Role of electron heating in efficient interaction of a nanosecond laser with the cluster media: a case study on tetrahydrofuran cluster system

Abstract

Interaction of tetrahydrofuran clusters with nanosecond laser pulses has been investigated at 532 and 1064 nm, using a time-of-flight mass spectrometer and home-built electron analyzer setup. An efficient laser–cluster interaction has been observed at both the laser wavelengths, based on detection of multiply charged atomic ions. At 532 nm, multiply charged atomic ions up to C⁴⁺ and O⁴⁺ have been observed, while at 1064 nm multiply charged atomic ions up to C⁵⁺ and O⁶⁺ have been detected. Such efficient laser cluster interaction is supposed to be facilitated by coupling of laser energy into the cluster by collisional heating of electrons confined within the cluster. Accordingly, kinetic energy distribution of electrons liberated upon interaction of tetrahydrofuran clusters with nanosecond laser pulses has been quantified using a home-built electron analyzer setup. A good correlation between the ionization energy of the highest multiply charged atomic ions observed at the two laser wavelengths and the measured kinetic energy of electrons (up to ∼80–100 eV at 532 nm and up to ∼300 eV at 1064 nm) has been obtained. Present studies suggest that upon initial ionization of the cluster by a multiphoton ionization mechanism, which is predominant under nanosecond laser conditions, further enhanced ionization of the cluster constituents during the time-span of the laser pulse is dominated by energetic electrons. These electrons are energized via inverse Bremsstrahlung absorption process, causing step-wise electron ionization of cluster constituents and augmentation of charge on the cluster, over a time scale where cluster expansion can be considered to be insignificant.

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1. Introduction

The interaction of intense ultra-short laser pulses with clusters has attracted a great deal of attention in the scientific community over the last few decades.^1–9 The main motivation driving these studies comes from the inherent ability of the cluster media to convert optical laser pulses into radiation sources of highly-charged ions,¹⁰ energetic electrons¹¹ and neutrons,¹² having the same order of pulse duration as that of the laser pulse.¹³ Such diverse transformation of the optical laser pulse is facilitated by efficient absorption of laser energy by the cluster media due to its near solid like density.

Consequently, evolution of different atomic and molecular cluster systems have been investigated, upon their interaction with laser pulses of intensity ≥10¹⁴ W cm⁻² and over wavelength range spanning from IR to X-ray region.^14–18 Various theoretical models have been proposed to explain different facets of laser–cluster interaction.^19–27 Mainly all these models consider laser–cluster interaction to be a multistep process – involving initial ionization of the cluster constituents at the leading portion of the laser pulse, subsequent energy absorption by the ionized cluster media from the remnant portion of the laser pulse – leading to enhanced multi-step ionization of the cluster constituents and finally disintegration of the excessively ionized cluster under the influence of the coulombic field. All these processes occur in the sub-picosecond time-span. Of all these theoretical models “nanoplasma model” has been extensively utilized for rationalizing different aspects of laser–cluster interaction.^26,27 This model considers that solid like density of cluster facilitates rapid energization of inner ionized electrons (ionized electrons confined within the cluster) via collisional inverse Bremsstrahlung (IBS) process, under the influence of laser pulse. These energized electrons facilitate further enhanced ionization of the cluster constituents.

In the last decade, there have been several reports regarding enhanced ionization and Coulomb explosion of clusters upon interaction with nanosecond laser pulses of intensity ∼10⁹ to 10¹¹ W cm⁻².^28–32 Unlike the extensive experimental studies carried out using ultrafast laser pulses over intensity range of 10¹⁴ to 10¹⁸ W cm⁻² and the theoretical models proposed to describe the evolution of clusters upon irradiation with laser pulses, the literature is sparse with theoretical models to account for interaction of clusters with nanosecond laser pulses over intensity range of 10⁹ to 10¹¹ W cm⁻². Consequently, to account for such efficient laser–cluster interaction under nanosecond laser field conditions, a three-stage cluster ionization model has been proposed by Wang et al.,³³ drawing analogy from the nanoplasma model. Although the proposed three-stage cluster ionization model qualitatively explains the wavelength dependent behavior, based on IBS heating of the clusters via quasi free electrons, concerns were raised regarding direct applicability of nanoplasma model under nanosecond laser conditions. Because, under femtosecond laser irradiation cluster expansion can be considered to be negligible (near solid like density), which facilitates laser energy absorption via IBS. On the contrary under nanosecond laser conditions, considering cluster expansion insignificant has been suggested to be inappropriate as under the influence of coulombic forces the cluster is expected to undergo significant expansion, consequently collisional heating via inverse Bremsstralgun is expected to be inefficient.

