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Quasi-monoenergetic proton beam generation from a double-layer solid target using an intense circularly polarized laser

Published online by Cambridge University Press:  17 July 2009

J.H. Bin ,
A.L. Lei ,
X.Q. Yang ,
L.G. Huang ,
M.Y. Yu ,
Wei Yu  and
K.A. Tanaka
J.H. Bin
Affiliation:
Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China
A.L. Lei*
Affiliation:
Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China
X.Q. Yang
Affiliation:
Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China
L.G. Huang
Affiliation:
Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China
M.Y. Yu
Affiliation:
Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou, China
Wei Yu
Affiliation:
Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China
K.A. Tanaka
Affiliation:
Graduate School of Engineering, Osaka University, Osaka, Japan
*
Address correspondence and reprint requests to: Anle Lei, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China. E-mail: lal@siom.ac.cn

Abstract

Monoenegetic ion beam generation from circularly polarized laser-pulse interaction with a double-layer target is considered. The front layer consists of heavy-ion plasma, and the rear layer is a small thin coating of light-ion plasma. Particle-in-cell simulation shows that the multi-dimensional effects in the ion radiation pressure acceleration are avoided and a highly monoenergetic light-ion beam can be produced. Our simulations reveal that the charge-mass ratio of heavy ions in the front layer and the thicknesses of both layers can strongly affect the proton energy spectra.

Keywords

Circularly polarized laserDouble-layer solid targetPIC simulationQuasi-monoenergetic proton generation

Information

Type
Research Article
Information
Laser and Particle Beams , Volume 27 , Issue 3 , September 2009 , pp. 485 - 490
Copyright
Copyright © Cambridge University Press 2009

1. INTRODUCTION

With the rapid advances in laser technology, energetic-ion-beam production from intense-laser interaction with matter have attracted much attention because of its compactness and many potential applications, such as in ion cancer therapy (Malka et al., Reference Malka, Fritzler, Lefebvre, d'Humieres, Ferrand, Grillon, Albaret, Meyroneinc, Chambaret, Antonetti and Hulin2004; Linz & Alonso, Reference Linz and Alonso2007; Yogo et al., Reference Yogo, Sato, Nishikino, Mori, Teshima, Numasaki, Murakami, Demizu, Akagi, Nagayama, Ogura, Sagisaka, Orimo, Nishiuchi, Pirozhkov, Ikegami, Tampo, Sakaki, Suzuki, Daito, Oishi, Sugiyama, Kiriyama, Okada, Kanazawa, Kondo, Shimomura, Nakai, Tanoue, Sasao, Wakai, Bolton and Daido2009), fast ignition in inertial confinement fusion (ICF) (Roth et al., Reference Roth, Cowan, Key, Hatchett, Brownl, Fountain, Johnson, Pennington, Snavely, Wilks, Yasuike, Ruhl, Pegoraro, Bulanov, Campbell, Perry and Powell2001), fast-beam injection in conventional accelerators (Krushelnik et al., Reference Krushelnick, Clark, Allott, Beg, Danson, Machacek, Malka, Nakmudin, Neely, Norreys, Salvati, Santala, Tatarakis, Watts, Zepf and Dangor2000), proton radiography and imaging (Borghesi et al., Reference Borghesi, Campbell, Schiavi, Willi, Mackinnon, Hicks, Patel, Gizzi, Galimberti and Clarke2002; Cobble et al., Reference Cobble, Johnson, Cowan, Renard-LeGalloudec and Allen2002; Breschi et al., Reference Breschi, Borghesi, Campbell, Galimberti, Giulietti, Gizzi, Romagnani, Schiavi and Willi2004), etc. Most of these applications require ion beams with small energy spread Δɛ/ɛ. For example, for cancer therapy, a proton beam with Δɛ/ɛ ≤ 2% would be needed (Khoroshkov & Minakova, Reference Khoroshkov and Minakova1998; Kraft, Reference Kraft2001). However, energetic ion beams obtained in the experiments usually have large (say 100%) Δɛ/ɛ.

