Clustered gas jets are shown to be an efficient means for plasma waveguide generation, for both femtosecond and picosecond generation pulses. These waveguides enable significantly lower on-axis plasma density (less than 1018 cm−3) than in conventional hydrodynamic plasma waveguides generated in unclustered gases. Using femtosecond pump pulses, self-guided propagation and strong absorption (more than 70%) are used to produce long centimetre scale channels in an argon cluster jet, and a subsequent intense pulse is coupled into the guide with 50% efficiency and guided at above 1017 W cm−2 intensity over 40 Rayleigh lengths. We also demonstrate efficient generation of waveguides using 100 ps axicon-generated Bessel-beam pump pulses. Despite the expected sub-picosecond cluster disassembly time, we observe long pulse absorption efficiencies up to a maximum of 35%. Simulations show that in the far leading edge of the long laser pulse, the volume of heated clusters evolves to a locally uniform and cool plasma already near ionization saturation, which is then efficiently heated by the remainder of the pulse.
Many of the exciting applications of intense laser fields demand large product of intensity and interaction length in plasma. These applications include laser-driven wakefield accelerators (Tajima & Dawson 1979; Esarey et al. 1996), X-ray lasers (Milchberg et al. 1995a; Korobkin 1996; Butler et al. 2003) and coherent radiation generation (Milchberg et al. 1995b), especially short-wavelength generation. For a Gaussian beam of given energy ϵlaser, pulse duration τ and wavelength λ, diffraction limits the product of intensity and interaction length to a constant ∼ϵlaser/λτ. Over the last 10 years or so, several schemes for guided propagation have been demonstrated to counter this limitation, wherein the refractive index profile of the medium balances the diffractive spreading and the intense pulse is guided at a constant small radius over many Rayleigh ranges. Apart from the length of the waveguide, the ability to control the guided mode structure and waveguide optical properties are critical for some of these applications. Finally, the waveguide lifetime should be sufficiently long to make employing it practical for applications. This means that waveguides produced synchronously with injected pulses should be reproducible at a high repetition rate for many shots, with a very high duty cycle. Steady state waveguides should survive for many laser shots. For a single guiding scheme to meet all these requirements is very challenging.
The guiding methods developed to date can be divided into three classes: self-focused propagation, hollow fibre structures and preformed plasma waveguides. The first method relies on relativistic self-focusing and ponderomotive charge displacement by the laser pulse, whereby the on-axis plasma refractive index increases by a relativistic enhancement of electron inertia near beam centre or by ponderomotive charge expulsion. Under a wide range of conditions, however, such effects are subject to instabilities, diffraction and ionization-induced defocusing (Sprangle et al. 1992; Antonsen & Mora 1992; Monot et al. 1995; Coverdale et al. 1995; Chessa et al. 1999). In practice, these effects have limited the self-guided propagation lengths to less than approximately 2 mm. Moreover, merely to guide the beam, relativistic intensities of approximately 1018 W cm−2 are needed—even in experiments where the main goal may be X-ray lasers or harmonic generation, where lower intensities may be preferable.
Hollow core glass fibres have been used in two ways: lowest-order mode (monomode) (Dorchies et al. 1999; Courtois et al. 2000) and multimode guiding (Jackel et al. 1995; Borghesi et al. 1998). For practical applications, the fibres would be first filled with gas. However, unless the gas density is extremely low (less than 1015 atoms cm−3), refraction from self-generated ionization gradients will result in strong laser coupling to the guide wall and eventual guide destruction. In monomode vacuum guiding, the injected pulse is mode matched to the EH11 lowest-order mode of the hollow fibre (Dorchies et al. 1999; Courtois et al. 2000). A linear modal analysis for the hollow fibre (Dorchies et al. 1999) predicts that the ratio of intensity at the guide wall to that at the centre is higher than 10−4 for guides smaller than approximately 100 μm in diameter. Femtosecond material breakdown thresholds of approximately 1012−1013 W cm−2 then imply that maximum monomode guided intensity must be less than 1017 W cm−2. In such guides, high-quality injected modes and exceptionally accurate alignment is needed: misalignment at the fibre entrance will result in breakdown at the front face of the fibre followed by fibre destruction. If an individual mode of the guide is represented by u(k⊥r⊥)×exp(ik∥z), where the waveguide axis is along z, r⊥ is a position vector perpendicular to that axis, u(k⊥r⊥) is the mode transverse spatial dependence and k∥ is the propagation wavenumber, then higher order modes, in larger diameter fibres, have larger values of k⊥/k∥ than monomodes. From a ray optics perspective, k⊥ can be viewed as an effective perpendicular wavenumber, so that multimode guiding implies larger wall-directed fluxes of laser power. This results in the generation of near solid density supercritical wall plasma (in the case of negligible prepulse), with Ne≫Ncr, where Ne is the electron density at the wall and Ncr is the plasma critical density. Here, the plasma generation is responsible for the confinement and total internal reflection guiding of the pulse via (ncore)2>(nwall)2, where ncore∼1 is the refractive index of the low density gas, low density plasma or vacuum in the interior of the guide and (nwall)2=1−Ne/Ncr∼−100 is the square of the refractive index of the solid density plasma. For laser systems with appreciable prepulse, plasma may evolve from the capillary wall in an uncontrolled manner well before the arrival of the pulse main peak, and this plasma may effectively act as the working medium (Kitagawa et al. 2004). However, the plasma generation is usually accompanied by capillary destruction on each shot (Kitagawa et al. 2004).
