel (5) because the ion-pair
formation is a very specific probe for superexcited states. A
full understanding of the channel mechanism is necessary for a
0034-6748/2016/87(2)/023107/15/$30.00
87, 023107-1
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quantitative description of processes (1)–(5), and it should also
help us to predict probabilities of ion-pair channels in other
molecules. Despite the long history and the large number of
photoion-pair studies, see reviews of Refs. 5–8, the mechanism
of the ion-pair formation is still being discussed controversially.9,10 Generally, typical probabilities of ion-pair formation
are rather small, 10−3 to 10−6, see review of Simpson.8 One
mechanism of the ion-pair formation is a direct photoinduced
transition from the ground state into the ion-pair state. In this
case, the low probability of the ion-pair channel arises from the
small Franck–Condon factors, resulting from a poor overlap of
the nuclear wave functions of the molecular ground state and
the ion-pair state.8 Another mechanism involves non-adiabatic
transitions from superexcited states into the ion-pair state.6 In
this case, the small probability for ion-pair formation arises
from the small probability of the non-adiabatic transition.
What is intriguing and stimulating the present study is the
existence of rather large probabilities of the ion-pair channel
in some cases. For example, for the two-photon transition in
REMPI of HCl X 1Σ+, v = 0 → → V 1Σ+, v ′ = 12, the relative
probability of the ion-pair channel (5) is close to 3%.1,4 For
this reason, this transition normally serves as a benchmark in
ion-pair studies.
For simultaneous detection of positive and negative photoproducts, ions or electrons, a double-arm time-of-flight (TOF)
mass spectrometer is normally used, where positive and negative photoions and electrons are accelerated in opposite directions by electric fields. While first experiments with such mass
spectrometers were already done in the 1970s,11 they became
really efficient only after the application of microchannel
plates (MCPs).12–14 A variety of configurations of such mass
spectrometers is known in the literature. Most of them are used
to detect photoelectrons and positive photoions. They may use
homogeneous electric fields (HFs),15–20 one-side velocity map
imaging (VMI),14,21–36 or two-side VMI;29,31,34,35,37,38 delay
line (DL) detectors,14–31,34–36 or charge-coupled device (CCD)
cameras,32,33,39 or both;38 pulsed lasers,15,17–20,29,30,32,34–36,38
or discharge lamps,14,21–26 or quasi-continuous synchrotron
radiation,28,31,36 or free-electron-laser radiation;38 simultaneous32,33 or coincidence14–19,21–23,26,28–31,34–36,38 detection;
the ionization by one-photon absorption,14,20–26 or REMPI,34,35
or by the strong electric field of femtosecond laser
pulses.15–20,28–31,33 Only a limited (and surely incomplete) set
of references to the studies published in the last 15 years is
shown here.
The first observation of ionic pairs has been reported in
1932 in the pioneering work of Terenin and Popov.40 Since
then, a lot of other ionic pairs have been observed, with
the list given in the review of Berkowitz6 including TlX,
X2, (X=F,Cl,Br,I), ClF, H2, O2, NO, CO, H2O, N2O, CO2,
COS, SO2, KrF2, XeF2, C2H2, CH4, CH3F, CH3Cl, CH3Br,
CF4, CF3Cl, CF2Cl2, CFCl3, C2H6, C3H8, C4H10, C2H5Cl,
SF6, cyclo-C6H11Cl, and CH3ONO2. Additional molecules
are listed in the review of Simpson,8 including CX4, C2X4,
C3X6, C3X8, (X=H,F), CHnCl4−n, where n = 0–4, CFmCl4−m,
where m = 1–3, CHF3, CH3Br, CF3Br, CF3I, SF6, SF5Cl, and
SF5CF3. All these systems have been studied at the Daresbury Synchrotron Radiation Source between 2005 and 2008.
Also, after 1996, ion-pair channels have been studied in the
Rev. Sci. Instrum. 87, 023107 (2016)
photodissociation of ICl,41 CH3Cl,42,43 CH3Br, C2H5Cl, and
C2H5Br.43 Recently, one interesting molecule, the ionic
liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([E+mim][Tf2N−]), was added to the lists by Koh and
Leone.33
However, a simultaneous or coincidence detection of
positive and negative photoions is rather rare. Our summary,
which is almost surely incomplete, includes H2,44 N2O,45–47
CH3F,48 CH3Cl,39 SF6,49 OCS,CO2,50 CH4,CD4,51 CF4,52 CH3
X (X=F,Cl,Br),53 SO2,54 H2S,55 CH3Br,32 O2,56 and the ionic
liquid [E+mim][Tf2N−].33 Ion-pair production is also used in
threshold ion-pair production spectroscopy (TIPPS), where
highly excited metastable Rydberg-like states are selectively
detected using dissociation induced by a weak Stark field.
TIPPS is used to investigate thermochemistry, spectroscopy,
and superexcited state decay dynamics at high resolution. For
example, it was successfully used to measure the dissociation
energies of HCl, H2, D2, and H2S.55
In the present work, a double-arm mass spectrometer was
constructed which allowed us to simultaneously measure the
3D velocity vector distributions of positive and negative ions.
The detection of negative ions is a much more difficult task
than might be expected initially. The main difficulty consists
of a large number of negatively charged particles appearing
at different times of flight. Main contributions are from the
electron emission from metal grids under ion bombardment
and from charge transfer between positive ions and the metal
surface of the grids. What is intriguing is the absence of
the description of these phenomena in the imaging literature,
although double-arm mass spectrometers are not a novelty.
Surely, all these phenomena are well known in the surface
sciences. For example, the emission of negative ions under the
bombardment of a surface by positive ions is used in secondary
ion mass spectrometry, a technique developed in the 1960s,
which is used in materials and surface sciences to analyze the
composition of solid surfaces.
Also, searching for negative ions from ion-pair channels
without imaging capability is very difficult, almost impossible,
mainly because of these secondary negative particles and also
because of some other problems. For example, we found that
the largest number of negative ions from channel (5) occurs
at some optimal laser energy, with their number not growing
monotonically with the laser energy.
Finally, the focus of the paper is on two areas.
The first one is the adaptation of an appropriate configuration of a double-side mass spectrometer to characterize
quantitatively radiative transitions (1), (3), and (5). Whereas
double-side mass spectrometers and measurements of twophoton cross sections are nothing new, the analysis of the
kinetics of competing transitions (one-photon, two-photon,
and non-radiative) between different states (X, IS1, and IS2)
leading to different ionic products, positive and negative
is demonstrated here for the first time.
