INSTITUTE OF PHYSICS PUBLISHING
JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS
J. Phys. B: At. Mol. Opt. Phys. 37 (2004) R57–R88
PII: S0953-4075(04)63251-2
TOPICAL REVIEW
Physics with electrostatic rings and traps
L H Andersen1, O Heber2 and D Zajfman3,4
1
2
3
4
Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark
Physics Service Units, Weizmann Institute of Science, Rehovot, 76100, Israel
Department of Particle Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
Max-Planck-Institut für Kernphysik, D-69117 Heidelberg, Germany
Received 26 February 2004
Published 17 May 2004
Online at stacks.iop.org/JPhysB/37/R57
DOI: 10.1088/0953-4075/37/11/R01
Abstract
The recent development of electrostatic devices which allow us to store keV
ion beams has launched several new kinds of investigations. We review the
basic ideas behind the development of the electrostatic ion storage ring and the
electrostatic ion beam trap techniques. The various experiments performed with
atomic and molecular ion beams, ranging from the measurement of lifetimes
of metastable atomic states up to biological applications and single component
plasma studies are discussed.
(Some figures in this article are in colour only in the electronic version)
1. Introduction
1.1. A short history
The physics of trapped ions has evolved into a very mature field since the invention of the ion
trap about 50 years ago [1]. As expressed by Wolfgang Paul, the inventor of the Paul trap, in
his Nobel Lecture, ‘Experimental physics is the art of observing the structure of matter and
of detecting the dynamic process within it’ [1]. Today, sophisticated schemes for trapping
and observing trapped ions are still being developed, and these techniques have yielded
an impressive list of results in various field of physics, such as atomic, molecular, optical
and nuclear physics, nonlinear dynamics, single component plasmas, mass spectrometry,
biophysics, quantum computation and others. It is interesting to note that the idea of building
ion traps grew out of molecular beam physics, mass spectrometry and accelerator physics in
the early 1950s. It is in fact the development of electric and magnetic multipole fields to
focus neutral particles [2–4] in two-dimensional space which triggered the question ‘What
happens if one injects charged particles, ions or electrons, in such multipole fields?’[1]. If one
extends the principle of two-dimensional focusing to three dimensions, one obtains the main
ingredients for particle traps. Ion traps are built to store ions for as long a time as possible and
in such a way that the particles are well localized in space.
0953-4075/04/110057+32$30.00 © 2004 IOP Publishing Ltd Printed in the UK
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Another type of storage device which has been developed during the eighties and early
nineties, to respond to the need of the atomic and molecular physics community, is the
heavy-ion storage ring [5–7]. These machines were designed on the basis of the high-energy
storage rings used in high-energy particle physics, in particular LEAR [8], and use mainly
magnetic bending and focusing elements. Atomic and molecular ion beams have been stored
in heavy-ion storage rings in the energy range between several keV and several tens of MeV.
During the last decade, the need to store fast beams of increasingly more massive particles
such as clusters and bio-molecules has triggered the development of electrostatic storage rings
and ion beam traps. As opposed to magnetic storage rings, these devices have essentially
no upper mass limit on the ions that can be stored. Moreover, they are usually smaller and
require neither high-energy (MeV) accelerators for injecting the beam, nor a sophisticated
energy ramping technique. These electrostatic machines are also easier to operate and cheaper
to build. It is the purpose of this review to present the development which has occurred during
the last eight years since the emergence of the electrostatic storage ring and ion beam traps.
1.2. Why trap ions?
Why do we want to trap ions? The reason can be understood if one realizes that longer
observation time means better precision. The Heisenberg uncertainty principle, Et h̄/2
(where E is the uncertainty in the energy measurement, t the interaction time or observation
time and h̄ is the Planck constant), simply states that precise energy measurements require
a long time. However, we clearly do not need to go deep into the quantum mechanical
world to understand that the more we measure a quantity, the better the precision will be.
Being important for very high precision measurements, the system under investigation has to
be isolated from external perturbation. It is basically this reason which prompted Dehmelt
to embark on the endeavour of using ion traps for precision measurements with ‘individual
particle freely floating in space’.
There are additional reasons to seek very long confinement times: for example, if one
wants to measure the lifetime of a system, for example of a metastable state of an atom, or of
a radioactive isotope. Long trapping time also allows cooling of internal degrees of freedom
(such as electronic, vibrational or rotational excitations of molecules), so that an ensemble of
internally cold particles can be obtained. Typical lifetimes of atomic and molecular transitions
range over several orders of magnitude, from microseconds to hours. Also, some chemical
reactions are so slow that they need a long time before one can identify the outcome. In
general, the isolation of the particles under study allows for better control of the experiment,
and avoids interferences with external perturbations. On the other hand, if required, it is
possible to influence the trapped particles with a well-controlled perturbation (light from a
laser beam for example), so that the effects of a given perturbation can be monitored under
well-defined conditions. Another advantage relies on the recycling of particles. By storing
particles which are difficult to produce, or are available only in small quantities, it is possible
to increase the signal to background ratio and efficiency of the experiments. Several excellent
reviews have been written on the subject [9, 10], describing the different methods of trapping
and their various applications.
1.3. Ion traps, storage rings and electrostatic storage devices
As pointed out before, one can divide the world of particle storage devices into two different
groups: those where ions are localized in space, and their kinetic energy is in the sub-eV
regime (Paul, Penning, Kingdon traps and their variances), and those where particles move
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at very high velocity (from MeV to GeVs), and circulate in a circular vacuum tube (storage
rings). For many years these two groups have been relatively well separated, the first one used
by the atomic physicist, and the second by the high-energy physics community. However, the
need to trap, in ion traps, fast particles produced by accelerators on the one hand, and the use
of the heavy-ion storage ring technique for precision measurement in atomic and molecular
systems on the other hand, have brought these two worlds together.
What are the advantages of each of these methods? Although there is no exclusivity for
the physics problems that can be addressed using either the ion trap or storage ring technique,
and many physical questions have been probed using both of them (such as the cooling of
ions, mass measurements, precision spectroscopy and others), some experiments are (almost)
unique to one single trapping method, such as the recombination of electrons with atomic
and molecular ions in storage rings, and the recent use of ion traps for quantum computing.
Of course, the localization in space obtained in ion traps allows for cooling to a very low
temperature, while the fact that the ions are moving in a well-defined direction in a heavyion storage ring allows for high efficiency detection of reaction products and the use of the
merged beams technique, as is regularly done with the so-called electron coolers existing in
all heavy-ion storage rings .
During the last few years, the technique of storage rings and ion traps have started to merge.
A typical example is the appearance of the ‘storage Paul trap’ (PALLAS) [11] which is a small
Paul trap shaped as a ring, allowing the ions to circulate and be stored with the help of a timedependent electric field. During the last half of the 1990s, ideas of building small electrostatic
storage rings and electrostatic ion beam traps were brought forward. Electrostatic beam
storage devices have the convenience of being more compact than the usual large magnetic
storage rings. However, their main advantage lies in the lack of an upper limit for the mass of
the stored particles. This opens new areas of research (such as cluster and biophysics) which
may benefit from the long storage times available in these devices. Additional benefits are the
lower construction and operation costs as well as the simpler operation and tuning.
Because of the use of electrostatic fields, these machines are usually limited to the keV
energy range (up to several hundred keV). The lifetime of the beams at these energies is
usually limited by the electron-capture processes as well as multiple scattering, while the
lifetime of MeV beams is mostly limited by electron-loss process. For singly charged ions,
and assuming identical vacuum conditions, the lifetime of keV and MeV beam is about the
same (i.e., typically 1–100 s) because the cross sections for electron capture and electron
stripping are of the same order of magnitude at these energies.
In the following, we describe the principle of operation of both the electrostatic storage
rings and the electrostatic ion beam traps, and we review the main results obtained with these
techniques.
2. Electrostatic storage rings
2.1. Introduction and history
The Danish storage ring ELISA, which is an acronym for electrostatic ion storage ring,
Aarhus [12, 13] was to our knowledge the first electrostatic storage ring built for the storage
of heavy ions. It was funded in 1996 and the first beams were already successfully stored
the following year. The concept of electrostatic storage in a ring was, however, used much
earlier for the storage of electrons. At Brookhaven [14] an electrostatic synchrotron for the
storage of 1–10 MeV electrons was built as a test facility. This particular storage ring was
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circular with a radius of about 7 m, but was never used as a dedicated research machine.
More recently, a second electrostatic heavy-ion storage ring has come into operation at the
KEK-High Energy Accelerator Research Organization in Japan [15, 16]. The design of this
ring (in short called the KEK ring here) is essentially a copy of ELISA, although cylindrical
deflectors were used instead of the spherical deflectors that were initially used in ELISA.
Cylindrical deflectors were used in the Japanese ring, and later also in ELISA, to avoid a
narrow focus of the ion beam and an unwanted loss of beam particles at high currents. Other
electrostatic storage rings are planned or under construction. One such ring is considered to
be built in Frankfurt am Main, Germany [17] and a double-ring storage device is planned in
Stockholm, Sweden [18].
