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Revealing of hydrodynamic and electrostatic factors in the center-of-mass velocity of an expanding plasma generated by pulsed laser ablation

Published online by Cambridge University Press:  15 March 2011

J. Krása ,
A. Lorusso ,
V. Nassisi ,
L. Velardi  and
A. Velyhan
J. Krása*
Affiliation:
Institute of Physics, ASCR, Prague, Czech Republic
A. Lorusso
Affiliation:
Department of Physics of Lecce, Laboratorio di Elettronica Applicata e Strumentazione, INFN of Lecce, Lecce, Italy
V. Nassisi
Affiliation:
Department of Physics of Lecce, Laboratorio di Elettronica Applicata e Strumentazione, INFN of Lecce, Lecce, Italy
L. Velardi
Affiliation:
Department of Physics of Lecce, Laboratorio di Elettronica Applicata e Strumentazione, INFN of Lecce, Lecce, Italy
A. Velyhan
Affiliation:
Institute of Physics, ASCR, Prague, Czech Republic
*
Address correspondence and reprint requests to: J. Krása, Institute of Physics, ASCR, Na Slovance 2, 18 221 Prague 8, Czech Republic. E-mail: krasa@fzu.cz
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Abstract

Time-of-flight spectra of C, Fe, and Si ions produced with the use of a KrF excimer laser have been analyzed. Ion currents were collected by Faraday cups and their responses were analyzed using a detector signal function. This function was derived from shifted Maxwell-Boltzmann velocity distribution, in order to uncover the contribution of partial currents of all the ionized species constituting the expanding plasma plume. The deconvolution method allowed to estimate parameters of the plasma, such as the ion temperature and the center-of-mass velocities of expanding ionized species. Furthermore, the linear charge-state dependence of the center-of-mass velocity has revealed the contribution of hydrodynamic and electrostatic forces to the expansion velocity of the plasma. The nearly isotropic distribution of the center-of-mass velocity indicates that the shape of the plasma plume is determined mainly by the angular distribution of the ionization degree of ions.

Keywords

Angular distribution of ionsFaraday cup signal functionPartial ion currents
Type
Research Article
Information
Laser and Particle Beams , Volume 29 , Issue 1 , March 2011 , pp. 113 - 119
Copyright
Copyright © Cambridge University Press 2011

