Accurate modelling of small-scale linear ion trap operating mode using He buffer gas to improve sensitivity and resolution for in-the-field mass spectrometry

Improved sensitivity and resolution of a small-scale linear ion trap is observed using He buffer.


Introduction
Research work involving portable mass spectrometry for in-thefield application has accelerated since 2000 1 . Different types of radio frequency (RF) trapping analysers can be used within small instruments, and their miniaturisation has several advantages. For instance, with smaller internal radii, lower confinement voltages can be used at the same frequency 2 . However, a small containment volume can increase the space charge effect 3 . A linear ion trap (LIT) has a quadrupole field in the radial direction and a static field in the axial direction. Its geometrical shape leads to improved trapping efficiency upon ion injection along axial direction with large containment capacity with equivalent space charge, in comparison with a 3D trap 4 .
The electronic control unit (ECU), which provides confinement and control voltages, requires functionality simplification for device portability. This can be achieved through the choice of the LIT operating mode. Only a single m/z ion is analysed with nonscanning mode 5  applied upon electrodes are switched for ion injection, isolation and ejection: the maximal amplitude of the isolation RF voltage is maintained constant during the sequence. The sequence can be reproduced with different maximal amplitudes of RF voltage to analyse a set of different m/z ions 6 . As a consequence, only DC potential changes are required with short rising/falling times at switching, without generating an RF voltage ramp. Operation in non-scanning mode has the advantages of faster operation (important for security applications in-the-field) and reduced false positives because possible interference compounds are screened out a priori.
In a portable instrument, air residue in the vacuum chamber is typically used as buffer gas as it may be easily introduced at gas/ion sampling. The collisions between confined ion and buffer gas result in a decrease of the ion kinetic energy with time.
With higher pressures (from 1 to 50 mtorr), ion neutral collisions reduce the stability region and the region in which massselective resonance ejection is performed. In addition, an increase of the pressure improves collision-induced dissociation efficiency and mass resolution 7 .
The use of a buffer gas at lower pressures improves ion injection 8 , resolution of mass-selective instability scan and ion isolation in 3D traps 9,10 . The effects of He buffer gas and ambient air have been characterised on the performance of a LIT with hyperbolic electrodes. An improvement of resolution and ion isolation was observed with He gas 11 .
In an earlier paper, the authors reported the development of a portable device comprising a LIT operated in non-scanning mode 12 . An experimental mass separation of 4 u was obtained for methyl benzoate, 2-nitrotoluene and dimethyl methylphosphonate 13 . Since then the authors have shown the possibility of decreased mass separation (increased resolution) with spatial-and velocity-reduced ion distributions, when the LIT is operated close to the stability diagram apex 14 . The conclusions of these studies led the authors to simulate the use of He buffer gas cooling in order to obtain a mass separation of 1 u. Prior to design and realisation of this new LIT device with an electrode arrangement allowing He entrance and fast pumping, they decided to simulate the effects of collisional cooling at each stage of a non-scanning LIT with hyperbolic electrodes. Although He buffer gas use could be disadvantageous for device portability, it was chosen instead of residual ambient air because of the improved performance that may be obtained. Many recent simulation papers neglect the influence of the RF trapping field by using the pseudo-potential approximation and consider that collisions induce a damping effect upon ion trajectories 15,16 . However, Schwarz emphasised in 2008 the necessity for a microscopic description of the RF heating and to take into account the statistical nature of the collisions 17 . If this is not done, the effectiveness of the cooling process can be significantly overestimated. The best visual evidence is given in Fig. 3 of Ref. 17 , where the radial position as a function of axial position of an ion is compared for a viscous damping approach and a microscopic description of collisions.
The simulation in this uses a realistic electrode design and an accurate Boundary Element Method (BEM) to calculate the electric field for computation of the individual ion trajectories using the Charged Particle Optics (CPO) software 18 . A collisional computation tool has been developed and added to CPO which allows LIT pressure dependence to be modelled which is essential for accurate simulation. The recommendations of Schwarz have been taken into account in our simulations at the expense of the computational time duration. Since an accurate characterisation of collisional effects is required for each time step of the nonscanning mode sequence, the instants of collision are computed by an event-driven m using randomised probability computation methodology. The ion-buffer gas interaction is simulated by a hard-sphere model leading to a modification of the ion velocities when collision occurs.
The aim of this simulation study is therefore the accurate modelling of the LIT configuration in non-scanning mode with collisional cooling to obtain a mass peak separation equal to 1 m/z with a greater sensitivity thanks to an increase of the number of ions.

