MeV proton generation and efficiency from an intense laser irradiated foil

High Energy Density Physics 3 (2007) 365e370 www.elsevier.com/locate/hedp

MeV proton generation and efficiency from an intense laser irradiated foil M.E. Foord*, P.K. Patel, A.J. Mackinnon, S.P. Hatchett, M.H. Key, B. Lasinski, R.P.J. Town, M. Tabak, S.C. Wilks Lawrence Livermore National Laboratory, University of California, Livermore, CA 94551, USA Received 30 November 2006; received in revised form 9 December 2006; accepted 9 December 2006 Available online 15 December 2006

Abstract The proton energy distribution generated from the interaction of an intense (Il2 z 1020 W/cm2 mm2) short-pulse (100 fs) laser with a thin foil is investigated using energy resolved measurements and 2D collisional PIC-hybrid simulations. The measured absolute proton spectrum is well matched by a 1.7 MeV exponential function for energies <11 MeV. The proton conversion efficiency from hot electrons z6%. Simulations pre˚ hydrocarbon depletion region. C and O ions in dict a strong radial dependence on the maximum proton energy and on the radial extent of 12 A the hydrocarbon layer gain significant energies, limiting the efficiency to the protons. The efficiency scaling for ion mixtures is derived using a simple model, and is shown to strongly depend on the cooling rate of the hot electrons. Simulations using hydrogen-rich, layered targets predict much higher efficiencies. Published by Elsevier Ltd. Keywords: Laser generated protons; Warm dense matter

The generation of multi-MeV protons from intense laser interactions with solid density targets is currently of much interest for potential applications in a number of areas, such as proton Fast Ignition [1e4], high energy density physics [5], medical research [6e10], radiography [11,12], and low emittance accelerators [13]. Well collimated proton beams with energies up to 60 MeV have been reported [14, 15] and much progress has been made in understanding the basic mechanisms of proton generation [16e19]. However, for most practical applications, much higher proton fluxes are needed than have been achieved to date. For example, in the area of Fast Ignition, Atzeni, et al. [3, 4] calculate that 10e40 kJ of protons in a Boltzmann energy spectrum with kT ¼ 3e 5 MeV are required to ignite a precompressed DT sphere at 500e250 g/cc, many orders of magnitude higher than currently available. Other applications such as proton therapy treatment will require much higher proton energies (60e * Corresponding author. Tel.: þ925 422 0990. E-mail address: [email protected] (M.E. Foord). 1574-1818/$ - see front matter Published by Elsevier Ltd. doi:10.1016/j.hedp.2006.12.001

200 MeV) and better control of the proton energy spectrum [10,20]. Recent theoretical works have suggested a path for reaching higher energies and fluxes, but are somewhat idealized and little tested [21e23]. Therefore, further experiments and development of computational models are needed to better understand and control the ion beam characteristics. An intense laser (I > 1018 W/cm2) incident on a solid density target quickly ionizes the surface material and transfers energy, via. collisionless processes, to a quasi Maxwellian distribution of forward directed electrons with energies characterized by kT > 200 keV. In the case of thin foil targets (10e100 mm), these hot electrons penetrate the foil and generate a Debye sheath on the back surface which field ionizes the surface material. The hot electron pressure drives the expansion of the quasi-neutral plasma of fast ions and hot electrons, with a non-neutral sheath at its leading edge [16]. The beam is typically composed of C, O and H ions that originate from the tens-of-Angstrom surface layer of hydrocarbons and water vapor, ubiquitous in target chamber environments [18,19,24,25].