1. INTRODUCTION

The shape of time-resolved ion collector signals induced by ions from laser-produced plasma reflects changes in the velocity distribution of ions during their expansion into the vacuum. The initial phase of plasma expansion is formed by the evolution of the hierarchy of processes occurring during and after the interaction of the laser pulse with the matter — by a pressure gradient, various electrical driving forces, and gradients of potentials, as e.g., target normal sheath acceleration, skin-layer ponderomotive acceleration, double-layer effect in the expanding plasma (Tajima & Dawson, Reference Tajima and Dawson1979; Gitomer et al., Reference Gitomer, Jones, Begay, Ehler, Kepphart and Kristal1986; Haseroth & Hora, Reference Haseroth and Hora1996; Badziak et al., Reference Badziak, Kozlov, Makowski, Parys, Ryc, Wolowski, Woryna and Vankov1999; Wilks et al., Reference Wilks, Langdon, Cowan, Roth, Singh, Hatchett, Key, Pennington, Mackinnon and Snavely2001; Torrisi et al., Reference Torrisi, Gammino and Andò2002; Hora Reference Hora2007; Láska et al., Reference Láska, Krása, Velyhan, Jungwirth, Krouský, Margarone, Pfeifer, Rohlena., Ryć., Skála., Torrisi. and Ullschmied2009; Liu et al., Reference Liu, Xie, Huang, Liu and Yu2009). Currently, the investigation of the early formation of plasma jets has become an interesting object for theoretical and experimental investigation for ion acceleration (Kasperczuk et al., Reference Kasperczuk, Pisarczyk, Kálal, Martínková, Ullschmied, Krouský, Mašek, Pfeifer, Rohlena, Skála and Pisarczyk2008, Reference Kasperczuk, Pisarczyk, Demchenko, Gus'kov, Kálal, Ullschmied, Krouský, Mašek, Pfeifer, Rohlena, Skála and Pisarczyk2009; Andreev et al., Reference Andreev, Platonov and Kawata2009; Bin et al., Reference Bin, Lei, Yang, Huang, Yu, Yu and Tanaka2009; Steinke et al., Reference Steinke, Henig, Schnürer, Sokollik, Nickles, Jung, Kiefer, Horlein, Schreiber, Tajima, Yan, Hegelich, Meyer-Ter-Vehn, Sandner and Habs2010). For the analysis and interpretation of experimental data, a real complex of studies is needed. Nevertheless, a decisive criterion for the interpretation of the experimental data is the distance of the probe from the target surface. For example, if the optical emission spectroscopy is applied for measuring the temporal evolution of plasma parameters at a fixed distance of a few millimeters to centimeters, a theoretical model taking into account a hierarchy of processes as well as a non-Maxwell velocity distribution should be a base for the data interpretation (Capitelli et al., Reference Capitelli, Casavola, Colonna and De Giacomo2004). If the probe is positioned outside the recombination zone (L > L CR, where L CR is the critical distance), the temperature is established, ion charge-states are frozen and ions freely drift into the vacuum. The determination of the critical distance is based on the analysis of ion currents, j(t) (i.e., time-of-flight (TOF) spectra), and of the total charge, Q, carried by ions using expressions t L1 = (L 1/L 2) t L2; j L1 = (L 1/L 2)3j L2 and Q L1 = (L 1/L 2)2Q L2, which allow to compare TOF spectra observed at different distances L 1 and L 2. Far from the target, i.e., for L > L CR, both the ion current and the total charge decrease with increasing L as j(t) ∝ L −3 and Q ∝ L −2, respectively. This analysis was demonstrated experimentally for Cu plasma produced with the use of 308-nm excimer laser (Lorusso et al., Reference Lorusso, Krása, Rohlena, Nassisi, Belloni and Doria2005). Since it was experimentally proven that recombination and collisional excitation processes are not important in the last zone of expansion, one can suppose that the Maxwell-Boltzmann shifted distribution of ions well characterizes the motion of ions far from the target (Lorusso et al., Reference Lorusso, Belloni, Doria, Nassisi, Krása and Rohlena2006).

The aim of our work is to analyze TOF spectra of ions, which is based on an ion collector signal function derived from a shifted Maxwell-Boltzman velocity distribution function. The signal function allows the uncovering of the partial ion currents from the ion collector signal and the distinguishing of the components of the center-of-mass (CM) velocity induced by hydrodynamic and electrostatic forces. Thermal ions were generated with the use of a KrF laser delivering the intensity of about 108 W/cm2 onto a target.

2. SIGNAL FUNCTION OF ION COLLECTOR

The diagnostics of expanding laser-produced plasma is based on the analysis of TOF spectra. The expression for the detector's signal was originally deduced for expanding neutral species into the vacuum considering an ablated flux $d\vec v \times v_x dN$ of particles characterized by a Maxwell-Boltzmann velocity distribution function $f_{MB} \, \lpar \vec v\,\rpar $ (Kelly & Dreyfus, Reference Kelly and Dreyfus1988; Miotello & Kelly, Reference Miotello and Kelly1999). This procedure was applied to derive a signal function equivalent to the current density of ions having a velocity distribution $f\, \lpar \vec v\,\rpar $:

(1)
\,j_{IC} \lpar t\rpar \propto v_x f\lpar \vec v\,\rpar \, d\vec v\, \propto {{L^2 } \over {t^5 }}\, f\left({{L \over t}} \right)\comma \; \eqno\lpar 1\rpar

where it is assumed that the ion collector is located at a distance x = L from the target and the y, z directions are considered parallel to the target surface (Krása et al., Reference Krása, Jungwirth, Krouský, Láska, Rohlena, Pfeifer, Ullschmied and Velyhan2007, Reference Krása, Velyhan, Jungwirth, Krouský, Láska, Rohlena, Pfeifer and Ullschmied2009). Furthermore, v x = L/t, |dv x| = Ldt/t 2, dv y = dy/t, dv z = dz/t and the detector size is dS = dzdy. Thus, $d\vec v=\lpar L/t^4 \rpar \, dSdt$. The influence of the center-of-mass (CM) motion of the plasma plume on the movement of ions can be expressed by a shifted velocity distribution $f\lpar \vec v - \vec u_{CM} \rpar $, where $\vec u_{CM} $ is the CM velocity. Finally, the ion current is the sum of partial currents j i,q of all ionized species, i, with a charge-state, q. Then the total current density can be expressed as:

