Non-destructive detection of large molecules without mass limitation
Adrien Poindron, Jofre Pedregosa-Gutierrez, Christophe Jouvet, Martina Knoop, Caroline Champenois
aa r X i v : . [ phy s i c s . i n s - d e t ] F e b Non-destructive detection of large molecules withoutmass limitation
A. Poindron, J. Pedregosa-Gutierrez, C. Jouvet, M. Knoop, and C. Champenois
Aix Marseille Univ, CNRS, PIIM, Marseille, France (Dated: 9 February 2021)
The problem for molecular identification knows many solutions which include mass spec-trometers whose mass sensitivity depends on the performance of the detector involved.The purpose of this article is to show by means of molecular dynamics simulations, howa laser-cooled ion cloud, confined in a linear radio-frequency trap, can reach the ultimatesensitivity providing the detection of individual charged heavy molecular ions. In our sim-ulations, we model the laser-cooled Ca + ions as two-level atoms, confined thanks to a setof constant and time oscillating electrical fields. A singly-charged molecular ion with amass of 10 amu is propelled through the ion cloud. The induced change in the fluores-cence rate of the lather is used as the detection signal. We show that this signal is due to asignificant temperature variation triggered by the Coulombian repulsion and amplified bythe radio-frequency heating induced by the trap itself. We identify the optimum initial en-ergy for the molecular ion to be detected and furthermore, we characterize the performanceof the detector for a large range of confinement voltages.PACS numbers: keywords: mass spectrometry, non-destructive detection, giant molecules I. INTRODUCTION
Mass spectrometry is among the most advanced techniques of precise identification and finger-printing today and covers a broad range of species from light atoms up to giant molecules, likeproteins or viruses. This method can reach extreme resolution by exploiting various techniques and in particular if coupled to sophisticated time-of-flight trajectories . The vast majority of massspectrometers identify the species by its mass-to-charge ratio which can be done by measuring ei-ther a characteristic frequency, arrival time, or any properties reflecting the ion trajectory withinelectromagnetic fields. For these mass spectrometry measurements, the sample species has to beionized, which can be done in different configurations (ESI, MALDI, electron impact). It will thenundergo a mass-filtering process in order to separate different species (TOF, quadrupole filter, traps,...), before finally reaching a detector. The need to expand the sensitivity range of charged particledetectors towards very large mass has appeared already in the 90’s with the achievement of heavymolecules ionising sources like MALDI and ESI.In mass spectrometry, the detection is most often done by accelerating the species under identi-fication (SUI) towards a charge detecting device (e.g. an electron multiplier, a micro channel plate(MCP), ...) . Such detectors are based on secondary electron emission: the incident particle mustgenerate the emission of at least one electron. This electron is then amplified in a cascade pro-cess, in order to generate a measurable current at the final anode. For increasing molecular mass,triggering the first electron by impact becomes less likely as velocities are getting smaller for agiven energy value . The low detection efficiency of electron multipliers and MCPs is known andunderstood for the mass range beyond 10 a.m.u and the strong dependence of the detectionefficiency with the incident ion mass, for a given impact energy, is an issue for a mass spectrometer.If not corrected by further amplification, this variable efficiency produces a mass spectrum whichdoes not accurately reflect the mass abondancy of the incoming ions. This drawback is circum-vented with calorimetric cryo-detectors whose application range now covers masses as large as fewMDa when coupled to TOF devices and which show a high detection efficiency independentof the mass but require a cryogenic environment.Interest in measuring accurate masses for species with molecular weights much greater than1 MDa has led to the development of single-particle techniques , like shown by the recentdetection of individual ions carrying a single charge by charge detection mass spectrometry . Inthis manuscript we propose an original detection method with the potential to non-destructively de-tect single molecules without limitation of the mass range. Our novel approach consists in a radicalchange in the detection principle of the molecular ion, based on the perturbation that it induces incrossing a laser-cooled cloud of trapped ions. The SUI deposits part of its kinetic energy in thetrapped ion cloud and the induced temperature increase is amplified by the radio-frequency (RF)heating, characteristic of