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Recent studies have reported on the proton conversion efficiency for a few cases [18,23]. In this paper, we present measurements and simulations of the absolute proton efficiency from a short-pulse laser experiment. The experimental conditions are well diagnosed, allowing absolute comparisons of the measured proton flux with simulations from the 2D collisional PIC-hybrid code LSP. The proton spectrum is well matched by the simulations and is used to determine the proton conversion efficiency from hot electrons z6%. Results indicate that approximately half the total beam energy is lost to the C and O ions, which is investigated using a simple ion mixture model. The energy transfer between the hot electrons and thermal electrons in the foil is shown to be important in determining the acceleration time and proton conversion efficiency. Using a hydrogen-rich back surface coating and a careful choice of target and laser conditions, simulations predict that much higher conversion efficiencies should be achievable. Experiments were performed at the JanUSP laser facility at the Lawrence Livermore National Laboratory (LLNL). JanUSP is a Ti:Sapphire laser that operates at 0.8 mm and delivered 9.8 J of energy in a pulse duration of 100 fs. The spatial profile of the laser focus is approximated as a double Gaussian with widths 5 and 15 mm FWHM, with approximately half the laser energy deposited within each Gaussian, yielding a peak target irradiance of Il2 z 1020 W/cm2 mm2. The ASE pre-pulse intensity fraction is typically 108, a few nanoseconds before the peak of the pulse. The targets used in the experiments were 15 mm thick Au foils. Using X-ray photoemission spectroscopy, the back surface hydrocarbon layer was measured to contain ˚ surface layer with approximate relative concentrations a 12 A of 83% CH2 and 17% H2O [19]. The proton energy distribution was measured using radiochromic multilayer film (RCF) placed 26 mm behind and normal to the surface of the target. RCF is a dosimetry film that measures deposited energy when exposed to ionizing radiation. As protons lose energy passing through the stacked film layers, the exposure images provide an energy record of the beam. The highly ionized C and O ions are absorbed by the 18 mm thick Al blast shield and do not penetrate the film. The film images for protons that are accelerated from the back of the thin foil are typically well collimated, having a decreasing angular divergence with increasing energy [19], as shown in RCF film images in Fig. 1a. Using the calibrated film response, the absorbed energy in each film layer is then determined (see Fig. 1b). The energy scale is determined by the energy for maximum deposition into each layer, which is a strongly peaked function of initial energy. Overall uncertainty in the energy absorption in each layer is estimated to be 25%. In order to unfold the proton energy distribution, an exponential function of the form dN/dE ¼ (Nt/Ep)exp(E/Ep) for E < Emax, dN/dE ¼ 0 for E > Emax, is assumed, where Emax and Ep are the proton cutoff energy [21] and exponential energy fall-off of the proton distribution, respectively. The proton energy distribution is then convolved with energy response of the multilayer film, allowing direct comparison

Fig. 1. (a) Radiochromic film images of the proton beam at various energies. (b) Proton energy deposition (>) at each energy. Uncertainties of 25% include film response and background subtraction. Also shown for comparison is the proton distribution function dN/dE ¼ (Nt/Ep)exp(E/Ep) for E < Emax with Emax ¼ 11 MeV and Ep ¼ 1.7 MeV (C), calculated using the film response and connected with dashed lines.

with the film data (see Fig. 1b). Agreement to within <5% in each of the five energy bins at energies 3.5, 6.1, 7.9, 9.5, and 10.8 MeV is found using Ep ¼ 1.7 MeV, Nt ¼ 1.2  1011 protons, and a cutoff energy Emax ¼ 11 MeV. Although, as shown below, simulations predict a more complicated spatially dependent distribution, Ep is useful in representing the spatially averaged value of the proton energy. Proton generation from the back surface of the foil is simulated using the collisional PIC-hybrid code LSP [26]. LSP solves the particle and field evolution in an ionized plasma using the direct implicit method [27]. This approach allows dense plasma phenomena on times scales t [ upe, to be simulated without the need for resolving the Debye scale length or plasma frequency, often a requirement in explicit PIC schemes. The LSP code includes particle collisions between different ion and electron species, as well as a simple ideal gas model to provide feedback between the fields and particle pressures. The particles are modeled as a hybrid-fluid [28]; the lower density energetic ions and electrons are treated kinetically, while the solid density background electrons and ions are treated particles with internal temperature. Unlike previous works [19,22,23] the progressive transfer of energy from the hot electrons to the thermal electrons and ions through direct collisions and resistive heating is included and found to have an important effect on the efficiency. Based on previous PIC simulations of relativistic laser interactions with solid targets [16], we assume in the simulations a forward drifting relativistic Maxwellian electron distribution that is applied to the front surface of the target. While understanding the laser coupling to solid matter is an active area of research, here we focus on understanding the coupling between the hot electron distribution and the resulting proton beam. This allows the hot electron source to be varied independently and its effects on the ion beam to be investigated and compared

