Laser system A femtosecond, CPA laser system based on titanium doped sapphire (Ti:S) provided pulses for the Imperial College cluster work, centred at a wavelength of 780 nm, with energy up to 60 mJ and a pulse duration of <200 fs [50]. The front end of the system is a Kerr lens mode-locked Ti:S oscillator that generates near transform-limited pulses of duration ~90 fs. The oscillator pulses are stretched in a diffraction-grating stretcher to a duration of ~250 ps, thus reducing the pulse power by a factor ~3000. This permits safe amplification first to the millijoule level in a Ti:S regenerative amplifier operating at 10 Hz and then to ~120 mJ in a multi-pass Ti:S power amplifier. The amplified pulses are then recompressed in a grating compressor to yield pulses at a power level of approximately 0.5 TW (60 mJ/ 150 fs) at a pulse repetition rate of 10 Hz. In conjunction with standard (single-shot) autocorrelation pulse duration measurements, and equivalent-plane focal spot characterisations, the focused laser intensity is inferred from ion appearance data using over-the-barrier ionization (OTBI) thresholds [51]. This is carried out in the same interaction chamber (described below) used for the low-density cluster studies, providing in situ intensity measurement.
Interaction chamber The interaction chamber, illustrated in Fig. 2, is essentially a TOF particle spectrometer coupled to a skimmed, gas-jet cluster source. It is used to measure the energies of electrons and ions as well as the charge states of ions produced in the laser induced explosion of isolated clusters. As outlined above, to achieve a relatively low density of clusters in the interaction region, a cluster jet produced from a solenoid pulsed-valve at the top of the chamber is skimmed to produce a much lower density cluster beam. The cluster beam intersects the laser focus at the centre of the high vacuum section of the chamber, some 50 cm below the nozzle. Differential pumping is employed to maintain the high vacuum in the main chamber. Typically, the density of clusters at the laser focus is ~1010 cm-3 corresponding to <1000 clusters in the laser focal volume.
The linearly polarised laser is focused at ~f/20 with plano-convex lens which gives an approximately Gaussian focal spot of ~20 µm (e-2 radius). By rotating a half-wave plate before the lens, the polarization vector can be rotated through 360°, enabling the angular distribution of particles in the plane perpendicular to the laser axis to be studied.
The energies of ions produced in the interaction are determined from their TOF from the laser focus to a microchannel plate (MCP) detector, without the use of an extraction field. The electrons produced in cluster explosions are too fast for standard TOF techniques to be used. Instead, a retardation method is employed. Two closely spaced grids are placed in the flight path. To the first, a voltage U is applied, the second is grounded. This introduces a potential barrier to electrons with energy less than eU, where e is the electron charge. The MCP signal is recorded as a function of U. The electron energy spectrum is then found by differentiating this distribution with respect to U.
With a small modification to the standard TOF apparatus, information can also be gained on the ion charge state, Z. Three closely spaced metal grids are placed in the flight tube. Applying a potential U to the middle grid, while keeping the front and back grids at earth introduces a barrier to ions with energy less than ZeU, without significantly altering the flight time of higher energy ions. By measuring the number of ions reaching the detector as a function of U, and then differentiating with respect to U, the charge state distribution of the ions as a function of their kinetic energy can be determined. However, this technique cannot measure the energy distribution of a given charge state. The complete charge state information can be gained by incorporating magnetic deflection into the ion flight path, as demonstrated in [49].
Ion energy spectrum Typical raw ion TOF spectra are shown in Fig. 3(a) for a range of angles between the laser polarization and the TOF axis. Each spectrum is averaged over several thousand laser shots. The target was 2500-atom Xe clusters irradiated at 2 x 1016 W cm-2. The fast unresolved feature in the TOF spectrum is due to the emission of ener- getic electrons (resolved in other studies [43]), the broader peak is due to the ions. The close similarity of the TOF spectra recorded for different angles is a clear signature of a spherically symmetric explosion. The energy spectrum corresponding to the 0° trace is displayed in Fig. 3(b) (the other angles give almost identical energy spectra). The mean ion energy is 45±5 keV, showing that the average laser energy deposited per ion is substantial. A remarkable aspect of the ion spectrum is the presence of ions with energies up to 1 MeV. This energy is four orders of magnitude higher than has previously been observed in the Coulomb explosion of molecules [52] and about 1000 times higher than the average energy of the highest charge state Ar ions ejected in the disintegration of small (<10 atoms) cluster. In fact 1 MeV is about a factor four higher than the predictions of the nanoplasma model for these parameter values. It has been suggested that the MeV ions do not result from the hydrodynamic expansion, but are the result of an electrostatic shock wave that Coulomb ejects the most highly charged ion that are close to the cluster surface [44]. (underline added)
Ion charge state distributions The production of highly stripped ions is another characteristic feature of the laser–cluster interaction. The charge state distributions of Xe ions (for the same conditions as Fig. 3) are shown in Fig. 4 as a function of their kinetic energy. For the high energy ions (>100 keV), the peak charge state is at Z = 18–25, with some ions, remarkably, having charge states as high as 40 [47]. These are much higher than the ~12 expected from laser field ionization of single atoms at these intensities according to an OTBI model [53]. In fact, the OTBI model predicts an intensity of nearly 1020 W cm-2 to produce such a high charge state. The nanoplasma model provides an explanation for these high charge states. Efficient collisional heating in the nanoplasma heats the electrons to several keV. These electrons strip the ions to high charge states through collisions. Modelling shows that it is largely thermal collisional ionization responsible, which occurs while the cluster is shielded from the external field. The ion charge state depends only weakly on ion kinetic energy, contrary to what would be expected from a pure Coulomb explosion. Using a magnetic deflection TOF spectrometer, the energy distributions of ion charge states in the range 1–30 from 2 million-atom Xe clusters interacting with 130-fs Ti:S pulses at an intensity of ~5 x 1017 W cm-2 have been measured [44]. This allowed the dependence of the ion energies upon the charge states to be investigated.