Apart from being relatively small and easy to operate there are numerous other advantages
of electrostatic storage rings. First of all there is, as already pointed out, in principle no
limitation to the mass of the stored particle. Ions of the same energy experience the same
deflection in an electric field irrespective of the mass. In magnetic rings the required magnetic
field is proportional to the momentum of the ion and hence the square root of the mass at
constant energy. This feature was indeed essential in the original proposal for ELISA in 1996,
where the possibility of storing amino acids and DNA fragments was discussed [19].
Avoiding magnetic fields in electrostatic devices is advantageous for studies where
mixing of magnetic substates is unwanted [20]. Especially, if energy splittings between
fine-structure components are small, the magnetic field can be strong enough to introduce a
mixing of magnetic substates with the same MJ -quantum number from different fine-structure
components. Such mixing may cause changes in the autodetachment rate and thus in the
lifetime [21]. The effect of magnetic fields may hence complicate the interpretation of
the data.
The modest size of electrostatic rings also allows for some control of the temperature,
which is important in connection with the study of the influence of black-body radiationinduced photodetachment of weakly bound negative ions [22]. Lowering the temperature also
improves the vacuum—a feature that can be utilized when processes, which proceed on a very
long time scale, are studied [23].
In the following sections we describe some technical aspects of ELISA. We choose to
focus on this ring since it has been in operation for the longest time. The other operating ring
in Japan is essentially a copy of ELISA and most of the discussion will also pertain to this
ring. Then we give examples of research conducted at ELISA as well as at the KEK ring.
2.2. Concept and characteristics
The electrostatic storage ring is, in principle, a bent vacuum pipe where charged particles
circulate, guided and focused by electrostatic steering elements. The ELISA ring has two
straight sections for experiments as seen in figures 1 and 2. ELISA was built without an
internal acceleration section and ions travel with constant speed in the ring except when
entering the electrostatic elements where some local acceleration is experienced. In this
respect, storage rings differ from ion traps of the cavity-type where ions come to a complete
stop at the ends (see the later discussion).
Different ion sources can be mounted on a high-voltage platform (see figures 1 and 2) and
used to produce a beam of ions to be stored in the ring. A maximum of 25 kV may be applied
to the ion–source platform giving the ions an energy of max z × 25 keV, z being the charge of
the ion in units of the elementary charge. After acceleration, an m/z analysis, where m is the
mass and z is the charge state of the ion, is performed by a 90◦ bending magnet with 1.5 m
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Pulsed lasers
Nd:YAG
Laser
power meter
ELISA
Magnet
OPPO
ETRAP
Particle
detector
H.V. platform
With ion source
Figure 1. The electrostatic ion storage ring ELISA equipped with pulsed lasers, internal electron
target (called ETRAP) and a detector for neutral products.
Figure 2. The electrostatic ion storage ring ELISA seen in 3D perspective. At the far end the ion
source and the injection magnet can be seen. The detector chamber for the neutrals detector (left)
and the laser (right) are seen at the nearest end. The coils for the electron beam are seen at the
experimental straight section to the left. The six vertical tubes on top of ELISA are sublimation
vacuum pumps.
radius capable of deflecting singly charged ions at 22 keV with masses up to 1650 amu. The
ions proceed as a bunch of µs duration into the ring.
Many ion sources give high dc currents and the filling of the ring is simply a matter of
directing the beam into the ring and filling it by a single-turn injection. Several high-current
ion sources have been used in this mode of operation such as the sputter-ion source [24, 25]
and a hollow-cathode glow discharge source [26] for negative ions, and the Nielsen-type ion
source [27] for positive ions. More recently, the electrospray ionization (EIS) technique [28]
has been applied to produce ions of molecules, clusters and biomolecules in ELISA [29, 30]
as well as in the KEK ring [31]. The ESI source is mounted on a high-voltage platform
and combined with an ion trap to accumulate ions between injections and hence increase the
number of ions in the injected ion bunch. The ion source ensemble was designed and built in
Aarhus [29] and is shown schematically in figure 1. A constant flow of the spray solution is
led through a stainless steel hypodermic needle biased at 2–4 kV relative to a heated capillary
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where solvent molecules are removed from the desired ion species. The ions are focused
and steered through an octupole beam guide and finally they enter a quadrupole ion trap with
cylindrical geometry. The trap is based on a design by Wells et al [32]. When the ions are
released from the trap, they exit through an Einzel lens into the acceleration tube where they
gain the final kinetic energy.
3. Physics with electrostatic storage rings
3.1. Lifetime measurements
While circulating in the ring, ions experience collisions with the background gas which is
mainly H2 . As a result the number of stored ions decays according to
N (L) = N0 × e−σ (Ek )ρL ,
(1)
where N0 is the initial number of stored ions, L is the distance travelled, ρ is the density of
atoms and molecules in the vacuum chamber (proportional to the pressure p) and σ is the total
cross section for a collision leading to loss of particles, i.e. changing the ratio Ek /z, where Ek
is the kinetic energy. For ions moving at a constant energy, or speed v, this translates into an
exponential decay in time:
N (t) = N0 × e−σ0 ρvt = N0 × e−t/τ ,
(2)
where σ0 is the cross section at the storage energy. For the storage of negative ions the
lifetime (τ ) is typically limited by electron-loss collisions whereas positive ions are lost as a
consequence of electron capture. If the beam contains particles in metastable states (i), which
decay spontaneously with a rate ki = 1/τi the total decay rate is [33]
α0 −t/τc αi −t/τi
R(t) = N0 ×
e
+
e
,
(3)
τc
τi
i
where α0 is the fractional population of the stable ions and (αi ) the fraction of metastable
components. Normally, the collision-limited storage lifetime (τc ) is of the order of 10–100 s.
Two studies of lifetimes of metastable atomic negative ions were performed in ELISA. In
the first [20] the decay of He− in the 1s2s2p 4 P state was studied. This state is bound by only
77 meV relative to the 1s2s 3 S excited state of helium. The 4 P state has three fine-structure
levels which autodetach with different strengths. It is predicted theoretically that the decay
is caused by the two-body spin–spin and spin–other-orbit relativistic interactions [34]. The
beam of He− was produced at 22 keV by a charge-transfer reaction in a K vapour cell. It
was found that the three fine-structure components were roughly statistically populated. The
revolution time in ELISA was 8 µs, just short enough to observe the fast decays of the J = 1/2
and 3/2 fine-structure components (see figure 3(c)). The J = 5/2 component decayed with a
lifetime of about 300 µs at room temperature and about 350 µs when ELISA was cooled to
−50 ◦ C. The temperature dependence was accounted for by black-body induced detachment
and the final J = 5/2 intrinsic lifetime was determined to be 365 ± 3 µs. This value is in
good agreement with an earlier measurement performed at the magnetic storage ring ASTRID
[21] (350 ± 15 µs), and slightly outside the one-standard deviation result of the more recent
ion-trap measurement (343 ± 10 µs) [35]. Compared to the first measurement at the magnetic
ring ASTRID, the lifetime at ELISA was determined with higher accuracy owing to a more
precise account of the black-body induced contribution and the avoidance of fine-structure
mixing in magnetic fields. The J = 1/2 and 3/2 components decay with almost identical
rates and an average lifetime of 11.1 ± 0.3 µs was determined in agreement with theoretical
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Counts
Counts
10
4
-
(a)
10
3
10
2
10
1
10
4
10
3
C2H2
-t/τ
e , τ=28 s
0 10 20 30 40 50
-
(b)
Ag5
10
6
10
5
10
4
10
3
10
2
10
1
(c)
3
10
2
10
1
10
0
-
τ5/2
0
10
He
τ<1/2,3/2>
0.002
(d)
0.004
-
RFP(1)
1+ δ
10
2
10
1
1/t
, δ=0.1
0 10 20 30 40 50
Time (s)
0
0.04
Time (s)
0.08
Figure 3. Counts in the neutral detector as a function of time. (a) Venylidene anions exponentially
decaying with a storage lifetime of 28 s, (b) Ag5 cluster anions which decay as 1/t 1.1 , (c) the atomic
He− with two very short exponentially decaying components, (d) the red fluorescent chromophore
molecule RFP(1)− being heated up after 50 ms of storage by absorption of photons from a laser
pulse.
predictions by Brage and Fisher [34]. As with the J = 5/2 state, a slightly shorter lifetime
was obtained in the electrostatic-trap experiment (8.9 ± 0.2 µs ), indicating that there might
have been unforeseen losses of ions in the trap (see the later discussion).