LIT design and operating conditions
The design of the LIT modelled in this study is schematically represented in Figure 1. It is composed of four hyperbolic electrodes whose ends are closed by two flat disks (lenses). The physical centre of the LIT is the origin of the coordinate system. The hyperbolic electrodes are truncated at 3r 0 . The smallest distance sepa-rating a hyperbolic electrode from the Oz axis is r 0 = 2 mm. The length of the hyperbolic electrodes is 2z 0 = 40 mm. An electron impact ion source and a set of extracting, focusing and grounded lenses are coupled to the LIT. The ions are injected with 3 eV energy. For more details on ion injection simulation with experimental results, see references 12,14 .
The non-scanning mode consists in a series of m/z mass analysis sequences 12,13 . Each sequence comprises four steps: injection, cooling, isolation and total ejection.  Figure 1 describes the potentials applied to the electrode for each step of the sequence. A symmetrical configuration is applied to the hyperbolic electrodes of the trap: V (t) = U 0 +V 0 cos(Ωt + ϕ) on the pair of x-axial electrodes and −V (t) on the pair of y-axial electrodes. The frequency is Ω/(2π) = 1 MHz. The maximal amplitude of the RF confinement voltages is maintained at a constant value during the steps of the sequence. Only the DC voltages applied to hyperbolic and end-cap electrodes are modified in order to: enter the ions, and then eject them from the trap; operate the LIT in RF only mode for ion injection and cooling; and operate the LIT close to the apex for ion isolation. This simplifies the conception of the voltage generating device (ECU) and guarantees a better stability of the voltages needed for ion confinement. During the injection step, 0 V is applied to the input disk of the trap, 20 V is applied to the output disk, and U 0 = 0 V and V 0 = V apex of the m/z ion being analysed. During the cooling step, the trap operates in RF only mode with both end-caps biased at 20 V. During the isolation step, the DC confinement voltage is instantaneously switched from U 0 = 0 to U apex . Finally, during the ejection step, the voltage applied to the output disk is switched to -100 V to extract the ions out of the trap and propel them towards the detector.

Ion/neutral collision modelling and computational tool
The ion/neutral interaction is assumed to be elastic and simulated by means of a hard-sphere model. With respect to this model, the ion and neutral velocities are modified by collision. In the centre-of-mass system, the total kinetic energy is conserved and scattering is isotropic.
For determination of instants of collision, an event-driven approach results in a more accurate and efficient simulation than a time-driven one.
Ion trajectories are computed using the CPO software 18 with a small constant step time ∆t = 5 × 10 −5 ms. At the end of each step time, an in-house subroutine is called for ion-neutral collision treatment.
The main event-driven simulation loop works as follows: At each step time of ion trajectory computation, an elementary probability, denoted as p ce , is computed from the following equation: with ρ G (atoms/m 3 ) the He buffer gas density; σ IG = 3.5 × 10 −19 (m 2 ) an estimation of the total scattering cross-section between m/z 100 ion and He atom (see Page 20 of Reference 19 ); − → v I the ion velocities computed by CPO; and − → v G the He buffer gas velocities. The He buffer gas velocities are drawn from three zero-centred Gaussian density functions with standard deviations σ Gx = σ Gy = σ Gz = k B T /m G , with k B = 1.38 × 10 −23 J×K −1 , the Boltzmann constant and T the buffer gas temperature (K).
At each step time, the elementary probability p ce is summed with the previously computed ones. This summation improves the estimation of each elementary probability computed from a single sample.
When the sum, denoted as p c , exceeds ε = 10 −2 , a value is drawn from a uniform distribution on [0, 1], and if this value is lower than p c then a collision occurs. The value ε = 10 −2 is the best compromise between precision and fast computation ensuring that no more than one collision occurs and that positions and velocities of ions are almost constant.
When a collision occurs, the final ion velocities are modified. In the centre-of-mass system, the velocity of the ion after the collision is expressed in accordance with energy and momentum conservation: with m G (kg) and m I (kg) the masses of He buffer gas and ion, respectively; and − → n a unitary vector defining the ion direction after collision. Hard sphere scattering is isotropic in the centre-of-mass and does not depend on incident ion direction. The two scattering angles θ and ϕ (using spherical coordinates) are drawn from θ = arccos(1 − 2u 1 ) and ϕ = 2πu 2 , respectively, with u 1 and u 2 two uniform distributions on [0, 1].
Then, the new ion velocity is calculated in the coordinate system from equation: After collision treatment, the sum p c is reset to zero. The trajectory computation stops when the confinement time exceeds a fixed value.