In a recent study, we investigated interaction of tetrahydrofuran clusters ((THF)_n) with nanosecond laser pulses over intensity range of 10⁹ to 10¹⁰ W cm⁻².³⁴ THF was used because of its high volatility, which facilitates generation of clusters upon supersonic expansion. In addition this cyclic ether forms clusters with cage like structure containing voids, which act as site for electron solvation.³⁵ Thus these sites might assist in confining the quasi-free electrons and aid in efficient coupling of laser-energy with the cluster media. A significant observation of the study was generation of multiply charged atomic ions up to C⁴⁺ and O⁴⁺ at 532 nm, while at 1064 nm multiply charged atomic ions up to C⁵⁺ and O⁶⁺ were observed. Also calculations based on the proposed three stage model, suggested that upon initial ionization, the cluster survives for sub-picosecond timescale under the influence of the laser pulse – coupling laser energy with the cluster media, prior to disintegration.³⁴ Here, as the ionization energy of the highest observed multiply charged atomic ions at 532 and 1064 nm, were 64.5 eV (C⁴⁺) and 392 eV (C⁵⁺) (Table 1), (THF)_n clusters provide an ideal system to verify the preposition of IBS heating of the cluster media by energized inner ionized electrons leading to generation of multiply charged atomic ions, under the influence of nanosecond laser field. As the kinetic energy of the electrons liberated upon disintegration of the (THF)_n clusters should be comparable with the ionization energy of the highest observed multiply charged atomic ions, at the two laser wavelengths. Accordingly, studies have been carried out to quantify the kinetic energy of the electrons liberated upon interaction of (THF)_n clusters, with 532 and 1064 nm using in house developed retarding field electron energy analyzer. In the following, we describe the indigenously developed electron energy analyzer and present the experimental findings to probe role of inner ionized electron in coupling laser energy with the cluster media.

Table 1 Ionization energies of multiply charged atomic ions of carbon and oxygen ions³⁶

Charge state	Ionization energy of isolated carbon ions (C^n+) (eV)	Ionization energy of isolated oxygen ions (O^n+) (eV)
+1	11.26	13.62
+2	24.38	35.12
+3	47.88	54.93
+4	64.49	77.41
+5	392	113.9
+6	490	138.12
+7		739.32
+8		871.39

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2. Experimental

Details of the experimental setup have been described in our earlier publications and only a brief account is given here.^28,29,34 Neutral clusters of (THF)_n were generated via supersonic expansion of room-temperature THF vapours seeded in helium/argon at a backup pressures of ∼3 bar. A pulsed valve (0.8 mm nozzle diameter and 300 μs pulse duration) was used for this purpose. The experimental results were found to be independent of the carrier gas. The gas jet so produced was skimmed at a distance of 5 cm from the pulsed nozzle and entered the interaction region located 17 cm downstream from the skimmer. Here the clusters were subjected to nanosecond laser pulses (i.e. 532 and 1064 nm), from a pulsed Nd:YAG laser (Quanta System, Olona, Italy; 10 ns, GIANT G790-10). At both the laser wavelengths, studies were carried out at threshold laser intensity where signal-to-noise ratio (S/N) for multiply charged atomic ions was satisfactory. Thus present studies at 532 and 1064 nm were carried out at laser intensity of ∼5 × 10⁹ and ∼1 × 10¹⁰ W cm⁻², respectively. The in house built electron energy analyzer was placed ∼8 cm away from the laser–cluster interaction zone, orthogonal to the direction of the laser and the cluster beam (Fig. 1). The electron energy analyzer is based on retardation field method. The analyzer comprises of an assembly of three stainless steel grids, placed 1 cm apart from each other, in front of channel electron multiplier detector, which was configured for detecting electrons and negative ions. Unlike some previous studies,^30,37 in the present setup no external field was applied at the laser–cluster interaction region to steer the liberated electrons towards the electron analyzer assembly, and the electrons reach the detector purely due to kinetic energy gained by them during the laser–cluster interaction process. Upon laser–cluster interaction as the electrons are liberated isotropically, only the fraction of electrons liberated at a narrow solid angle are probed by the electron energy analyzer. To obtain the kinetic energy distribution of electrons, time-of-flight traces were recorded as a function of increasing retarding potential applied to the central grid of the grid assembly (0–V–0). Increasing values of retarding potential gives rise to signal due to those electrons which have enough kinetic energy to overcome the retarding potential, thus providing information regarding the kinetic energy of the electrons. The electron energy distribution was subsequently obtained upon differentiating the obtained retardation potential curve. In addition, under identical experimental conditions ions formed upon laser–cluster interaction were also characterized using time-of-flight mass spectrometer in positive ion mode, to correlate the highest observed multiply charged atomic ions with the electron energy data.