The lifetime of metastable Be− (2s2p2 4 P, J = 3/2) was also studied in the electrostatic
trap [36] and at ELISA [37]. The lifetime of this state was first determined by Balling
et al [38] at ASTRID. Magnetic mixing between the J = 3/2 fine-structure component and
the other two fast-decaying components, J = 1/2 and 5/2, complicated the measurement,
but in the limit of vanishing magnetic fields (towards low storage energy) one obtained the
lifetime of the pure J = 3/2 state. In ELISA it was determined to be 43.40 ± 0.10 µs, which
represents a fifty-fold improvement compared to the initial data from ASTRID. In the trap
measurement [36] a lifetime of 42.07 ± 0.12 µs was obtained; again slightly shorter than the
lifetime obtained at ELISA.
The two ions just discussed decay very fast and the collisionally induced destruction rate
is of little significance. In the measurement of the stability of the vinylidene anion (C2 H−
2)
ground state in ELISA [23], the intrinsic decay is very slow and great effort is needed to
extract it from the decay dictated by collisional destruction. By measuring the decay rate as
a function of background pressure it was possible to establish that the isomerization process
involving detachment from the vinylidene anion to neutral acetylene has a long lifetime of
about 100 s [23]. In this experiment it was also utilized that the ring could be cooled down, in
this case to improve the vacuum.
If the intrinsic decay rates are constant in time pure exponential decays are observed
as outlined above. This is normally the case when the system is in a well-defined energy
state, or a few substates are populated as in the case of He− . A new situation arises,
however, when clusters and large molecular ions are considered under circumstances where
there is a significant heat capacity and when ion sources are used which provide ions at
finite, non-negligible temperature and hence with a large variation in the internal degree of
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excitation. With stored ions we deal with isolated systems of well-defined energy (if we
neglect weak radiative couplings) and we thus deal with a microcanonical ensemble. At a
given microcanonical temperature T the energy distribution G(E) is approximately Gaussian
with a width [39]
(4)
σ = kB CT
where kB is Boltzmann’s constant and C is the microcanonical heat capacity [39] which
asymptotically (i.e. at high temperature) is C = (3N − 6)kB − kB = (3N − 7)kB , N being
the number of atoms in the molecule. C is reduced by kB , because the system is not in
equilibrium with a heat bath, as is normally the case. Inside an oven, which is kept at
a constant temperature there are frequent collisions with walls and other molecules which
ensure a rapid energy exchange. When particles have left the ion source they travel basically
as isolated species and the energy of each particle is conserved, that is the ensemble of ions in
the ring or trap is a microcanonical ensemble characterized by the energy E and level density
ρ(E), which defines the microcanonical temperature [39]:
Tm =
1/kB
.
d/dE(ln ρ(E))
(5)
The internal energy at a given temperature may be calculated from the normal mode frequencies
(νi ) [40]:
E=
[hνi /(exp(hνi /kB T ) − 1)],
(6)
i
where the sum is over all the normal mode frequencies. They may be calculated with semiempirical methods using for example the PM3 Hamiltonian (Gaussian98 [41]). Accordingly,
the canonical heat capacity is
[(hνi /kB T )2 × exp(−hνi /kB T )/(1 − exp(−hνi /kB T ))2 ].
(7)
C = kB
i
The microcanonical heat capacity is approximately equal to the canonical heat capacity minus
kB . Molecules with about 30 atoms easily have a heat capacity of 20–40kB and hence an energy
spread of 0.1 to 0.2 eV (equation (4)) when produced at room temperature, for example, by
the electrospray-ion source. Ions produced by the sputter-ion source may, however, be much
hotter and this has severe consequences for the decay [42] as will be discussed below.
For a system with an initial internal energy distribution G(E) the rate of emission of a
fragment with binding energy Eb is [42]
(8)
I (t) = dE k(E)G(E) e−k(E)t ,
where k(E) is the energy-dependent rate constant. If G(E) is a delta function around some
fixed energy E0 , k(E) = k(E0 ) = k0 one obtains the usual exponential decay. If, on the
other hand, G(E) corresponds to a broad distribution in energy and varies slowly compared
to k(E), k(E) exp(−k(E) t) peaks at an energy Em where k(E) = 1/t and a power law is
obtained after integration [42]:
I (t) ∼ 1/t.
(9)
Indeed such time-dependent decays (yield of neutral fragments as a function of time) have
been observed for many hot cluster ions at ELISA [43]. We show data obtained by Hansen et
al [42] with silver cluster anions in ELISA in figure 3(b). The decay here is due to electron
emission (thermionic emission) [44] and it almost follows the predicted 1/t decay law. The
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10
2
10
1
10
0
Lifetime (s)
-1
10
-1
10
-2
10
-3
OH (3600 cm )
-1
CO (1800 cm )
500
1000
2000
T (K)
Figure 4. Calculated decay times for energy loss from the harmonic oscillator for OH and CO
vibrations. Equation (11) was used for the calculation and the effective charge was set equal to e.
small correction (causing a slightly faster decay) may be explained by the explicit form of
k(E) and is related to the effective number of degrees of freedom [42].
If the decay is relatively slow (on the ms time scale or longer) the individual molecules
may lose energy by photon emission. The way to correct for this effect is to make the
substitution −k(E)t → −(k(E) + 1/τc )t in equation (8), τc being the cooling decay time. This
gives an additional factor exp(−t/τc ) to I (t). Radiative cooling and its effect on thermionic
emission from hot clusters and amino acids are treated in several papers by Andersen et al
[42, 45, 46]. IR emission from molecules was earlier investigated by Dunbar et al (see,
for example, [47]). The power radiated from a charge undergoing one-dimensional periodic
oscillations at frequency ω is [48]
2ω4 q 2 /4π 0
· x 2 ,
(10)
3c3
where q is the effective charge and c the speed of light. For a harmonic oscillator x 2 is equal
to Eosc /Mω2 , where M is the mass and Eosc the energy which is a function of temperature
since each oscillator is populated with the Boltzmann weight factor. The resulting radiated
power is
P =
P =
h̄ω
2ω2 q 2 /4π 0
.
·
3Mc3
exp(h̄ω/kB T ) − 1
(11)
Energy loss from low-frequency oscillations (vibrations and rotations) is avoided by the
appearance of the ω2 factor. It is seen that at low temperature also high-energy oscillations are
damped by the Boltzmann factor. The exponential lifetime associated with radiation emission
(energy loss) is h̄ω/P which may be estimated from equation (11). The lifetime associated
with a CO stretch mode at 1800 cm−1 is about 0.2 s at T = 1000 K and the corresponding
lifetime for an OH vibration at 3600 cm−1 is 0.1 s, both significant for lifetime measurements
in traps and storage rings. Due to the Boltzmann factor, the two vibrational modes have
different significance at high and at low temperature as seen in figure 4.
Large molecules, clusters and biomolecules may possess an internal energy of several eV
and the rather slow emission of infrared radiation will eventually cool the stored particle down
to a temperature where they no longer decays by fragmentation and where the production of
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4
10
415 nm
96 µs
-
HOOC
Counts
3
10
1.5 ms
COO
N
H
N
N
H
N
2
10
0
5
10
15
Time after photon absorption [ms]
20
Figure 5. The counts of neutral products from deprotonated protoporphyrin after being exposed to
a single laser pulse at 415 nm. The fast-decaying component (96 µs) was ascribed to a thermally
activated dissociation process and the ms-time component is due to population trapping in the
triplet state.
detectable neutral fragments hence stops. Deviations from the simple power law caused by
infrared emission have recently been discussed in connection with collisionally excited amino
acids in ELISA [30].
Before ending the discussion of lifetime studies in electrostatic ion storage rings, we draw
attention to the recent experiment by Calvo et al [49]. They measured the lifetime of the first
electronic triplet state of protonated and deprotonated protoporphyrin, which are important
photoactive molecules in biology. The creation of these molecules in the electronic triplet
state (parallel spins of the outermost electrons) can be hazardous since it may interact with
3 ground-state triplet oxygen O2 and convert it into the reactive species in the excited singlet
1 state O2 . The triplet state of protoporphyrin chromophore was excited by a laser at 415 nm
and found to have lifetimes of 1.5 ms (deprotonated form) and 0.6 ms (protonated form). It
was also found that the quantum yield for the triplet states was about 0.60–0.70. Figure 5
shows the counts of neutral products from deprotonated protoporphyrin after being exposed
to a single laser pulse at 415 nm. The fast-decaying component (96 µs) was ascribed to a
thermally activated dissociation process in the singlet manifold and the ms-time component
to population trapping in the triplet state. When trapped in the triplet state, the decay rate for
neutral formation is limited by the intersystem crossing time to the electronic singlet ground
state from which fragmentation eventually takes place.
3.2. Biophysics
3.2.1. Absorption profiles. The combination of the electrospray ionization technique as an
efficient method for the production of large gas-phase molecules and the mass-independent
electrostatic storage of molecules has turned out to be very successful for studies of gas-phase
molecular ions of biological relevance. The fact that we deal with molecules in the gas phase
is essential, and new information is gained by studying property differences in the gas phase,
the liquid phase and in biological systems such as proteins. Such comparisons give insight
into the perturbations that are encountered in biomolecules. And perturbations can have very
significant effects on, for example, the absorption properties of photoactive biomolecules.
