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Shockwaves and filaments induced by counter-streaming laser-produced plasmas
High Energy Density Physics 9 (2013) 239e242
Contents lists available at SciVerse ScienceDirect
High Energy Density Physics journal homepage: www.elsevier.com/locate/hedp
Shockwaves and filaments induced by counter-streaming laserproduced plasmas D.W. Yuan a, Y.T. Li a, *, X. Liu a, Y. Zhang a, J.Y. Zhong b, W.D. Zheng c, Q.L. Dong a, M. Chen a, Y. Sakawa d, T. Morita d, Y. Kuramitsu d, T.N. Kato d, H. Takabe d, Yong-Joo Rhee e, J.Q. Zhu f, G. Zhao b, J. Zhang a, g a
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China Institute of Applied Physics and Computational Mathematics, Beijing 100094, China d Institute of Laser Engineering, Osaka University, 2-6 Yamada-oka, Suita, Osaka, 565-0871, Japan e Laboratory for Quantum Optics, Korea Atomic Energy Research Institute, 1045 Daedeok Street Yuseong-gu, Daejon 305-353, South Korea f National Laboratory on High Power Lasers and Physics, Shanghai, 201800, China g Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 31 May 2012 Received in revised form 26 October 2012 Accepted 4 January 2013 Available online 28 January 2013
The interaction between two counter-streaming laser-produced plasmas is studied with shadowgraph and interferometry on the Shenguang II (SG-II) laser facility. Shockwaves and filaments are observed at different timing. The simulation and theoretical analysis indicate that these structures are probably induced by collisionless mechanisms. Ó 2013 Elsevier B.V. All rights reserved.
Keywords: Shock waves Filaments
1. Introduction Collisionless shockwave is defined that the shock transition occurring on a length scale is much shorter than the particle mean free paths. Coulomb collisions between particles are unimportant for the shockwave generation. This concept was first proposed in 1966 [1]. The collisionless shockwave is one important phenomenon in astrophysics. It has been observed in many astronomical phenomena such as solar winds and supernova remnants. It is believed that the dissipation process and the energy transformation happened in the shockwave are relative to the generation of the high energy particles and cosmic rays [2e4]. The idea using the laser-produced plasmas to simulate astrophysical phenomena has been proposed since the invention of the laser [5]. The rapid development of high-power laser technology and the proposed similar principle [6], which allows to scale the laboratory plasmas to the astrophysical objects such as supernova remnants, have brought new opportunities to laboratory astrophysics. Theoretical and experimental researches about the
* Corresponding author. Tel.: þ86 10 82649355; fax: þ86 10 82649356. E-mail addresses: [email protected], [email protected] (Y.T. Li). 1574-1818/$ e see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.hedp.2013.01.008
generation of the collisionless shockwave have been performed by several groups [7e13]. In this paper, we present our observation of shockwaves and filaments induced by two counter-streaming plasmas produced by the high-power SG-II laser facility. The simulation and theoretical analysis indicate that these structures are probably induced by collisionless mechanisms. 2. Experimental setup The experiments were performed at the SG-II laser facility, which can deliver a total energy of 2.0 kJ in 1 ns at 3u (351 nm). Fig. 1 shows a schematic view of the experimental setup. The eight laser beams of SG-II laser were divided into two bunches. Here, two 2 mm 2 mm 0.1 mm thin separate hydrocarbon (CH) foils facing each other were used as the targets. The distance between foils is 4.5 mm. The two laser bunches were focused onto the facing surfaces of the CH foils to generate two counter-streaming plasmas. The focal spots, 400 mm 25 mm apart, have diameters about 150 um FWHM, giving a laser intensity of 5.7 1013 W/cm2. The interactions of two plasma streams were probed by another laser pulse with a wavelength of 526 nm and a duration of 30 ps parallel to the surface of target foils using a modified Nomarski
240
D.W. Yuan et al. / High Energy Density Physics 9 (2013) 239e242
Fig. 1. Schematic view of the experimental setup. The target is double CH foils. The size of a CH foil is 2 2 0.1 mm3 and the distance between foils is 4.5 mm. A Nomarski interferometer is used to measure the electron density of plasma. The shadowgraph gives the shape of two counter-streaming plasmas. Two pinhole cameras are used to monitor the X-ray emission from the CH targets.