M.E. Foord et al. / High Energy Density Physics 3 (2007) 365e370

1011

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Energy (MeV) Fig. 3. Simulated spatial profile of the proton distribution function. Protons that originate from radii r < 10 mm are depleted below E < 1.5 MeV. The peak energies from each radial region decrease with increasing radius. The 3 MeV curve is an exponential fit to the r < 5 mm distribution.

decrease in field strength with time. At larger radii, the proton spectra are not depleted, but reach lower maximum energies, due to the radial decrease in the hot electron temperature. The time-history of the particle and field energies are shown in Fig. 4. The hot electrons are seen to lose the majority of their energy to the thermal electrons in the foil within z300 fs, with much less energy going into the field. The H, C and O ions acquire final energies of 31, 27 and 7 mJ, respectively. Using the 0.5 J hot electron energy, the conversion efficiencies from hot electrons into the H, C, and O ions are (.031/0.5) ¼ 6.2%, (.027/0.5) ¼ 5.4%, and (.007/0.5) ¼ 1.4%, respectively. The oxygen and carbon ions are predicted to gain more than half the total ion beam energy, limiting the energy available to the protons. It is therefore of interest to better understand the partitioning of energy between the ion species, especially as it relates to improve the efficiency for proton generation. To calculate the efficiency scaling for an ion mixture, it is useful to first consider the self-similar solution for an

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Energy (MeV) Fig. 2. Simulated time-evolution of the proton distribution function. Near t ¼ 4 ps, the protons approach their asymptotic distribution. For comparison, the experimental distribution derived from the RCF data is shown (dashed) along with the self-similar form (dotted).

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with experimental data. The model target is a 150 mm diameter, 15 mm thick Au foil, coated on the backside with a thin hydrocarbon layer. A 100 fs electron pulse is injected with the energy equally divided between 5 and 15 mm FWHM Gaussian spots, similar to the experiment. The initial Au foil temperature is Ti ¼ Te ¼ 10 eV, with a fixed charge Auþ10, ion density nAu ¼ 5.9  1022 cm3 and thermal electron density ne ¼ 5.9  ˚ hydrocarbon layer of 1 g/cc (CH2)0.83 1023 cm3. A 1000 A (H2O)0.17 is included and is assumed to be fully ionized, due to strong field ionization (E > 1012 V/m) in the sheath [24]. To account for possible depletion from the hydrocarbon layer, ˚ , only ions that originate which has a measured thickness of 12 A from within this depth are included in the analysis of the ion distributions. This approach allows an increase in the computational speed of the 2D simulations by allowing larger zone sizes and time steps, which are determined in the implicit scheme by the Courant limit, Dt  Dx/vemax z Dx/c. Comparisons with ˚ zoning of the 12 A ˚ layer 1D simulations that included sub-A gave similar results for maximum energies and lower energy cutoffs due to depletion of the ion distributions. The simulations employ a hot electron distribution with a forward drifting Maxwellian, with energies Edrift ¼ Thot ¼ 800 keV and total energy z0.5 J. These values were determined by varying the hot electron flux and temperature to approximately match the measured absolute proton flux and slope, respectively. The time-evolution of the distribution is shown in Fig. 2, reaching an asymptotic limit near t ¼ 4 ps. Also shown is the measured distribution, which agrees well with the absolute flux, the 1.7 MeV exponential fall-off energy, and the 11 MeV cutoff energy. Further analysis of the calculated spectrum shows that protons that originate from small radii (r < 10 mm) are depleted below E < 1.5 MeV (see Fig. 3). The low energy cutoff is from particles that originate from the ˚ layer, which are accelerated less due to the back of the 12 A

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Time (ps) Fig. 4. Simulated time-history of the particle and field energies for a 15 mm Au ˚ hydrocarbon layer. foil with a 12 A