The second concern of this work is to elucidate the origin
of the secondary negative ions and electrons and quantitatively
characterize the loss of produced ions of interest (H+, HCl+,
Cl+, Cl−) before the detection. This characterization is necessary for the first aim, the measurements of one- and two-photon
absorption cross sections.
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Rev. Sci. Instrum. 87, 023107 (2016)
II. EXPERIMENTAL SETUP
A. TOF mass spectrometer
Our TOF mass spectrometer with 3D ion imaging capability was previously used in a single-arm version to detect
positive ions only,2,3,57–59 it has previously been described in
detail.60–62 In the present study, the setup was modified to
enable the detection of negative ions as well. The extended
setup differs from the original version by an additional, second
TOF mass spectrometer which is the mirror reflection of the
first, sharing the symmetry axis and equipped with two independent ion detectors.
A pulsed nozzle (General Valve Series 9) is installed
oriented perpendicularly to the mass-spectrometer axis. The
nozzle injects a supersonic molecular beam (MB) between
the two mass spectrometers, where it is intersected by a
laser beam (LB) propagating perpendicularly to the molecular
beam and to the mass-spectrometer axis likewise. Laser beam
(X), molecular beam (Y ), and mass-spectrometer axis (Z)
define the Cartesian coordinate system of the experimental
setup.
The principal electric scheme and the dimensions of our
double-arm mass spectrometer are presented in Fig. 1. These
two mass spectrometers have one common acceleration region, which is placed between two field-free drift regions and
contains 10 metallic ring electrodes kept apart by glass rods.
Thus, the acceleration region is a 100 mm tube with eleven
1 mm gaps. This is done in order to shield the spectrometer interior from external electric fields. All metal parts are
covered by graphite spray (GRAPHIT 33) to decrease the
scattering of light. In the homogeneous electric field configuration, the voltages on the ring electrodes change linearly
from 0 to 2Ua , it was varied from 50 to 2000 V in different
measurements.
The elementary composition of the grids was studied by
energy dispersive X-ray fluorescence (EDX) using a scanning electron microscope (JEOL JSM 6400). The results
are as follows (mass, in %): Cr (18.52), Fe (73.32), and
Ni (8.15). The diameter of the grid wires was 52 µm, each
grid occupied 19% of the area of the TOF tube of the mass
spectrometer.
Our setup has a rare option:61 we can easily switch from
outside between a space-focusing configuration63 and the VMI
configuration of Eppink and Parker.64,65 By space focusing,
we mean that the TOF is unaffected by a small uncertainty
dZ in the position where the ion has been created on the Z
axis (d TOF/dZ = 0). In the space-focusing configuration,
the acceleration voltage 2Ua is split by 11 equal resistors in
order to obtain a HF throughout the acceleration region of
the spectrometer. The VMI results from adding an ionic lens
(IL) which arises from application of 2.9Ua voltage to the 8th
electrode, while the remaining voltages remain unchanged,
with electrodes 7 and 9 now being connected by two resistors.
In this case, the electrode 8 serves as Einzel lens and its field is
superimposed by the homogeneous field. The first configuration is useful, when high time resolution is necessary, allowing
us to resolve fine structures in the TOF profiles of negative
particles. However, the VMI configuration was always used in
order to obtain speed distributions of ions with high resolution.
We should note that our electric field configuration is
not that of Wiley and McLaren,66 as we wrongly wrote in
our review.62 Both configurations use homogeneous electric
fields and both are space-focusing. But in our configuration,63
there is one acceleration region and one drift region, while in
the Wiley-McLaren configuration, there are two acceleration
regions and one drift region.
In the present work, we have installed the VMI option
only at one side. When operating the spectrometer in VMI
FIG. 1. Electrodes configuration, dimensions, and voltages to the double-arm mass spectrometer (not to scale). Constructions from metal and notations,
dimensions, glass, plastic, and electric scheme details are shown in black, red, green, blue, and violet colors, respectively. The plane with the laser beam (LB)
and molecular beam (MB) is shown by red dotted-dashed line, four grids are shown by black dashed lines. Details of the left- and right-side mass spectrometers
are labeled by letters L and R, respectively. The units are volts and millimeters.
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mode, the TOF profile of the VMI side and the spatial image
on the other side are distorted and unsuitable for a quantitative
analysis. If double-side VMI is desirable, a second ionic lens
should be installed on the other side.29,31,34,35
perpendicular (Σ → Π → Σ), and the value b2 = 2.01 ± 0.15
was obtained. In the experiments, we found IQ(0)/IQ(1) ≈ 2.
Therefore, from Eqs. (6) and (7), we obtain the rotational
temperature to be Trot = 17 K, and the relative population of
the J = 0 state to be 0.66.
B. Laser system, vacuum system, and ions detector
Laser radiation for the excitation of HCl molecules
(10 Hz, up to 100 µJ/pulse) in the spectral region 234–240 nm
is produced by BBO frequency doubling of the output of a
tunable Nd:YAG-pumped dye laser (Lambda Physik Scanmate). The laser polarization is linear and usually oriented
along the mass-spectrometer axis.
The vacuum chamber is pumped by two turbomolecular
pumps (Pfeiffer, TMU 260 and TMH 521 P), background
pressure is ∼10−6 mbar. The pumps are forepumped by a rotary
vane pump filled with oil. When the nozzle is operating, the
time-integrated pressure is ≈10−5 mbar.
Positive and negative ions fly in opposite directions, pass
the acceleration and the drift regions, and hit the two commercial 3D imaging detectors. Each detector consists of a double
stage MCP assembly (Hamamatsu) with a DL detector (Roentdek).67,68 Each DL detector has 4 outputs; the signals which
are recorded by a 500 MHz oscilloscope (LeCroy Waverunner
6050) and analyzed by a custom program which decomposes
the signals on each line into individual pulses. Usually, each
pulse has almost Gaussian shape, with known width and amplitude; this knowledge is used to distinguish ion signals and
noise. The program is self-learning, from statistical analysis,
it determines the average values for the widths, amplitudes,
and TOF profile areas (A) of the pulses and uses them in
consequent analysis.
D. Determination of the ion number
It is easy to measure the average number of ions projected on a detector per laser pulse at reduced laser energies,
when the number of ions per laser pulse ñ is small, ñ ≤ 1.