electrodynamic traps. The exploited signal is the corresponding changein the laser induced fluorescence of the laser-cooled stored ion cloud, which can be tuned to besufficiently long-lasting to be observable. As the ion cloud is just heated and not lost, it can eas-ily be reset to initial (cold) conditions by the tuning of the laser according to a cooling protocol.Therefore, this method provides a non-destructive detection system without mass limitation, neithercharge number requirement, for individual molecules .This article presents the operation principle of this novel detector, demonstrated by means ofmolecular dynamic simulations, which allow to scan a vast range of parameters. The followingsection describes the scheme of the detection process, and introduces its main properties. We thendescribe the details of the simulation, which takes up the realistic environment and follows theinjected species throughout the detection cloud. Section IV describes a full sequence of the detectionprocess for one particular set of parameter. The best choice for the SUI initial energy and the cloudtrapping parameters are discussed in section V. The experiment under construction will be brieflyoutlined in the conclusions. II. WORKING PRINCIPLE OF THE DETECTOR AND OF ITS SIMULATION
The key element of the detector is a cloud of laser-cooled atomic ions stored in a linear RFquadrupole trap, very similar to many other experiments . Ca + ions have been chosen due tothe commercial availability of lasers at the required wavelengths for photoionisation and laser-cooling, as well as for the observation efficiency . These ions are trapped in a linear RF trap (innerradius r =2,5 mm) as depicted in figure 1, built and connected as the one in , which leaves thetrap’s z -axis free of electrodes and allows easy injection. The radial trapping potential is given by: Φ ( x , y , t ) = ( U st + U RF cos Ω t ) ( x − y ) r (1)where U st is a the static voltage and U RF is the amplitude of the oscillating voltage applied to therods, see figure 1. The potential along the trap axis, z , can be considered as harmonic on the lengthscale of the ion cloud and is well represented by U H ( z ) = m ω z z / ω z scaling linearly withthe voltage difference U DC = V out − V in (see figure 1 for the voltage definition). FIG. 1. Schematic of the rf trap and the voltages applied to each electrode. The inner radius of the trap is r =2,5 mm and the central electrodes are 4 mm long. A cloud of 1024 Ca + -ions is laser-cooled to a temperature below 10 mK, and its fluorescenceis monitored with the cooling laser set at fixed frequency. A heavy molecule with mass m SUI = amu and a unit charge Q = + e is injected into the trap, at a distance larger than 1 mm fromthe ion cloud with an initial position exactly on the trap symmetry axis and a given initial kineticenergy. The injected molecule is heavy enough not to be deviated by the trap potential nor bythe interaction with the ion cloud. In our simulation we can extract its energy loss, an importantparameter in the understanding of the energy exchange between the injected molecule and trappedion cloud. The equilibrium state of the laser-cooled ion cloud is perturbed by the molecule crossingand the kinetic energy of the cloud increases. In a second step, the heating process is amplified byradio-frequency heating . The temperature of the cloud is not accessible to measurements and itsindirect observation is based on the collection of the laser induced fluorescence. It is numericallycomputed by the number of photons emitted by the ion cloud in a time cell duration ∆ t . At fixedlaser frequency ω L , this number is sensitive to the ion velocity ~ v i through the Doppler effect whichshifts the laser frequency seen by the ion to ω L − ~ k L .~ v i with ~ k L the laser wave-vector. The probabilityfor ion i to be in the excited state is then P e ( i ) = Ω r / ( δ − ~ k L .~ v i ) + Γ / + Ω r / Ω r is the Rabi frequency standing for the atom-laser coupling strength, Γ is the spontaneousemission rate of the excited level and δ is the laser detuning ω L − ω with respect to the atomictransition frequency, for an atom at rest. On average, the number of photons emitted by an ionduring ∆ t is P e ( i ) × Γ × ∆ t .To have a better understanding of the phenomena that are discussed in the following, somefeatures concerning the self-organization of a laser-cooled ion cloud are useful. They can bedemonstrated in the static picture where the cloud can be considered as trapped by a static pseudo-potential which is the sum of the harmonic approximation of the DC potential designed to trapalong the axis z , U H ( z ) and a radial potential which is also harmonic and can be written as U pp ( r ) = m ω r ( x + y ) / ω r = ω x − ω z / ω x = e √ U RF / ( mr Ω ) with e the elemen-tary charge. Rigorously, this static