Preformed subcritical density plasmas can act as waveguides when the electron density increases with radius from the beam propagation axis: the index of refraction is peaked on axis, slowing the centre of the propagating phase front and continuously balancing diffraction. For the highest intensity guiding in a given preformed plasma waveguide, the injected pulse transverse mode must be matched to the lowest-order mode of the waveguide. Approximate relations (Durfee et al. 1995; Clark & Milchberg 2000) for mode confinement (cut-off) and lowest-order mode matching are given by, respectively, ΔNemax≥(2p+m+1)2/πrerm2 and ΔNe(wch)=1/πrewch2, where ΔNemax=Ne(rm)−Ne(0) is the electron density difference between the channel centre and the maximum electron density at the channel wall, and ΔNe(wch)=Ne(wch)−Ne(0), where r=wch is the 1/e2 intensity radius of the lowest-order guided mode. Here, re is the classical electron radius (2.8×10−13 cm), and p≥0 and m≥0 are radial and azimuthal mode indices, respectively. Guiding of a lowest-order mode with spot size w0=wch=10 μm therefore requires ΔNe(wch)∼1018 cm−3. Note that this requirement is independent of wavelength (Milchberg et al. 1995b), which is of significant importance for coherent X-ray generation and propagation in plasma waveguides. The desired on-axis density of a plasma waveguide is determined by the application. For resonant wakefield generation, the optimum laser pulse duration scales as Ne−1/2, with optimum density less than 1018 cm−3 for approximately 100 fs pump pulses (Leemans et al. 1998). Thus, the maximum guide density at its walls should not exceed a few times 1018 cm−3.
Guided propagation of high-intensity pulses was first demonstrated in preformed channels generated by laser heating of gases (Durfee et al. 1995; Clark & Milchberg 2000). High aspect ratio channels up to 3 cm long, generated by radial propagation of a laser-induced hydrodynamic shock, were produced in the axicon (or Bessel beam) line focus breakdown of a gas using a 100 ps laser pulse. Subsequently, femtosecond pulses from a Ti : sapphire laser synchronized with the waveguide-generation laser were guided through these channels at 1017 W cm−2 (Nikitin et al. 1999; Kim et al. 2002). The mode structure of the guided pulse could be tuned by adjusting the gas target parameters or the delay between the waveguide generation pulse and the injected pulse. A variant of the hydrodynamic shock technique has also been developed, in which collisional gas breakdown is promoted by an auxiliary femtosecond pulse which generates the initial free electrons by optical field ionization (OFI) (Volfbeyn et al. 1999). In another similar scheme, gas breakdown is assisted by an electrical discharge (Gaul et al. 2000). Monoenergetic acceleration of electrons has recently been demonstrated in preformed plasma waveguides (Geddes 2004) (and also in unguided configurations (Mangles et al. 2004; Faure et al. 2004)). Non-laser generated waveguides have also been formed in vacuum and gas-prefilled slow capillary discharges (Ehrlich et al. 1996, 1998; Butler et al. 2002), in gas discharges (Lopes et al. 2003) and in Z pinches (Luther et al. 2004). In particular, waveguides generated by slow capillary discharges offer an appealing blend of simplicity, low cost, high lifetime and very high aspect ratio. Moreover, this method, especially in the hydrogen gas prefilled version (Butler et al. 2002), can produce reproducible guides at controllable densities of approximately 1018 cm−3 and somewhat lower. Plasma waveguides generated in the closed geometry of capillaries have been difficult to diagnose except through Stark broadening measurements of ionic lines from end-viewed plasma (Ehrlich et al. 1996), or from axial interferometry of very short discharges (Spence et al. 1999). The recent advent of square cross-section sapphire capillaries allows transverse optical probing (Hooker 2005). The main drawback of discharge capillary plasma waveguides is their wide fundamental mode diameter, which is set by the equilibrium plasma radial pressure balance, where the radial variation of the temperature gradient is determined by plasma heat flow to the capillary wall (Bobrova et al. 2001). As modern multi-terawatt laser systems continue to increase in power, the wide mode diameter may cease to be a concern.