At higher laser energies, when ñ significantly exceeds unity,
the ion signals on the delay lines overlap, the procedure of
individual ion identification fails, and the value ñ cannot be
determined directly. In this case, the value was determined
as ñ = At /A, where At is the total area of the overlapped
signal of the DL detector, and A ≈ 1 ns × V is the mean area
of the signal of the individual ion obtained at reduced laser
energy.
E. Determination of the molecule concentration
in the molecular beam
For the determination of the absolute values of absorption
cross sections, we need to know the concentration [HCl] on the
molecular beam axis. This concentration was calculated from
the equations
[HCl(L, θ)] = [HCl(L, θ = 0)] cosn θ,
 π/2
NHCl = 2πL 2V t˜
[HCl(L, θ)] sin θdθ,
In the present study, we show experimental results for
only two transitions, the lower state was always X 1Σ+(v = 0,
J = 0), and the upper I S1 states were V 1Σ+(v ′ = 12, 15; J ′
= 0); wavenumbers are 84 745.60 cm−1 for v ′ = 1269 and
86 401.6 cm−1 for v ′ = 15.70 The chlorine isotope shift is rather
large, 4.5 cm−1 for v ′ = 12 and 6.1 cm−1 for v ′ = 15;70,71
therefore, only H35Cl was detected in the present study.
The rotational temperature Trot of HCl in the molecular
beam was determined from the relative line intensities of
REMPI signals of rotational Q(0) and Q(1) transitions into the
(V, v ′ = 12) excited state. For Q branches of two-photon electronic transitions with ∆Ω = 0, the rotational line intensities
are
IQ(J) = e−B0J (J +1)/kTrot S(J),
(6)
where B0 = 10.5 cm is the ground state rotational constant
and S(J) are line strengths. For REMPI transitions they may
be taken from our work,2 see also Refs. 72 and 73,

J(J + 1)
2J + 1  2
b +
,
(7)
S(J) =
9
5(2J − 1)(2J + 3)
−1
where the parameter b depends on the nature of the transition. For the 2-photon transitions to the (V, v ′ = 12) state,
it was measured previously,2 the transition was found to be
(9)
0
NHCl = ⟨dNHCl/dt⟩/ν,
V ≈ Vma x = {2kT0 ϱ/(ϱ − 1)MHCl}1/2,
C. Spectroscopy of HCl
(8)
(10)
(11)
where L = 10 cm is the distance from the nozzle to the laser
beam, θ is the azimuthal angle in the spherical coordinate
system aligned with the molecular beam, NHCl is the number of
HCl molecules ejected from the nozzle in one molecular beam
pulse, ⟨dNHCl/dt⟩ is the long-term averaged flow of HCl molecules (typically 3 × 1017 s−1), t˜ = 165 µs is the duration of the
molecular beam pulse, V is the speed of the molecular beam,
Vmax = 696 m/s is the maximum speed of the molecular beam,
when the internal temperature is zero, ν = 10 Hz is the laser
pulse repetition rate, MHCl = 36 a.m.u. is the mass of the H35Cl
molecule, k is the Boltzmann constant, ϱ ≡ CP/CV = 7/5, and
T0 = 300 K is the temperature. The first formula (8) describes
the angular distribution of the molecular concentration in the
molecular beam, formula (9) averages the concentration over
the angle θ, formula (10) calculates the number of molecules
per pulse from the long-term averaged flow of HCl molecules,
and expression (11) yields the maximal possible speed of
the cold molecular beam. If we assume that the translational
and rotational temperatures of HCl are similar, Ttr ≈ Trot, then
from the ratio Ttr/T0 = 1 − (V/Vmax)2, we obtain V = 0.93Vmax.
However, the rotational quanta in HCl are normally larger
than typical translational energies; therefore, the rotationaltranslational energy exchange may be inefficient and hence, it
is probable that Trot > Ttr. Thus, the speed V should be between
0.93Vmax and Vmax. Finally, we assume V ≈ Vmax.
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From Equations (8)–(11), one obtains the final expression
[HCl(L, θ = 0)] = (n + 1)⟨dNHCl/dt⟩/2πνL 2V t˜.
The value of ⟨dNHCl/dt⟩ was measured from the decrease
of the gas pressure in the calibrated volume before the nozzle.
The time profile of the molecular beam was recorded by
observing HCl+ ions from REMPI of HCl at different delays
between the laser pulse and the valve-opening electric pulse. It
was found that it has an approximately rectangular shape with
duration of t˜.
It is known from the literature74 that the angular distribution of molecules in the molecular beam should be proportional to cos4 θ. We confirmed this law, n = 4, using the experimental setup shown in Fig. 2. In these measurements, we
carefully arranged eleven flexible plastic wires in vacuum
(10−4 mbar) and took a video of the wire movement through a
glass viewport. The distances between the wires and the nozzle
were the same for all wires, but the θ angles were different. The
frequency of the nozzle was very low (0.1 Hz); therefore, the
oscillations of the wires completely finished at the start of a
new nozzle pulse. It was assumed in these measurements that
the deviations of the wires from their equilibrium positions
after the blow by the molecular beam are proportional to the
gas flow.
Finally, we obtained that the typical concentration in our
experiments was [H35Cl(J = 0)] = 3.4 × 1012 cm−3.
F. Reconstruction of the speed distribution
from 3D VMI
In order to obtain speed and angular distributions of the
ions produced by REMPI, one should analyze the experimental
3D distributions of the ions, over the surface of the detector
and over arrival times. The analysis of these 3D distributions
obtained in the HF configuration63 is simple and straightforward, because the movements of the ions along the axis of
⃗ and along the radial direction R
⃗
the mass spectrometer Z
⃗
are independent. Cylindrical coordinates are assumed here, R
⃗
⊥ Z.
When we use VMI in the IL configuration64,65 in combination with the 3D detection of the ions, the analysis is
more complicated. Therefore, a reconstruction of the HFdistribution from the observed IL-distribution is necessary. In
our previous paper, the solution of this problem is described
in detail.61
Here, we use a simpler approach. First, the electric field
in the mass spectrometer is calculated analytically.61 The basic
⃗
assumption is the independence between movements along Z
⃗ directions. This assumption was checked by numerical
and R
calculations and was found to be very good.
