Laser ionization and charge state distribution above the saturation level

An unavoidable property of studies performed in focused laser light is the presence of a broad range of peak intensities across the focal region. Experimentally, this results in the acquisition

of a volume-integrated product yield S(I0)

0 0 0 0 ( , ) ( ) ~ ( ) I dV I I S I P I dI dI

∫

V(I,I0) : Volume where I> I0

The probability P(I) that should be investigated is therefore different from the measured yield

S(I0) due to the volumetric weighting. Even though the focal geometry might be described analytically, the unambiguous deconvolution of the measured yield according to the above formula is prevented by the lack of precise knowledge about the ionization process. Since for

intensities above the assumed saturation intensity (for which P(I)→1), the measured yield

becomes proportional to I3/2, the decrease of P(I) for higher intensities is camouflaged in the

acquired signal. This behavior is widely studied in experiments dealing with the generation of highly charged ions in intense laser foci [84, 85] and several efforts where attempted to con- fine the detection volume at least along on dimension like intensity selective detection (ISS)

[86, 87]. The direct measurement of P(I) requires the confinement of the detection region to a

Fig. 4.12: Intensity selective detection of ions in a focused laser beam. The upper panel shows the occurrence of Ar+_{, Ar}++ _{and Ar}3+ _{across the focus of 1,8 µJ, 48 fs laser beam along with the sum over all generated ions. It}

is clearly visible, how the higher charged states are generated in a more and more narrow area around the beam-axis. The lower panel shows the higher charged states (Ar4+ _{- Ar}6+_{) again along with the sum over all}

ions. Up to Ar4+_{, the observed ion yield drops around the beam center, i.e. for high intensities. This clearly}

indicates saturation of the process and constitutes a direct measurement of intensity dependant ionization probability. The survival of lower charge states in the beam center where Ar6+ _{is generated is a challenging}

observation. The occurrence of lower charge states in the focus can not be attributed to beam inhomogeneities and pointing instabilities as witnessed by in-depth studies of the laser focus and the beam-pointing-stability with optical methods.

The measurements presented here rely on the reflectron mass spectrometer presented in chap- ter 3.3.2 and make use of its capability to trace back the origin of ions along the spectrometer axis as encoded in their arrival time on the detector. To confine the detection volume in the two dimensions transverse to the laser beam, the spectrometer was equipped with a 10 µm wide entrance aperture. In total, the detection region was constricted to a cylindrical volume of 10 µm diameter and < 5 µm height. A comparison of the measured traces with a simple model yielded a half-width of the focused beam of 14 µm, detailed optical measurements of the laser focus have not yet resulted in a conclusive number. It should be noted, that the satu- ration of the lower charge states sets in already at distances distinctively larger than the given half-width.

Fig. 4.13: Ion-knife-edge. The upper panel shows data acquired by scanning the position of the detection volume across the beam. The charged states set in according to the extent of their respective generation volume that is large for low-charged states. The kink in the traces of Ar+ _{- Ar}3+ _{is indicative for the depletion of these states in}

In addition, the focus appears in the optical imaging not to be a perfect Gauss-mode; a com- plex intensity rise in the slopes of the laser focus on the other hand dramatically influences the occurrence of the different charged states. In contrary, the measured yields give a handsome tool to observe the extent of the focus and its structure with µm resolution. This fact suggests the application of the described technique to analyze focal intensity distributions. The meas- urements confirm the known rise of the signal with increasing intensity, but furthermore allow investigating the observed drop of the signal if the intensity becomes larger then the saturation intensity.

Across the confined, µm-sized detection volume, the variation of the local peak intensity is

tolerable enabling direct measurements of P(I) for the first time. In Fig. 4.12, the detected

yields across the laser focus is shown for Argon ions generated by a focused laser beam with 1,8 µJ pulse energy at a duration of 48 fs. The repetition rate is 1 kHz. The focusing is

achieved by a achromatic lens with f=15 cm. The measurement was performed at a pressure

of 3 x 10-7 mbar and with a peak intensity on-axis of 5 x 1015 W/cm². The detection volume is

moved by scanning the voltage settings of the ion-reflector in the spectrometer and thus scan- ning the generation volume across the laser beam. From the voltages applied to the R-TOF spectrometer (cp. Fig. 3. 12) the ion-flight-time dispersion-relation can be extracted and thus the actual displacement of the detection volume. The axis in both Fig. 4.12 and 4.13 are given in µm and highlight the spatial resolution the technique offers, exceeding by far any method to investigate intensity distributions in the focus that is based on optical imaging. In addition, the method is applicable to the full beam without any need for attenuation as optical methods in general are.

Fig. 4.13 shows the result of a connatural idea: The detection volume in this case is an elon- gated cylinder perpendicular to the laser beam. This idea, similar to knife-edge methods that are employed in optics, is put into practice by stepwise moving the on one side sharply bor- dered detection region (i.e. the energy filter acceptance range of the R-TOF) in the laser focus. The charge states appear subsequently as the beam-axis is approached according to the con- centric alignment of their generation volumes. The lower panel of the figure shows how the structure of the generation volumes can be imagined. By approaching the laser focus from the

side, first Ar+ ions are detected since their formation requires the least intensity. By further

moving the detection range to the beam axis, the cloud in which the intensity is high enough to generate doubly ionized Argon is adding contributions to the signal.

As a consequence of the small confinement of the area from which ions are collected, the measurements presented here, in principle, are in the position to clarify quantitatively how the depletion of low charged states in the most intense part of the laser focus takes place. To this end, space charge effects have to be efficiently excluded, what, according to the latest find-

ings, is only ensured for pressures below ~ 5 x 10-7 mbar [88]. The data presented in Fig. 4.14

are taken at a pressure of 1 x 10-6 mbar and show a charge state distribution that becomes

broader as the overall charge is increasing (at high intensities many charge states are present). However, the charge-state distribution is necessarily very susceptible to space charge effects.

Fig. 4.14: Charge state distributions inside the laser focus. By shifting the detection volume (here 60 x 20 x 10 µm) along the beam axis through the focus, effectively the constant intensity inside this volume is changed. The different z-positions correspond to different intensities, position 11 relates to the highest intensity (i.e. the geo- metrical focus). Obviously, even for the highest intensities, lower charged states survive suggesting the presence of re-neutralization processes (e.g. High-harmonic-generation, recollision, plasma effects).

In the future, detailed studies on this have to be performed with a low pressure ensuring the absence of space-charge effects. So far, measurements at very low pressures have already proven that a complete depletion of ions in a specific area is detectable based on the presented technique. For Oxygen, a diatomic molecule that breaks apart before being ionized, no recol- lision channels like for Argon atoms are possible (i.e. re-neutralization is prohibited). The first

measurements focused on this idea showed an entirely vanishing O+ signal in a volume that