Testing the validity of the computational tool
For testing, the operating conditions are: number of ions = 200; m/z = 100; V 0 = 28.9 V; U 0 = 0 V.
As expected, the number of collisions is proportional to the pressure ( Table 1). The mean value of p c is slightly higher than ε = 10 −2 and increases with pressure. The number of values involved in computation of p c decreases when pressure increases. By this means the model could produce results corresponding to higher values of He gas temperature or density (pressure) than the input values. The highest pressure value used in simulation, i.e. p G = 1 × 10 −3 torr, gives p c ≈ 1.0517 × 10 −2 with σ p c = 0.0388 × 10 −2 . It is the maximal value of the buffer gas pressure that can be used within this model, with the time step duration ∆t = 5 × 10 −5 ms for ion trajectory computation. The set of times at which collision occurs is recorded. The set of time intervals between two collisions (denoted as τ c ) can be then computed. The number of collision occurrences versus time interval between two collisions is then computed by time intervals of 20 µs ( Figure 2). Assuming that the number of collision occurrences can be interpolated by an exponentially decreasing function for values greater than zero: exp(−x/τ c ) with τ c the mean value. From results of Figure 2, it is found that τ c is inversely proportional to the buffer gas pressure. The variable τ c can be then used as a criterion for studying the time to reach the ion equilibrium state.

Injection step
For ion injection, the trap is operated in RF only mode with U 0 = 0 V and V 0 = 28.9 V for m/z 100 ions. We have previously estimated that the trap filling time (or maximal residence time of ions in the trap) from a short-time pulse ion injection is almost 150 µs for m/z 100 ions 14 . Additional computations have been performed with the same design and operating conditions except that simulation tool involves collisional processing.
Results are given in Figure 3 for RF confinement potential phase ϕ = 0 and three values of the buffer gas pressure.

Number of ions
Injection time (ms) Only a small increase of the number of ions is observed for the highest pressure p G = 1 × 10 −3 from the injection time 40 µs. The ions undergo an average of 2 collisions during injection. The maximal number of collisions, i.e. 9 collisions, has been observed for two ions having the highest residence times and a complete path in the LIT.
As demonstrated in the next section, we can assume that the position and velocity distributions of ions at steady-state are not modified by collisional processes due to the small number of collisions.

Cooling step
For ion cooling, the trap is operated in RF only mode with U 0 = 0 V, and V 0 = V apex = 28.9 V for m/z 100 ions and V 0 = V apex = 86.7 V for m/z 300 ions. The initial ion distributions of cooling step are the ion distributions at the end of collision-free injection 14 . The main objective is to determine the influence of the collisions on the number of confined ions and on the evolution of position and velocity ion states, and the minimum time of the ion cooling step, time from which we can consider that the ion cloud has reached the equilibrium state.

