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Fast electron beam with manageable spotsize from laser interaction with the tailored cone-nanolayer target

Published online by Cambridge University Press:  01 August 2012

Huan Wang ,
Lihua Cao ,
Zongqing Zhao ,
M.Y. Yu ,
Yuqiu Gu  and
X.T. He
Huan Wang
Affiliation:
Center for Applied Physics and Technology, Peking University, Beijing, China Key Laboratory of High Energy Density Physics Simulation of the Ministry of Education, Peking University, Beijing, China
Lihua Cao*
Affiliation:
Center for Applied Physics and Technology, Peking University, Beijing, China Key Laboratory of High Energy Density Physics Simulation of the Ministry of Education, Peking University, Beijing, China Institute of Applied Physics and Computational Mathematics, Beijing, China
Zongqing Zhao
Affiliation:
Laser Fusion Research Center, China Academy of Engineering Physics, Mianyang, China
M.Y. Yu
Affiliation:
Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou, China Institute for Theoretical Physics I, Ruhr University, Bochum, Germany
Yuqiu Gu
Affiliation:
Laser Fusion Research Center, China Academy of Engineering Physics, Mianyang, China
X.T. He
Affiliation:
Center for Applied Physics and Technology, Peking University, Beijing, China Key Laboratory of High Energy Density Physics Simulation of the Ministry of Education, Peking University, Beijing, China Institute of Applied Physics and Computational Mathematics, Beijing, China Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou, China
*
Address correspondence and reprint requests to: Lihua Cao, Institute of Applied Physics and Computational Mathematics, Beijing, China, 100088. E-mail: cao_lihua@iapcm.ac.cn

Abstract

An advanced cone-nanolayer target with nanolayers on both inside and outside of the hollow-cone tip is proposed. Two-dimensional particle-in-cell simulations show that laser interaction with such cone-nanolayer targets can efficiently produce fast electron beams with manageable spotsize, and the beams can propagate for a relatively long distance in the vacuum beyond the cone tip.

Keywords

Advanced cone-nanolayer targetFast electron beamParticle-in-cellPropagation distanceSpotsize

Information

Type
Research Article
Information
Laser and Particle Beams , Volume 30 , Issue 4 , December 2012 , pp. 553 - 558
Copyright
Copyright © Cambridge University Press 2012