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expanding plasma of temperature Thot and charge Zi. The isothermal solution is ni(x, t) z nioexp(v(x, t)/Cs) [29], and the energy distribution per unit area for ions of charge Zi can be rewritten as:  h i dNi ðEÞ  1=2 1=2 ¼ nio Cs t=ð2EZi Thot Þ exp  ð2E=Zi Thot Þ dE

ð1Þ

where Cs is the ion sound speed defined for a single ion species as Cs ¼ (ZiThot/mi)1/2. This solution is valid for density scale lengths Cst [ lD or times t [ 1/upi. While the isothermal solution predicts no cutoff in the energy spectrum, more detailed analysis pffiffiffiffiffiyields a maximum energy Emax ¼ 2Zi Thot ½lnð2upi t= 2eÞ2 [21], which occurs near the non-neutral front of the beam. The solution does not include hot electron energy loss to heating the foil and so has no specific limit on the time. For the case of a finite laser pulse, t may be approximated by the effective coupling time t, between the hot electrons and the ions. As discussed below, in cases where the hot electrons quickly lose energy to the foil, the coupling time is limited by the laser pulse length, while in case of weak coupling, t depends more on the expansion time, L/Cs, of the hot electrons. In Fig. 2, the normalized self-similar function (using Thot ¼ 0.7 MeV) is compared with simulation results, showing somewhat better agreement than with the simple exponential function. RE Defining the beam energy as Ei ¼ 0 max EðdNi =dEÞdE and integrating Eq. (1) yields the total energy in the beam per unit area, Ei ¼ nio Zi Thot Cs tgðEmax Þ, where nio is the ion beam density near the solid density interface, R x and g is an integral function defined as gðEmax Þ ¼ ð1=2Þ 0max x2 expðxÞdx, where xmax ¼ (2Emax/ZiThot)1/2 and g(Emax) / 1 for Emax [ ZThot or upit [ 1. For a beam composed of a mixture Pof ions, the total beam energy per unit area is given by Eb ¼ nio Zi Thot Cs tgðEmax Þ ¼ nehot Thot Cs tg, where g is averaged overi ion species. This gives the heuristically correct result that the beam energy per unit area equals the pressure, nehotThot, exerted over the scale length of the beam, Cst, In 1D geometry relevant for thin foils, nehot ¼ Ne/LA, where Ne is the total number of hot electrons, L is the foil thickness and A is the sheath area. The total beam energy per unit area can then be written as: Eb ¼ ðNe =LAÞThot Cs tg

ð2Þ

For a homogeneous mixture of ions, the sound speed is given by Cs hðThot hZi2 =mi i=hZi iÞ1=2, where h i is averaged over ion concentration [30]. The sound speed limits the rate at which ions can expand from the surface and therefore is an important parameter determining the efficiency. We now define the ion beam conversion efficiency, e, as e ¼ Eb/Ehot, where Ehot is the hot electron energy per unit area. Using Eq. (2) and assuming gz1ðupi t[1Þ yields the scaling expression: ezðNe =LAÞThot Cs t=ðNe Thot =AÞ ¼ ðCs =LÞt

ð3Þ

As mentioned above, this result is derived based on the assumption of a constant temperature hot electron plasma that is maintained during time period t, while in fact, Thot decreases