Let us compare, for example, HF- and IL-distributions of
the ions over TOF. The first one is narrower than the second
one. In this discussion, the relative TOF for the ith ion dt i,C
= t i,C − ⟨t C ⟩ is introduced, where C denotes the configuration,
C=HF or C=IL, t i,C is the TOF of the ith ion, and ⟨t C ⟩ denotes
the time of the center of the TOF profile. For each ion i, the
difference dt i,IL is known and we want to know what would be
the dt i,HF value if we change from IL to HF configuration. The
time dt i,HF is equal to63
dt i,HF = Vi, Z /aHF,
(12)
where Vi, Z denotes the initial speed of the ion along the Z
axis, and aHF is the acceleration in the homogeneous electrical
field. According to our simulations, the TOFs for HF- and ILconfigurations may be related by
dt i,HF = dt i,IL(a + bVi, Z + cVi,2Z ),
(13)
where the coefficients a, b, and c may be obtained from
modeling. They depend on the voltage configuration, massspectrometer geometry, and ion mass. Thus, each ion has its
own scale factor dt i,HF/dt i,IL which depends on its initial speed
Vi, Z . In Equations (12) and (13), the values for dt i,IL, aHF, a, b,
and c are known, and therefore, the values for dt i,HF and Vi, Z
may be calculated.
The same approach is used to transform IL-distributions
to HF-distributions in the XY -plane.
G. Absolute detection efficiency (ADE) of MCP
The knowledge of the ADE of the MCP is necessary in
the present study. Under our experimental conditions, it may
be given by75
FIG. 2. (a) Experimental study of the angular distribution of molecules in the molecular beam. I: Nozzle, II: metallic screen, III: video camera. The angle
between the axis of the nozzle and the direction of interest is θ. The wires are labeled as 1, 2, ..., 11. (b) The initial amplitudes of the wire oscillations vs angles
θ. The curve is a fitting by cos4 θ, see Eq. (8).
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ADE = OAR × f (P, Et ,UMCP),
Rev. Sci. Instrum. 87, 023107 (2016)
(14)
where OAR means Open Area Ratio, the ratio of integrated
pore area to the total disc area. It is 0.65 for our MCP. This
expression assumes that particles incident on the MCP between channels are not detected.
f (P, Et ,UMCP) is the efficiency function which depends on
the nature of the particle P, the kinetic energy of the particle Et ,
the voltage between front and back sides of the MCP UMCP, and
many other factors, like the angle between the axis of the MCP
channels and the velocity vector of the incident ion. We also
include in the f function the efficiency for assigning DL pulses
to ions. We estimated that in our case, f (P, Et ,UMCP) ≈ 0.9.
The deviation from unity is mainly due to the analysis
being unable to assign all DL pulses to ions. This may be the
case, first, when the intensity of some DL pulses drops below
the noise level due to fluctuations; second, when the pulses
overlap in time; third, when two ions hit the same place of the
MCP.
H. Mass-spectrometer detection configurations
Our double-arm mass spectrometer has several detection
configurations, some of which are shown in Fig. 3. The main
one is configuration (b), where positive and negative ions are
detected simultaneously.
Configuration (c) of Fig. 3 is a trap for negative ions, with
detection of positive ions. This configuration was used to prove
that negative ions never produce positive ions in collisions with
the grids. We attempted to detect these recharged positive ions
by both mass spectrometers, but were unsuccessful.
Configuration (d) of Fig. 3 is a “double trap,” which was
used to study the production of negative ions and electrons in
collisions of positive ions with the grids, see Sec. V.
III. DOUBLE-ARM MASS SPECTROMETER
EXPERIMENT
A. H+ and Cl− detection
In our recent preliminary study, the list of the ion-pair
channels in REMPI of HCl was significantly extended.77
Now this list includes the intermediate states I S1 = V 1Σ+(v ′
= 8, 9, 11, 12, 13), E 1Σ+(v ′ = 0, 1), and g 3Σ−(0+)(v ′ = 0). This
extension has become possible due to the detection of the Cl−
ions, while all other investigations of the ion-pair channels
in HCl before us were performed with imaging of H+. The
example of our speed and angular distributions of the Cl− ions
are shown in Fig. 4.
All studies of the ion-pair channel yielded the anisotropy
parameter76 of the H+ ion angular distributions to be β ≈ 2.4,77
This means that only excited states with the symmetry Σ are
involved in the process of ion-pair photodissociation.
The speeds of the ion pair were measured in several
studies,4,77 in all cases, it was proven that the ion-pair channel
is caused by the absorption of exactly three photons. This result
is an important proof of the scheme of the ion-pair channel (5).
B. Imaging and angle-speed distributions
The detection of negative ions has several advantages over
the detection of positive ions.
First, the study of the ion-pair channel (5) by observation
of H+ ions is usually hindered by the presence of the H+ ions
produced in channels (2) and (4). Very often, the speed distributions of the ions for all three channels overlap, therefore
identifying the ion-pair channel becomes questionable, see
Fig. 4. In contrast, the study of the ion-pair channel by the
detection of Cl− ions is easy because there exist no competing
channels and hence, the detection sensitivity is large.
FIG. 3. (a) Schematic representation of the double-arm mass spectrometer. LB and MB are laser beam and molecular beam, respectively. Grids are shown by
vertical dashed lines. Mass-spectrometer detection configurations are: (b) double-arm, positive and negative ions are detected, (c) one-arm, positive ions are
detected, negative ions are trapped, and (d) double trap, both positive and negative ions are trapped. ((b)–(d)) Voltages are shown by black lines.
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FIG. 4. Meridian plots3 for REMPI of HCl via transition X 1Σ+(v = 0, J = 0) → V 1Σ+(v ′ = 15, J ′ = 0). Left: H+ ions, right: Cl− ions. The relative scale is arbitrary.
The speed of Cl− is 503 m/s, anisotropy parameter76 β ≈ 2. The width of the speed distribution for the case of H+ ions is much larger than the width for the case
of Cl− ions because the H+ ions are produced via several pathways.
Second, while in the REMPI of HCl, the Cl− ions are
produced via only one potential energy surface with a well
defined speed, the H+ speed distribution is broad, see Fig. 4,
because in channels (2) and (4), the kinetic energy of the
emitted electron may vary in a broad range. In addition, even
the ionization step also slightly contributes to the speed of H+
in these last two channels due to electron recoil,78 while it
has no influence on the ion-pair channel. Therefore, the speed
distribution of the Cl− ions produced in the REMPI of HCl is
very narrow and hence may be used as benchmark for testing
imaging techniques.