INTRODUCTION

The interaction of an ultrashort intense laser pulse with a solid target has been of considerable interest because of its many applications, such as in producing high-brightness K α and X-rays (Rousse et al., Reference Rousse, Rischel and Gauthier2001), laser-driven accelerators (Eliezer, Reference Eliezer2012), high-order harmonics generation (Teubner & Gibbon, Reference Teubner and Gibbon2009), high resolution radiography (Theobald et al., Reference Theobald, Akli, Clarke, Delettrez, Freeman, Glenzer, Green, Gregori, Heathcote, Izumi, King, Koch, Kuba, Lancaster, Mackinnon, Key, Mileham, Myatt, Neely, Norreys, Park, Pasley, Patel, Regan, Sawada, Shepherd, Snavely, Stephens, Stoeckl, Storm, Zhang and Sangster2006; Courtois et al., Reference Courtois, Edwards, Compant La Fontaine, Aedy, Barbotin, Bazzoli, Biddle, Brebion, Bourgade, Drew, Fox, Gardner, Gazave, Lagrange, Landoas, Ledain, Lefebvre, Mastrosimone, Pichoff, Pien, Ramsay, Simons, Sircombe, Stoeckl and Thorp2011), fast ignition in inertial confinement fusion (Tabak et al., Reference Tabak, Hammer, Glinsky, Kruer, Wilks, Woodworth, Campbell, Perry and Mason1994), diagnostics of high energy density physics (Borghesi et al., Reference Borghesi, Campbell, Schiavi, Willi, Mackinnon, Hicks, Patel, Gizzi, Galimberti and Clarke2002), etc. In general, the target configuration plays an important role in laser-electron energy conversion as well as the quality of the fast electron beams (FEBs). Specially designed targets with structured surfaces can enhance the laser energy absorption by the plasma particles, the brightness of the x and Kα radiations, the collimation of the hot electrons as well as their propagation distance (Murnane et al., Reference Murnane, Kapteyn, Gordon, Bokor, Glytsis and Falcone1993; Nishikawa et al., Reference Nishikawa, Nakano, Ahn, Uesugi and Serikama1997; Kulcsár et al., Reference Kulcsár, Al Mawlawi, Budnik, Herman, Moskovits, Zhao and Marjoribanks2000; Kahaly et al., Reference Kahaly, Yadav, Wang, Sengupta, Sheng, Das, Kaw and Kumar2008; Renard-Le Galloudec et al., Reference Renard-Le Galloudec, D'Humieres, Cho, Osterholz, Sentoku and Ditmire2009; Zhou et al., Reference Zhou, Wu, Cai, Chen, Cao, Chew and He2010b, 2010a; Cao et al., Reference Cao, Gu, Zhao, Cao, Huang, Zhou, He, Yu and Yu2010a, Reference Cao, Gu, Zhao, Cao, Huang, Zhou, Cai, He, Yu and Yu2010b; Zhao et al., Reference Zhao, Cao, Cao, Wang, Huang, Jiang, He, Wu, Zhu, Dong, Ding, Zhang, Gu, Yu and He2010; Ovchinnikov et al., Reference Ovchinnikov, Kostenko, Chefonov, Rosmej, Andreev, Agranat, Duan, Liu and Fortov2011), etc. The hollow cone target enhances both the energy coupling and the electron yield since the inner cone wall not only provides the fast electrons but also guides them to the cone tip (Kodama et al., Reference Kodama, Norreys, Mima, Dangor, Evans, Fujita, Kitagawa, Krushelnick, Miyakoshi, Miyanaga, Norimatsu, Rose, Shozaki, Shigemori, Sunahara, Tampo, Tanaka, Toyama, Yamanaka and Zepf2001; Sentoku et al., Reference Sentoku, Mima, Ruhl, Toyama, Kodama and Cowan2004; Nakamura et al., Reference Nakamura, Sakagami, Johzaki, Nagatomo and Mima2006, Reference Nakamura, Sakagami, Hohzaki, Johzaki, Nagatomo, Mima and Koga2007; Cai et al., Reference Cai, Mima, Zhou, Jozaki, Nagatomo, Sunahara and Mason2009). It has also been shown that a cone target with nanolayers inside its tip can more efficiently convert the laser energy into the electron energy and increase fast electrons yield (Cao et al., Reference Cao, Chen, Zhao, Cai, Wu, Gu, Yu, Yu and He2011). However, the hot electrons in the originally vacuum region behind the cone tip, as well as the FEB itself, generates a strong quasistatic space-charge or sheath electric field that tends to slow down the FEB.

In this paper, an advanced design of the cone-nanolayer target is proposed: nanolayers are attached to both the inside and outside of the hollow-cone tip. Two-dimensional particle-in-cell (PIC) simulations are used to investigate the interaction of a short high-intensity laser pulse with tailored cone-nanolayer targets of three different configurations. It is found that the spotsize of resulting FEB can be easily managed by adjusting the nanolayers at the cone tip, and the highly charged FEB can propagate a long distance into the initial backside vacuum.

TARGET CONFIGURATIONS AND SIMULATION PARAMETERS

Four cone-nanolayer target configurations are schematically shown in Figure 1. Figure 1a corresponds to the classical cone-nanolayer target T1, which consists of a hollow cone with parallel nanolayers inside its tip. Figure 1b is for the target T2, which consists of a classical cone-nanolayer target with three additional nanolayers outside its tip. The target T3 in Figure 1c has nine parallel nanolayers outside, each similar to that in T2. The target T4 in Figure 1d has a central nanolayer outside the cone tip and four converging nanolayers with the inclination angle ±12°. The cone has a 30° full-opening angle and the nanolayers are of length 5λ, width 0.4λ, and interlayer spacing 0.4λ, where λ = 1.06 µm is the initial laser wavelength.