Laser-driven waveguides, when generated with conventional backfill or gas jet targets, have three significant drawbacks. First, efficient collisional breakdown for channel generation requires high gas density N0 due to the early exponential growth of electron density Ne(t)=Ne0 exp(SN0t), where Ne0 is the initial electron density and S is the collisional ionization rate. In practice, this has resulted in typical waveguide central densities higher than 5×1018 cm−3, which may not be optimum for some applications as described previously. The requirement for high gas density imposed by efficient collisional breakdown is not mitigated by auxiliary pre-ionization schemes (Volfbeyn et al. 1999; Gaul et al. 2000), which increase Ne0 but not the exponent. Second, the requirement for adequate ionization and heating for channel formation demands the use of high energy, long-duration pulses from an auxiliary laser. At best, the channel heating efficiency of such pulses is 10–15% under special resonant conditions which apply to Bessel beams (Fan et al. 2000, 2002). Finally, there is significant taper at the waveguide ends, which results in inefficient coupling of injected pulses. This is due to the fall-off of gas density at the edges of gas jets (Nikitin et al. 1999), where reduced ionization and heating result in slower radial expansion of the guide ends. In the ignitor-heater scheme, the end-injected ignitor pulse (which provides Ne0 to initiate the avalanche) can mitigate this problem somewhat by increasing efficiency of the subsequent heater pulse (Geddes 2004), but the issue of the axial gas density gradient at the jet edge remains.
2. Plasma waveguides generated in clustered gases by femtosecond end-pumping
The use of atomic clusters provides a new scheme for generating plasma waveguides that addresses the issues of density control, absorption efficiency and waveguide end taper. Clusters are van der Waals-bonded assemblies of approximately 102–107 atoms produced by rapid cooling during high-pressure gas flow through a gas jet nozzle into vacuum (Hagena & Obert 1972; Hagena 1987). A clustered gas introduces two novel and important features: efficient absorption of femtosecond pulses (Ditmire et al. 1997; Kim et al. 2003a,b) and their self-guided propagation (Alexeev et al. 2003; Chu et al. 2004). The laser breakdown of a cluster is initiated by OFI, which produces the first generation of free electrons, followed by efficient collisional ionization under local solid density conditions, where the local atomic density N0 is approximately 1000 times greater than in typical gas targets. The heated clusters explode on a sub-picosecond time-scale, eventually expanding and merging to form a locally uniform plasma in approximately 10–100 ps (Milchberg et al. 2001; Kim et al. 2003a). This hot plasma expands radially, leading to the formation of a shockwave and subsequent waveguide structure over a nanosecond time-scale in a manner similar to ordinary gas targets. The clusters radially surrounding the hot plasma of the laser interaction region are preheated by a precursor from radiation and fast electrons (Ditmire et al. 1997), which ionizes and disassembles them in advance of the shockwave arrival. The cluster method provides a route to control waveguide density: since efficient heating is local to a cluster, independent of the cluster density in the gas, cluster size and density can be adjusted to give desired levels of merged plasma density.
A gas of clusters also has unique optical properties due to the dynamics of the laser–cluster interaction. According to a one-dimensional hydrodynamic model (Milchberg et al. 2001), the real part of the polarizability of the cluster is positive during the early parts of cluster evolution after irradiation by an intense femtosecond pulse. This reflects the fact that the heated cluster excludes the laser field when it is above critical density. In a laser beam with intensity peaked on axis, the evolving gas of clusters local to the beam cross-section has a positive and concave-shaped refractive index profile during this phase, which induces self-focusing. As the cluster expands to critical density, the imaginary part of the polarizability increases and reaches its peak. Thus, the process of self-focusing of the pulse is accompanied by its efficient absorption. The predictions of the model for the complex polarizability, self-focusing and frequency shifts have been experimentally confirmed (Kim et al. 2003a, 2005; Alexeev et al. 2003; Chu et al. 2004). The combination of highly efficient absorption with weak self-focusing of femtosecond pulses makes possible the generation of femtosecond end-pumped waveguides that are much longer than the Rayleigh range of the focused pulse.