In the case of retinal, the light-absorbing molecule (chromophore) of the rhodopsin protein
responsible for vision [50], different perturbations of the same chromophore molecule tunes
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the wavelength of the absorption maximum from about 450 nm to 600 nm. It is found that the
replacement of a polar with a nonpolar residue near the chromophore shifts the absorption by
about 10 nm [50]. Studies of such effects at the single molecule level are indeed challenging
and may lead to a more detailed understanding of proteins. Another motivation is related
to molecular theory [51–57]. We may provide data to guide further theoretical development
by measuring absorption bands of bare chromophores and chromophores with well-defined
perturbations (for example a few water molecules) since absorption data from chromophores
in liquids as well as in biological systems are still too complicated for ab initio theory. A
different area of research is related to the radiation damage of biomolecules in large biological
molecules such as DNA [58–61]. It has been shown that low-energy electrons can cause
considerable damage via the dissociation of specific basic molecular units [60–63] both in
single oligonucleotides [64, 65] and double-stranded DNA [58–60]. Such damage was found
to be strongly influenced by electron resonances. Recently, the first reports have emerged on
studies where stored ions of biomolecules [31] and small solvated anions [66] are bombarded
by free electrons in electrostatic storage rings. In the following, we discuss these areas of
research in relation to storage rings: photophysics of gas-phase chromophores and collision
physics with free electrons.
Chromophores are found in many proteins where they serve as signal mediators in the
sense that light absorption by the chromophore has clear detectable consequences. Typically,
they have absorption bands in the visible or near visible part of the spectrum. In the visual
rhodopsin protein mentioned above, the absorption of light triggers a fast isomerization of the
chromophore [67] producing an active signalling state, which eventually generates a visual
nerve impulse [50]. Other proteins emit light as a consequence of the primary excitation
of the chromophore. Such light-emitting proteins as the green fluorescent protein (GFP)
from the jellyfish Aequorea victoria [68–71] have immense practical applications in biology
for continuously monitoring gene expression and developments in living cells. Many GFP
mutants have a high fluorescence quantum yield whereas others only have poor quantum
yields [72]. The interaction between the chromophore and the protein environment plays a
crucial role for the preferred response, for example isomerization versus fluorescence. Despite
the many applications, important aspects of the photophysics of these chromophores are still
incompletely understood. At the electrostatic storage ring ELISA we have addressed the
basic problem of photo response of chromophores at the most fundamental level, i.e. in the
completely isolated form—the gas phase.
In a series of recent experiments at ELISA, gas-phase absorption spectroscopy of model
chromophore ions (protonated/deprotonated) of proteins such as GFP [75, 76], the GFP mutant
called W7 [77] and the red fluorescent protein DsRed [78, 79] has been addressed. The basic
idea in these studies is to use the electronic excitation energy (i.e. the absorption wavelength)
as a means to monitor perturbations on the electronic structure of the chromophores in different
media such as protein cavities and liquids. The applied experimental technique is based on
photodestruction: chromophores in the gas phase are exposed to a laser pulse, and experience
single or multiple absorptions of photons at a given laser wavelength. As a consequence of
the absorption, the chromophores are heated to a degree where they dissociate by thermal
activation. Briefly the experiment was conducted as follows. After a preselected storage
time, typically 5–50 ms corresponding to about 102 –103 revolutions in the ring, the ions were
irradiated by a laser pulse in the straight section opposite the place of injection (see figure 1).
Storage before irradiation ensured that ions collisionally excited during production and
injection had at least partially decayed. Tunable, visible laser light was provided by an optical
power parametric oscillator laser (ScanMate OPPO from Lambda Physik) pumped by the third
harmonic of a Nd:YAG laser (Infinity-Coherent, 355 nm, 3 ns pulse). Frequency-doubled light
Topical Review
differential absorption cross section [arb.units]
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1
0.8
0.6
0.4
0.2
0
0
0.5
tim
ea
fte
1
r ir
rad
1.5
iat
ion
[m
s]
2
500
520
540
560
580
600
620
640
660
wavelength [nm]
Figure 6. The differential absorption cross section (arbitrary units) as a function of time after laser
excitation and wavelength for the deprotonated DsRed chromophore (RFP2− ).
from a dye laser (Lambda Physik), pumped by the second harmonic of the Nd:YAG laser, was
used for wavelengths shorter than 430 nm. Tuning the laser wavelength to an absorption band
resulted in electron detachment and/or bond dissociation and hence production of neutrals.
A 10 Hz repetition rate was applied and counts of neutrals were normally accumulated over one
thousand injections where each injection and storage was associated with only one laser pulse.
A particle detector counted neutrals formed in the straight section opposite the laser-interaction
region.
The yield of neutrals was recorded as a function of time after laser excitation and
wavelength. Figure 6 shows absorption data with the deprotonated red fluorescent protein [80]
model chromophore called RFP(2) [78, 79]. The absorption of light leads to the formation
of neutral products which stops after less than a millisecond, and the absorption profile was
obtained by integration over time. A measure of the absorption cross section at a specific
wavelength was obtained from
(12)
Nneutrals = Nions × σ (λ) × dt
or
1
Nneutrals
×
,
(13)
Nions
Elaser × λ
where Nneutrals is the number of laser-induced neutrals (integrated over time), Nions the number
of ions in the ion bunch (proportional to the neutrals arriving at the detector prior to firing the
laser), σ the photo-absorption cross section, the photon flux, Elaser the laser-pulse energy
and λ the wavelength.
The first absorption spectra recorded at ELISA were performed with a chromophore of
the green fluorescent protein [75, 76]. The measured absorption bands are shown in figure 7,
where the absorption of the chromophore in three different media are shown: the protein [68],
σ (λ) ∝
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R69
GFP
1.0
neutral
Absorption cross section [arb. units]
0.5
0
300
anion
400
500
gas phase
1.0
0.5
0
300
1.0
600
cation
anion
400
500
600
H2O
pH=7 pH<1
pH=13
0.5
0
300
400
500
600
λ [nm]
Figure 7. The absorption cross section (arbitrary units) as a function of wavelength for the GFP
chromophore in the protein (top), in the gas phase (middle) and in water (bottom). The gas-phase
data were recorded at the ELISA storage ring.
the gas phase (ELISA) and aqueous solutions of different pH. The absorption spectrum of the
protein shows two absorption bands that are ascribed to a neutral chromophore (absorption
maximum at 395 nm) and a deprotonated (anion) chromophore (absorption maximum at
477 nm). The absorption spectrum of the gas-phase chromophore anion reveals that the
absorption band has a maximum at 479 nm. There is, thus, almost no difference between
the absorption bands obtained with the protein and the chromophore in vacuo. It is seen that
the absorption maximum for the anion form of the chromophore is shifted to 426 nm when
recorded in an alkaline aqueous solution. This large shift may be explained by hydrogen
bond interactions, which localize the active electrons of the chromophore in the anion form.
There is a significant amount of electron delocalization for the anion form, which makes the
chromophore sensitive to perturbations from the environment.
The similarity between the absorption band of the gaseous anion and the second absorption
band of the protein is striking. In the protein, the chromophore is covalently attached to an
α-helix that runs up the axis of a hollow cylinder formed by eleven β-strands [68]. The
cylindrical shape of the rigid β-can protects the buried chromophore from the solvent and the
results indicate that the actual environment of the chromophore inside the protein cavity is
much closer to vacuum than to bulk solution. In other words, the electron delocalization in the
Aequorea victoria GFP chromophore matches that of the gaseous anion. The chromophore
cation in the gas phase exhibits an absorption maximum at 406 nm. It is not possible to
make direct comparisons with protein data as this chromophore charge state is not present in
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Topical Review
GFP. The absorption in the acidic solution (pH< 1) has a maximum at 396 nm, i.e. a blue
shift of only 10 nm with respect to the gas-phase case. It may be argued that the shift is
significantly smaller for cations than for anions because of less electron delocalization for
GFP-chromophore cations [75].
3.2.2. Dissociation dynamics. The decay leading to the emission of neutral particles after
n-photon absorption (see, for example figure 6) is assumed to proceed through a decay channel
with activation energy Ea , and the Arrhenius expression for the decay constant is expected to
be applicable:
kn = A × exp(−Ea /kB Tn∗ ),
(14)
where A is the pre-exponential factor for the mode of decay and Tn∗
is the effective temperature
of the molecule after absorption of n photons. Since the molecules are not in equilibrium with
a heat bath which keeps its temperature constant an effective temperature Tn∗ is used, which is
the temperature corresponding to the mean energy before and after the decay [39]:
Tn∗ = Tn − 1/Cn × Ea /2,
(15)
where Tn and Cn are the temperature and heat capacity, respectively, after n-photon absorption.