Fig. 1.

(a) The classical cone-nanolayer target T1, the tailored cone-nanolayer targets (b) T2, (c) T3, and (d) T4. The cone has a 30° opening angle and the nanolayers are of length 5λ, width 0.4λ, and interlayer spacing 0.4λ.

To investigate the generation and propagating of electrons generated by laser interaction with the cone-nanolayer targets and the corresponding field structures, we use a two dimensions in space and three dimensions in velocity (2D3V) particle-in-dell (PIC) code (Ruhl et al., Reference Ruhl, Bonitz and Semkat2006). The targets are assumed to be pre-ionized Au5+ plasma with initial electron density 10n c, where n c is the critical density. A p-polarized Gaussian laser pulse with strength a = a 0 exp [−(t − t 0)2/τ2]exp[−(y − y 0)2/w 2] is incident normally from the left. The laser strength parameter is a 0 = eE 0/mω0c ~ 6.4, the pulse duration is τ = 15T, and t 0 = 50T, the spot radius is w = 10λ, and the laser axis is at y = y 0 = 20λ, where −e, m, ω0, T, E 0, and c are the electron charge, electron rest mass, laser frequency, laser period, maximum laser electric field amplitude, and the speed of light in vacuum, respectively. The size of the simulation box is 40 × 70 µm2. The laser propagates along the z axis and (y, z) is the simulation plane.

MANAGING THE BEAM SPOTSIZE AND ENHANCING THE NUMBER OF FORWARD-GOING FAST ELECTRONS

Irradiation of cone-nanolayers target by the intense laser (I ≈ 5.6 × 1019 W/cm2) pulse produces a lot of fast electrons with several-MeV mean energy inside the target. Before the FEB reaches the rear surface of the cone tip, the hottest laser generated electrons can escape from the cone, establishing around the latter a space-charge sheath potential that hinders further electron escape (Quinn et al., Reference Quinn, Yuan, Lin, Carroll, Tresca, Gray, Coury, Li, Li, Brenner, Robinson, Neely, Zielbauer, Aurand, Fils, Kuehl and McKenna2011). The induced sheath electric field is roughly E sheath ~ T h/eλD (Mora, Reference Mora2003), where λD = (T hɛ0/n ee 2)1/2 is the Debye length, n e and T h are the number density and temperature (in eV) of the hot electrons in the sheath region, and ɛ0 is the vacuum permittivity. This field hinders the lateral spread but also the forward propagation of the FEB, which can rapidly lose energy working against the sheath field.

For the laser and target parameters of the present simulations, the forward moving fast electrons appearing near the cone tip has mean energy ~2.7 MeV and density ~6n c. Thus, the sheath electric field E sheath ~1.81 × 1013 V/m can prevent the FEB from propagating forward. Some of the fast electrons are even pushed backward by the sheath electric field, as can be observed in Figure 2 for the distribution of the momentum vectors of the forward (black arrows) and backward (red arrows) fast electrons with energies >1 MeV at t = 145T. Figure 2a for the classical cone-nanolayer target T1 shows that the forward and backward moving fast electrons have almost the same spotsize (~ 13 µm), which is larger than the width (~ 8 µm) of nanolayer region in the inner cone tip. In contrast, with the tailored cone-nanolayer targets, the forward-going fast electrons can propagate longer distances beyond the cone tip at remarkably smaller spotsize, which depend strongly on the configuration of the nanolayers outside the cone tip. As shown in Figures 2b, 2c, and 2d, the spotsize of the forward-moving fast electrons is approximately 1.8 µm and 7 µm for T2 and T3, respectively, and for T4 it reduces gradually from 7.4 µm to 3.3 µm. Thus, the present tailored cone-nanolayer target can efficiently manage the spotsize of the FEB. On the other hand, we note that the backward moving electron bunches have a similar spotsize for all the targets considered here.