In the present study, a slightly different approach is used
where the rate is defined as
W (2) = σ (2)Φ2(r, z,t),
where σ (2) is a lineshape-dependent “cross section” in
cm4 s/photon2. In our approach, time averaging of the photon
flux is not used; therefore, the statistical factor G(2) disappears,
and the lineshape function g(ω) is included in the definition of
the “cross section” σ (2). The photon flux may then be described
as
Φ(r, z,t) = Nhν
IV. PROBABILITIES OF 2- AND 3-PHOTON
TRANSITIONS
A. Definition of 2-photon “cross sections”
The rate for a one-photon transition between two states is
usually defined as
W (1) = σΦ(r, z,t),
(15)
where σ is a one-photon cross section (in cm2/photons), and
Φ(r, z,t) is a photon flux (in photons/cm2 s). Hereafter, new
cylindrical coordinates (r,z) are introduced with the reference
point in the focus of the lens and the axis z along the laser beam
(axis X in Figs. 1 and 3).
The notations and approach introduced by Saxon and
Eichler79 are usually used to describe the two-photon absorption “cross sections.” In their notation, the rate for a twophoton transition in s−1 is described by the expression
W (2) = σ0(2)g(ω)G(2)Φ2(r, z,t),
(16)
where σ0(2) is a lineshape-independent “cross section” in
cm4/photon2, the area-normalized
lineshape function g(ω)

expressed in seconds ( gdω = 1), and the photon statistical
factor G(2) is dimensionless. The factor G(2) is the secondorder intensity autocorrelation function of the laser,80 G(2)
≡ ⟨ f 2(t)⟩/⟨ f (t)⟩2, where the angular brackets denote time
averaging.
(17)
f (t) U(r, z)
,
∆t πr z2(z)
(18)
where Nhν = I/hν, I, and ∆t represent the number of photons,
the energy, and the effective duration of the laser pulse, respectively, and r z (z) is the effective radius of the laser beam.
The dimensionless functions f (t) and U(r, z) are normalized to unity
 +∞
[ f (t)/∆t] dt = 1,
(19)
−∞
 +∞
U(r, z)
2πr dr = 1,
(20)
πr z2
0
where the second equation implies a constant radiation flux
along the z-axis.
We have measured the functions f (t), [HCl(z)], and g(ω)
experimentally. The laser pulse function f (t) was recorded
by a quick photomultiplier, transferred to the LeCroy oscilloscope, and analyzed by Origin program. We tested different
fitting functions and finally found that the best one is the
extreme function, see Fig. 5,
f (t) = e− exp(−t /∆τ) e−t /∆τ ,
(21)
where ∆τ = 1.58 ± 0.02 ns. This function obeys condition
(19), it has its maximum at t = 0, f (0) = e−1, and it has a
full width at half maximum of 2.44∆τ. We prefer the extreme
function over the Gaussian because the former is very easy to
integrate, and because it reflects the reality: the time shape of a
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FIG. 5. Comparison of fittings of the experimental time profile of the laser pulse by extreme and Gaussian functions.
Nd-Yag laser pulse is known not to be symmetric, but to have
a “quick” rise, a “slow” fall, and a “long” tail.
In the simplified approach to the theory of laser beams, the
spatial distribution U(r, z) of the radiation intensity is usually
assumed to be Gaussian along the radius r,
U(r, z) = 2 exp(−2r 2/r z2)
(22)
and Lorentzian along the symmetry axis z,
r z2 = r 02 [1 + (z/z0)2],
(23)
where r 0 is the diffraction limited effective radius of the laser
beam in the focus plane and z0 is the confocal parameter
of the beam (Raleigh range), z0 = 2 f r 0/d, f = 20 cm is the
focus length, and d is the diameter of the laser beam just after
the aperture placed close to the lens. The radius r 0 may be
predicted theoretically from the Airy pattern theory to be r 0 =
λ f /d = 0.031 mm for an aperture of d = 1.5 mm. Also, the
radius was measured experimentally. As shown in Sec. IV B,
the dependence [HCl+(z)], the ion density along the laser
beam, is given by
[HCl+(z)] ∼ 1/r z2 ∼ (1 + z 2/z02)−1.
(24)
The experimental dependence [HCl+(z)] was measured by
REMPI and fitted by this expression, and thus, the values of
z0 and r 0 were determined.
The intensity of the Fraunhofer diffraction pattern of a
circular aperture, the Airy pattern, is given by
U(r, z) = π 2(J1(x)/x)2,
has Lorentzian shape with full width at half maximum of
1.08 cm−1; hence, g(ω) = 1.96 × 10−11 s.
Note that the Doppler broadened spectrum of H(n = 2)
atoms produced in channel (4) is only slightly narrower than
the spectrum of the laser radiation; hence, a correction factor should be used. Mathematically, this factor is a convolution of the radiation spectrum and the absorption spectrum of
the atoms. In the present work, we neglected this correction,
because it was small.
(25)
where x ≡ πr/r z (z). In our experiment, we prefer the Gaussian
shape (22), because Airy theory does not work far away from
the focus plane.81 However, the Airy theory yields the correct
value of r 0.
The Doppler broadening in the molecular beam is negligibly small; the decay time of the upper state IS1 of the REMPI
transition, spontaneous as well as radiation-induced, is ≈3
ns;82 hence, for our case, the lineshape function g(ω) almost
coincides with the spectrum of laser radiation. This spectrum is determined mainly by the cavity of the dye laser and
B. Determination of the 2- and 3-photon
“cross sections”
When discussing 2- and 3-photon REMPI processes, the
major steps in the kinetic scheme are
W (2)
W (1)
X(r, z,t) → B(r, z,t) → C(r, z,t) → D P ,
(26)
where X, B, C, and D P denote ground, excited, superexcited,
and ionic states of HCl. The states D P lead to ionic products
P, which may be either H+ or Cl+ or HCl+ or Cl−. In the case of
HCl, there are five ionic channels, see Eqs. (1)–(5), but in the
present study, we normally do not distinguish between H+ ions
produced via different channels. Under the assumption that the
last step is quick, it is taken into account by branching ratio
coefficients γ P only, [P] = γ P [C],
[P] = γ P [HCl(C)] =
[P]
[HCl(C)].