With specially structured targets, quasi-monoenergetic ion beams with Δɛ/ɛ ≤ 20% have been achieved using linearly polarized (LP) laser pulses (Hegelich et al., Reference Hegelich, Albright, Cobble, Flippo, Letzring, Paffett, Ruhl, Schreiber, Schulze and Fernandez2006; Schwoerer et al., Reference Schwoerer, Pfotenhauer, Jackel, Amthor, Liesfeld, Ziegler, Sauerbrey, Ledingham and Esirkepov2006). Both works were based on the ion acceleration mechanism target normal sheath acceleration (TNSA) (Wilks et al., Reference Wilks, Langdon, Cowan, Roth, Singh, Hatchett, Key, Pennington, MacKinnon and Snavely2001; Esirkepov et al., Reference Esirkepov, Bulanov, Nishihara, Tajima, Pegoraro, Khoroshkov, Mima, Daido, Kato, Kitagawa, Nagai and Sakabe2002; Flippo et al., Reference Flippo, Hegelich, Albright, Yin, Gautier, Letzring, Schollmeier, Schreiber, Schulze and Fernandez2007; Nickles et al., Reference Nickles, Ter-Avetisyan, Schnürer, Sokollik, Sandner, Schreiber, Hilscher, Jahnke, Andreev and Tikhonchuk2007). In TNSA, the hot electrons are generated by the LP laser pulse at the target front and are transported through the target to the backside vacuum, forming a strong electrostatic space-charge sheath field there. The sheath field is normal to the target rear surface and can accelerate some of the ions in the latter to high energy. Recently, with LP laser pulses, Yin et al. (Reference Yin, Albright, Hegelich and Fernandez2006, Reference Yin, Albright, Hegelich, Bowers, Flippo, Kwan and Fernandez2007) have shown in the particle-in-cell (PIC) simulations that monoenergetic ion beams up to GeV are generated due to laser breakout afterburner (BOA) acceleration mechanism (Davis & Petrov, Reference Davis and Petrov2009).

Using circularly polarized (CP) laser pulses, a new mechanism radiation pressure acceleration (RPA) was considered for monoenergetic ion beam generation (Macchi et al., Reference Macchi, Cattani, Liseykina and Cornolti2005; Kado et al., Reference Kado, Daido, Fukumi, Li, Orimo, Hayashi, Nishiuchi, Sagisaka, Ogura, Mori, Nakamura, Noda, Iwashita, Shirai, Tongu, Takeuchi, Yamazaki, Itoh, Souda, Nemoto, Oishi, Nayuki, Kiriyama, Kanazawa, Aoyama, Akahane, Inoue, Tsuji, Nakai, Yamamoto, Kotaki, Kondo, Bulanov, Esirkepov, Utsumi, Nagashima, Kimura and Yamakawa2006; Liseikina & Macchi, Reference Liseikina and Macchi2007; Zhang et al., Reference Zhang, Shen, Li, Jin, Wang and Wen2007; Klimo et al., Reference Klimo, Psikal, Limpouch and Tikhonchuk2008; Robinson et al., Reference Robinson, Zepf, Kar, Evans and Bellei2008; Yan et al., Reference Yan, Lin, Sheng, Guo, Liu, Lu, Fang and Chen2008). Without high-frequency oscillating component of the v × B force for a CP laser pulse, there is no heating originating from the hot electron oscillations when it is normally incident on a target (Macchi et al., Reference Macchi, Cattani, Liseykina and Cornolti2005). The electrons are pushed forward steadily and compressed by the light pressure. An intense electrostatic field is thus formed, which then accelerates ions inside the target. One-dimensional (1D) simulations show that fairly monoenergetic ion beams can be generated (Macchi et al., Reference Macchi, Cattani, Liseykina and Cornolti2005; Zhang et al., Reference Zhang, Shen, Li, Jin, Wang and Wen2007; Klimo et al., Reference Klimo, Psikal, Limpouch and Tikhonchuk2008; Robinson et al., Reference Robinson, Zepf, Kar, Evans and Bellei2008). However, in reality higher-dimensional effects such as hole boring and filamentation (Liseikina & Macchi, Reference Liseikina and Macchi2007; Klimo et al., Reference Klimo, Psikal, Limpouch and Tikhonchuk2008; Robinson et al., Reference Robinson, Zepf, Kar, Evans and Bellei2008; Yan et al., Reference Yan, Lin, Sheng, Guo, Liu, Lu, Fang and Chen2008) can significantly increase Δɛ/ɛ and thus reduce the quality of the ion beam.

In this paper, we show by two-dimensional (2D) PIC simulation that a CP laser pulse of intensity 2.5 × 1021 Wcm−2 irradiating a double-layer (DL) target can produce a highly localized monoenergetic ion beam of ~156 MeV with Δɛ/ɛ ≈ 4%. The target is made up of two layers of different materials. The intense CP laser is normally incident on the dense front layer of heavy ions. The rear layer is a thin dot of light ions. The front-layer electrons driven forward in the overdense plasma by the laser ponderomotive force form in front of the pulse a thin highly compressed electron layer. An electron depletion region (EDR) with very intense space-charge field is thus created (Macchi et al., Reference Macchi, Cattani, Liseykina and Cornolti2005). When it propagates to the rear surface of the front layer of heavy ions, light ions in the rear layer are then accelerated. With the DL target, the multi-dimensional effects in the light ion RPA are avoided and a highly monoenergetic light-ion beam can be produced. The regime of ion acceleration here is also quite different from that of the existing TNSA scheme (Schwoerer et al., Reference Schwoerer, Pfotenhauer, Jackel, Amthor, Liesfeld, Ziegler, Sauerbrey, Ledingham and Esirkepov2006).