(2)
\,j_{IC} \lpar L\comma \; t\rpar =\sum {\,j_{i\comma q} \lpar L\comma \; t\rpar =L^2 t^{ - 5} \sum {\,j_{i\comma q}^0 \, f_{i\comma q} \left({{L \over t} - u_{i\comma q} } \right)} }\comma \; \eqno\lpar 2\rpar

where $j_{i\comma q}^{\,0} $ is the term for calibration of the peak amplitude of partial currents.

The presence of hydrodynamic and electrostatic forces in the expanding plasma can be established by analysis of values of all velocities u i,q obtained by fitting Eq. (2) to the TOF spectrum as both the forces contribute to u CM by particular components (Torrisi et al., Reference Torrisi, Gammino and Andò2002):

(3)
u_{CM} = u_{HD} + u_{EL}\comma \; \eqno\lpar 3\rpar

where u HD is the velocity component corresponding to the effect to hydrodynamic forces, while u EL is the velocity contribution deriving from the presence of the ambipolar electric field. Since the term u HD is a part of the total CM velocity, u HD is not related to the temperature of the ablated neutral gas (Kelly & Dreyfus, Reference Kelly and Dreyfus1988; Miotello & Kelly, Reference Miotello and Kelly1999).

The u CM velocities as well as the kinetic energy of ionized species are quantities reflecting the acceleration of ions by fast electrons. For thermal ions generated by laser intensities lower than a threshold value of about 1 × 1014W cm−2 (Gitomer et al., Reference Gitomer, Jones, Begay, Ehler, Kepphart and Kristal1986; Láska et al., Reference Láska, Badziak, Boody, Gammino, Jungwirth, Krása, Krouský, Parys, Pfeifer, Rohlena, Ryć, Skála, Torrisi, Ullschmied and Wołowski2007a, Reference Láska, Badziak, Gammino, Jungwirth, Kasperczuk, Krása, Krouský, Kubeš, Parys, Pfeifer, Pisarczyk, Rohlena, Rosiński, Ryć, Skála, Torrisi, Ullschmied, Velyhan and Wołowski2007b) the charge-state dependence of u CM was established experimentally (Krása et al., Reference Krása, Jungwirth, Krouský, Láska, Rohlena, Pfeifer, Ullschmied and Velyhan2007) as:

(4)
u_{CM}\lpar q\rpar = u_{0} + u_{q} q. \eqno\lpar 4\rpar

This linear charge-state dependence of u CM reflects the dominant effect of collisions on slowing down the acceleration of ions because the relative velocity Δu  ≡  u 2 – u 1 of the species 1 and 2 in the collisional regime is:

(5)
\Delta u=\lpar q_2 - q_1 \rpar {{eE} \over {m {\rm \omega} }}\comma \; \eqno\lpar 5\rpar

where E is the ambipolar electric field responsible for the ion acceleration and ω is the collision frequency between the species of the kinds 1 and 2, which decreases the contribution of the acceleration, as derived by Forslund (Reference Forslund1980). Finally, comparing Eq. (3) and Eq. (4) the term u 0 may be interpreted as the term u HD. Than the signal function (2) takes the form:

(6)
\eqalign{\,j_{IC} \lpar L\comma \; t\rpar & =\sum j_{i\comma q} \lpar L\comma \; t\rpar = L^2 t^{ - 5} \sum j_{i\comma q}^{\,0} \exp \cr &\quad \times \left\{- {m_i \over 2kT}\lpar L/t - u_{HD} - u_i \, q\rpar ^2 \right\}\comma \; } \eqno\lpar 6\rpar

where m i is the atomic mass of the i th ion species, k is the Boltzmann constant, T is the equivalent ion temperature, and u i q represents u EL in (3).