It is assumed that the dissociation of the molecule yields neutral fragments which may
be detected in the experiment. Dependent on A and Ea it may take one or several photons
to effectively heat up the molecule to cause fragmentation. In the absorption region (400–
600 nm), temperatures of 800–1000 K (n = 1) and 1300–1500 K (n = 2) are typically reached
[84]. The decay in time of an excited chromophore having absorbed n photons is
Yn (t) = kn exp(−kn t) = A × exp(−Ea /kB Tn∗ ) × exp(−A × exp(−Ea /kB Tn∗ )t).
(16)
To get a proper description of the decay, the energy spread of the initial energy distribution
G(E) at the appropriate temperature before the photon absorption T0 (here room temperature)
is taken into account. Normally a Gaussian function with the width given in equation (4) is
used [39]. The finite width is causing deviations from a perfect exponential decay as will
be seen in an example given below. The final expression for the intensity of fragments as a
function of time is
(17)
In (t) = dE G(E)kn (E) exp(−kn (E)t).
It is possible to determine both Ea and A with only a single measurement at a given
wavelength under certain favourable conditions. However, recording the decay rate at different
wavelengths (and hence different temperatures) provides a better way of determining these
parameters simultaneously [84]. The applied formalism is demonstrated in figure 8 where
the yield of neutral fragments from GFP chromophore cations is shown as a function of
time, when excited by 266 nm photons (single-photon absorption) [84]. An activation energy
of about 3 eV and a pre-exponential factor A of 5× 1016 s−1 was found from a fit to the
data [84].
The decay after photoabsorption may take place after considerable time (µs–ms) as
discussed above. In other words, there is normally ample time for the energy to be distributed
over the many degrees of freedom (3N-6) in the molecule. When located in a medium
other than vacuum the medium may take part in the dissipation of the energy. In biological
environments this is normally a good thing because it prevents dissociation (destruction)
of the chormophores. In a recent photo-destruction study at ELISA [85] of the RNA and
DNA building blocks, the adenosine 5’-monophosphate (AMP) nucleotide, it was found by
a depletion technique that the protonated AMP molecules had a significant, very fast decay
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R71
Yield
1000
experiment
Fit
100
10
+
GFP
266 nm
1
50
60
Time (ms)
70
Figure 8. The yield of neutral fragments from protonated GFP chromophores as a function of
time after exposure to a single laser pulse at 266 nm. The laser was fired 46 ms after injection into
ELISA. The solid line is based on the calculation described in the text. Note that the decay is not
exponential in time.
component (non-statistical process), whereas the deprotonated AMP (natural form at normal
pH) decayed significantly slower due to a process where the energy is statistically distributed
over the many degrees of freedom in the molecule. Thus, the AMP form of biological relevance
(the deprotonated form) has a good ability to survive upon exposure to UV radiation.
3.3. Collisions with electrons
To keep a beam in a storage ring for a considerable time (many revolutions) the interaction with
a given target medium must be weak or the medium thin. In the laser excitation experiments
for example, ions are exposed to laser light for only a very short time (ns). We now turn to
a discussion of experiments where stored ions are exposed to a beam of free electrons with a
rather low density (106 –107 cm−3 ). Such experiments have been conducted for many years
at the magnetic heavy-ion storage rings with both negative and positive ions and atomic and
molecular species; for reviews the reader may consult the papers by Larsson [86], Andersen
[87] and Schuch [88].
In studies of electron-capture processes, it may be desirable to obtain low relative energy
between the electrons and the stored ions because of the increasing cross section for capture
at low energy. In storage rings where storage is based on magnetic fields, the stored ion beam
may have considerable energy and the merged beam configuration is pertinent. The electron
energy that provides zero relative energy in the merged beam case is Ee (eV) ∼ 550 eV ×
Eion (MeV)/M (amu). From this relation it is immediately seen that for a heavy molecule
(several hundred amu), stored in an electrostatic ring (at tens of keV) the energy of the electrons
that provides zero collision energy is only a fraction of an eV. Thus for practical purposes,
zero relative energy in small electrostatic rings may only be obtained for very light ions. In
the KEK ring a merged-beam configuration was chosen whereas in ELISA a crossed-beam
geometry is used.
The electron target at the KEK ring is described by Tanabe et al [89]. Briefly, it has an
interaction length (overlap with the stored ion beam) of 20 cm, a guiding magnetic field in the
interacting region of 10–100 G and very low longitudinal and transverse temperatures [92]
(energy spread) in the meV region. The low energy spread is obtained by adiabatic expansion
[90] of the electron beam from a radius of 0.175 cm at the cathode to 1 cm in the interaction
region. The electron current at 7 V acceleration is 0.012 mA scaling with voltage as V3/2 [91].
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7
Rate coefficient (arb.)
6
(a)
5
4
(a) Asp-Arg-Val-Tyr-Ile-His-Pro-Phe-His-Leu
(b) Asp-Arg-Val-Tyr-Ile-His-Pro-Phe
(c)
Arg-Val-Tyr-Ile-His-Pro-Phe
(b)
3
2
(c)
1
0
0
5
10
15
20
25
E r (eV)
Figure 9. The rate for neutral fragment production as a function of the electron energy. The data
were obtained by Tanabe et al at the KEK ring.
Hence, the electron density at this energy is 1.5 × 105 cm−3 and the target thickness as seen
by the ion beam is 3 × 106 cm−2 .
The electron target at ELISA is described by Jensen [93]. Here electrons intersect the
stored ion beam in a crossed-beam geometry. The cathode radius is 0.7 cm and the electron
beam is guided by a constant magnetic field of up to 200 Gauss. The electron–target device is
called ETRAP since it is designed in such a way that it may work as a Penning trap, capable
of trapping slow electrons with a 38 s storage time [93]. The interaction length is only 1.4 cm
(equal to the electron-beam diameter), but the density of electrons is quite high. As a result
the target thickness is equal to that of the electron device at the KEK ring. As a consequence
of the higher electron density and the fact that the ions probe all electron trajectories across the
electron beam, the electron-energy spread at ETRAP/ELISA is not as good as at the KEK ring.
Tanabe et al have performed electron scattering experiments with singly protonated
peptides (angiotensin I, II and III) at the KEK ring [91]. More specifically, the electroninduced production of neutral fragments was measured as a function of the electron energy
from about 1 eV to 22 eV. The electrospray technique was used in the production of the
protonated gas-phase biomolecules. A main resonance-like structure was observed at about
6.5 eV (see figure 9). The structure was ascribed to a resonant electron-capture process. It
was also observed that the rate of neutral formation decreases with a decrease in the number of
amino-acid residues and it was concluded that not all bonds participate equally in the process,
leading to cleavage. Only a few of them play an important role in the reaction and the bonds
adjacent to the basic amino-acid residues Arg and His were assigned the responsibility for
the cleavage. Experiments with other peptides, singly protonated bradykinin (Arg-Pro-ProGly-Phe-Ser-Pro-Phe-Arg) and tuftsin (Thr-Lys-Pro-Arg) revealed similar structures which
indicate that the physics involved may be common to singly protonated light peptides.
Electron-impact detachment from negative ions were studied at ELISA. The first
investigations were concerned with the detachment process near the threshold and the possible
formation of doubly charged negative ions (dianions). Dianion resonances were observed for
a number of small molecular ions at ASTRID (for example C2 [94], CN [95] and NO2 [96]).
Figure 10 shows the ground-state resonance of NO2−
2 as obtained earlier with the merged-beam
setup at ASTRID as well as the crossed-beam setup at ELISA. The ground-state resonance at
Topical Review
R73
8
-
NO2 + e
-
4
σ (10
-16
2
cm )
6
2
0
0
5
10
Energy (eV)
15
20
Figure 10. The cross section for electron-impact detachment of NO−
2 as a function of the electron
energy near the threshold. The solid curves were obtained at the ASTRID storage ring and the
dots at ELISA. The ELISA data were normalized to those obtained at ASTRID. The ground state
dianion resonance at 7 eV is clearly detected at both ring experiments.
about 7 eV is clearly seen in both sets of data. These experiments are unique in the sense that
dianions which are electronically unstable, i.e. in the electronic continuum (positive energy)
may be studied. Not only is the mere existence of these rare and unstable species established,
but also their energy which may be compared to calculations.
To elucidate the stabilizing effect at the single molecule level and the physical
2−
properties of NO2−
2 in water microsolutions, the positive ground-state energy of the NO2 ,
2−
2−
NO2 · (H2 O), and NO2 · (H2 O)2 dianions were recently measured at ELISA [66]. Thus the
first controlled steps towards liquid-phase properties were taken by determining the stabilizing
effect on dianion states upon solvation of single water molecules. It was found that the
stabilizing contribution to the dianion ground-state energy from a single water molecule is
about 0.8 eV for the first few water molecules. From a model calculation it was moreover found
that when about n = 100 water molecules are attached, binding of an electron to NO2 · (H2 O)n
becomes favourable, whereas the transition already occurs at n = 3 in the case of SO4 · (H2 O)n
[66]. The experimental data for the bare NO2 dianion resonance as well as the resonances
observed with micro-solvated NO2 were accounted for by ab initio calculations and the overall
trend was also perfectly well explained in a model [66] based on the known water cluster data
[97].