Parameter scalings In this section we look at how the ion energies from cluster explosions scale with two important experimental parameters, the cluster size and the laser intensity [54]. These scaling provide tests of the models and help identify the conditions that maximise the ion energies, which is important for applications.
Cluster size Fig. 5 shows how the maximum ion energy varies with the number of atoms in a Xe cluster in the range 200–74,000 Xe atoms [54]. A laser intensity of 3 x 1015 W cm-2 was used. The threshold size for energetic ion production (>1 keV) appears to be ~200–400 atoms. The maximum ion energy rises from 8 keV at 200 atoms/cluster to a peak of ~53 keV for clusters of ~8000 atoms before falling to ~28 keV as the cluster size is increased beyond 50,000 atoms/cluster. Kr and Ar clusters show a qualitatively similar behavior.
The solid curve is a numerical simulation from the nanoplasma model, which is in reasonable agreement with the experimental data, though the calculated optimum size is somewhat larger. However, there is a factor of two uncertainty in the cluster size measurements and further, the calculation does not take into account the distribution of cluster sizes present in the laser focus. The modelling has recently been improved to include a realistic cluster size distribution [55].
The existence of an optimum cluster size is strong evidence for the ne = 3ncrit resonance predicted by the nanoplasma model. The maximum ion energy is determined largely by the laser intensity when the cluster experiences the resonant heating. The highest ion temperatures are obtained when the cluster passes through the ne = 3ncrit point near the peak of the laser pulse. Small clusters expand too quickly and reach this point before the peak. Larger clusters pass through 3ncrit well after the peak intensity is reached. This also ex- plains the existence of an optimum laser pulse-width for a given cluster size seen in [33,56].
An empirical formula for the optimum cluster size has been determined from the results of numerous simulations using the nanoplasma model 57:
Nc(opt) = 1.8 x 10-13Z-1I0.75t3,
where Nc is the number of atoms in the cluster, Z is the atomic number, I is the laser intensity in W cm-2 and t is the laser pulse duration in fs.
Laser intensity Fig. 6 shows how the maximum ion energies vary with the peak laser intensity (230 fs, 780 nm pulses) for 5300-atom Xe clusters and 6200-atom Kr clusters [54]. In Xe, a sharp onset of fast ion production is seen at 6 x 1014 W cm-2. The ion energies rise steeply up to ~1015 W cm-2, to an energy of ~50 keV. Above 1015 W cm-2, the ion energies saturate, increasing as ~I0:2 (the integrated ion yield scale as ~I1.4, consistent with the increase in focal volume). At 1016 W cm-2, the maximum ion energy is 90 keV. The Kr ion energies follow a similar trend to the Xe, with a sharp increase up to a mean energy of 9 keV at 1015 W cm-2, followed by a slow increase up to energies of 75 keV at 1016 W cm-2. For Kr the ion energies are about 20% lower. The solid and dotted curves are the nanoplasma calculations for Xe and Kr, respectively. Again, the agreement is reasonable.
The modelling provides explanations for the well-defined ‘‘appearance intensity’’ for energetic ion production, as well as the eventual saturation in the ion energies with increasing intensity. Referring back to Fig. 1(c), we see that the energetic cluster explosion is triggered by the second occurrence of the ne = 3ncrit resonance, since the first one occurs very early in the laser pulse when the intensity is low. Modelling shows that the appearance intensity is just the minimum peak intensity required to ensure two occurrences of the resonance during the laser pulse. Below this intensity, the resonance is achieved only once, early in the laser pulse, because the expansion velocity is insufficient compared to the ionization rate to drop 'ne back down to 3n''crit. The saturation in the ion energies with increasing intensity is a product of the increased ionization that occurs on the rising edge of the pulse. This results in the cluster expanding faster and reaching the second resonance earlier in the pulse. It therefore does not experience a substantially higher laser intensity at the point of resonant heating. (underline added)
See Also
3.14 - Vortex Theory of Atomic Motions 13.04 - Atomic Subdivision atomic Atomic Cluster X-Ray Emission Atomic Clusters Atomic Force atomic mass atomic number atomic theory atomic triplet atomic weight Debye Continuum Debye length Debye length in a plasma Debye length in an electrolyte Debye, Peter Debye Sphere diatomic Etheric Orbital Rotations Figure 13.06 - Atomic Subdivision Force-Atomic Formation of Atomic Clusters Inert Gas Interaction of Intense Laser Pulses with Atomic Clusters - Measurements of Ion Emission Simulations and Applications TD69.pdf InterAtomic Laser Cluster Interactions Law of Atomic Dissociation Law of Atomic Pitch Law of Oscillating Atomic Substances Law of Pitch of Atomic Oscillation Law of Variation of Atomic Oscillation by Electricity Law of Variation of Atomic Oscillation by Sono-thermism Law of Variation of Atomic Oscillation by Temperature Law of Variation of Atomic Pitch by Electricity and Magnetism Law of Variation of Atomic Pitch by Rad-energy Law of Variation of Atomic Pitch by Temperature Law of Variation of Pitch of Atomic Oscillation by Pressure Models of Laser Cluster Interactions monatomic Nanoplasma Plasma Plasma holes Quasi-neutrality Quasi-neutrality and Debye length Specific Heat Violation of quasi-neutrality