In contrast to the thermal ions, the fast ions exhibit different charge-state dependence because no “friction” forces balance the effect of the electric field as they do in the case of thermal ions (Krása et al., Reference Krása, Velyhan, Jungwirth, Krouský, Láska, Rohlena, Pfeifer and Ullschmied2009). The analysis of TOF spectra of fast ions generated by intensity I > 1 × 1014 W cm−2 shows that the u CM (q) dependence can be expressed as:

(7)
u_{CM} \lpar q\rpar = u_{0} + u_{q} \surd q. \eqno\lpar 7\rpar

Both the dependencies (4) and (7) indicate, respectively, the limits for a strong or insignificant influence of ion-ion collisions and recombination on acceleration of ions by fast electrons.

3. EXPERIMENTAL SETUP

C, Fe, and Si plasmas were generated with the use of a KrF excimer laser (Lambda Physics, Compex) operated at 248-nm wavelength. Laser pulses of 23 ns in duration were tilted by 70° with respect to the target normal. The focus spot area was about 1 × 10−3cm2 and the focused fluence ranged up to 120 J/cm2. A set of Faraday cups (FC) was placed in front of the target at a distance ranging from 9 cm to 24 cm as shown in Figure 1. The operating circuit of FC was described by Doria et al. (Reference Doria, Lorusso, Belloni and Nassisi2004).

Fig. 1. Scheme of the experimental apparatus equipped with Faraday cups array placed in front to the target. A beam splitter (BS) is utilized in order to measure the laser energy by a joule meter.

The cups are 9 mm in diameter and 11.5 mm in distant from each other. Such configuration is able to diagnose the radial profile of the expanding plasma from −30° up to +30° with respect to the target normal direction for the 9-cm distance of the FC to the target. All the cups are inserted in the grounded flange, insulated among them and coaxially connected to a BNC (Bayonet Neill-Concelman) connector of 50Ω, which is able to derive the ion current signal to the oscilloscope.

4. RESULTS AND DISCUSSION

4.1. Ion Emission along Target Normal

Typical pulse-to-pulse fluctuations of time-resolved currents (TOF spectra) are shown in Figure 2a for ions emitted from a C plasma generated with a laser fluence of 12.5 J/cm2. The TOF signals were observed in the direction of the target normal (ϕ = 0°). Partial currents of Cq+ ions uncovered by deconvolution of a TOF spectrum using Eq. (3) are shown as an example in Figure 2b. The best fit was obtained when besides the partial currents of Cq+ (1 ≤ q ≤ 4) ions also the contribution of a particular group of slow C+ ions was included into the tail of the TOF spectrum. We note that the presence of this particular group of slow singly-charged ions is a general characteristic of all IC signals induced by impacting ions generated by sub-joule laser beams. Fitted values of u CM (q) velocity are plotted in Fugure 3.

Fig. 2. (Color online) Pulse-to-pulse fluctuations of TOF spectra of C ions generated with 12.5 J/cm2 fluence focused onto a graphite target (a). Deconvolution of TOF spectrum using the Faraday cup signal function (6); the uncovered peaks are ascribed to partial currents of Cq+ (1 ≤ q ≤ 4) ions (b). The distance of the Faraday cup from the target was 24 cm.

Fig. 3. (Color online) Charge-state dependence of fitted values of u CM velocity of Cq+ (1 ≤ q ≤ 4) ions composing the hidden partial currents (see Fig. 1).