Fig. 1 (a) In-house built electron energy analyzer setup. (b) Electron energy analyzer setup, mounted inside the experimental chamber. (c) Schematic of the electron energy analyzer.

3. Results

A typical trace obtained from electron energy analyzer at zero retardation potential, for tetrahydrofuran clusters irradiated with 532 nm laser pulse of intensity ∼5 × 10⁹ W cm⁻², is depicted in Fig. 2(a). As illustrated in the figure, three distinct signals due to photon, electron and negative ion are clearly observed. Signal due to photon, electron and ion were distinguished by applying retarding voltage on the grid assembly. It was observed that on increasing retarding potential, signal due to electron and ion was found to decrease, while the photon signal remains unaffected. Also, upon placing a strong permanent magnet outside the vacuum system, near the laser–cluster interaction region drastically reduces the electron signal.³⁸ Fig. 2(b) illustrates systematic decrease in electron signal due to filtering out of lower energy electrons at 532 nm, upon increasing the retarding potential. For studies carried out at 1064 nm, signal due to photon and electron was not well resolved due to overlapping of photon signal with electron signal of higher kinetic energy generated upon interaction of (THF)_n clusters with 1064 nm laser pulses (as discussed later).

Fig. 2 (a) Typical time-of-flight trace obtained from electron energy analyzer, at zero retardation potential for tetrahydrofuran clusters irradiated with 532 nm laser pulse of intensity ∼5 × 10⁹ W cm⁻². (b) Traces depicting systematic decrease in electron signal, as a function of retarding potential due to filtering of lower energy electron component for (THF)_n clusters irradiated with 532 nm laser pulse of intensity ∼5 × 10⁹ W cm⁻².

Fig. 3 illustrates positive ion time-of-flight mass spectrum obtained, upon interaction of 532 nm laser pulses of intensity ∼5 × 10⁹ W cm⁻². Under identical experimental conditions, the kinetic energy distribution of electrons is presented in Fig. 4. Similarly, Fig. 5 depicts positive ion time-of-flight mass spectrum obtained, when clusters of (THF)_n were irradiated with 1064 nm laser pulses of intensity ∼1 × 10¹⁰ W cm⁻². The corresponding plot for kinetic energy of electrons is shown in Fig. 6. These studies suggest that at 532 nm, along with fragment ions, the highest observed multiply charged atomic ions are C⁴⁺ and O⁴⁺. While for studies carried out at 1064 nm, multiply charged atomic ions up to C⁵⁺ and O⁶⁺ have been observed. As these multiply charged atomic ions are associated with large kinetic energy, often ion signals arising from multiply charged atomic ions exhibited significant peak broadening in the time-of-flight mass spectra. As a result, the ion signal for an individual multiply charged atomic ion comprises of a broad forward component and a sharp energy-focused backward component, thus complicating assignment of m/z value to the particular ion.³⁴ In order to overcome this issue, several mass spectra were recorded by varying extraction/acceleration voltage, for a given set of experimental conditions. These recorded spectra are then individually calibrated using different reference fragment ions. Since the variation of extraction and acceleration voltage leads to variation in the arrival time of individual ion, upon calibration precise m/z assignment to all the ion signals recorded in the mass spectrum aids in resolving this complexity. Alongside, based on electron energy distribution derived from the integrated electron signal as a function of retardation potential, it is observed that at 532 nm, the electron energy distribution peaks at ∼15 eV, with mean electron energy of ∼24 eV and the distribution tails ∼80–100 eV. Similarly at 1064 nm, the electron energy distribution is found to peak at ∼80 eV, with mean electron energy of ∼72 eV and the tailing of electron energy distribution is observed up to ∼300 eV. Here it is worth mentioning that, in the present setup the laser–cluster interaction region is devoid of any extraction electrodes or other surfaces in its close vicinity to avoid contribution from potential artifacts and alteration of electron energy distribution.