picture is a close description of the RF-trapping only for U RF values lower than the ones used for the simulations presented here. Nevertheless, it gives usefulclues to understand the impact of the trapping parameters. In the pseudo-potential picture, it hasbeen shown that a cold ion cloud has a uniform density over the whole sample and forms aspheroid with radius R and half-length L , with an aspect ratio α = R / L that depends on the aspectratio of the 3D-potential ω z / ω r . For prolate clouds like used in the present simulations, the relationis ω z ω r = − − ( α − − ) / − α ( α − − ) / sinh − ( α − − ) / − α − ( α − − ) / (3)which can be simplified in ω z / ω r ≃ α ln ( / α ) for α < . U RF and/or U DC are changed, the shape of the cloud is modified according to Eq. (3)but one can show that the cloud density depends only on U RF and scales like U RF . The nextsection describes the numerical simulations built to produce a signal useful to evaluate the detectionefficiency of this cloud. III. MOLECULAR DYNAMIC SIMULATIONS
The molecular dynamics simulations presented in the following numerically integrate the equa-tions of motion of N interacting ions within the trapping potential oscillating at frequency Ω / π = U st = π / Ω / = U RF ,2. the thermalization process is replaced by laser-cooling, modeled by the recoil induced byabsorbed and emitted photons,3. linear increase of the RF voltage until the desired U RF is reached keeping the same laser-cooling protocol,4. injection of the SUI by setting it on the trap axis, off the ion cloud, with a given energy,5. observation of the post-crossing dynamics of the ion cloud, calculation of the cloud tempera-ture evolution and record of the number of emitted photons.In the first step, ions created with a null velocity and a position randomly chosen in a Gaussian dis-tribution evolves in a low-RF trapping field ( U RF =26.9 V, corresponding to a Mathieu parameter q x = . m ∂ tt x i = Q k C N ∑ j = , j = i (cid:18) x i − x j | ~ r i − ~ r j | (cid:19) − QU RF cos Ω tr x j − γ∂ t x i + p Γ k B T b θ xi m ∂ tt y i = Q k C N ∑ j = , j = i (cid:18) y i − y j | ~ r i − ~ r j | (cid:19) + QU RF cos Ω tr y j − γ∂ t y i + p Γ k B T b θ yi m ∂ tt z i = Q k C N ∑ j = , j = i (cid:18) z i − z j | ~ r i − ~ r j | (cid:19) − (cid:12)(cid:12)(cid:12)(cid:12) dU G ( z ) dz (cid:12)(cid:12)(cid:12)(cid:12) z i − γ∂ t z i + p Γ k B T b θ zi , (4)where ~ r = ( x , y , z ) , k C = / ( πε ) , U G ( z ) is the axial potential given by Eq. (5), γ a friction coeffi-cient, k B Boltzmann’s constant, T b is the temperature of the thermal bath and θ x j , θ y j and θ z j are acollection of independent standard Wiener processes . The equations of motion in this first codeare numerically solved using the vGB82 algorithm as described in and already implemented in .The rest of the simulation codes do not include any friction term or thermal bath and use theVelocity-Verlet algorithm. Laser-cooling is introduced in step 2 by an algorithm which uses a two-level atom model to compute the recoil induced by photon emission and absorption. When in theground state, the probability for an ion to absorb a photon depending on its instantaneous velocity ~ v i , is based on Eq. 2, and at each time step, it is compared is to a random number to decide if theion is excited or not at the next time step. If excited, the ion velocity is modified according to therecoil of a photon momentum ¯ h ~ k L . Once the ion is classified as excited, the algorithm computes theprobability for spontaneous and stimulated emission and compares them to another random numberto decide if the ion emits a photon. In the case of spontaneous emission, the photon emissiondirection is random with an isotropic probability in space. Such an approach allows to model arealistic laser cooled ion cloud upon which the external particle can be injected. Moreover, by usinga photon absorption / emission approach, it is possible to record the total number of emitted photonswhich represents one of the few quantities accessible to measurement in a real experiment. Step 3continues with the same processes but the radio-frequency voltage amplitude U RF is increased toreach the value chosen for the SUI-cloud interaction step.At the beginning of step 4, the SUI is initialized on the trap axis at x = y = z = − z i = − . E SUI . The variation of the electrostatic potential along z drives theSUI to the ion cloud and the code stops when the SUI reaches z = + z i , with z = z i , to make possible situations where the chosen initial energy E SUI is lowerthan m ω z z i /
2. The potential equation is adapted for long distance | z | to the trap center by fittingthe axial potential generated by the trap geometry and calculated by the commercial FEM softwareSIMION8.0 . This leads to the equation U G ( z ) = m ω z L ( − e − z / L ) (5)where L = .