Fig. 2.

(Color online) The momentum vectors of the forward (black arrows) and backward (red arrows) fast electrons with energies E ≥ 1 MeV for (a) T1, (b) T2, (c) T3, and (d) T4 at t = 145T. The arrows show the magnitude and direction of the momentum of the fast electrons.

The left column of Figure 3 shows the spatial distribution at t = 85T of the time-averaged (over 5 laser periods) electric field E y (normalized by mω0c/e) outside the cone tip (i.e., 50 µm < z < 62 µm) for T2, T3, and T4, respectively. The right column of Figure 3 shows the corresponding lateral distribution of the averaged (over 5 laser periods) magnetic field B x (normalized by mω0/e) and electric field E y (normalized by mω0c/e). The magnetic field B x at the outside edge of the nanolayers is ~1.37 × 104 T. The electron gyroradius is r c ~mv/eB x, or r c /λ = (mω0/2πeB)(v/c), where v is the electron speed. For a 1 MeV electron around the nanolayers behind the cone tip, we have v/c ≈ 0.9411 and r c ≈ 0.1λ. The latter is smaller than the interlayer spacing 0.4λ, so that the fast electrons around the adjacent nanolayers do not mix. The space-charge field is given by E y ~ −n eeL y/ɛ0, where L y is the scale length of electric field in the y direction. Thus, for n e ~ 4n c (at z = 52.5 μm) and L y ~r c we obtain E y ~8 × 1012 V/m, which agrees well with the simulation result E ysimulation ~ 6 × 1012 V/m.

Fig. 3.

(Color online) Contours of the time averaged (over 5 laser periods) electric field E y outside of the cone tip (50 μm < z < 62 μm) for the targets (a) T2, (b) T3, (c) T4, and (d) T4 at t = 85T, where the black dashed lines mark the position z = 52.5 μm. The lateral distribution of the time averaged (over 5 laser periods) magnetic (B x, black solid line) and electric (E y, red dashed line) fields for the targets (d) T2, (e) T3, and (f) T4. The magnetic and electric fields are normalized by mω0c/e and mω0/e, respectively.

Figure 4 is a schematic diagram for the forces on the fast electrons along the nanolayers outside of the hollow-cone tip in the presence of the induced electric and magnetic fields. The forward fast electrons (red balls) in the vacuum gap induce a lateral electric field E y (indicated by orange colored ‘ ↑ ’ and ‘ ↓ ’) and a strong azimuthal magnetic field B x (indicated by red colored ‘ ⊗ ’ and ‘⊙’) around the nanolayers. Balancing return currents of cold electrons (indicated by blue balls) on the surfaces of the nanolayers generates a nearly symmetric but reverse magnetic field B x, indicated by blue colored ‘ ⊗ ’ and ‘⊙’. The combined magnetic field acting on the fast electrons is negative (positive) around the upper (lower) surfaces of the nanolayers, and E y is positive (negative) around the upper (lower) surfaces of the layers. This scenario corresponds to the simulation results shown in Figures 3d, 3e, and 3f for T2, T3, and T4, respectively. Accordingly, the electric field force (F electric =−eE y) tends to drive the fast electrons back to the surface of nanolayers and the y component of the Lorentz force F Lorentz1 = −ev zB x tends to pull the fast electrons into the vacuum gap between the nanolayers. It is worth noting that amplitude of normalized electric field E y is greater than that of the normalized magnetic field B x, as shown in Figures 3d, 3e, and 3f and v y < c, so that |F electric| > |F Lorentz1|. Thus the fast electrons have a net transverse velocity directing inward to the surfaces of the nanolayers, so that the z component of the Lorentz force F Lorentz2 = −ev yB x accelerates the fast electron forward and prolong the propagating distance along the nanolayers. We also note that there is a small gap between the peaks of B x and E y, as shown in Figures 3d, 3e, and 3f, i.e., the magnetic field is closer to the surfaces of nanolayers than the electric field (Kodama et al., Reference Kodama, Sentoku, Chen, Kumar, Hatchett, Toyama, Cowan, Freeman, Fuchs, Izawa, Key, Kitagawa, Kondo, Matsuoka, Nakamura, Nakatsutsumi, Norreys, Norimatsu, Snavely, Stephens, Tampo, Tanaka and Yabuuchi2004).