Number of confined ions
From trajectories computed by CPO, the number of ions can be computed for different confinement times. The relative number of confined ions of m/z 100 is plotted versus cooling time in Figure  4.  A first ion loss (the decrease from 1 to 0.8) is observed for the first confinement times, corresponding to a micro period of the confinement field (1 µs). One can assume that these lost ions have initial conditions that fall outside the phase-space acceptance ellipses in the radial directions. Then, a progressive loss of ions occurs due to non-linearities.
Between 15 and 20 µs the curves have different behaviours: an ion loss is observed for the lowest pressures while not for p G = 1 × 10 −3 torr. One can assume that a collision has occurred leading to stabilisation of the ion trajectory for p G = 1 × 10 −3 torr. Over a time interval of 10 ms, more ions remain trapped with collisions: the higher the pressure, the greater the number of confined ions. For a cooling time of 4.5 ms, the number of confined ions increases with He buffer gas pressure, until about 0.66 for p G = 1 × 10 −3 torr.
In Figure 5, the relative number of confined ions of m/z 100 is plotted versus He buffer gas pressure at cooling time 4.5 ms. The number of confined ions starts to increase from p G = 1×10 −5 torr, then tends to stabilise to 0.66 from p G = 1 × 10 −3 torr. The same shape of variation in the number of ions has been observed in experiments, for instance, to fill up a 3D Paul trap of 1 cm 3 volume when ions are injected along the axial direction (see Figure  17 in Page 52 of Reference 20 ) and to accumulate ions in a linear radiofrequency trap of the ISOLTRAP mass spectrometer (see

Equilibrium state and cooling time
For each ion, the pair "time interval between two collisions" and "confinement time" or "instant of collision", denoted as (τ c ,t c ) has been recorded when collision occurs. The mean value τ c (t i ) is calculated from pairs such as the value of t c ∈ [t i − T e /2,t i + T e /2], with t i = iT e , and T e = 90 µs for m/z 100 ions and 180 µs for m/z 300 ions. τ c (t i ) is plotted in Figure 6 for p G = 1 × 10 −3 torr.
The central limit theorem establishes that the values of τ sc (t i ) are normally distributed around the mean value τ c (t i ) with standard deviation : the number of collisions in time interval [t i − T e /2,t i + T e /2]. In Figure 6, the error bars represent the two standard deviation limits around the mean.
The computed values are interpolated by the curve τ c (t i ) = (τ c (∞) − τ c (0)) (1 − exp (−t i /τ r )) + τ c (0) (curve of Figure 6). The mean value of the time interval between two collisions tends to the constant value τ c (∞) = 0.067 ms for m/z 100 ions, with the relaxation time τ r = 1.5 ms. The parameters of the interpolation curve are valid as these curve falls within the error bars.
One can assume that the equilibrium state is reached when the criterion τ c (t i ) does not evolve. The equilibrium time or cooling time is expressed as: τ eq = 3τ r = 4.5 ms for m/z 100 ions. The number of collisions necessary to cool the ion cloud is calculated by: N col,eq = τ eq /τ c (∞) 70 collisions.
As a result, the time duration of the cooling step is T cool = 4.5 ms for m/z 100 ions and 14 ms for m/z 300 ions with p G = 1×10 −3 torr. For lower values of the buffer gas pressure over few orders of magnitude, the cooling time can be estimated being linearly related in inverse proportion to the buffer gas pressure.