Figure 1 shows a schematic of the experimental setup. The inset is an interferogram of an approximately 8 mm long plasma waveguide produced by a 25 mJ, 70 fs, λ=800 nm pump pulse in an elongated argon cluster jet. The slight axial taper of the guide is caused by absorption of the pump as it propagates. Owing to guiding of the pump pulse in the clustered gas, these channels are considerably longer than the pump pulse Rayleigh range (200 μm), and are the longest and most uniform hot plasma structures produced to date by laser end pumping. Figure 2a,b shows time-resolved electron density profiles of the resulting waveguide near its centre for high (gas valve temperature and backing pressure 190 K and 27 bar) and low (170 K, 20 bar) gas densities, measured using femtosecond interferometry. Pump pulse absorption was measured to be 85 and 70%, respectively, for the high- and low-density jets. Mean cluster radius was measured to be approximately 6 and 2.5 nm, respectively (the jet was optimized after these measurements, so these values represent lower limits) (Kim et al. 2003b). A central minimum in electron density develops in approximately 1 ns. These results illustrate the ability to control the guide density to low levels of 1018 cm−3. For the minimum density profile shown in figure 2a, the matched spot size of the channel is w0=20 μm. Note that the pump pulses are only 30 mJ, approximately 10 times less energy than required for heating conventional gas targets for plasma waveguide generation (Durfee et al. 1995). Figure 2d shows the electron density profile measured at the entrance of the waveguide. The channel develops into a waveguide over a short distance (approx. 100 μm) along the pump laser propagation direction. This represents a substantial improvement over waveguides generated in conventional gas jets, where 500 μm tapering at the entrance hinders efficient coupling of the injected pulse (Nikitin et al. 1999). Even though the cluster density gradient at the edge of the gas jet can be as large as 500 μm (Nikitin et al. 1999; Kim et al. 2003b), the strong heating of individual clusters ensures an axially uniform rate of radial plasma expansion, and a much-reduced waveguide-entrance taper. Delayed probe pulses were injected into and guided by these channels, and exit modes of the probe were relay imaged to a CCD camera. Figure 2c shows the smallest exit mode of the laser pulse achieved at the delay of 1.3 ns, obtained for a 25 mJ pump and a 40 mJ injected probe. The guided mode is remarkably stable on a shot-to-shot basis, and this image is a 50-shot average. The coupling efficiency and channelled intensity of the guided pulse were determined using such images. The highest transmitted intensity is 3×1017 W cm−2 at 1.3 ns delay, where w0=8 μm and with 50% coupling efficiency. At shorter delays, the energy transmitted is lower, and at longer delays, the mode becomes larger. In order to avoid further ionization by even higher intensity pulses than guided here, it is desirable to form the waveguide in a low-Z medium which can be fully ionized. We have guided 1016 W cm−2 pulses in 3 mm long plasma waveguides generated in weakly clustered hydrogen jets, and we are currently working on improving the clustering efficiency and waveguide length.
3. Plasma waveguides generated in clustered gases by long pulse (100 ps) side-pumping
In this section, we describe the generation of plasma waveguides in clustered gases by axicon-line-focusing long-duration laser pulse into an extended clustered gas jet. Using clustered gas targets and long 100 ps heating pulses, absorption can be increased by as much as a factor of approximately 10 compared to unclustered gases of the same volume average atomic density. The 100 ps pulse appears to be a surprisingly efficient heater of the cluster plasma despite the fact that individual clusters disassemble to below critical density on a time-scale of only a few hundred femtoseconds, and thus might be expected to be strongly absorbing only during that period (Milchberg et al. 2001; Kim et al. 2003a).