4. Electrostatic ion beam traps
4.1. Concept and characteristics
The basic concept of the electrostatic ion beam trap (EIBT) is based on the analogy with
classical optics. It is well-known that it is possible to ‘store’ a beam of photons between
two mirrors if a well-defined condition for stability is fulfilled. For symmetric mirror, this
condition is given by [98, 99]:
L
< f < ∞,
(18)
4
where L is the distance between the two mirrors, and f the focal length. It is also well known
that the motion of an ion in an electric potential V can be shown to be equivalent
√ to the motion
of a photon in a material with index of refraction n, by substituting n with V . It is through
this similarity that the concept of storing ions between two electrostatic mirrors came about.
Clearly, the mirrors do not need to be spherical, and with the freedom given by the different
type of electrodes and potentials that can be used to create electrostatic mirrors, the simple
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k
ENTRANCE
V1 V3
V2 V4
Vz
Vz
V3 V1
V4 V2
Micro-channel
plate detector
Amplifier
Digital
oscilloscope
Figure 11. Schematic view of the EIBT developed at the Weizmann Institute. The various
electrodes are connected to independent power supplies. The ions are injected through the lefthand side mirror. The ring pick-up electrode is also shown in the centre of the trap.
Figure 12. Geometry of the Conetrap. Voltages are applied to the two conical electrodes, while
the central one is grounded. The dimension are given in mm.
model described by equation (18) can be extended to more complex schemes, as described
in [100].
A schematic drawing of an ion trap which is based on the above idea and has been
developed at the Weizmann Institute of Science in 1996 is shown in figure 11. A similar
system was later built at Oak Ridge [101]. The two mirrors are made of eight electrodes
each, allowing different voltages to be applied so that the stability condition described in
equation (18) can be fulfilled. The mirrors can be made of any number of electrodes, and
they only influence the shape of the potential in which the ions are moving. As will be seen
later, changing the shape of the potential (within the stability criteria) allows one to observe
interesting dynamical effects or to vary the diameter of the trapped beam. An interesting
example is the CONETRAP [102], developed at the University of Stockholm [103] (see
figure 12). In this case, the mirrors are made out of only one electrode, whose shape is such
that it produces an electric field so that the focal point of the mirrors obeys equation (18).
Another similar setup was constructed at Lawrence Berkeley National Laboratory [104] for
the purpose of mass spectrometry of biomolecules.
In the Weizmann setup, the four electrodes (shown as V1 to V4 in figure 11) are used to
produce the needed longitudinal potential barriers, while the larger electrode (Vz in figure 11) is
Topical Review
R75
used for focalization purpose. In general, several voltage configurations are possible to obtain
trapping. It was found that the stability of the system can be deduced by calculating single
particle trajectories, using a computer program which allows one to track particle trajectories
in electric fields (such as SIMION5 ). The calculations consist of launching particles with a
well-known energy, parallel to the optical axis of the trap, towards the mirror, and to register
the focal point (which is the position at which the bouncing particles cross the optical axis of
the trap). As long as this focal point obeys equation (18), the chosen mirror configuration will
produce stable trajectories.
The injection of particles in an EIBT system is done by lowering the voltages on one
mirror, injecting a bunch of particles, usually with a kinetic energy of several keV per charge
and raising the voltages once the bunch is located inside the trap. It is important to raise the
voltage fast, about an order of magnitude faster than the typical oscillation time of the ions in
the trap (usually on the scale of several µs). Once trapped, the number of ions can be detected
using a pick-up ring electrode which is located between the two mirrors [104, 105]. Such a ring
electrode (see figure 11) measures the image charges which are induced by the ions when they
pass through the ring. In order to obtain a strong signal, it is advantageous to bunch the beam
using an external RF signal, tuned to the natural oscillation frequency of the ions, connected
to any of the trap electrodes. The Fourier transform of this signal yields a power spectrum
whose intensity is directly proportional to the number of ions in the trap. An additional but
more indirect detection can be applied by counting the number of neutral particles which exit
the trap, through one of the mirrors. These neutral particles are created by charge changing
collisions with the atoms or molecules of the residual gas, and can, for example, be counted
with the help of a micro-channel plate (MCP) detector located at the exit of the trap (see
figure 11). Measuring the rate of these neutral particles allows one to extract directly the
lifetime of the stored beam. This lifetime is inversely proportional to the pressure in the trap,
see equation (2) (working pressure is < 2×10−10 Torr). The two most important factors which
influence the lifetime of the beam are the neutralization and the multiple scattering processes
[100]. Figure 13 shows the count rate measured on the MCP detector when a beam of
4.2 keV Au+ is stored in the trap at a pressure of 1× 10−10 Torr. The rapid decay at the
beginning is most probably due to the space charge effect, which represents an additional loss
contribution for high intensity beams.
4.2. Physics with electrostatic traps
4.2.1. Lifetime measurements. Lifetimes of metastable negative ions can easily be measured
with the ion beam trap in a way which is identical to the one described in section 3.1. When
decaying, the neutralized particles exit the trap, and half of them can be detected by the MCP
detector which is located after the exit of the trap. As long as the intrinsic lifetime is much
shorter than the beam lifetime, the decay rate measured on the detector can be interpreted as
being directly related to the intrinsic lifetime of the ions. Otherwise, corrections due to the
finite lifetime of the beam must be taken into account as well.
Measurements for both He− and Be− have been performed with the ion beam trap
[35, 36]. The beams were produced with an energy of 4.2 keV, which correspond to an
oscillation time in the trap of the order of 2 to 3 µs, allowing measurements of relatively short
lifetimes. Details concerning the electronic structure of these ions have already been given in
section 3.1, and the measurement technique is similar to the one used at ELISA [20, 37],
although the trap could not be cooled, and hence only room temperature experiments were
performed. For He− , the lifetime of the 4 P5/2 state, after including the effect of black-body
5
SIMION, V.6.0 Ion Source Software.
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4
Rate on MCP (arb. units)
10
3
10
2
10
1
10
0
10
0
10
20
30
40
50
60
Time (s)
Figure 13. Rate of neutral particles exiting the EIBT when a beam of 4.2 keV Au+ is stored.
radiation was found to be τ5/2 = 343 ± 10 µs, while the mean lifetime for the 4 P3/2 and
4
P1/2 was found to be τ3/2,1/2 = 8.9 ± 0.2 µs. As pointed out in section 3.1, these values
deviate slightly from the values measured by ELISA [20], which are 365 ± 3 µs and 11.1 ±
0.3 µs, respectively. For the Be− ion, the lifetime of the metastable (2s2p2 4 P, J = 3/2) state
was measured to be 42.07 ± 0.12 µs again slightly different than that measured in ELISA
43.40 ± 0.10 µs [37]. Comparison of the numbers between ELISA and the EIBT shows that
the lifetimes measured by the latter are always shorter than by the former. What could be the
reasons for such deviations? First of all, we observe that the largest relative difference between
the two types of measurement is obtained for the shortest lifetime. This may indicate that some
initial instability exist in the ion trap, where ions are lost not only because of neutralization,
but because of unstable trajectories. Space charge effect can be neglected as the number of
injected ions (about 10 per injection) was very small. Experiments made with a beam of Ar+
did show that shortly after injection, and for several µs, the exponential decay has a weak
modulation which could be due to the presence of a ‘hole’ in the distribution of ions in the
trap. This hole is due to the fact that no ions are trapped in the entrance mirror, when the
voltages of its electrodes are being raised. Similar type of measurements were performed with
the Oak Ridge electrostatic trap [101] for CS−
2 [106].
The lifetime of metastable states of positive ions has also been measured with the EIBT.
The charge of the stored ions does not change, and a direct detection of the product of
the decay is not possible. There are two ways to measure such lifetimes: either by detecting
the photons emitted during the decay, or by measuring the change in the stored beam lifetime
due to the difference in the charge exchange cross section of the excited and ground states. In
the following we describe two different techniques based on these concepts.
In the first case [107], the lifetime of 1 S0 metastable state of Xe2+ was measured by
counting the 380 nm photons emitted by the decay of the 1 S0 state. This state mainly decays
to the 3 P1 level, through a magnetic dipole (M1) transition. A photomultiplier tube (PMT)
with a 3 mm photocathode was mounted on the side of the ion trap (see figure 14) and its solid
angle was increased by a pair of sapphire lenses attached to the sapphire viewport of the trap.