Fig. 4.

(Color online) Schematic diagram describing the induced electric and magnetic fields, and the forces acting on the fast electrons. The inset at the top right corner is the configuration segment of Target 3, and the central figure represents the part in the red box. The regime in beige color represents the nanolayers outside the cone tip, the red (blue) balls represent the fast electrons (cold return-current electrons) moving forward (backward) in vacuum gap near the surface of nanolayers (inside the nanolayers). Correspondingly, the magnetic fields B x induced by the fast electrons (cold return-current electrons) are indicated by red (blue) colored ‘⊗’ (in the x direction) and ‘⊙’ (in the –x direction), and the combined magnetic field is indicated by black colored ‘⊗’ and ‘⊙’. The electric fields E y in y (–y) direction are indicated by orange colored ‘↑’ (in the y direction) or ‘↓’ (in the –y direction) near the upper (lower) surface of the nanolayers. On the right side, the component of electric force F electric = −eE y is marked by orange colored arrow, and the two components of Lorentz force in y and z-directions (F Lorentz1 = −ev zB x and F Lorentz2 = −ev yB x) are indicated by black colored arrows.

The key for decreasing the spatial divergence of the fast electrons is to manage the distribution of energetic electrons in the lateral direction. Figure 5 gives the lateral distribution of the number of forward fast electrons with energies E ≥ 1 MeV at 145T. One can see that there is a remarkable increase in the number and decrease in the spotsize of the forward propagating fast electrons for the tailored cone-nanolayer targets T2, T3, and T4 as compared to the classical target T1. For all the three tailored cone-nanolayer targets, the lateral size of the FEB is close to the width of the nanolayer stack outside the cone tip.

Fig. 5.

(Color online) The transversal distribution of the number of forward propagating fast electrons with energies E ≥ 1 MeV at t = 145T, for (a) T1, (b) T2, (c) T3, and (d) T4.

Figure 6 shows the time evolution of the forward moving fast electrons with E ≥ 1 MeV. We see that with the tailored targets, there are significantly more fast electrons propagating for a longer distance than that with the classical cone-nanolayer target T1. This increase in the number of fast electrons can be attributed to the guiding effect of the nanolayers outside the cone tip. The laser-to-beam conversion efficiency has also been enhanced for the tailored targets, that is, the maximum efficiency for T2 is approximately 2.5%, for T3 is 7.5%, for T4 is 4.4%, compared with 1.1% for T1. Figure 7 shows the energy distribution of the fast (E ≥ 1 MeV) forward propagating electrons in the (y,z) plane. Here one can clearly see that the tailored cone-nanolayer targets can limit the spotsize, enhance the number of forward-going fast electrons, and prolong the propagation distance of FEB.

Fig. 6.

(Color online) Time evolution of the number of forward-going fast electrons with energies E ≥ 1 MeV for T1 (blue dash-dotted line), T2 (red dotted line), T3 (black solid line), and T4 (cyan dashed line).

Fig. 7.

(Color online) The spatial energy distribution of forward-going fast electrons with energies E ≥ 1 MeV within 50 μm < z < 62 μm and 10 μm < y < 30 μm) for (a) T1, (b) T2, (c)T3, and (d) T4 at t = 145T.