in time due to continuous energy loss into heating the foil and accelerating the ions. Therefore, this expression is approximate in the sense that both the sound speed and the coupling time are changing in time, but is still useful in allowing the efficiency scaling to be examined. For example, the efficiency scaling for ion mixtures is compared with 1D LSP simulations using ˚ layer of Cþzi Hþ (1 < Zi < 6), Cþ6 a thin Au foil with 1000 A þ or H . For the CH calculations the density is assumed to be r ¼ 1 g/cc, giving ion densities of nC ¼ nH ¼ 4.6  1022 cm3. For the cases of pure Cþ6 and Hþ, the same density is assumed to allow the scaling with other parameters to be compared. As shown in Fig. 5, the simulations predict a strong dependence on the ion charge. The simulations also agree with scaling results derive above. For example, comparing pure Hþ with Cþ6Hþ, the ratio of Cs is 1:[(1 þ (36/12))/(1 þ 6)]1/2 ¼ 1:0.75, which agrees well with the simulation results shown in Fig. 5. Ratios for other ion mixtures and for the case of pure Cþ6 also show good agreement. For example, the ratio between pure Hþ and Cþ6 is predicted to be 1:[(36/12)/6]1/2 ¼ 1:(1/2)1/2 z 0.71, in agreement with the result shown in Fig. 5. The conversion efficiency for individual ion species is also shown in Fig. 5. As the carbon ion charge decreases, Hþ gains a larger fraction of energy. Assuming that the energy gain scales as Z2i /mi, good agreement is found for the separate efficiency curves for each ion. Of particular interest is that the proton efficiency is enhanced by a factor of three for the case of pure Hþ vs. Cþ6Hþ. Thus, significant improvements in proton efficiency are predicted with a high fractional abundance of H and low Zi/mi contaminants. The efficiency is predicted to improve with thinner foils, due to the inverse dependence of the hot electron density on foil thickness, nehott ¼ Ne/(LA). Other LSP simulations have verified the w1/L scaling for foils with L ¼ 5, 10 and 15 mm. As discussed elsewhere, this simple linear scaling 35

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˚ Fig. 5. LSP simulation results for the ion conversion efficiencies of a 1000 A surface layer of pure Hþ and Cþ6, and for an ion mixture of CþZiHþ. The total (>), proton (B), and carbon (,) conversion efficiencies are shown for each case. Dashed lines connect the modeling results (x, þ, D) discussed in the text, normalized to the pure Hþ case.

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may not hold in practice for very thin targets, which are limited by problems from preheat [23] or by the Debye length of the hot electron gas (typically a few microns) [31], or in much thicker foils (where L is much larger than the laser spot size) where 2D expansion of the hot electron gas reduces the density and pressure of the hot electrons [23]. In this formulation, t is the energy exchange rate between the hot electrons and the thermal particles and field. The efficiency is predicted to increase with t. However, from a simple consideration of energy conservation, t is constrained by (Cs/L)t  1, i.e. t is roughly limited by the expansion time of the hot electrons which are initially confined by the foil thickness, L. In the collisionless limit where resistive and collisional heating of the foil is minimal, higher efficiency is possible due to most of the hot electron energy eventually being converted into the ion kinetic expansion energy. It is therefore useful to consider t as a competition between the energy exchange rate into the non-dissipative process of accelerating the ions from the expansion of the hot electron plasma, and the dissipative process of heating the thermal electron and ions in the foil, or 1/t ¼ 1/ taccel þ 1/theat. When resistive or collisional losses dominate, t w theat, and the hot electrons cool rapidly after the laser is off. In this regime, the energy exchange rate is limited by the laser pulse length. For example, in Ref. [23], based on an empirical fit to data, good agreement is found using the ad hoc assumption t ¼ 1.3tlaser while similarly t ¼ tlaser is assumed in Ref. [32]. As shown in Fig. 4, in our experiments, the hot electrons also cool relatively quickly (w300 fs) and transfer most of their energy to the thermal electrons in the foil soon after the laser pulse. In cases where dissipative losses are relatively small, t is mainly determined by the expansion time of the hot electron plasma, t w taccel w L/Cs, and efficiencies approaching unity are predicted. At high electron temperature, the hot electrons are less coupled with the thermal background plasma. Improved efficiency with hot electron temperature has been previously reported [18,31], and in fact, the highest proton conversion efficiency reported to date (12% from laser light to protons) was in a high power PW laser experiment with temperature Thot z 6 MeV [15]. To illustrate these scaling results, a 5 mm Al foil with ˚ layer of methane (CH4) is simulated in 1D. A a 1000 A 200 fs pulse of hot electrons is injected with Edrift ¼ Thot ¼ 2.5 MeV. The foil temperature is initially Ti ¼ Te ¼ 10 eV and ionized to Alþ6, with ion density nAl ¼ 6.0  1022 cm3 and a thermal electron density of ne ¼ 2.4  1023 cm3 (see Fig. 6). The proton conversion efficiency from the hot electrons reaches z50%, a factor of 10 increase over the Au experiment. This improvement can be roughly attributed to ˚ ) surface the three times thinner foil, a much thicker (1000 A layer having twice the concentration of hydrogen, and a three times higher electron temperature which improves the efficiency by increasing the sound speed, (Cs w T1/2 hot), as well as reducing the cooling rate of the hot electrons (as seen from comparing Figs. 4 and 6). The lower density Al was chosen in this example to further reduce the coupling rate to the hot electrons. Although in practice, using such thin foils may require very low pre-pulse levels to maintain the foil integrity,