45 mm is the relevant length as given by the fit which behaves like a harmonic potentialat its bottom, characterised by ω z / π = . U DC = −4 −3 −2 −1 T [ K ] P M s i g n a l cts/µscts/ms7.50 7.5510 −3 −2 −1 FIG. 2. Results of the simulation with parameters given in section IV. Top : temperature of the cloud duringone run. The framed numbers indicate which part of the simulation is being executed according to descriptionof section III. The inset focuses on the fourth part where the SUI is injected. The grey rectangle indicates whenthe SUI is actually crossing the ion cloud. Bottom : ion cloud fluorescence. The blue line represents all thephotons emitted by the cloud integrated during 1 µ s. The black marks represent the fluorescence signal S as itwould be measured with realistic conditions : a 1 ms integration time and a 10 − detection efficiency. While the SUI is present in the simulation, the time integration concerning the dynamics drivenby the Coulomb interaction and the RF trapping is run with a variable time step Velocity-Verlet al-gorithm adapted to the closest distance between the charged particles, to make sure the interaction isproperly described . This variable time step procedure demands extra computations and thereforeis limited to step 4. The algorithm describing the laser-ion interaction keeps the same constant timestep of 5 ns and with an excited state lifetime of 7 ns for the chosen Ca + -ion, it is justified to usethe stationary limit of Eq. 2 to compute the fluorescence for each ion, even if its velocity changesin time . To avoid irrelevant statistical fluctuations, the number of emitted photons is recorded ontime bins of size ∆ t = µ s. IV. RESULTS OF A FULL DETECTION SIMULATION
Figure 2 shows the result for a complete simulation run for N = + ions. The trap pa-rameters for this case are U RF = . U st = U DC = q x = . ω z / π = . m SUI = amu, a unit chargeand its initial energy E SUI is such that its kinetic energy at the minimum of the trapping potentialwell E is equal to 50 eV. The top part of Fig. 2 shows the time evolution of the ion cloud tempera-ture while the bottom part traces the fluorescence signal, with two different average time scales. Thetemperature of the cloud is computed from the sample averaged squared velocities, averaged overone RF-period. This strategy to compute time-averaged values is used to eliminate the RF-drivenmotion contribution from the velocity . The number of photons emitted by the entire cloudis given for a 1 µ s acquisition time, which is a time scale relevant for the simulation. The signal S expected from a realistic experiment is also plotted, assuming a detection efficiency of 10 − and anacquisition time of 1 ms, which is typical for this kind of experiment, to reach a relevant signal tonoise ratio (SNR) equal to 1 / √ S when taking into account the photon counting noise.The first step, from t = t = . ms , corresponds to the preparation of the cloud in theradio-frequency trap with a low RF voltage, which brings it in equilibrium with a thermal bathtemperature. The value of the thermal bath temperature, T b = . + limit temperature of the Doppler laser cooling. At such temperature, the ion cloud forms a Coulombcrystal with the shape of a spheroid with a length of 470 µ m and a radius of 47 µ m. During thesecond step, covering t = . t = . z . The laser detuning used for all the results presented in this paperis δ = − Γ . The choice for this laser detuning results from a compromise between cooling efficiencyand signal discrimination as it controls the velocity class with the highest probability of excitationand the fluorescence rate for a given velocity distribution. With the typical temperatures of a largeset of simulations, a detuning of δ = − Γ appears to be the best compromise to keep the ion cloudcold before the SUI crossing and reach a large fluorescence signal difference when the SUI has left.The choice for the coupling strength Ω r is governed by a compromise between the temperature thatcan be reached by laser cooling and the photon diffusion rate . For all the simulations discussed inthis paper, it is chosen such that Ω r = Γ .At the end of step 3, the ion cloud has reached a stationary state in the RF-trapping field definedby U RF = . q x = . − z i = . + z i from the trapping well minimum are the beginning and end ofstep 4 and are materialised by a vertical line on the inset of Fig. 2, which shows a zoom into thetemperature evolution of the ion cloud for steps 4 and 5. This value was chosen far enough from thetrap center so that the initialisation of the SUI does not perturb the trapped ion cloud. The first sharpjump of the temperature around t ≈ .