Position and velocity distributions of the ion cloud
The position and velocity distributions at the end of injection step and at the end of cooling step are compared for m/z 100 ions in Figure 7. The duration of the cooling stage is 4.5 ms with p G = 1 × 10 −3 torr. The final time of cooling step corresponds to the phase zero of the RF confinement field.
When they are injected the ions enter the LIT at different RF phases of the confinement field. As a consequence, the radial distributions in position and velocity are identical and differ from Gaussian in that the distributions have a heavier tail than a Gaussian distribution. The axial-position distribution is quasi-uniform due to the U-shaped potential well along the axial direction. The axial-velocity distribution shows two classes of velocities corresponding to the outward and return paths of the ions in the trap. Using equation (1/2)m(∆v) 2 = q(∆V ) (difference of kinetic and potential energy between source and trap centre) and assuming that initial velocity of neutral in the ion source is negligible, with ion source biased at 3 V and trap centre at 0 V, the estimated value of maximal axial velocity in the trap is 2500 m/s for m/z 100 ions and 1400 m/s for m/z 300 ions. When the ion cloud is cooled at equilibrium state (at 4.5 ms with p G = 1 × 10 −3 torr) the radial distributions tend to Gaussian functions with different standard deviations between to x-and y-direction, and between position and velocity. The ion cloud is cooled and the ions oscillate synchronously according to RF confinement field. The ions remain quasi-uniformly distributed in the axial direction with lower trajectory extensions. The axial velocity distribution tends to a Gaussian function.

Standard deviation of ion velocities and mean kinetic energy
The standard deviation of ion velocities and mean ion kinetic energy versus confinement/cooling time are plotted in (Figure 8) for p G = 1 × 10 −3 torr. For ion kinetic energy and for standard deviations of ion velocity in x-and y-directions, four curves are plotted for 0, π/2, π and 3π/2 phases of the RF confinement field. For each phase, the points are separated by 1 µs. The standard deviation of ion velocities and mean value of ion kinetic energy decrease with time. These values tend to a constant value from about 4.5 ms confinement time for m/z 100 ions and about 14 ms for m/z 300 ions. This confirms the previous estimation of the cooling time for p G = 1 × 10 −3 torr.
The minimal values of the standard deviation of x-direction are obtained for 0 phase. At equilibrium, the value is lower than k B T /m I = 155 m/s for m/z 100 ions and 89 m/s for m/z 300 ions.
The mean value of kinetic energy is maximal for π/2 and 3π/2 phases and minimal for 0 and π phases. At equilibrium, the kinetic energy remains slightly higher than 3k B T /2 = 0.0388 eV as the ions experience RF field (RF heating).

Isolation step
The isolation step allows us to trap ions of given m/z. In this simulation work, it is assumed that U 0 is instantaneously switched from zero to U apex , a value close to the apex of the stability diagram. The stability diagram is that of a m/z 100 ion (or m/z 300 ion) crossing through an "equivalent" quadrupole mass filter (the term is defined just below). In order to have a finer characterisation of the step, the spectral response has been calculated for the scan line giving a mass separation of 1 m/z. The influence of the number of ions involved and step duration has been studied for mass separation of 1 m/z.

Stability diagram close to apex
The theoretical stability diagram of an "equivalent" Quadrupole Mass Filter (QMF) has been compared to the stability diagram of the LIT.
The equivalent QMF is a mass filter having hyperbolic electrodes located at a same distance (i.e. r 0 = 2 mm) than the LIT and having an infinite length. The boundaries of the theoretical stability diagrams for m/z 99, 100 and 101 ions have been computed by means of the matrix method 22 and plotted in Figure 9. For the QMF, the scan line U 0 = 0.17 × V 0 − 0.096 provides mass separation of 1 m/z (Figure 9).
To delimit the boundaries of the LIT stability diagram, the numbers of m/z 99 and m/z 100 ions have been computed from CPO trajectories for a great number of operating points in the plane (U 0 ,V 0 ) close to the apex ( Figure 9). As it is very time consuming, the contour lines of only two different m/z values have been calculated and plotted for LIT, while the theoretical stability diagrams of three different m/z values have been plotted in order to show the scanline providing separation of 1 m/z. The initial conditions of ion cloud are the final conditions of the cooling stage with p G = 1 × 10 −3 torr. The ions are confined collision-free for 100 µs.
A shift has been observed between QMF and LIT diagrams. In Figure 9

diagrams.
The static electric field introduces a defocusing effect in both radial directions leading to a stability diagram different from that of the equivalent QMF 23,24 . By limiting the development of the potential to the quadruple term, the apex of the LIT can be shifted to a higher value of V 0 and to a lower of U 0 . This is therefore not compatible with the observed shift that comes from electrode segmentation in CPO. The potential is applied at the centre of the segment. Due to the convex shape of the electrodes inside the LIT, the electric potential is applied at a distance larger than that expected. The upper potential correction must be applied and is taken into account in the entire simulation process.