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Time (ps) Fig. 6. Simulated time-history of the particle and field energies for a 5 mm Al ˚ CH4 layer. The energy fraction into protons reaches z50%. foil with a 1000 A

this example illustrates the effects of varying each of these factors on improving the efficiency. We note that in experiments and PIC simulations the hot electron and proton temperatures are often compared to the pondermotive potential of the laser, Thot w Up w mec2(g  1), where g ¼ (1 þ (Il2/2.74  1018 W/cm2 mm2))1/2 [33]. In our experiment, the average intensity over the 5 mm center spot diameter was Il2 z 7  1019 W/cm2 mm2 and thus, Up z 2.1 MeV, close to the measured (and simulated) 1.7 MeV proton temperature, but somewhat greater than z1.1 MeV rms hot electron temperature. As shown in Fig. 3, it is difficult to glean much information from such comparisons, due to the strong radial dependence of the proton spectrum, which is averaged in the experiments. Using the measured laser energy on target of 9.8 and 0.5 J of hot electrons in the simulations, we estimate that the conversion from laser energy to hot electrons w(0.5/ 9.8) ¼ 5.1%. From other simulations and based on the uncertainty in the measured proton flux, we estimate w30% uncertainty in this absorption fraction. We note that this absorption fraction is much lower than typically reported for total laser absorption in high power laser experiments (25e50%) [15,23,34]. However, depending on factors such as the laser pre-pulse level [32] and the recirculation of the hot electrons [35,36], the total absorption efficiency and the fraction into suprathermal electrons can vary substantially between experiments [37]. Perhaps more relevant in our case, is that this conversion percent only includes the fraction of laser energy that goes into the suprathermal component of the electron distribution, and therefore does not include a possible lower energy component. In summary, the absolute proton flux from the back surface of a thin foil is measured in experiments where the hydrocarbon layer and laser conditions are well diagnosed, allowing direct comparisons with the collisional PIC code LSP. We believe that these simulations are the first to model realistic experimental conditions, that include both collisional and collisionless processes, and that incorporate the actual foil density and multi-species surface layer. This allows effects such as surface

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depletion, energy losses to C and O ions, and the conversion efficiency to protons to be determined self-consistently. Acknowledgements The authors thank A. Kemp for helpful discussions. This work was performed under the auspices of the Department of Energy Contract # W-7405-Eng-48. References [1] R. Kodama, et al., Nature 412 (2001) 798. [2] M. Roth, et al., Phys. Rev. Lett. 86 (2001) 436; M. Key, et al., Fusion Sci. Tech. 49 (2006) 297. [3] S. Atzeni, M. Temporal, J.J. Honrubia, Nucl. Fusion 42 (2002) L1. [4] S. Atzeni, M. Tabak, Plasma Phys. Control. Fusion 47 (2005) B769. [5] P. Patel, et al., Phys. Rev. Lett. 91 (2003) 125004. [6] K. Ledingham, et al., J. Phys. D 37 (2004) 2341. [7] B.M. Hegelich, et al., Nature 439 (2006) 441. [8] H. Schwoerer, et al., Nature 439 (2006) 445. [9] S. Bulanov, V. Khoroshkov, Plasma Phys. Rep. 28 (2002) 453. [10] E. Fourkal, Med. Phys. 30 (2003) 1660. [11] J.A. Cobble, R.P. Johnson, T.E. Cowan, et al., J. Appl. Phys. 92 (2002) 1775. [12] M. Borghesi, et al., Phys. Rev. Lett. 92 (2004) 055003.

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