CONCLUSION

In conclusion, tailored cone-nanolayer targets with nanolayers at the outer tip of cone-nanolayer target are proposed and investigated. Two-dimensional PIC simulations show that the tailored cone-nanolayer targets can efficiently limit the spotsize of the FEB and increase its charge and propagation distance beyond the cone tip, as compared to that from the classical cone-nanolayer target. These improvements can be attributed to the confining magnetic and electric fields induced by the fast electrons propagation along the plasma layers behind the cone tip. Therefore the tailored cone-nanolayer target may be useful for generating collimated or microfocused FEBs for various applications.

ACKNOWLEDGMENTS

This work is supported by the Natural Science Foundation of China (Grants 11175030, 10835003, 11175029, and 10975025), the National High-Tech ICF Committee of China, and the Science and Technology Foundation of China Academy of Engineering Physics (Grant 2011A0102008). H. Wang would like to thank B. Liu, D. Wu, H. C. Wu and Q. Jia for their discussions.

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Figure 0

Fig. 1. (a) The classical cone-nanolayer target T1, the tailored cone-nanolayer targets (b) T2, (c) T3, and (d) T4. The cone has a 30° opening angle and the nanolayers are of length 5λ, width 0.4λ, and interlayer spacing 0.4λ.

Figure 1

Fig. 2. (Color online) The momentum vectors of the forward (black arrows) and backward (red arrows) fast electrons with energies E ≥ 1 MeV for (a) T1, (b) T2, (c) T3, and (d) T4 at t = 145T. The arrows show the magnitude and direction of the momentum of the fast electrons.

Figure 2

Fig. 3. (Color online) Contours of the time averaged (over 5 laser periods) electric field Ey outside of the cone tip (50 μm < z < 62 μm) for the targets (a) T2, (b) T3, (c) T4, and (d) T4 at t = 85T, where the black dashed lines mark the position z = 52.5 μm. The lateral distribution of the time averaged (over 5 laser periods) magnetic (Bx, black solid line) and electric (Ey, red dashed line) fields for the targets (d) T2, (e) T3, and (f) T4. The magnetic and electric fields are normalized by mω0c/e and mω0/e, respectively.

Figure 3

Fig. 4. (Color online) Schematic diagram describing the induced electric and magnetic fields, and the forces acting on the fast electrons. The inset at the top right corner is the configuration segment of Target 3, and the central figure represents the part in the red box. The regime in beige color represents the nanolayers outside the cone tip, the red (blue) balls represent the fast electrons (cold return-current electrons) moving forward (backward) in vacuum gap near the surface of nanolayers (inside the nanolayers). Correspondingly, the magnetic fields Bx induced by the fast electrons (cold return-current electrons) are indicated by red (blue) colored ‘⊗’ (in the x direction) and ‘⊙’ (in the –x direction), and the combined magnetic field is indicated by black colored ‘⊗’ and ‘⊙’. The electric fields Ey in y (–y) direction are indicated by orange colored ‘↑’ (in the y direction) or ‘↓’ (in the –y direction) near the upper (lower) surface of the nanolayers. On the right side, the component of electric force Felectric = −eEy is marked by orange colored arrow, and the two components of Lorentz force in y and z-directions (FLorentz1 = −evzBx and FLorentz2 = −evyBx) are indicated by black colored arrows.

Figure 4

Fig. 5. (Color online) The transversal distribution of the number of forward propagating fast electrons with energies E ≥ 1 MeV at t = 145T, for (a) T1, (b) T2, (c) T3, and (d) T4.

Figure 5

Fig. 6. (Color online) Time evolution of the number of forward-going fast electrons with energies E ≥ 1 MeV for T1 (blue dash-dotted line), T2 (red dotted line), T3 (black solid line), and T4 (cyan dashed line).

Figure 6

Fig. 7. (Color online) The spatial energy distribution of forward-going fast electrons with energies E ≥ 1 MeV within 50 μm < z < 62 μm and 10 μm < y < 30 μm) for (a) T1, (b) T2, (c)T3, and (d) T4 at t = 145T.