Fig. 3 Positive ion time-of-flight mass spectrum obtained upon interaction of (THF)_n clusters with 532 nm laser pulse of intensity ∼5 × 10⁹ W cm⁻².

Fig. 4 Integrated electron signal as a function as a function of retarding potential, obtained for (THF)_n clusters subjected to 532 nm laser pulse of intensity ∼5 × 10⁹ W cm⁻². Inset shows electron energy distribution obtained upon differentiating the integrated electron signal curve.

Fig. 5 Positive ion time-of-flight mass spectrum obtained upon interaction of (THF)_n clusters with 1064 nm laser pulse of intensity ∼1.1 × 10¹⁰ W cm⁻².

Fig. 6 Integrated electron signal as a function as a function of retarding potential, obtained for (THF)_n clusters subjected to 1064 nm laser pulse of intensity ∼1.1 × 10¹⁰ W cm⁻². Inset shows electron energy distribution derived from the integrated electron signal curve.

For studies carried out at 532 nm, based on time-of-flight mass spectrum it was considered that contribution to m/z = 4 in the mass spectrum recorded at 532 nm, was mainly due to C³⁺ and contribution from O⁴⁺ was negligible. However, the electron energy measurement studies carried out at 532 nm, where electrons with kinetic energy higher than ionization energy of O⁴⁺ (Table 1) are observed suggest that there is significant contribution to m/z = 4 ion signal from O⁴⁺ ion as well.

Thus the kinetic energy of electrons liberated upon laser–cluster interaction, is in qualitative agreement with the ionization energy of highest observed multiply charged atomic ions observed at the two laser wavelengths.

4. Discussion

Generation of multiply charged atomic ions and detection of energetic electrons, liberated upon laser–cluster interaction can be explained on the basis of proposed three-stage cluster ionization model. i.e. “multiphoton ionization ignited-inverse Bremsstrahlung heating-electron impact ionization”.^33,39 The model considers that under the influence of nanosecond laser pulse, clusters undergo multi-photon ionization (dominant ionization mechanism under nanosecond laser conditions) at the leading edge of the laser pulse. Subsequently, some of the ionized electrons get confined within the cluster (i.e. inner ionized electrons). These electrons having initial kinetic energy ∼ n(hν) − I.E._(cluster) (n = no. of photons required for multiphoton ionization of cluster at 532/1064 nm and I.E._(cluster) is ionization energy of cluster), which is of the order of 1 to 2 eV, get further energized by extracting energy from the remnant laser pulse via inverse Bremsstrahlung (IBS) process under the influence of Coulomb field within the cluster. In turn, these energized electrons cause further indiscriminate stepwise ionization of cluster constituents. This sequence of events leads to augmentation of charge on the cluster, until the duration of the laser pulse or to a stage where the charged cluster disintegrates under the influence of coulombic forces. As a result energetic multiply charged atomic ions and electrons are generated.

The rate of energy extraction from the laser pulse by the confined electrons via IBS process^40,41 is given by eqn (1)

here ν is the collision frequency of the inner ionized electrons and is of the order of ∼10¹⁴ to 10¹⁵ Hz (i.e. order of laser frequency) and ponderomotive energy (U_p) is given by the eqn (2)

U_p = 9.33 × 10⁻¹⁴I (W/cm²)λ² (μm)² (2)

From eqn (1) and (2), it is obvious that the total energy gained by the inner ionized electrons, in the time span starting from initial ionization till the disintegration of cluster, is dictated by the product of ponderomotive energy and the total number of effective electron-ion/neutral collision frequency. Eqn (2) further suggests that as the wavelength (λ) increases, ponderomotive energy (U_p) of electrons and in turn total extracted energy increases quadratically for a given laser intensity. Hence, higher level of ionization is expected at longer laser wavelengths. This qualitatively explains our results obtained at 532 and 1064 nm, where higher multiply charged atomic ions and electrons with comparatively enhanced kinetic energy were obtained at longer laser wavelength.