[H+] + [Cl+] + [HCl+]
(27)
Hereafter, [S] denote [HCl(S)], with S = X, B, and C. As it
follows from Eqs. (1)–(5), the REMPI of HCl produces exactly
one positive ion; hence, γH+ + γCl+ + γHCl+ = 1 and γCl− is the
relative probability of the ion-pair channel (5).
The rate equations for the above reaction scheme are
d/dt [X] = −k 2[X],
d/dt [B] = k 2[X] − k 3[B],
d/dt [C] = k 3[B],
where concentrations [X], [B], and [C] and rate constants k2
and k3 depend on r, z,t variables. The initial conditions are
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[X(r, z,t = 0)] = [X0(r, z)] and [B(r, z,t = 0)] = [C(r, z,t = 0)]
= 0. According to definitions (15) and (17), the rate constants
in these equations may be expressed as
k2 = σ (2)Φ2(r, z,t),
(28)
k3 = σΦ(r, z,t).
(29)
Under the assumption that the decrease of the number of
molecules in the ground state X is negligible, [X] ≈ [X0], and
assuming the time shape of the laser pulse to be of extreme
form (21), the solution of the equations system at the t → ∞
limit is
[B(r, z, +∞)] + [C(r, z, +∞)]
(
)2

σ (2) 2 U(r, z)
Nhν
, (30)
≈ [X0] k2 dt = [X0]
4∆τ
πr z2(z)
where expressions (17)–(21) and (28) have been used.
If the probability of the one-photon step is assumed to be
small, k3∆τ ≪ 1, then we obtain
)3
(
5σ (2)σ 3 U(r, z)
.
(31)
Nhν
[C(r, z, +∞)] = [X0]
36∆τ
πr z2(z)
To calculate NB, Nc , and NP , the numbers of molecules
in the states B, C, and D P , respectively, their concentrations should
be integrated over the volume. For example,

NC =
[C(r, z, +∞)] 2πr dr dz. After the integration, the
final formulae are
σ (2) 2
N ,
∆τλ hν
σ (2)σ 3
N ,
NP = γ P NC = γ P [X0] C3
∆τλr 02 hν
NP = γ P (NB + NC ) = γ P [X0] C2
(32)
(33)
where C2 and C3 are coefficients, which depend on the choice
of the U(r, z) function: C2 = 1/4 = 0.250 and C3 = (5/36)(2/
3π) = 0.0295 for the Gaussian pattern (22) and C2 = Υ2π 2/4
= 0.284 and C3 = (5/36)Υ3π 4/2 = 0.0423 for
 ∞the Airy pattern
(25), where Υ2 and Υ3 are integrals Υn ≡ 0 2π 2−n (J1(x)/
x)2n dx, with n = 2,3. Whereas we have used the coefficients
for the Gaussian pattern, the difference between the two patterns yields an estimate of the diffraction modeling uncertainty. Note that the first expression is more accurate, because
there it does not contain geometrical properties of the laser
beam.
We did not detect all produced ions, thus the number of
detected ions ÑP is related to NP by correction factor, ÑP ≡
ADE(1 − p)2 NP , where ADE is the absolute detection efficiency from Eq. (14), and the parameter p describes the ion loss
in collisions with grids, see Subsection V D. This correction is
used when experimental data are fitted by Eqs. (32) and (33).
Let us illustrate our logic by two examples.
First, let us suppose that the dependence of NP on I 2 is
linear for all observed ions P, like in Fig. 6 for small laser
pulse energies I. Then, the 2-photon step is a “bottle neck,”
a limiting step, and all other transitions are very quick, so
that they have no influence on the dependence of NP on I.
Using expression (32), from the initial slopes of the curves
in Fig. 6, we obtained σ (2) = 3.2 × 10−49 cm4 s/photon2 and
four branching ratios γ P . For example, the relative probability
of the ion-pair channel (5) is γCl− = (5% ± 1%). Applying
Eq. (16) gives the lineshape-independent cross section, σ0(2)
= σ (2)/g(ω) = 1.6 × 10−38 cm4/photon2.
Second, let us suppose that the ionic signals are proportional to the third power of the laser energy, NP ∼ I 3, like at the
top of Fig. 6. It means, that in addition to the two-photon step,
there is also a one-photon transition occurring on a time scale
comparable with ∆τ. In the cases of P = Cl− and P = HCl+,
it is evident that this is the transition from the excited state
IS1 to the superexcited state IS2 in HCl. Then, expression (33)
should be used to obtain the values γ P σ (2)σ from the initial
slopes of the experimental curves for each ion P. If the values
γ P and σ (2) have already been determined from the NP ∼ I 2
dependencies, the absolute values of the cross sections σ may
be determined. In our case, it is σ = 1.2 × 10−16 cm2/photons.
This cross section is very large, but seems to be possible,
because it corresponds to transitions to several superexcited
states of HCl.3
FIG. 6. REMPI of HCl via the excited state V 1Σ+(v ′ = 12) at 84 745.60 cm−1.69 Displayed is the average number of detected ions vs the square of the laser
energy. Inset at the top: The average number of detected Cl− ions vs third power of the laser energy.
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An interesting case is demonstrated in Fig. 6, where the
dependence of NCl− on I k is linear at small energies for k = 3
and at moderate energies for k = 2. Therefore, the initial part
of the curve (shown at the top) is described by Eq. (33) and
the slope of the curve is proportional to γCl− σ (2) σ, while the
rest of the curve is fitted by Eq. (32) and the slope of the
curve is proportional to γCl− σ (2). Hence, the ratio of these
two slopes provides the cross section σ. This procedure does
not require the knowledge of the [X0] concentration and the
duration ∆τ of the laser pulse and should therefore be rather
accurate.
Interestingly, the ratio of the relative yields of Cl− and
+
H ions from REMPI via the state V 1Σ+(v ′ = 12) may be
determined from Fig. 1 of the study of Romanescu and Loock,4
[Cl−]/[H+] = γCl−/γH+ = 0.15 ± 0.015. Our value, as one can
obtain from Fig. 6 by comparison of initial slopes, is almost
the same, γCl−/γH+ = 0.18. This difference is probably due
to the smaller laser power in our study, because the ratio
[H+]/[Cl−] increases with I, see Fig. 6, This rise is partly due
to competition between 3-photon processes (1) and (5) and 4photon processes (2)–(4), while the role of the HCl+ photodissociation rises with I. Hence, we believe that the determination
of relative probabilities of different ionic channels by scanning
the laser power is a more correct procedure than measurements
at fixed laser power.