interferometer with a magnification of 3.5. A time series of snapshots were obtained by changing the delay between the probe pulse and the main pulse. Two pinhole cameras with magnification of 10 were also used to monitor the X-ray emission from the CH targets. 3. Results and discussion Fig. 2 shows the interferograms taken at delay times of 1 ns, 2 ns, 3 ns, 5 ns, 9 ns and corresponding measured density profiles along the blue line in Fig. 2(b), respectively. The delay is defined as the time separation between the falling edges of the probe and the main pulses. The main laser spots are labelled by the red circles in Fig. 2(a) and the initial position of the CH foils is marked by the red columns in Fig. 2(c). Two dark regions in Fig. 2 are owing to that the density gradient is much higher and the probing light is refracted out of the collective optical system. At 1 ns, the fringes near the target surface are shifted due to two plasmas expanding. The fringes in the middle are still straight. This indicates that both of
plasma streams meet each other but no shockwaves form. At 2 ns, the fringes in the middle become discontinuous. The width of this density jump region is about 150 mm. At 3 ns, two plasma streams continue to propagate after collision and then penetrate through each other. The fringes in the middle are shifted less, illustrating the interaction between streams becoming weak. At 5 ns, there are some filamentous structures appeared in the middle region caused by some plasma instability. At 9 ns, a density jump region appears again. Fig. 2(f) shows the density profiles obtained by using Abel inversion of the measured interferograms. The horizontal coordinate represents the distance between CH foils. The longitudinal coordinate represents the electron density. An obvious density jump arises in the regions from 2350 mm to 2500 mm. This abrupt density change indicates that there is the formation of shock and the width of shock is about 150 mm. The electron density of the plasmas in the interaction region is about 1019 cm3. The expansion velocity is 1.1 108 cm/s calculated by irradiating only a target with one bunches of four laser pulses. Using the formula for the mean free paths [14],
Fig. 2. Panels (a)e(f) are the interferograms obtained at delay times of 1 ns, 2 ns, 3 ns, 5 ns, 9 ns and corresponding measured density profiles along the blue line in Fig. 2(b), respectively. Red circles in (a) represent the laser focal spots. The green boxes in (b) and (e) indicate the density jump regions. The red columns in (c) represent the initial position of the targets. The green box in (d) indicates the filamentous structures. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
D.W. Yuan et al. / High Energy Density Physics 9 (2013) 239e242
lii ¼
m2i v412 4pe4 Z 4 nLnL
12
where n is the ion density, v12 is the relative plasma expanding velocity, Z is the ionization state of plasma, mi is the ion mass, e is the elementary electric charge and LnL12 is Coulomb logarithm. In our experiment, n ¼ 1019 cm3, Z ¼ 6, LnL12 ¼ 6; v12 ¼ 2.2 108 cm/s, mi ¼ 20.04 1027 kg, e ¼ 1.6 1019 C, the low limit of lii is estimated to be 110 cm. Since the width of the measured density jump is much shorter than lii, the interaction between plasma streams at 2 ns and 3 ns in our experiment is believed to be collisionless. Previous works with particle-in-cell (PIC) simulations [15,16] show that the electrostatic instability (ESI), which is driven by the large difference between the electron temperature and ion temperature, can excite the collisionless shockwaves in counterstreaming plasmas. We have carried out hydrodynamical simulations with the same conditions of our experiment. The electron and ion temperatures are obtained by 2D radiative-hydrodynamics simulations with XRL2D codes, which is a two temperature model. In this model, the evolution of electron temperature and ion temperature are not the same. The results show that the electron temperature is much higher than ion temperature before two plasma streams colliding. Moreover, the larger the distance between plasma and the surface of CH target, the larger the ratio of the electron temperature to ion temperature. Fig. 3 shows the distribution of the ratio of the electron temperature to ion temperature at 2.5 ns. The X-axis represents the distance from the CH target surface and the Y-axis represents the position along the target surface. From Fig. 3 we can see the large difference between the electron and ion temperatures, particularly at the plasma edge. Such differences may induce the shockwave observed at 2 ns due to the electrostatic interaction between the two plasmas. According to the previous PIC simulations [17,18], electromagnetic Weibel-type instability (WBI) beside ESI could be also excited during the interaction between two counter-streaming plasmas. The growth rate of ESI grows up much quicker than that of WBI at the early stage. Therefore, ESI plays a major role in the interaction between plasma streams at the beginning. Meanwhile, ESI could produce an electric field heating the ion, and reduce the difference between electron and ion temperature. This will result in
Fig. 3. Distribution of the electron to ion temperature ratio at 2.5 ns, obtained with the hydrodynamics code. The X-axis represents the distance from the CH target surface and the Y-axis represents the position along the target surface. The scale on the right stands for the ratio of the electron temperature to ion temperature.