Thus the three stage cluster ionization model accounts for energization of electrons and generation of multiply charged atomic ions, however generation of hydrogen like C⁵⁺ ions at 1064 nm having ionization energy of ∼392 eV cannot be explained based solely on the three-stage model, since the electron energy measurement studies suggest observation of electrons with kinetic energy ∼300 eV. To account for this anomaly observed between the ionization energy of the highest observed multiply charged atomic ion and the kinetic energy of electrons, one has to invoke the effect of screening within the highly charged cluster under the influence of laser field.^42–44 Screening effects arise due to presence of charged particles in close proximity, within the solid density cluster. Consequently the internal electric field produced by ions and electrons, generated upon initial ionization significantly suppresses the ionization potential of species (atoms/molecules/ions) present within the cluster as compared to its isolated counterpart. The extent of ionization potential suppression depends on the overall intra-cluster electric field experienced by the species. In addition, the local cluster electric field also facilitates electron ionization.⁴⁵

The degree of ionization potential suppression can be estimated using eqn (3), which is derived from Debye potential using the first-order perturbation theory⁴⁶

where, E_I.E. = ionization energy of atomic ions after considering screening effects, Z_eff = effective charge of the atomic core = , E_Z = ionization energy of isolated atomic ion, n = principal quantum number, l = azimuthal quantum number, R = Debye radius = , T_e = electron energy (also referred as electron temperature), n_e = electron density = Q(n_a∑Z_im_i), Q = fraction of molecules that are ionized in cluster medium, n_a = number density of molecules in clusters, Z_i = charge state of atomic ions, m_i = number of particular element in a molecule.

Using eqn (3), suppression of ionization potential of multiply charged atomic ions upon interaction of tetrahydrofuran clusters has been estimated. All calculations presented here are performed in atomic units (a.u.). Calculations were performed for different charge state of carbon and oxygen ions at varying electron energy for the case of 532 and 1064 nm, assuming neutral cluster density as liquid density of tetrahydrofuran i.e. 0.0011 a.u. (0.8892 g cm⁻³). For 532 and 1064 nm, calculations were carried out considering different level of cluster ionization, as the average charge state of atomic ions observed at 532 and 1064 nm are different. At 532 nm, for estimating the suppression in ionization energy for O³⁺ → O⁴⁺, the parameters were derived considering that at the stage when the multiply charge ions are generated the cluster has sustained at least 10% ionization, causing cluster expansion by an order of magnitude. At this stage, n_e = Qn_a(3 × 4)_C + (8 × 1)_H + (1 × (4 − 1)_O), where Q = 0.1, n_a = 0.00011. Based on these values Debye radius (R) is calculated to be . Substituting the value of Debye radius and Z_eff = 4.77 (for O⁴⁺ n = 2 and E_z = 77.41 eV = 2.844 a.u.) in eqn (3) one obtains ionization energy of O⁴⁺ as a function of electron temperature. Fig. 7 and 8 depicts ionization energy of highest observed multiply charged atomic ions as a function of electron energy, at 532 and 1064 nm respectively. As can be seen from Fig. 7 and 8, the ionization energy of atomic ion significantly decreases at lower electron energy. At 532 nm, the ionization energy of O⁴⁺ at electron energy of 24 eV (mean electron energy measured at 532 nm) decreases from 77.41 to 69.3 eV. Similarly, ionization energy of C⁵⁺ as a function of electron energy is depicted in Fig. 8. For C⁵⁺, ionization energy decreases from 392 eV to 327 eV, at electron energy of 72 eV (mean electron energy measured at 1064 nm). While at lower electron temperature of ∼25 eV, the ionization energy of C⁵⁺ is estimated to be ∼300 eV. Thus screening effect considerably decreases ionization energy of the atomic ions at lower electron energy. Consequently, it was justifiable to investigate effect of screening on ionization energy of O⁵⁺ (at 532 nm), C⁶⁺ and O⁷⁺ (at 1064 nm) as a function of electron energy. These ions are the next higher analogues of highest multiply charged atomic ions detected under our experimental conditions (i.e. O⁴⁺ and C⁵⁺ and O⁶⁺). Though these higher analogue ions were below the detection limit in the recorded time-of-flight mass spectra, does screening effect predict generation of these multiply charged atomic ions? For comparison, ionization energy of these multiply charged atomic ions are also illustrated in Fig. 7 (O⁵⁺) and 8 (C⁶⁺ and O⁷⁺). As shown in the figures, the effect of screening significantly reduces the ionization energy of these multiply charged atomic ions: however the extent of ionization potential lowering is not adequate to facilitate generation of higher multiply charged analogues upon electron ionization, under our experimental conditions.