Note that our present data about REMPI of HCl are
preliminary only, further work is in progress to measure the
cross sections accurately.
V. ELECTRON EMISSION AND ION CHARGE
EXCHANGE ON THE GRIDS
For the measurement of absorption cross sections, we
have to characterize quantitatively all possible processes leading to ion number changes in the mass spectrometer. Three
kinds of such processes have been observed and are described
Rev. Sci. Instrum. 87, 023107 (2016)
below. For all of them, the detection of negative photofragments by the right-hand side mass spectrometer in detection
configurations (b) and (d) shown in Fig. 3 is assumed; the laser
polarization is oriented along the axis of the mass spectrometer; all formulae are obtained in assumption of free flights in
a homogeneous electric field.
A. Effect 1, electron emission: Cl− + grid→ e−
Fig. 7 shows the TOF profiles of the negative photofragments produced in the ion-pair channel in REMPI of HCl,
where the double-arm detection configuration shown in Fig.
3(b) is assumed. Large signals in the 5.20–5.30 µs region
belong to Cl− ions with an anisotropy parameter β ≈ 2, while
small signals at shorter time are produced by electrons emitted
from grid 2 R . The speed of the ions is negligibly small relative
to the speed of the electrons; therefore, the time shift between
the arrival of emitted electrons and Cl− ions is essentially equal
to the TOF of the ions from grid 2 R to the MCP R . The time shift
may be calculated by the formula


∆s 2MCl 
( Ua + ∆U − Ua ),
(34)
δτ =
∆U
|e|
where ∆s = 8 mm is the distance between grid 2 R and MCP R ,
and MCl is the mass of the Cl− ion. The calculated value of the
time shift δτ is in good agreement with the observed value in
Fig. 7 and supports our interpretation of the TOF spectra.
We found that not only TOF but also the spatial distribution of the electrons produced on grid 2 R mimicks the space
distribution of the Cl− ions, that is related with relatively
high voltage ∆U and short distance ∆s. Therefore, under our
experimental conditions, the study of the electron angular
distribution was difficult.
The same electron emission should also occur on grid 1 R ,
which separates acceleration and drift regions. In contrast to
FIG. 7. TOF profiles of the Cl− ions and the electrons emitted from the grid 2 R in the REMPI of HCl via excited state V 1Σg+(v ′ = 12).
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TABLE I. The relative efficiency of electron production by the Cl− ion with
different kinetic energies eUa , electrons per one Cl− ion.
eUa (eV)
Efficiency
150
0.08
300
0.14
450
0.18
600
0.19
750
0.22
the situation with grid 2 R , most of the produced electrons were
turned to the walls of the drift region by magnetic fields and
were lost upon impact on the walls, and only a small portion
of them was detected.
A nontrivial fact is that the efficiency of electron production increases with the kinetic energy eUa of Cl−, impacting
on grid 2 R , see Table I. We roughly assume here that this
efficiency is equal to the ratio of e− and Cl− signals; this
assumption neglects the difference in MCP R detection efficiency, f (e−, 0,UMCP) = f (Cl−,Ut ,UMCP), see Eq. (14).
B. Effect 2, ejection of electrons from the MCP
surface: H+, Cl+, HCl+ + MCP → e−
In the first experiments with HCl photoionization, we
found that at almost all laser energies, the number of photoelectrons was large enough to saturate the MCP and therefore
make it almost blind, see Fig. 8, blue line. In this subsection,
the detection configuration shown in Fig. 3(b) is assumed.
The disturbing effect of the photoelectrons was eliminated by
the installation of four permanent magnets (NdFeB, 40 × 20 ×
5 mm), see Fig. 8, black line. These magnets produced a homogeneous field oriented perpendicular to the axis of the mass
spectrometer. The magnetic field turned the electrons to the
wall of the drift region. Unfortunately, high-energy electrons
eject secondary electrons from the surface and therefore, their
signals were not eliminated completely. One pair of magnets
was installed at the beginning of the drift region of the rightside mass spectrometer, the second pair was installed at the
end of the drift region. The experiment shows that the most
effective orientation of the second field is perpendicular to the
first one. The mass of the ion Cl− is much larger than the mass
of the electron; therefore, the trajectory of the ion was not
noticeably affected.
The broad and the sharp peaks shown in Fig. 8 at approximately 9.7 µs mimick the TOF profile of Cl+ and HCl+ positive ions and disappear if the left-side mass spectrometer is
switched off. The peaks obviously reflect the ability of the
left-side mass spectrometer MCP L to emit electrons after the
impact of positive Cl+ and HCl+ ions. The integrated pore
area of our MCP is only 65% of the total MCP surface, see
Subsection II G, so the other 35% of the surface emits electrons
into the space between the front side of the MCP L and the
grid 2 L . If the positive ion falls into one of the pores, it produces
electrons which are then accelerated into the MCP L . However, if the positive ion hits the surface between the channels,
the electric field accelerates the emitted electrons away from
the MCP L surface towards the right-side mass spectrometer.
On the way towards the negative ion detector, they are once
again accelerated in the acceleration region. Because of the
small mass of the electrons relative to ions, they cover the
distance between the two detectors in a very short time. As
a result, the time of impact of these electrons on the negative
ion detector almost coincides with the time of impact of the
negative chlorine ion. To guarantee the correct separation of
negative photoions and secondary electrons emitted from the
opposite-side MCP R one needs to install the set of magnets
and have a sufficiently high TOF resolution of the imaging
detector.
C. Effect 3, forward/backward scattered electrons
and positive ion recharge: Cl+, HCl+ + grid → e−,
Cl−, HCl−
The emission of negative ions and electrons under the
bombardment of a surface by positive ions is known since
1931.83 We observed these emission processes also. They were
studied with the “double trap” detection configuration shown
in Fig. 3(d). In the right-side mass spectrometer, a trap for positive ions (H+, Cl+, and HCl+) produced after REMPI of HCl
is organized. Moving periodically in the trap, the positive ions
impact on grid 2 R two times per period. The first impact occurs
on the way towards the right MCP R , the second impact occurs
on the way back from the MCP R . In both cases, we detect negative particles emitted from grid 2 R and flying to the MCP R ;
the first are forward scattered secondary particles, the second
are backward scattered secondary particles. These forward and
backward scattering processes are shown in Fig. 9, and the
corresponding TOF profiles are shown in Fig. 10. In Figure 10,
peaks 1 and 2 correspond to the forward scattered secondary
electrons, produced in the processes Cl+ + grid 2 R → e− and
HCl+ + grid 2 R → e−. Peaks 4 and 5 represent the backward
scattered secondary electrons, produced by the ions Cl+ and
HCl+. The peak 3 reflects the recharge of forward scattered
HCl+ ions.