241
the electrostatic interaction between the plasmas to become weak with time. This process agrees with experimental results at 3 ns, at which the fringes in the interaction region are shifted less. Fig. 4 shows a shadowgraph taken at 5 ns [The corresponding interferogram shown in Fig. 2(d)]. The filamentous structures are much clear in the shadowgraph. The length of the filaments is about 550 mm. The filaments observed are not well understood till now. There are some instabilities inducing filamentary structures, such as electrostatic instability (ESI), electromagnetic Weibel-type instability (WBI), RayleigheTaylor instability (RTI) and so on. According to the theoretical simulations [17,18], the length of filaments excited by the WBI is larger than that caused by the ESI, moreover, larger than the plasma wavelength, i.e., LESI < l < LWBI, where L is the length of the filamentous structures. The wavelength, l ¼ c=upe ¼ cð4pne0 e2 =me Þ1=2 , where ne is the electron density, and c is the light speed, is estimated to be 2 mm. It is smaller than the length of the filaments (w550 mm). This may indicates that the filaments are not caused by ESI. Simulations show that WBI induced filaments can be generated only when the flow velocity [18] or the shock velocity is extremely high [19]. Such high velocity may be reached only on NIF laser facility. As for RTI, it is an instability of an interface between two fluids of different densities, which occurs when the lighter fluid is pushing the heavier fluid [20]. In our experiments, the two target foils were irradiated by the identical laser pulses with basically same energy, durations, and focal spots, so the parameters (density, temperature and pressure) of the two plasmas should be symmetrical. Therefore, the filaments are also not caused by the RTI. Understanding the filamentous structures observed in our experiment needs to further experimental and theoretical investigation. In addition, we observed the interaction for a nonsymmetrical laser driven condition in the experiment. The right CH foil was heated by four laser beams with a focal spot of 350 mm FWHM, while the left CH foil heated by three laser beams with a focal spot of 150 mm FWHM at a delay time of 1.5 ns. Fig. 5(a) and (b) shows the interferogram and the shadowgraph at 2 ns after the three laser beams heating on the left target. The expansion velocity of plasma from the left target is about 1.1 108 cm/s, the right one about 0.8 108 cm/s. The width of interaction region is about 500 mm. The electron density is 1019 cm3. The mean free path is about 59 cm using the above formula. It is smaller than the width of interaction
Fig. 4. (a) Shadowgraph obtained at delay time of 5 ns. (b) Post-processed shadowgraph at the same delay time to reduce the noise. The green boxes in (a) and (b) show the region where the filaments are induced. The length of the filaments is about 550 mm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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D.W. Yuan et al. / High Energy Density Physics 9 (2013) 239e242
Fig. 5. (a) The interferogram obtained at delay time of 1.5 ns. The red columns represent the position of the CH foils. The green circles represent the laser focal spots. The pink circle represents the left plasma edge at delay time 2 ns and the yellow circle represents the right plasma edge at delay time 3.5 ns. The width of interaction region is about 500 mm. (b) The shadowgraph at the same delay time. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
region. Therefore, the interaction is also collisionless. Note that the structures are mushroom-like, instead of filaments. 4. Conclusion The interaction between two counter-streaming laser-produced, low-density, non-relativistic plasmas is investigated by using the SG-II laser beams to irradiate double-foil targets. During the interaction density jump and filamentous structures are observed. The structures are probably due to collisionless mechanisms. However, understanding the jump and the filamentous structures observed in our experiment needs further experimental and theoretical investigations. Acknowledgements This work is supported by the National Nature Science Foundation of China (Grant Nos. 11135012 and 10925421). The authors thank the staff of SG-II laser facility for operating the laser and target area. References [1] R.Z. Sagdeev, Cooperative phenomena and shock waves in collisionless plasmas, Rev. Plasma Phys. 4 (1966) 23. [2] A.R. Bell, S.G. Lucek, Cosmic ray acceleration in pulsar-driven supernova remnants: the effect of scattering, Mon. Not. R. Astron. Soc. 283 (1996) 1083e1088. [3] R.D. Blandford, J.P. Ostriker, Particle acceleration by astrophysical shocks, Astrophys. J. Lett. 221 (1978) L29. [4] W.I. Axford, E. Leer, J.F. McKenzie, The structure of cosmic ray shocks, Astron. Astrophys. 111 (1982) 317e325. [5] J.M. Dawson, On the production of plasma by giant pulse lasers, Phys. Fluids 7 (1964) 981.