An image of a Bessel-beam line focus breakdown in an elongated argon cluster jet is shown in figure 3. The ring on the screen at left is nonlinear fluorescence of the locus of rays from the axicon which heat the plasma and are transmitted through it, and the central spot is from the central part of the input beam which passes through a 2.5 mm diameter hole in the centre of the axicon. (This hole is used in experiments where secondary delayed pulses are injected through the axicon and coupled into the plasma waveguide and optically guided (Durfee et al. 1995; Nikitin et al. 1999).) Visually, Bessel-beam breakdown of a clustered gas jet is significantly brighter than similar breakdowns in unclustered jets or in backfill targets.
Figure 4a–c shows grayscale images of the extracted electron density at three probe delays for the case of argon at valve temperature −100 °C, backing pressure of 800 psi and pump laser energy of 150 mJ. The images were obtained from two-dimensional phase extraction from interferometric images at three probe delays. Assuming cylindrical symmetry, Abel inversion was used to convert the two-dimensional phase into grayscale plots of refractive index (or plasma density) versus radial and axial coordinates. For waveguides of similar electron density produced in non-clustered argon, the pump energy required was approximately 500 mJ, and a seed gas (N2O at 10–20% partial pressure) was needed to provide OFI electrons to seed the avalanche breakdown (Clark & Milchberg 1997). In the present case, the lower laser energy and lack of a seed gas means a much reduced OFI rate. But the much higher local atomic density in a cluster ensures that even with the lower yields of OFI electrons, the subsequent collisional breakdown is far more vigorous than in the seeded unclustered gas case. This will be seen in the later simulations.
Figure 5a shows Bessel-beam absorption versus backing pressure of argon and nitrogen clusters for Tvalve=−100 °C and laser energy of 315 mJ and figure 5b shows absorption as a function of pump energy for argon clusters (Pvalve=800 psi and Tvalve=−100 °C) and for argon gas (Pvalve=800 psi and Tvalve=25 °C). The level of absorption in unclustered nitrogen jets was below the sensitivity level of the measurement. It is seen that the maximum absorption is approximately 35%. While not at the level of more than 80% absorption of femtosecond pulses in clustered gases as discussed in §1, the absorption of these long 100 ps pulses is much greater than that achievable in unclustered gas jets.
Insight into how a 100 ps pulse interacts with a cluster first requires considering our earlier femtosecond experiments. Those time-resolved measurements showed that heating of few hundred angstrom diameter clusters by 1015 W cm−2, λ=800 nm, 70 fs pump pulses induces an ultrafast cluster plasma explosion, wherein the peak electron density drops from solid levels of approximately 1023 cm−3 to subcritical levels below 2×1021 cm−3 within approximately 0.5 ps (Milchberg et al. 2001; Kim et al. 2003a), and the plasmas from nearby cluster explosions merge in approximately 10–100 ps, depending on cluster density. The implication of this for the current experiment is that the majority of the 100 ps pulse envelope will encounter low subcritical density, uniform plasma arrived at from expansion and merging of individual cluster explosions that are initiated very early in the pulse. Therefore, an explanation for the surprisingly high absorption efficiency resides in the cluster plasma dynamics in the leading edge of the 100 ps pump pulse.
Figure 6 shows results from our laser cluster hydrodynamic code (Milchberg et al. 2001), for a 200 Å argon cluster exposed to a 100 ps, λ=1064 nm pulse for a range of laser intensity. The figure plots the log of cluster central electron density as a function of time for peak pulse intensities in the range 1013–1014 W cm−2, corresponding to the range of experimental intensities in the central maximum of the Bessel beam. The pulse starts near t=−300 ps at 1.5×10−11 of peak intensity (e.g. the starting intensity is 1500 W cm−2 in the case of the peak 1014 W cm−2 pulse), where the initial electron density is taken to be 2 electrons cm−3, giving effectively zero electrons over the cluster volume. The laser pulse peak is at t=0. The ionization onset time varies over an approximately 40 ps range as the peak intensity varies from 1013 to 1014 W cm−2, but the onset always remains in the far leading edge of the pulse. The onset location is not affected by the choice of (small) initial electron density. For all curves, the electron density peaks at in excess of 1023 cm−3, giving an average degree of ionization Zavg∼8 corresponding to the Ne-like Ar8+ ion, which is stable below approximately 1018 W cm−2 against further ionization. The sharp decline in central density after each curve's peak corresponds to cluster explosion to below critical density. As the density rapidly drops, Zavg∼8 is ‘frozen in’ owing to recombination occurring at a much slower rate than expansion. Once the exploding cluster plasma has dropped below critical density, it cools by expansion well before the pulse intensity increases sufficiently to contribute to heating. During this phase, the expanding and merging cluster plasma is also cooled via thermal conduction to the neutrals and weakly pre-ionized gas on the periphery of the main plasma. From single cluster calculations alone (Milchberg et al. 2001) (ignoring thermal conduction to the gas jet periphery), expansion cooling can decrease the temperature from a peak of a few hundred electron volts down to a few electron volts.