Fig. 7 Calculated ionization energy of O⁴⁺ and O⁵⁺ as a function of electron energy for studies carried out at 532 nm. Vertical dotted line corresponds to mean electron energy obtained from electron energy distribution studies carried out at 532 nm.

Fig. 8 Calculated ionization energy of C⁵⁺, C⁶⁺ and O⁷⁺ as a function of electron energy for studies carried out at 1064 nm. Vertical dotted line corresponds to mean electron energy obtained from electron energy distribution studies carried out at 1064 nm.

Thus generation of multiply charged atomic ions, upon interaction of clusters with nanosecond laser pulses can be explained on the basis of three stage cluster ionization model discussed above. The electron kinetic energy distribution profiles support the vital role played by inner ionized electrons in efficient coupling of laser energy with the cluster media, leading to enhanced electron ionization of cluster constituents and augmentation of charge on the cluster. Concurrently, augmentation of charge on the cluster instigates screening effect which significantly suppresses the ionization energy of cluster constituents: thereby facilitating their ionization to higher charged states. These sequence of events i.e. electron energization – ionization of cluster constituents – generation of additional electrons – further suppression of ionization potential continues until the cluster disintegrates or till the duration of the laser pulse. Above discussed model is a simplified version of the actual cluster ionization mechanism. For example, in ionization energy suppression calculations involving screening effect within ionized cluster, the calculations have been carried out for discrete distribution of ion charge and electron energy. However, in actual scenario there is a dynamic distribution of ions of varying charge state within the cluster, which progressively increases along the duration of the laser pulse, preceding cluster disintegration. Similarly, the inner ionized electrons within the cluster are also associated with varying electron energy distribution. Consequently at any given instance, following initial ionization of the cluster the electric field and accordingly the ionization energy suppression of ion is an average quantity, characterizing collective effect of all ions and electrons on a particular ion within the cluster. This explains the complexity of laser–cluster interaction upon interaction with nanosecond laser, which involves multi-step interdependent excitation process leading to generation of multiply charged atomic ions.

5. Conclusions

Kinetic energy distribution of electrons liberated upon interaction of (THF)_n clusters with nanosecond laser pulses has been investigated at 532 and 1064 nm, using home-built electron energy analyzer setup. The kinetic energy distribution of electrons obtained has considerable correlation with the ionization energy of multiply charged atomic ions obtained at the two laser wavelengths. Under cluster conditions energization of electrons under the influence of laser pulse has been observed, in line with the proposed three-stage cluster ionization model, suggesting that the step-wise multiple ionization of cluster is facilitated by energetic electron ionization. Also higher energization and charging of clusters is observed at longer laser wavelength. In addition, our studies suggest that though the initial ionization of the cluster is initiated via multiphoton ionization of the cluster, the major contribution to overall ionization of the cluster leading to generation of multiply charged atomic ions is via electron ionization of the cluster constituents by energized electrons. In addition, cluster expansion upon initial multiphoton ionization of the cluster is expected to be insignificant even under nanosecond laser conditions, following quantification of wavelength dependent electron kinetic energy distribution. The rate of electron energization and subsequent ionization by the energetic electrons, far exceed the cluster expansion during the initial laser–cluster interaction phase.

Acknowledgements

The authors thank Dr V. K. Jain, Head, Chemistry Division and Dr B. N. Jagatap, Director, Chemistry Group for constant encouragement.

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