[6] D. Ryutov, R.P. Drake, J. Kane, E. Liang, B.A. Remington, W.M. Wood-Vasey, Similarity criteria for the laboratory simulation of supernova hydrodynamics, Astrophys. J. 518 (1999) 821. [7] L. Romagnani, S.V. Bulanov, M. Borghesi, P. Audebert, J.C. Gauthier, K. Löwenbrück, A.J. Mackinnon, P. Patel, G. Pretzler, T. Toncian, O. Willi, Observation of collisionless shocks in laser-plasma experiments, Phys. Rev. Lett. 101 (2008) 025004. [8] Y. Nagamine, H. Nakashima, Analysis of plasma behavior in a magnetic thrust chamber of a laser fusion rocket, Fusion Technol. 35 (1999) 62. [9] G. Sorasio, M. Marti, R. Fonseca, L.O. Silva, Very high Mach-number electrostatic shocks in collisionless plasmas, Phys. Rev. Lett. 96 (2006) 045005. [10] B. Lembege, F. Simonet, Hybrid and particle simulations of an interface expansion and of collisionless shock: a comparative and quantitative study, Phys. Plasmas 8 (2001) 3967. [11] R.P. Drake, The design of laboratory experiments to produce collisionless shocks of cosmic relevance, Phys. Plasmas 7 (2000) 4690. [12] C. Courtois, R.A.D. Grundy, A.D. Ash, D.M. Chambers, N.C. Woolsey, Experiment on collisionless plasma interaction with applications to supernova remnant physics, Phys. Plasmas 11 (2004) 3386. [13] X. Liu, Y.T. Li, Y. Zhang, J.Y. Zhong, W.D. Zheng, Q.L. Dong, M. Chen, G. Zhao, Y. Sakawa, T. Morita, Y. Kuramitsu, T.N. Kato, L.M. Chen, X. Lu, J.L. Ma, W.M. Wang, Z.M. Sheng, H. Takabe, Y.-J. Rhee, Y.K. Ding, S.E. Jiang, S.Y. Liu, J.Q. Zhu, J. Zhang, Collisionless shockwaves formed by counter-streaming laser-produced plasmas, New J. Phys. 13 (2011) 093001. [14] C. Chenais-Popovics, P. Renaudin, O. Rancu, F. Gilleron, J.-C. Gauthier, Kinetic to thermal energy transfer and interpenetration in the collision of laserproduced plasmas, Phys. Plasmas 4 (1997) 190. [15] D.W. Forslund, C.R. Shonk, Formation and structure of electrostatic collisionless shocks, Phys. Rev. Lett. 25 (1970) 1699. [16] R.J. Mason, Ion and electron pressure effects on magnetosonic shock formation, Phys. Fluids 15 (1972) 845. [17] T.N. Kato, H. Takabe, Nonrelativistic collisionless shocks in unmagnetized electron-ion plasmas, Astrophys. J. 681 (2008) L93. [18] T.N. Kato, H. Takabe, Electrostatic and electromagnetic instabilities associated with electrostatic shocks: two-dimensional particle-in-cell simulation, Phys. Plasmas 17 (2010) 032114. [19] F. Fiuza, R.A. Fonseca, J. Tonge, W.B. Mori, L.O. Silva, Weibel-instabilitymediated collisionless shocks in the laboratory with ultra-intense lasers, Phys. Rev. Lett. 108 (2012) 235004. [20] D.H. Sharp, An overview of RayleigheTaylor instability, Phys. D 12 (1984) 3e18.