The conclusion from these calculations is that essentially the full 100 ps pulse envelope encounters highly ionized, uniform and relatively cold plasma as its effective initial target. In typical pre-ionization schemes, the initial ionization level per atom is less than unity, Zeff<1 (Volfbeyn et al. 1999; Gaul et al. 2000). With clusters as the target, one can have Zeff≫1, as seen in figure 6. The effects of this on the further breakdown and heating of the target can now be investigated by utilizing our self-consistent Bessel-beam plasma interaction code (Fan et al. 2000), which simulates pulsed Bessel-beam heating of gas-density plasmas.
For this calculation, we use conditions corresponding to experimental parameters of figure 5: axicon ray approach angle γ=15°, λ=1064 nm, a peak intensity of 2.5×1013 W cm−2 and gas densities Nn=0.7×1019, 1.0×1019 and 1.4×1019 cm−3. The results are shown in figure 7a–c, respectively. The figures show the time-dependent absorption for initial ionization levels in the range Zinit=10−7–8. This corresponds to the initial plasma conditions encountered by a long pulse interacting with targets spanning the range of initially unclustered gas to a gas of large clusters. Overlaid on these curves is the incident pulse envelope, normalized to unity. The table insets in the plots give the curve legend for the various values of Zinit and the total absorption fraction, η, which is the integral of each curve. It is seen for the Nn=0.7×1019 cm−3 plot (figure 7a) that absorption for the ‘clustered’ case of Zinit=8 (η=0.10) is approximately 10 times greater than for the ‘unclustered’ case of Zinit=10−7 (η=0.012). For Nn=1.0×1019 cm−3 (figure 7b), the maximum absorption is η=0.33, while it decreases for Nn=1.4×1019 cm−3 (figure 7c) to η=0.25. In both the latter cases, a high degree of initial ionization increases the subsequent absorption by a factor of approximately 3 compared to the low initial ionization case. In the higher density case, the absorption is somewhat reduced owing to the incipient exclusion of the axicon field from the plasma caused by the increase in the effective critical density Ncr,eff=Ncr sin2 γ seen by the Bessel beam. In general, low average density cluster gases show the greatest relative absorption enhancement over their non-clustered counterparts, while the largest absolute absorption takes place at intermediate pressures, before the density is large enough to effect Bessel-beam field exclusion. In all cases, the absorption of long-duration laser pulses in clustered gases is significantly greater than in neutral gases of equivalent average density.
We have demonstrated that clustered gas jets are an efficient means to produce laser-generated plasma waveguides. The highest heating efficiency is obtained with femtosecond pump pulses injected into the end of the jet. The self-guiding and strong absorption (more than 70%) of the pump pulse, which occur in tandem, provide a hot, high aspect ratio plasma, which generates the plasma waveguide through transverse shock expansion. The use of clustered jets realizes the possibility of achieving on-axis plasma densities less than 1018 cm−3 by making local pump laser heating independent of average gas density. Preliminary experiments with hydrogen clusters indicate that long fully ionized waveguides may be formed with a more efficient cluster source. We have also demonstrated that clustered gases are an excellent medium for use in plasma waveguide generation using long pulse (100 ps) Bessel beams. The resulting waveguides can have both low central density and small diameter, a desirable but hard to achieve combination for Bessel beam-generated waveguides using conventional gases. The extremely efficient absorption of laser pulses in clustered gas jets is shown to extend to pulses that are significantly longer than the time-scale for cluster explosive disassembly. This is due to the fact that a clustered gas is very strongly preionized in the far leading edge of a long pulse; the remaining pulse envelope acts to heat a relatively cool, highly ionized plasma.
The authors thank Andy York for help with improving the analysis programs, and also thank E. Parra and J. Fan for help with the cluster jet cooling block design. This work is supported by the US Department of Energy and the National Science Foundation.
One contribution of 15 to a Discussion Meeting Issue ‘Laser-driven particle accelerators: new sources of energetic particles and radiation’.
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