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R77
Electron-Impact
Ion Source
4.2 keV
20o Magnet
Slits
Entrance
electrodes
Exit
electrodes
Microchannel
Plate
Wien
Filter
Ion Optics
Corning Glass Filter
PMT ( Hamamatsu R2295)
Multichannel
scaler
Single channel
analyser
Pulse shaping
amplifier
Pre-Amp
Figure 14. Schematic of the experimental setup used for measuring the lifetime of the 1 S0
metastable state of Xe2+ .
Figure 15. Photon decay curve for Xe2+ . The solid line is the result of a nonlinear least-squares
fit to the data.
Using a Monte Carlo simulation, the total efficiency for photon detection was estimated to be
∼3 × 10−4 . For each trapping cycle (lasting 50 ms) an average of 1.2 photon was measured.
Figure 15 shows the time dependence of the signal measured by the PMT. Fitting the data
using a single exponential decay and a time-independent background resulted in a lifetime of
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4.46 ± 0.08 ms. This is almost four times more accurate than the previous measurement made
by Calamai and Johnson (4.6 ± 0.3 ms) [108] and by Walch and Knight (4.5 ± 0.3 ms) [109].
1
A semiempirical calculation by Garstang [110] for the M1 and E2 S0 → 3 P2 tansition rates
using parametric least-squares fit for the observed energy levels yielded a mean lifetime of
4.4 ms. A revised calculation by Hansen and Persson [111] using a similar method, but after
proper assignment of the 1 S0 level, yielded a value of 4.9 ms for the lifetime. Thus the EIBT
result is in agreement with the calculation of Garstang [110], but such agreement is purely
coincidental as the identification of the 1 S0 level in the 5p4 configuration was in error. More
theoretical calculations are needed to clarify the situation.
The second technique [112] was used to measure the decay rate of a metastable state
whose reactivity (electron-capture cross section) with the residual gas is very different than
for the ground state. Such a method works only if the excitation energy is rather large, so
that the difference with the ground state is significant. A good candidate for this is the a 3 +
metastable state of NO+ . This state is 6.4 eV above the ground X1 + state, and because of spin
selection rules, the transition between these two states has to proceed through the perturbation
by other electronic states [113]. It is interesting to point out that the lifetime of the a 3 + state
has been the subject of five experiments [114–118] producing results which differ by about an
order of magnitude. The theoretical values of the a 3 + lifetime also vary widely, indicating
that the lifetime is very sensitive to the perturbation due to other states [114, 115, 119, 120].
The basic idea for the lifetime measurement of the a 3 + state relies on the difference
between the destruction cross sections for the a 3 + and the X1 + states. This difference leads
to a time dependence of the ion loss rate from the trap which itself depends on the lifetime of
the metastable state. More specifically, for NO+ , it has been measured that the electron-capture
cross section for the metastable state is much larger than for the ground state, at keV energies
[121]. Since all other excited states of NO+ have much shorter lifetime than the one expected
for the a 3 + state [117], one is left with a ‘two-level’ system after ∼10 ms of trapping time,
and the lifetime of the beam can be described using three independent decay rates. The first
one is the radiative decay rate from the a 3 + state (kr ), which is the quantity of interest. The
other two decay rates, ke and kg , are related to the destruction cross sections due to collisions
with the atoms and molecules of the residual gas of the excited a 3 + and ground 1 + states,
respectively. Thus, the time-dependent behaviour of the excited and ground state population
of NO+ , Ne (t) and Ng (t) can be described by two rate equations, with these solutions [112]
Ne (t) = Ne0 exp[−(kr + ke )],
kr
kr
exp[−kg t] − Ne0
Ng (t) = Ng0 + Ne0
exp[−(kr + ke )t],
kr + k e − kg
kr + k e − kg
(19)
where Ng0 and Ne0 are the initial ground- and excited-state populations.
The measured quantity is the count rate R(t) on the MCP detector located at the exit of
the ion trap, which is given by the sum of the contributions of the ground- and excited-state
populations, given by
d
R(t) = α [Ng (t) + Ne (t)]
dt
ke − kg
kr
= α(kr + ke )Ne0
exp[−kg t],
exp[−(kr + ke )t] + αkg Ng0 + Ne0
kr + k e − kg
kr + k e − kg
(20)
where α is the detection efficiency. Given that the decay rates ke and kg are not identical
and that the initial population in the excited state Ne0 is nonzero, equation (20) describes a
Topical Review
R79
double exponential decay curve. Note that the coefficient preceding the first component can
take positive or negative values, so that an increase in the count rate as a function of storage
time can also be observed, a somewhat counter-intuitive behaviour. By measuring these decay
curves for different background pressures, the radiative decay constant kr can be obtained by
extrapolating to zero-pressure. It is also interesting to point out that a precise measurement of
the pressure is not needed for this. Since both ke and kg are proportional to the pressure, their
ratio is a constant, and is only a function of their respective destruction cross sections. Thus,
one can find a linear relation between the total decay rate of the excited state (kr + ke ) and the
decay rate of the ground state kg :
(kr + ke ) = kr + Bkg ,
(21)
where B is the ratio between the destruction cross section of the excited state and the ground
state. Thus, plotting (kr + ke ) versus kg , one expects a straight line which intersects the abscissa
(kg = 0) at the values of kr . Figure 16 shows the decay curves measured for 4.2 keV NO+ at
four different background pressures. The presence of the initial fast decay is clear in each of
these data sets, and using a standard fitting procedure based on equation (3), one obtains the
different decay rates. Figure 17 shows the total decay rate of the excited state versus the decay
rate of the ground state. As expected (see equation (21)), a linear dependence is observed,
and an extrapolation to kg = 0 yields a collision-free radiative lifetime for the a 3 + state of
τr = 760 ± 30 ms. This result supports the value measured by Calami and Yoshino [117],
as well as the corrected value of Marx et al [118]. On the theoretical side, only the lifetime
estimated by Kuo et al [115], using first-order perturbation theory turns out to be in very good
agreement with the experimental result. More details can be found in [112].
4.2.2. Electron-impact experiments. The interaction of electrons with molecular ions is
a fundamental process which takes place in many environments such as laboratory and
astrophysical plasmas. The two main advantages of using storage devices for performing
such experiments is that (1) most of the molecular ions can be cooled to the lowest vibrational
ground state and (2) the merged electron–ion beam configuration makes possible to reach
very low energy with high resolution for low-energy collisions in the centre of mass system.
Advantage (1) is still available in an EIBT, but it is technically difficult to produce a merged
electron beam, as it would require very low-energy electrons (<1 eV).
An EIBT which includes an all electrostatic electron target has recently been built at the
Weizmann Institute [122, 123]. The system was specially designed to avoid influences on the
stored ion trajectories. The device produces an approximatively rectangular electron beam
(about 50 mm × 7.5 mm) and currents varying between 10 and 200 µA for an electron energy
between 5 and 30 eV, respectively. The device is mounted in a scattering chamber which
includes both the ion trap and the electron target, see figure 18, so that the ion beam is crossed
by the electron beam at an angle of 90◦ . The interaction region is free of any electrical and
magnetical field (except for the small space charge fields of the ions and electrons).
The first experiment performed with this setup was a measurement of the relative cross
section for electron-impact detachment of negative carbon (C−
n , 1 n 9) and aluminium
,
1
n
5)
clusters,
for
electron
energies
between
5
and
30 eV [124]. Figure 19 shows
(Al−
n
,
between
5 and 30 eV, compared
the relative electron-impact detachment cross section for C−
2
to the results obtained at ASTRID [125]. A very good agreement between the data exists (the
trap results are normalized to the ASTRID data at 20 eV), and the low energy resonance is
well reproduced by the EIBT data. Figure 20 shows results for the relative electron-impact
detachment cross sections for negative carbon clusters, at an electron energy of 20 eV, as a
function of their size n [124] as measured with the setup shown in figure 18. Also shown, in
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Topical Review
Figure 16. Decay curves for 4.2 keV NO+ as measured by the MCP located at the exit of the trap
at four diferent background pressures in the ion trap.
the insert, are the respective electron binding energies. An interesting feature appears: on one
hand the well known odd–even effect of the binding energy [126] is well reproduced in the
cross section, i.e., larger binding energies correspond to lower cross section. On the other hand,
although the average binding energy increases with n, the detachment cross section also keeps
increasing. Thus, the data show one trend and its opposite at the same time. The increasing
general trend
is also in contradiction with the known scaling laws for the cross section, which
predict a 1 Eb2 dependence [127–129], where Eb is the electron binding energy. The reasons
for such a behaviour are still unclear at this time, but it is suggested that the large increase
in polarizability as a function of n for the carbon clusters is responsible for it. Preliminary
results of a similar experiment performed on Al−
n clusters tend to support this suggestion.
These experiments demonstrate one of the main advantages of the EIBT: since the whole
system is electrostatic (including the electron target), no tuning is needed when changing the
mass of the trapped particles, as long as their energy is constant. This also increases the
precision of relative measurements, as the electron–ion beam overlap is constant for all ions.
More details can be found in [122, 124].