52 ms is a signature of the passage of the SUI through the ioncloud. The time actually spent by the SUI inside the ion cloud is materialised by a grey shadow onthe results and lasts 2.5 µ s. The following simulation sequence represents the evolution of the ioncloud under laser cooling after the passage of the injected SUI.Following the SUI injection, the fluorescence rate shows a short-lived increase during and shortlyafter the passage of the projectile followed by a significant drop to a stationary value which is 6times smaller than the value it had before the molecule passage. This behavour is different from thetemperature profile which increases in two steps : starting from the initial equilibrium value closeto 0.5 mK, a first jump is observed to values of the order of few tens of millikelvin, as a direct con-sequence of the perturbation caused. Then, once the projectile has left the cloud, the temperaturekeeps increasing to reach values of the order of several hundreds of Kelvin. The correlation be-tween temperature and fluorescence rate sits in the Doppler effect which impacts the laser inducedexcitation probability. As shown by the plot of the fluorescence signal S on Fig. 2, the instantaneousincrease of the fluorescence synchronised with the SUI crossing cannot be observed in typical exper-imental conditions where a photon detection efficiency of 10 − is assumed . Therefore, a successfuldetection requires that the difference between the stationary signal before and after the SUI crossingis larger than the detection noise and is persistent for a few ms. Like shown by the comparison ofthe top and bottom curves of figure 2, the long term decrease of the fluorescence is correlated withthe increase of the cloud temperature to several hundreds of Kelvin. This post-crossing temperatureincrease is due to RF-heating, a side-effect of RF-trapping when trapped particles collide with eachother or with a background gas or when non-linear resonances occur between the rf-frequencyand the oscillation frequencies of the ion in the trap . Here, the simulated collisions are theCoulomb collisions between the projectile and each ion of the target cloud, as well as the Coulombcollisions between the ions of the target. The two-step evolution of the temperature can be under-stood as first, an energy increase induced by the energy lost by the SUI inside the cloud, followedby a larger energy increase induced by RF-heating.For an efficient detection, the energy loss of the SUI must be sufficient to trigger a perturbationof the cloud large enough to ignite the increase of the RF-heating rate. In the present simulation, theenergy lost by the SUI is 11.48 meV. If we assume that this energy is transferred only to the thermalkinetic energy of the cloud, it would result in a temperature increase of 86 mK. The numericalsimulations give a value close to 40 mK, showing that part of the lost energy is transferred also tothe potential energy of the cloud, most probably the Coulomb interaction potential energy as ionshave moved from their equilibrium position.The dependence of the heating rate with the ion cloud temperature studied numerically in shows −50−40−30−20−100 U RF = 53.85 VU RF = 53.85 VU RF = 53.85 VU RF = 53.85 VU RF = 53.85 VU RF = 53.85 VU RF = 53.85 V U RF = 59.23 VU RF = 59.23 VU RF = 59.23 VU RF = 59.23 VU RF = 59.23 VU RF = 59.23 VU RF = 59.23 V −50−40−30−20−100 U RF = 64.61 VU RF = 64.61 VU RF = 64.61 VU RF = 64.61 VU RF = 64.61 VU RF = 64.61 VU RF = 64.61 V U RF = 70.0 VU RF = 70.0 VU RF = 70.0 VU RF = 70.0 VU RF = 70.0 VU RF = 70.0 VU RF = 70.0 V U D C [ V ] E SUI [eV] Δ Δ S U I [ m e V ] FIG. 3. Energy lost by the SUI ∆ E versus the SUI kinetic energy E at the center of the trap. 28 different setsof ( U RF , U DC ) are tested. Each of the four subplots stands for one U RF , and the colour code translate the valuesof U DC (see the color chart on the right side of the figure). that, for given trapping parameters, it increases by several orders of magnitude when the temperatureof the cloud increases from 0.1 to 1 K. This increased slope is also visible in the results of Fig. 2 forthe same range of temperature. If the heating rate in a perturbed cloud is higher than the laser coolingrate for the corresponding velocity distribution, the temperature of the cloud keeps increasing untilit reaches a stationary value where the RF-heating rate is negligible because the ions do not interactstrongly any more. The numerical results in also show a strong dependence of the heating ratewith the RF amplitude voltage U RF . It is then possible to tune the RF-heating rate to adapt it tothe temperature of the cloud after the SUI crossing. The next section focusses on the dependenceof this initial energy deposition on the energy E of the SUI and on the influence of the trappingparameters on the overall detection efficiency. V. EFFICIENCY OF THE DETECTOR