2. BRIEF ARGUMENT

As mentioned above, when a CP laser pulse is normally incident on the front layer, the electrons there are ponderomotively driven forward and compressed into a thin electron layer, whose spatial extent is on the order of the skin depth l s = c/ωp, where c is the light speed and ωp is the plasma frequency. While the intense space-charge electrostatic field is formed in front of the laser increases with time, further numbers of electrons are kicked into the compression layer until it reaches a maximum when the electrostatic pressure balances the light pressure. The optimum thickness of the front target layer can be obtained when the highest space-charge field is formed just at its rear surface, and can be written as (Yin et al., Reference Yin, Wei, Yu, Lei, Yang, Xu and Senecha2008) $d_{{\rm opt}}=\sqrt {I_L /\pi c} /en_{e1}$, where I L is the laser pulse intensity and n el is the initial electron density for the front layer. This intense space-charge field then accelerates the light ions in the rear layer. Since the laser pulse and its ponderomotive force are spatially nonuniform, which may lead to nonuniformity in the space-charge field, the thickness d 2 of the rear layer is taken to be close to the skin depth l s and its transverse size is taken to be smaller than the laser-pulse waist. We define that in the present scheme, the acceleration phase is separated from the space-charge-field-establishing phase, so that undesirable longer-timescale effects such as hole-boring, filamentation, etc. are avoided and a light-ion beam of high energy and small energy spread can be obtained.

3. SIMULATION PARAMETERS

To verify the above argument, we have carried out simulations using the 2D PIC code LAPINE (Xu et al., Reference Xu, Chang, Zhuo, Cao and Yue2002). A Gaussian CP laser pulse with wavelength λ0 = 1 µm and beam waist radius ω0 = 4λ0 is normally incident from the left side. The laser amplitude a = eA/m ec 2, where A is the vector potential, e and m e are the electron charge and mass, respectively, and c is the light speed, rises from zero to 30 (corresponding to a laser intensity of I L = 2.5 × 1021 Wcm21) in one laser period T 0 and remains constant for 30T 0. The simulation box is 60λ0 in the laser propagation (x) direction and 20λ0 in the y direction. The front layer consists of a carbon plasma with an electron density n e1 = 10n c, where n c is the critical density, and the rear-layer consists of protons with an electron density n e2 = n c. The front layer is at x = 20λ0 and has a diameter D 1 = 10λ0 and thickness d 1 = 1λ0 (which is near the optimum thickness d opt). The rear, or proton, layer has a diameter D 2 = 1λ0 and thickness d 2 = 0.05λ0 (which is near the skin depth l s = c/ωp) is attached directly to the rear side of the front layer. That is, the parameters chosen are near that for optimum ion beam production as estimated above.

4. SIMULATION RESULTS AND DISCUSSION

Figure 1a shows the evolution of the energy spectra of protons produced by the DL target. One can see that a highly monoenergetic proton beam of ~156 MeV and Δɛ/ɛ ≤ 4% is produced by the laser plasma interaction, and it maintains its monoenergetic characteristics as it is accelerated, even up to t = 90T 0. For comparison, Figure 1b shows the evolution of the energy spectrum of the protons produced from a single-layer proton target of thickness of 1λ0 and density of 10n c. We see that in this case, the proton energy peaks at an early stage (t < 30T 0) with a broad spectrum, and the peak disappears quickly as the proton beam propagates forward.

Fig. 1.

(Color online) The proton energy spectra from 2D PIC simulations. (a) From a double-layer target at near-optimum conditions from the simple theory. (b) From a simple proton target. The double-layer target consists of a front carbon (Z 1 = +4) layer and rear proton layer. The laser parameters are I L = 2.5 × 1021 Wcm−2, λ0 = 1 µm, and ω0 = 4λ0. The target parameters are n e1 = 10n c, D 1 = 10λ0, d 1 = 1λ0, n e2 = n c, D 2 = 1λ0, and d 2 = 0.05λ0.