The pulse-to-pulse fluctuations of the ion emission result in variations not only of the ion current and the total charge carried by them but also of the ion temperature and corresponding CM velocities, as Table 1 summarizes. The most affected characteristics of ions by pulse-to-pulse fluctuations are the ion temperature and CM velocity following the fluctuations of the width of TOF spectrum, which corresponds to the total charge carried by ions. The mean values of the fitted parameters in Eq. (6) are: T = 2.6 eV, u HD = 6.8 × 103 m/s, and u q = 8.1 × 103 m/s. The linear regression of the obtained values of u CM clearly shows that the linear function (4) can be used as a suitable model in which the term u 0 can be interpreted as a part of u HD corresponding to the hydrodynamic forces, while the term u qq reflects the electric forces, which are responsible of the acceleration of Cq+ ions.

Table 1. Standard deviations of parameters of ion-currents due to pulse-to-pulse fluctuations

4.2. Energy Dependence of CM Velocity

The dependence of u CM on the deposited laser energy was measured for Fe ions. Figure 4 shows an example of uncovered partial currents of Feq+ (1 ≤ q ≤ 5) ions generated with fluence of 122 J/cm2. It is obvious that the dominant peak is constituted by Fe2+ ions. An entirely insignificant peak at TOF ≅ 7 µs is constituted by Fe5+ ions. Nevertheless, the corresponding value of u CM (5) well matches the linear charge-state dependence plotted in Figure 4b. The dependence of obtained values of u HD and u q velocities on the laser fluence is shown in Figure 5. The values of u HD are about six times lower than the u q values, and u HD exhibits weaker increase with the increasing laser fluence than u q does.

Fig. 4. (Color online) Partial currents of ion Feq+ uncovered from TOF spectrum of ions produced with KrF laser beam delivering the fluence of 122 J/cm2 onto Fe target; L = 44 cm (a). Charge-state dependence of u CM for Feq+ (1 ≤ q ≤ 5) ions (b).

Fig. 5. (Color online) Dependence of u HD and u q of Feq+ ions on laser fluence.

The deconvolution of TOF current signals also allowed the determination of the ion temperature as a function of the laser fluence, as Figure 6 shows. Evidently, the temperature increases much more than u q (see Fig. 5). Similar increase is exhibited by the peak current or by the total charge carried by ions.

Fig. 6. Dependence of ion temperature of Feq+ ions on laser fluence.

4.3. Angular Distribution of Ion Emission

The angular distributions of ion peak current or the charge of ions is expressed by the following function:

(8)
S\left({\rm \phi} \right)=a\cos \left({{\rm \phi} - {\rm \phi} _0 } \right)- b\cos ^n \left({{\rm \phi} - {\rm \phi} _0 } \right)\comma \; \eqno\lpar 8\rpar

where S(ϕ) is the density of particles in the zenithal direction (ϕ) and a, b, and ϕ0 are fit parameters (Thum-Jäger & Rohr, Reference Thum-Jäger and Rohr1999; Láska et al., Reference Láska, Jungwirth, Krása, Krouský, Pfeifer, Rohlena, Velyhan, Ullschmied, Gammino, Torrisi, Badziak, Parys, Rosiński., Ryć and &Wołowski2008). The first term of Eq. (6) concerns the contribution of multiply charged particles with a rapid diminishing of a parameter during the ions' charge-state increasing: if q  ≥  2, then the angular distribution S(ϕ) can be well described by the cos n alone (Thum-Jäger & Rohr, Reference Thum-Jäger and Rohr1999).

An example of angular distribution of the peak current (maximum value of the time-resolved current) of Si ions generated by 8-J/cm2 laser fluence is shown in Figure 7. It is evident that the direction of the ions emission slightly turns toward the direction of the incoming laser beam as observed in other experiments (Thum-Jäger & Rohr, Reference Thum-Jäger and Rohr1999; Láska et al., Reference Láska, Jungwirth, Krása, Krouský, Pfeifer, Rohlena, Velyhan, Ullschmied, Gammino, Torrisi, Badziak, Parys, Rosiński., Ryć and &Wołowski2008). We should note that the declination from the target normal direction is not a general phenomenon arising from the laser beam interaction with the expanding plasma. In our measurements, the angular distribution was observed only for the range of angles from 30° to −30° with respect to the target normal due to constraints given by the dimensions of the interaction chamber (Fig. 1).

Fig. 7. (Color online) Angular distribution of peak current of Si ions generated with a laser fluence of 8 J/cm2.