The energy exchanged by a cold charged ensemble and a charged projectile has been studied inthe frame of the stopping power of a plasma . Simulation runs for the particular case of cold ionsin a RF trap consider the energy transfer between the projectile and the trapped ion cloud with adetailed analysis of the projectile’s energy evolution during its passage through the ion cloud. It hasbeen shown that two different mechanisms contribute to the energy interchange: collective effectsand Coulomb binary collisions and that the energy exchange rate depends on the kinetic energyof the projectile. An analytic estimation of the energy loss is extremely complex, and the detailedstudy of the interaction between the injected particle and the trapped ion cloud goes beyond the aimof the present work. To estimate the most adapted kinetic energy E to be used for the injectedparticle, to favor a large SUI energy loss ∆ E , 5 different kinetic energies E have been studied:1000 eV, 100 eV, 50 eV, 10 eV and 6 eV. For different combinations of U RF and U DC , the SUIis launched with an initial energy calculated such that its kinetic energy at the trapping potentialminimum is E . The results are shown in figure 3 where each data point represents the mean of 20independent simulations. The large deviation observed on ∆ E can be attributed to the contributionof binary collisions, that are very sensitive to the exact position of the trapped ions at the momentof the passage of the particle. DC [V]55606570 U R F [ V ] q x = 0.6q x = 0.5 D e t e c t i o n r a t e [ % ] FIG. 4. Detection rate as a function of U RF and U DC for E =
50 eV. q x is the Mathieu parameter associated tothe RF trapping. See the color chart that codes the detection rate. Some trends can be identified on Fig. 3 : for the 4 different U RF values, ∆ E increases when U DC decreases. Furthermore, the results show that ∆ E increases with U RF . Depending on the ( U RF , U DC )combinations, the variations of ∆ E with E are flat or show an extremum for E =
50 eV. This valueis chosen for the next simulations.To identify the conditions for an efficient detection, we have performed simulations over a rangeof values of U RF and U DC , keeping the other simulations parameters identical to those of figure 2.The detection efficiency is defined by a criteria based on the signal-to-noise ratio SNR of the es-timated experimental signal. The detector is assumed to be efficient if the variation in the usefulsignal S is larger than the statistical noise √ S of the signal before the SUI passage. The detectionrate, shown on Fig. 4, indicates the probability of detection for 100 independent simulation runs .Figure 4 shows that the detection rate increases with U RF and a 100% efficiency is reached forthe highest value of U RF , for nearly all values of U DC . These observations are consistent with thedependence of E shown in Fig. 3 and of the heating rate demonstrated by molecular dynamicsimulations with unbounded system. Regarding the influence of U DC , Fig 4 shows that as U RF is lowered, a high detection efficiency is still achieved for the lowest values of U DC . For afinite size system as a cold ion cloud, Eq. 3 shows that decreasing U DC increases the cloud length,suggesting that a lower heating rate and a lower ion density can be compensated by an increasedinteraction length. The role of the cloud length is more visible on Fig. 5 where the same results areplotted against the mean value of the measured half-length L of the ion cloud just before the particleinjection, h L i . This representation confirms our previous interpretation that longer clouds gives ahigher detection rate for the lowest U RF values. As the RF-heating is lowered with lower U RF , wecan conclude that an efficient detection relies on the value of the energy transferred to the cloud bythe SUI, that must be sufficient to trigger RF-heating. A lower heating-rate can be compensated byan increased interaction length of the SUI with the cloud which is independently controlled by thetrapping along the axis U DC . VI. CONCLUSION
In the present manuscript we have described the working principle of a new charged particle de-tector, which is based on the observation of the fluorescence of a cold ion-cloud perturbed by thecrossing of a large mass projectile. This detection method is non-destructive and has no upper limitfor the mass range, allowing to directly detect giant molecules and (corona-)viruses. We identifiedthe parameters controlling the detection efficiency for a chosen mass of 10 amu. The correspond-ing experimental set-up is under construction, and combines a molecular source by electro-sprayionisation with the above described linear trap in a differentially pumped vacuum set-up of 1 meterlength. The very good control of all parameters makes this set-up interesting also for fundamentalexplorations. As the radio-frequency heating signal amplification works only for a sufficient energytransferred from the projectile to the cloud, the signal detection can be used to study the experi-
120 160 200 240 280 320 360 400⟨L⟩⟨[µm]020406080100 D e t e c t i o n ⟨ r a t e ⟨ [ ⟩ ] U RF U D C ⟨ [ V ] FIG. 5. Detection rate as a function of the average cloud half-length h L i . The marker indicates the U RF and thecolor codes for the U DC values. mental conditions that favour this transfer. This will offer an experimental platform to study thestopping power of finite-size one-component plasma, in a regime of large plasma parameter that areout-of-reach of conventional neutral plasma. A better comprehension of the rf-heating mechanismwill be an asset for the control of the detection rate . ACKNOWLEDGMENTS
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