4.2.3. Beam dynamics and mass spectrometry. A unique feature of the EIBT is the special
oscillatory motion of the ions and the fact that the ions are brought to a full stop at the edges of
the trap. Thus, strong effects due to the ion–ion Coulomb interaction in the mirror region are
Topical Review
R81
Figure 17. Decay rate of the metastable state (kr + ke ) versus the decay rate of the ground state kg .
The radiative lifetime of NO+ (a 3 + ) was obtained from the straight-line fit when kg = 0.
Figure 18. Schematic view of the electrostatic trap including the electron target. The diameter of
the chamber is 451 mm.
expected. The most interesting dynamical behaviour which has been studied using the EIBT
is the so-called negative mass instability. Negative mass instability was first introduced by
Nielse, Sessler and Symon, in 1959 [130] for relativistic circular accelerators or storage rings.
It has been extensively considered in a number of both experimental and theoretical works
[131]. In these high-energy machines, the negative mass instability occurs when, for example,
the angular velocity decreases with increasing energy, a situation occurring above the socalled transition energy. This effect has, to our knowledge, been observed only in accelerators
operating at relativistic energies, and the theoretical treatment has been implemented using
the Vlasov equation [131]. It is also interesting to point out that this instability is considered
as a nuisance in these large machines, since it disturbs the time structure of the stored beam,
and as such, many efforts are made to avoid the onset of this instability. However, this feature
R82
Topical Review
6
Cross section (10−16 cm2)
5
4
3
2
1
0
5
10
15
20
Electron energy (eV)
25
30
Figure 19. Electron-impact detachment cross section of C−
2 as a function of electron energy. The
open squares are the results from the ASTRID storage ring [125], and the triangles are the EIBT
results [122], normalized at 20 eV.
80
E.A. [eV]
70
60
5
n
40
10
σ
exp
2
0
0
2
[au ])
50
4
30
20
10
0
0
2
4
6
8
10
n
Figure 20. Measured [124] (squares, dashed line) and calculated [129] (circles, full line) electronimpact detachment cross sections at Ee = 20 eV as a function of the number of atoms n for C−
n.
Data and theory are normalized to the absolute cross section of C−
2 [125]. Inset: electron binding
energy for negative carbon clusters as a function of n [126].
(which is also sometimes called self-bunching) can have practical application in the EIBT, as
will be shown below.
In the EIBT, this instability was initially observed by injecting a relatively narrow bunch
in the trap and observing its length as a function of trapping time (or number of oscillations)
[105, 132]. There are three main reasons for the bunch to broaden: (1) not all the particles
in a bunch have exactly the same velocities, (2) not all the trajectories in the trap have the
Topical Review
R83
−20
−20
150 µs
−25
−30
W
0
5
10
15
−8
Voltage (mV)
Voltage (mV)
−30
−35
0
−11
0
5
10
15
5
10
15
5
10
Time (µs)
15
−8
−14
650 µs
−12
0
−9
150 µs
650 µs
5
10
15
0
−8
−14
1650 µs
1650 µs
5
10
Time (µs)
15
0
Figure 21. The signal observed with the pick-up electrode for an initially short bunch of Ar+ at
4.2 keV for three different time windows of 15 µs after injection: the three left panels are in the
dispersive mode, while the three right panels are in the self-bunching mode. The initial value of
the time window is written in each plot.
same length and (3) the Coulomb repulsion between the ions tends to push the particle apart.
When a bunch is injected into the EIBT, its oscillation frequency and width can be measured
by the pick-up electrode. Figure 21 (left panel) shows the signal measured with the pick-up
electrode when a bunch of 4.2 keV Ar+ , with an initial length of 3 cm (corresponding to W0 ∼
200 ns) is injected into the trap. The three different left panels, taken at three different time
windows, show that the pulse broadens, and after a storage time of ∼1 ms, no clear signal can
be detected, indicating that the bunch size is equal to the trap size. Such debunching can be
characterized by a typical time spread [132] which can be obtained by fitting the width of the
(negative) peaks.
By changing the slope of the potential in the mirror regions, a different behaviour could
be obtained [132]. Figure 21 (right panel) shows the evolution of a bunch injected into the
trap with an initial length of W0 ∼ 200 ns, when the potential in the mirror regions is flatter
than in the previous case. In contrast to the dispersive behaviour observed in figure 21 (left
panel), the width of the bunch is preserved over the 1.65 ms shown. Similar signals can be
observed even after very long trapping times (several seconds). A fit to these peaks shows that
their width is now independent of the number of oscillations [132].
The reason behind this curious phenomenon is related to the dispersion dT /dE of the
trap, just as for the negative mass instability. Two quite similar models have been developed
to explain this phenomenon [133, 134] and both of them demonstrated that this effect occurs
only for dT /dE > 0. A detailed mathematical modelling of the situation shows that in such
a situation, the effective mass of the oscillating ions is negative [133]. The physical picture
which emerges from these models is that in this situation, the Coulomb force tends to slow
down the fast particles and speed up the slower ones [135].
An immediate application of the negative mass instability was found in the field of mass
spectrometry [133, 135, 136]. Since the ions stay bunched for a long time, it is possible to
measure their oscillation frequency, which is proportional to the square root of their masses,
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Topical Review
8
6
132
Xe
4
131
Xe
FFT (Arb. Units)
2
0
10
8
6
4
2
0
1182
1183
1184
1185 1186 1187
Frequency (kHz)
1188
1189
1190
Figure 22. Frequency spectrum obtained by fast Fourier transform of the pick-up signal when
a bunch comprising two isotopes of singly charged xenon ions is injected into the trap in the
self-bunching mode. Only the seventh harmonics are shown.
very precisely. The frequency measurement is performed by the Fourier transform of the
pick-up signal. An example is shown in figure 22 where two different isotopes of Xe+ are
stored in the trap. A mass resolution better than 7 × 10−6 is obtained. However, since the high
resolution is obtained because of the Coulomb interaction between the ions, it is unavoidable
that for very high masses, coalescence will take place, and although the resolution will be quite
high, the separation will not be enough to separate single masses. Experiments are underway
to measure the highest possible mass for which single mass separation is achievable.
An additional contribution to the field of mass spectrometry was made by Benner [103]
who showed that it is possible to measure the charge over mass ratio of a single highly charged
biomolecule with a mass in the range of 106 amu. The detection method is similar to that
described above.
Another type of beam dynamics that has been studied with the EIBT is the so-called
delta-kick cooling where the phase space of the stored particles is manipulated, using timedependent electric fields [137]. In this case, one takes advantage of the kinematical order
which develops when the ions are stored in the trap to influence their velocity distribution.
The method might be useful to reduce the velocity spread of the stored ions by applying
successive kicks.
5. Conclusions
We have reviewed the different type of experiments carried out with both the electrostatic
ion storage ring and the electrostatic ion beam trap. Although the devices are different in
size, they allow somewhat similar experiments to be performed. Each geometry has its
own advantage. The electrostatic storage ring benefits from (1) a slightly longer lifetime
of the beam at a given energy and pressure, probably due to the ion optics which gives
better beam confinement and weaker ion–ion interactions, (2) the fact that the beam is always
moving in one direction with a more or less constant energy, (3) and the possibility of having
Topical Review
R85
electron–ion merged beam configuration, as demonstrated at the KEK storage ring [89] as
well as the crossed beam configuration at ELISA [66]. For the electrostatic ion trap the main
advantages are (1) a compact size, (2) the interesting dynamical behaviour of the ions and (3) the
easier cooling of the device to very low temperatures (although ELISA has already been cooled
by liquid nitrogen as well). These devices have extended the range of species (beams) which
may be stored, thus greatly expanding the area of work accessible to the heavy-ion storage
rings. Research in biophysics and on clusters were the first to benefit from these developments,
and there is room for a large variety of applications which will, without any doubt, appear in
the near future. The authors are aware of new developments in the field of the electrostatic
storage ring. Among them is the double electrostatic ring DESIREE in Stockholm [18], which
will allow collisions between positive and negative ions to be studied and may be cooled to
10–20 ◦ C. Also, a liquid nitrogen cooled electrostatic ring at the Tokyo Metropolitan University
is under construction for the study of ionic clusters, and a He cooled (2 ◦ C) electrostatic ring
at the Max-Planck Institute for Nuclear Physics, Heidelberg, Germany is being designed. The
latter ring will allow us to store rotationally cooled molecular ions, and will be equipped with
both an electron target and a merged-neutral-beam setup. Also, electrostatic traps are being
built in Orsay, France (for studying the interaction of femtosecond laser pulses on trapped
ions) as well as in Heidelberg, Germany, and at the Bhabha Atomic Research Center, Mumbai,
India.
Acknowledgments
We thank JU Andersen, T Tanabe and S Brøndsted Nielsen for providing figures with data
from their works. This work was supported by the Danish National Research Foundation
through the Aarhus Center for Atomic Physics (ACAP), and by the Israel Science Foundation.
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