Minimal length of equivalent QMF
It is interesting to estimate the minimal length of the equivalent QMF using the same initial conditions than the LIT.
For m/z 100 ions, the trajectories in the equivalent QMF have been computed by solving 2D Mathieu equations using an RK4 method with 400 points per period of the confinement field. Ion confinement is He-free here. The initial conditions are those at the end of cooling at T cool = 4.5 ms, except for the following modifications: the axial positions are set to 0 mm and the axial velocities are centred on the equivalent velocity corresponding to a kinetic energy of 3 eV (the potential energy difference between ion source and the centre of the LIT).
The number of confined ions has been computed from trajectories for several operating points located on the scan line to obtain the mass spectrum of m/z 100 ions at different mean values of time-of-flight (curve (d) of Figure 13). Separation of 1 m/z is obtained for a mean value of time-of-flight greater or equal to 200 µs.
The optimal operating point U 0 = 4.817 V and V 0 = 28.9 V is chosen on the scan line inside the stability diagram of m/z 100 ion. The evolution of axial position distribution of m/z 100 ions according to the time-of-flight in the equivalent QMF is given in    . To obtain a separation of 1 m/z for a time-of-flight greater or equal to 200 µs, the equivalent QMF must be at least 500 mm long, while LIT length is 40 mm and this comparison demonstrates the advantages of the LIT in comparison to a QMF.

Number of ions at the optimal operating point
The optimal operating point at U 0 = 4.817 V and V 0 = 28.9 V was chosen on the scan line for the stability diagram of m/z 100 ion. The number of ions has been computed versus confinement time for the equivalent QMF and for the LIT with initially cooled or nocooled ions (during the cooling step) and different He gas pressures during the isolation step ( Figure 11).
Without a cooling prior to the isolation step, when collisions occur (with p G = 1 × 10 −3 torr), the ions are instantaneously lost. With a cooling step, the lower the He pressure, the greater the number of confined ions. Even without cooling prior to the isolation step, the greatest number of confined ions is obtained collision-free during isolation step (with p G = 1 × 10 −10 torr).
In Figure 12, the locations in the y-and z-directions of ions lost in the x-direction are plotted versus confinement time for p G = 1 × 10 −10 and 1 × 10 −3 torr. During collision-free trapping, the ions are preferentially lost in the y-direction, due to phase of the RF confinement field. During the initial instants of confinement, the ion loss is not linked to the axial ion position. The lost ions have stable radial trajectories but with large excursions resulting in collision with trap electrodes, mainly in the y-direction and this is because the trap operating point is close to iso-beta line β y = 1. For larger confinement times, ion loss occurs when the ions are axially located at both ends of the trap, where non-linearities exist. This mode of ion loss is due to energy exchanges from the axial to the radial direction.
With collisions (p G = 1 × 10 −3 torr), additional ion losses occur in both radial directions, even when ions do not experience nonlinearities.

Spectrum of m/z 100 ions
To establish the spectrum of m/z 100 ions, the trajectories of 100 ions have been computed for the maximal confinement time of 500 µs. The spectrum comes from a series of non-scanning mode sequences with the same cooled-ion cloud as the initial condition, and with different operating points belonging to the scan line providing mass separation of 1 m/z. As a consequence, it is not a spectrum measured by moving the operating point along the scan line. In the cooling step, the necessity of ion cooling to greatly increase the number of ions has been shown. So, only a cooled-ion cloud has been considered here.
In Figure 13, spectra have been plotted for different isolation step durations and He gas pressures during the isolation step. Contrary to quadrupole mass filter (curve (d)), the maximal number of ions decreases with time in the collision-free case with He pressure equal to p G = 1 × 10 −10 torr (curve (a)). This ion loss is due to non-linearities: there are a large number of resonance lines close to the stability diagram apex 23 . This ion loss increases when He gas pressure increases (curves (b) and (c)). Consequently, collisions induce additional ion losses when the trap is operated close to apex of the stability diagram.