The ratio Z 1/A 1 of the charge number to the atomic mass of the heavy ions in the front-layer obviously plays a crucial role in accelerating the much lighter protons in the rear layer. The evolution of the electrostatic space-charge field established by the laser-expelled front-layer electrons is shown in Figure 2a. We see that the field profile is almost linear in both its rising and falling segments. For convenience, one can divide the field into two regions (Macchi et al., Reference Macchi, Cattani, Liseykina and Cornolti2005): I and II, as shown in Figure 2b. In region I with the rising field, the protons have lower velocities and never pass through the peak of field. On the other hand, in region II with the falling field, the protons are accelerated and are compressed. In the DL, the space-charge field established by the laser displaced front-layer electrons can accelerate the heavy ions there to a velocity (Macchi et al., Reference Macchi, Cattani, Liseykina and Cornolti2005) 2ν0 where ${\rm v}_0 /c=\sqrt{Z_1\, m_e n_c /A_1m_p n_{e1}}a$, and m p is the proton mass. In the time t = (d 1 + d 2)/2v0 for the heavy ions to pass through the DL, the protons will obtain a velocity ${\rm v}_1=\displaystyle {({Z_2 eE_0 } / {2A_2\, m_p })}({{\lpar d_1+l_s \rpar } / {2{\rm v}_0 })}$, where E 0 = 4πen e1d 1 is the peak value of the electrostatic field and we have substituted d 2 by l s. Therefore, there can exist three different cases. Case 1 for v1 < 2v0; before the light ions are sufficiently accelerated, the heavy ions pass them, and neutralize much of the space-charge field, so that the light ions can only gain little energy. Case 2 for v1 > 2v0; the light ions always remain in front of the heavy ions, so that they are accelerated efficiently in the falling segment of the space-charge field and can achieve high energies with a narrow spectrum because of the narrow acceleration region due to the limited thickness (acceleration distance) of the rear layer. Case 3 for v1 ~ 2v0; a part of the light ions remains at low speeds in the region I of the space-charge field. Others will be in the region II, where they are compressed and attain high energies with small Δɛ/ɛ, as in Case 2.

Fig. 2.

(Color online) (a) Evolution of the space-charge field normalized by m eωc/e, where ω is the laser circular frequency. The laser and target parameters are the same as for Figure 1a. (b) Sketch of the profile of the electrostatic field (pink dashed line) in the two regions of the simple model.

In order to see the sensitivity on the charge-to-mass ratio, we have carried out simulations for different charge states of the front-layer heavy ions. The rear-layer light ions are still protons. Figure 3 shows the proton energy spectra, and the electric field and proton density profiles for the charge states Z 1 = +4, +5, and +6. When Z 1 = +4 corresponding to Case 2, we see that the accelerated protons have a narrow energy peak around 150 MeV. From the electric field and density profiles, one can see that the protons are in front of the electrostatic field. When Z 1 = +6, corresponding to Case 1, the protons are behind the electrostatic field and can only reach a relative low energy of 50 MeV. When Z 1 = +5, corresponding to Case 3, there are two peaks in the energy spectrum. From the proton density distribution, we see that a part of the protons are in the falling region of the electrostatic field and these protons can be accelerated to ~150 MeV. The protons in the ascending region of the space-charge field can only reach 50 MeV. From the simple model, we can calculate the proton speeds. For Z 1 = +4, we obtain v1 = 0.399c, which is higher than 2v0 (=0.256c). For Z 1 = +6, we get v1 = 0.326c, which is close to 2v0 (=0.313c). For Z 1 = +5, we have v1 = 0.357c, which is also higher than 2v0 (=0.286c). Thus, the results obtained from the simple model agree quite well with that from the simulations. In particular, the charge-to-mass ratio of the front layer should not be too large; otherwise the light ions cannot be efficiently accelerated. That is, the ions in the front layer should be heavy enough to make sure a low charge-to-mass ratio, for example, using gold ions in experiments instead of the carbon ions in the PIC simulations.

Fig. 3.

(Color online) Effect of the charge-to-mass ratio. (a) and (b) Z 1/A 1 = 4/12, (c) and (d) Z 1/A 1 = 5/12, and (e) and (f) Z 1/A 1 = 6/12. The left column shows the space-charge field (red solid lines) at t = 45T 0. The profiles (small blue patches) of the nearly monoenegetic proton bunch at the same instant is also shown. The right column shows the proton energy spectra at t = 90T 0 (blue solid lines). The laser parameters and the target structure are the same of Figure 1a except that n e2 = 2n c.