The angular distribution of the ion current is formed by angular distributions of ion velocity and of charge curried by ions, as Figure 8 shows. Values of velocities u PEAK, u HD, and u q as well as total charge Z q of Siq+ (1 ≤ q ≤ 4) ions were obtained by uncovering the partial ion currents from TOF spectra (Figs. 2 and 4). Figure 8a shows that the angular distribution of the charge of ions is similar in shape to the ion current distribution (Fig. 7) but the currents of Si3+ and Si4+ ions are not detectable at ϕ = 28°, as Figure 9 demonstrates. Conversely, velocities u PEAK, u HD, and u q exhibit a weak angular dependence, as Figure 8b shows. The value of the ratio of the lowest velocity to the highest one u PEAK(28°)/u PEAK(343°)  =  0.67 is about four times higher than the value of the corresponding ratio of peak currents j PEAK(28°)/j PEAK(343°)  =  0.16. Strong variations in angular distribution of ion currents are mainly caused by the narrow angular distribution of the charge curried by ions having the highest charge-states; the width of the stream of ions, in fact, decreases with increasing ion charge-state (Thum-Jäger & Rohr, Reference Thum-Jäger and Rohr1999). Figure 9 demonstrates this effect for TOF spectra observed at ϕ = 343° and 28°. Evidently, two peaks of partial ion currents are absent in the TOF spectrum observed at ϕ = 28° for TOF ranging from about 2 µs to about 4 µs. A small difference between the summa of uncovered Si2+ and Si+ peaks for ϕ = 343° and the TOF spectrum observed at 28° elucidates small variations in both the angular distributions of u HD and u q velocities.

Fig. 8. (Color online) Angular distribution of (a) total charge Z curried by Siq+ (1 ≤ q ≤ 4) ions and (b) peak velocity, u PEAK, corresponding to peak current shown in Figure 6 and of u HD and u q obtained as explained in Section 4.1.

Fig. 9. (Color online) TOF spectra of Si ions observed at angles of 343° and 28° with respect to the target normal; L FC = 9 cm. Uncovered partial ion currents are labelled as Si+ to Si4+ and their summa “FIT” is the fit by Eq. (5) to the observed TOF spectrum observed at ϕ = 343°.

Another example of significant variations in the angular distribution of the partial currents emitted from a C plasma is shown in Figure 10. While along the target normal the partial currents of C+ to C4+ ions are emitted, the number of charge-states is reduced from 4 to 3 as well as the total number of C ions significantly decreases in the direction ϕ = 11°. The small decrease of peak velocities of Cq+ ions correlates with the small decrease of velocities of Siq+ ions, as Figure 8b confirms. Considering other observed angular distributions (Thum-Jäger & Rohr, Reference Thum-Jäger and Rohr1999; Láska et al., Reference Láska, Jungwirth, Krása, Krouský, Pfeifer, Rohlena, Velyhan, Ullschmied, Gammino, Torrisi, Badziak, Parys, Rosiński., Ryć and &Wołowski2008) one can compile that the angular distribution of the number of ionized species N q(ϕ) significantly affects the angular distribution of ion emission driven by laser pulses.

Fig. 10. (Color online) Time-of-flight spectra of C ions observed at angles of 0° and 11° with respect to the target normal; L FC = 24 cm, F = 12.5 J/cm2. The corresponding groups of uncovered partial ion currents are labelled as C+ to C4+ and C+ to C3+.

This phenomenon forms a characteristic behavior of expanding laser-produced ion beams. The jet-like structure of an ion current observed is shaped by the jet structure mainly of partial currents of ions with the highest charge-states. Since the CM velocity of all the ionized species constituting the plasma plume exhibit insignificant angular distribution, the shape of the plasma plume corresponds to the angular distribution of the charge states. The width of the expanding plasma is inversely proportional to the highest charge-state generated inside the plasma, as Figures 9 and 10 demonstrate and an empirical law for the atomic mass dependence of the exponent n ≈ A 3/4 in Eq. (8) specifies (Thum-Jäger & Rohr, Reference Thum-Jäger and Rohr1999).