Spectrum of m/z 300 ions
To achieve 1 m/z mass separation in the equivalent QMF with m/z 300 ions, the scan line used is: U 0 = 0.17 × V 0 − 0.225. Spectra have been calculated for different durations of isolation step in the collision-free case (with p G = 1 × 10 −10 torr) with cooled initial ion distributions (cooling step at p G = 1 × 10 −3 torr) ( Figure  14). The relative number of ions is almost the same than with m/z 100 ions. Mass separation is 1 m/z.
For m/z 100 and 300 ions, with collision-free confinement in the LIT, mass separation of 1 m/z is achieved for an isolation step duration of about 200 µs with a relative number of ions of 30 % at peak maximum. So, it is important to adapt the operating mode to increase the number of ions.

Discussion and conclusions
The performance comparison, i.e. sequence duration and number of ions, for m/z 100 ions and mass separation of 1 m/z is given in Table 2 according to He pressure and non-scanning mode sequence, either with constant He pressure, or with an additional He removal step. The relative number of ions is calculated by dividing the number of ions measured with a LIT by the number of ions measured with an equivalent QMF of infinite length. The Table 2 Comparison of LIT performances (i.e. sequence duration and number of ions) for m/z 100 ions according to non-scanning mode sequence either with constant He pressure, or with an additional He removal step. (*) estimated value deduced from simulation. (**) estimated value according to 11,25 .  Table  2 equal to 0.2 ms, as required mass separation is 1 m/z. The first three horizontal blocks of the table concern the nonscanning mode sequence with constant He pressure for three different values of He pressure. For p G = 1 × 10 −4 torr, the cooling step duration has been estimated at 45 ms, if we assume that the cooling duration is inversely proportional to He pressure. For the isolation step, the number of ions has been estimated between those obtained with p G = 5 × 10 −4 torr and He-free. There exists an optimal value of the number of ions of about 43% remaining at the end of the isolation step with this operating mode for p G = 5 × 10 −4 torr. In that case the sequence duration is less than 10 ms.
The last horizontal block concerns the non-scanning mode sequence with an additional He removal step. The He gas in this case may be introduced by means of a pulse valve. A He removal step is added prior to isolation step with He valve closed, in order to operate He-free the LIT at apex during isolation step 11 . Its duration has been estimated at 1 s according to work described in 25 . With this operating mode, the number of ions remaining at apex is increased to a value of about 64% at the expense of the sequence duration estimated to a few seconds. For m/z 300 ions, a same number of ions is obtained, however the cooling time is 14 ms.
In order to reduce analysis time duration, two LIT devices could be used: the first one operated in the cooling mode with He buffer gas and the second one operated He-free for mass isolation providing that the maximum number of ions can be transferred between the two devices and the ion states in the radial directions are not modified.
In order to increase mass separation, the operating point of the isolation step can be chosen closer to the stability diagram apex, however the initial number of ions will be lower. For instance, deduced from Figure 9, the relative number of ions is 30 % for mass separation of 1 m/z, and less than 10 % for 0.5 m/z. Furthermore, both the sensitivity and mass separation could be increased by using a specific potential ramp to move the LIT operating point in the stability diagram from the centre (RF only mode for cooling step) toward apex (for isolation step). These promising results indicate the feasibility of this nonscanning technique for portable in-the-field mass spectrometer. Applications include detection of drugs of abuse, explosives and other security threats as well as point-of-use biomedical analyses for healthcare diagnostics.

Conflicts of interest
There are no conflicts to declare.