This interpretation of the observed TOF profiles was
confirmed by simple quantitative calculations. Thus, the time
between forward and backward impacts ∆t is equal to the turn
around time of positive ions in the space between grid 2 R and
FIG. 8. Influence of the magnet installation in the drift region of the righthand side mass spectrometer on TOF profiles of negative ions.
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FIG. 9. Schematic representation of the processes occurring on grid 2 R : (a) forward scattered electron production, (b) HCl+ ion recharge, (c) positive ions are
⃗ (d) backward scattered electron production.
reflected in opposite direction by the electric field E,
MCP R . It may be calculated by the formula

4∆s
MHClUa
,
∆t =
UMCP
2|e|
D. Periodic motion of ions in the mass spectrometer
(35)
where ∆s is the distance between the grid 2 R and the MCP R .
The calculated ∆t values are in perfect agreement with the
experimental ones, as well as the times δτ between signals of
the HCl− ions and electrons produced by the forward scattered
HCl+ ions, where the δτ values were calculated with Eq. (34).
In Subsection V C, we have described forward and backward scatterings of trapped positive ions on grid 2 R during
one period of the ionic motion. We continue the discussion of
the same experiments, but now we extend the time window
of observation in order to include the scattering on both grids
during several periods. The detection configuration shown in
Fig. 3(d) is assumed. The scheme of periodic motion as well
as the TOF profile is shown in Fig. 11.
The period starts and finishes in the acceleration region in
the point where the positive ions were produced by REMPI.
During the period, the positive ions may impact on each grid
two times, producing emission of electrons and negative ions.
If these emitted particles fly towards MCP R , they may be
detected.
The time τ is equal to the TOF of the positive ion in the
classical experiment and does not change for the subsequent
cycles of motion. Thus, the period of motion is equal to the
doubled TOF of the positive ion. The TOF profile shown in
Fig. 11(b) confirms the idea that the first signature of electrons
and recharged ions produced on grid 2 R takes place at time
τ, τ + ∆t, the second one occurs at time 3τ + ∆t, 3τ + 2∆t,
and the third one at the time 5τ + 2∆t, 5τ + 3∆t. Here, ∆t
is the time between the production of forward and backward
scattered electrons. Also, Fig. 11(b) shows the formation of
backward scattered electrons on grid 1 R at times 1.5τ + ∆t and
3.5τ + 2∆t, produced by positive ions flying in the direction
of the acceleration region. The forward scattered electrons are
less probable than backward scattered electrons, see Fig. 10,
which is why we have not observed the electrons on grid 1 R at
times 0.5τ, 2.5τ + ∆t, 4.5τ + 2∆t.
FIG. 10. TOF profile of negative particles observed in the REMPI of HCl
via the excited state V 1Σ+(v ′ = 12) at Ua = 800 V. Positive ions (H+, Cl+,
and HCl+) oscillate in the right-side mass spectrometer and produce negative
particles in collisions with grids 1 R and 2 R . The TOF profile shows the
processes occurring on grid 2 R .
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Poretskiy et al.
Rev. Sci. Instrum. 87, 023107 (2016)
FIG. 11. Periodic motion of positive ions in the mass spectrometer at Ua = 1500 V. (a) Scheme of three cycles of motion. (b) TOF profile of negative particles
produced in collisions of the positive ions with the grids 1 R and 2 R during three cycles. Fig. 10 shows a small part of such a profile in detail.
The number of produced electrons decreases with each
new cycle of motion. This results from the decrease of the
number of positive ions owing to the impacts on the grid and
to the formation of negative ions and neutral atoms on the grid.
Let us introduce the flight direction independent probability p
of ion loss on the grid. For N positive ions flying to the grid,
only (1 − p)N positive ions continue their flight after the grid.
Before the first cycle of electrons and recharged particles
(time gate around τ), N ions approach grid 2 R from the drift
region. Before the second cycle, the ions pass the grids four
times: two times near the MCP R (τ, τ + ∆t), one time entering
the acceleration region (1.5τ + ∆t) and another time exiting it
(2.5τ + ∆t). Thus, the number of the positive ions and the number of electrons produced on grid 2 R are reduced by the factor
(1 − p)4. From the intensities of the peaks in the experimental
time-of-flight profile, corresponding to the electrons produced
in the first and in the second cycles, one can then calculate the
probability of positive ion loss on grid 2 R .
The probability is measured for Cl+ and HCl+ ions with
different kinetic energies. It is found to be independent on the
ion nature or the kinetic energy of the ion and equal to 19.5% ±
0.05%. With the value p, it is possible to obtain the exact
number of ions produced as a result of HCl photodissociation
or ionization, from the number of ions detected in the classical
configuration experiment. To do this, one needs to divide the
number of detected ions by the factor (1 − p)2.
like HCl∗ + hν → HCl∗∗, and the probability of the nonadiabatic transitions HCl∗∗ → HCl(B) → H+ + Cl−, leading to
ionic pairs. All these data should be obtained from the analysis
of the dependencies of the number of ions on the laser energy.
Further work is in progress to measure accurately 2- and
3-photon cross sections and to analyze the mechanism of the
ion-pair channel in REMPI of HCl. A full characterization of
the laser beam and the knowledge of the probability for ion
detection are necessary parts of the analysis.
A detailed knowledge of losses of produced ions in the
mass spectrometer before detection requires understanding
and characterization of such processes like the electron emission from metal grids under ion bombardment and charge
transfer between positive ions and the metal surface of the
grids, Cl+ + grid → Cl−, e−.
An additional special configuration of the mass spectrometer was proposed where only the directions of the electrical
fields are different from the directions in the main configuration. This configuration organizes a trap for positive ions.
Moving periodically in the trap, the ions collide with two
grids of the mass spectrometer placed at both sides of the
drift region. This configuration allowed us to measure the
probabilities of production, branching ratios, time distribution,
and space distributions of electrons and negative ions produced
on the grids after the impact of positive ions. It was found, for
example, that each grid eliminates approximately 20% of the
positive ions.
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