As for the peak velocity u PEAK, which belongs to the maximum of the total current j(t), its value merely reflects the velocity of ions having the highest partial current j q(t) (Figs. 9 and 10). Thus, u PEAK corresponds to the velocity u CM = u q q of ion groups reaching the highest value of the current at the end of the recombination zone. It is useful to note that the peak velocity of the expanding plasma does not correlate with a mean velocity <u >  corresponding to the mean charge-state <q> which was determined by the uncovering the partial ion currents to be <q> = 2.3. The value of <u >  is lower than u peak about 0.75 times as can be estimated from Figure 9.

5. CONCLUSION

The uncovering of partial currents of ionized species constituting the expanding plasma generated with the use of pulsed lasers allows the determination of the number of ions contained in the corresponding partial currents, the CM velocities, and the temperature. It was shown that the linear regression of the charge-state dependence of the CM velocity of thermal ions could be interpreted in terms of hydrodynamic and electrostatic forces (u CM = u HD + u q q) balanced by collisions among ions, which result in the creation of a jet of plasma. The term u HD of the CM velocity was ascribed to the effect of the hydrodynamic forces. The other term u q related to the charge-state q is proportional to the ratio of the ambipolar field and the collisional frequency. The values of u HD and u q are comparable. In addition, the uncovering of partial ion currents observed in various directions also shows that the angular distribution of the expanding plasma is determined primary by the angular distribution of the ionization degree of the plasma plume. The CM velocity exhibits a slight angular distribution.

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Figure 0

Fig. 1. Scheme of the experimental apparatus equipped with Faraday cups array placed in front to the target. A beam splitter (BS) is utilized in order to measure the laser energy by a joule meter.

Figure 1

Fig. 2. (Color online) Pulse-to-pulse fluctuations of TOF spectra of C ions generated with 12.5 J/cm2 fluence focused onto a graphite target (a). Deconvolution of TOF spectrum using the Faraday cup signal function (6); the uncovered peaks are ascribed to partial currents of Cq+ (1 ≤ q ≤ 4) ions (b). The distance of the Faraday cup from the target was 24 cm.

Figure 2

Fig. 3. (Color online) Charge-state dependence of fitted values of uCM velocity of Cq+ (1 ≤ q ≤ 4) ions composing the hidden partial currents (see Fig. 1).

Figure 3

Table 1. Standard deviations of parameters of ion-currents due to pulse-to-pulse fluctuations

Figure 4

Fig. 4. (Color online) Partial currents of ion Feq+ uncovered from TOF spectrum of ions produced with KrF laser beam delivering the fluence of 122 J/cm2 onto Fe target; L = 44 cm (a). Charge-state dependence of uCM for Feq+ (1 ≤ q ≤ 5) ions (b).

Figure 5

Fig. 5. (Color online) Dependence of uHD and uq of Feq+ ions on laser fluence.

Figure 6

Fig. 6. Dependence of ion temperature of Feq+ ions on laser fluence.

Figure 7

Fig. 7. (Color online) Angular distribution of peak current of Si ions generated with a laser fluence of 8 J/cm2.

Figure 8

Fig. 8. (Color online) Angular distribution of (a) total charge Z curried by Siq+ (1 ≤ q ≤ 4) ions and (b) peak velocity, uPEAK, corresponding to peak current shown in Figure 6 and of uHD and uq obtained as explained in Section 4.1.

Figure 9

Fig. 9. (Color online) TOF spectra of Si ions observed at angles of 343° and 28° with respect to the target normal; LFC = 9 cm. Uncovered partial ion currents are labelled as Si+ to Si4+ and their summa “FIT” is the fit by Eq. (5) to the observed TOF spectrum observed at ϕ = 343°.

Figure 10

Fig. 10. (Color online) Time-of-flight spectra of C ions observed at angles of 0° and 11° with respect to the target normal; LFC = 24 cm, F = 12.5 J/cm2. The corresponding groups of uncovered partial ion currents are labelled as C+ to C4+ and C+ to C3+.