In each simulation above, the heavy ions in the front-layer are in one charge state. In an experiment, the heavy ions will be field ionized to multiple charge states by the accelerating sheath. In order to see the effect of multiple charge states on the proton energy spectra, we have carried out the simulation with multiple charge states of the front-layer heavy ions. In the simulation, the charge states of the front-layer carbon ions are Z 1 = +4 and +6. The densities of C4+ and C6+ ions are 5/4n c and 5/6n c, respectively, which results in the electron density in the front layer being 10n c. The other parameters are the same of Figure 3. The proton energy spectrum is shown in Figure 4, which still shows monoenergetic characteristics.

Fig. 4.

(Color online) The proton energy spectrum for the front-layer carbon ions with charge states Z 1 = +4 and +6. The densities of C4+ and C6+ ions are 5/4n c and 5/6n c, respectively. The other parameters are the same of Figure 3.

We consider now the effect of the thickness of the target layers. Figure 5a shows that proton acceleration is inefficient if the thickness d 1 of the heavy-ion layer is too small, since the space-charge field inside the DL cannot reach a high value. If the heavy-ion layer is too thick, the space-charge field will be partially neutralized by the accelerated heavy ions (corresponding to Case 3), and the protons also cannot gain much energy. Maximum proton energy is obtained when the front-layer thickness is equal to the estimated optimum thickness. Our estimate also shows that the thickness d 2 of the rear, or proton, layer should be close to the skin depth l s, so that all the protons in the rear layer can be accelerated by the same space-charge field. If the proton layer is too thick, the protons will be accelerated by the space-charge field at different local intensities. In Figure 5b, one sees that with increase of the proton-layer thickness, the proton energy spectrum becomes less monoenergetic. Thus, in order to obtain high quality ion beams, the rear layer should be sufficiently thin.

Fig. 5.

(Color online) (a) The proton energy spectra t = 90T 0 for different thicknesses of the front-layer ions. (b) The proton energy spectra at the same instant for different thicknesses of the proton layer. Other parameters are the same of Figure 1a.

5. CONCLUSION

In summary, a scheme of monoenergetic light-ion beam generation from the interaction of a circularly polarized laser pulse with a double-layer target is proposed. When the charge-to-mass ratio of the heavy ions is small and the conditions $d_1 \sim d_{opt}=\sqrt {I_L /\pi c} /en_{e1}$ and $d_2 \sim l_s=c/\omega _p$ are satisfied, a high quality monoenergetic proton beam can be generated. The 2D PIC simulation results agree quantitatively with that of a simple model. Our results should be useful in the design of practical applications of the monoenergetic light-ion beams generated by laser-target interaction.

ACKNOWLEDGMENTS

The work was supported by the Natural Science Foundation of China under Grant Nos. 10734130, 10775165, 10875158, and 10835003, the NSAF under Grant Nos. 10876011 and 10676010, the Science and Technology Commission of Shanghai Municipality under Grant No. 08PJ14102, and the JSPS Japan-China Core University Program.

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Figure 0

Fig. 1. (Color online) The proton energy spectra from 2D PIC simulations. (a) From a double-layer target at near-optimum conditions from the simple theory. (b) From a simple proton target. The double-layer target consists of a front carbon (Z1 = +4) layer and rear proton layer. The laser parameters are IL = 2.5 × 1021 Wcm−2, λ0 = 1 µm, and ω0 = 4λ0. The target parameters are ne1 = 10nc, D1 = 10λ0, d1 = 1λ0, ne2 = nc, D2 = 1λ0, and d2 = 0.05λ0.

Figure 1

Fig. 2. (Color online) (a) Evolution of the space-charge field normalized by meωc/e, where ω is the laser circular frequency. The laser and target parameters are the same as for Figure 1a. (b) Sketch of the profile of the electrostatic field (pink dashed line) in the two regions of the simple model.

Figure 2

Fig. 3. (Color online) Effect of the charge-to-mass ratio. (a) and (b) Z1/A1 = 4/12, (c) and (d) Z1/A1 = 5/12, and (e) and (f) Z1/A1 = 6/12. The left column shows the space-charge field (red solid lines) at t = 45T0. The profiles (small blue patches) of the nearly monoenegetic proton bunch at the same instant is also shown. The right column shows the proton energy spectra at t = 90T0 (blue solid lines). The laser parameters and the target structure are the same of Figure 1a except that ne2 = 2nc.

Figure 3

Fig. 4. (Color online) The proton energy spectrum for the front-layer carbon ions with charge states Z1 = +4 and +6. The densities of C4+ and C6+ ions are 5/4nc and 5/6nc, respectively. The other parameters are the same of Figure 3.

Figure 4

Fig. 5. (Color online) (a) The proton energy spectra t = 90T0 for different thicknesses of the front-layer ions. (b) The proton energy spectra at the same instant for different thicknesses of the proton layer. Other parameters are the same of Figure 1a.