Contents lists available at SciVerse ScienceDirect
High Energy Density Physics journal homepage: www.elsevier.com/locate/hedp
Shockwaves and filaments induced by counter-streaming laserproduced plasmas D.W. Yuan a, Y.T. Li a, *, X. Liu a, Y. Zhang a, J.Y. Zhong b, W.D. Zheng c, Q.L. Dong a, M. Chen a, Y. Sakawa d, T. Morita d, Y. Kuramitsu d, T.N. Kato d, H. Takabe d, Yong-Joo Rhee e, J.Q. Zhu f, G. Zhao b, J. Zhang a, g a
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China Institute of Applied Physics and Computational Mathematics, Beijing 100094, China d Institute of Laser Engineering, Osaka University, 2-6 Yamada-oka, Suita, Osaka, 565-0871, Japan e Laboratory for Quantum Optics, Korea Atomic Energy Research Institute, 1045 Daedeok Street Yuseong-gu, Daejon 305-353, South Korea f National Laboratory on High Power Lasers and Physics, Shanghai, 201800, China g Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 31 May 2012 Received in revised form 26 October 2012 Accepted 4 January 2013 Available online 28 January 2013
The interaction between two counter-streaming laser-produced plasmas is studied with shadowgraph and interferometry on the Shenguang II (SG-II) laser facility. Shockwaves and filaments are observed at different timing. The simulation and theoretical analysis indicate that these structures are probably induced by collisionless mechanisms. Ó 2013 Elsevier B.V. All rights reserved.
Keywords: Shock waves Filaments
1. Introduction Collisionless shockwave is defined that the shock transition occurring on a length scale is much shorter than the particle mean free paths. Coulomb collisions between particles are unimportant for the shockwave generation. This concept was first proposed in 1966 [1]. The collisionless shockwave is one important phenomenon in astrophysics. It has been observed in many astronomical phenomena such as solar winds and supernova remnants. It is believed that the dissipation process and the energy transformation happened in the shockwave are relative to the generation of the high energy particles and cosmic rays [2e4]. The idea using the laser-produced plasmas to simulate astrophysical phenomena has been proposed since the invention of the laser [5]. The rapid development of high-power laser technology and the proposed similar principle [6], which allows to scale the laboratory plasmas to the astrophysical objects such as supernova remnants, have brought new opportunities to laboratory astrophysics. Theoretical and experimental researches about the
* Corresponding author. Tel.: þ86 10 82649355; fax: þ86 10 82649356. E-mail addresses: [email protected], [email protected] (Y.T. Li). 1574-1818/$ e see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.hedp.2013.01.008
generation of the collisionless shockwave have been performed by several groups [7e13]. In this paper, we present our observation of shockwaves and filaments induced by two counter-streaming plasmas produced by the high-power SG-II laser facility. The simulation and theoretical analysis indicate that these structures are probably induced by collisionless mechanisms. 2. Experimental setup The experiments were performed at the SG-II laser facility, which can deliver a total energy of 2.0 kJ in 1 ns at 3u (351 nm). Fig. 1 shows a schematic view of the experimental setup. The eight laser beams of SG-II laser were divided into two bunches. Here, two 2 mm 2 mm 0.1 mm thin separate hydrocarbon (CH) foils facing each other were used as the targets. The distance between foils is 4.5 mm. The two laser bunches were focused onto the facing surfaces of the CH foils to generate two counter-streaming plasmas. The focal spots, 400 mm 25 mm apart, have diameters about 150 um FWHM, giving a laser intensity of 5.7 1013 W/cm2. The interactions of two plasma streams were probed by another laser pulse with a wavelength of 526 nm and a duration of 30 ps parallel to the surface of target foils using a modified Nomarski
240
D.W. Yuan et al. / High Energy Density Physics 9 (2013) 239e242
Fig. 1. Schematic view of the experimental setup. The target is double CH foils. The size of a CH foil is 2 2 0.1 mm3 and the distance between foils is 4.5 mm. A Nomarski interferometer is used to measure the electron density of plasma. The shadowgraph gives the shape of two counter-streaming plasmas. Two pinhole cameras are used to monitor the X-ray emission from the CH targets.
interferometer with a magnification of 3.5. A time series of snapshots were obtained by changing the delay between the probe pulse and the main pulse. Two pinhole cameras with magnification of 10 were also used to monitor the X-ray emission from the CH targets. 3. Results and discussion Fig. 2 shows the interferograms taken at delay times of 1 ns, 2 ns, 3 ns, 5 ns, 9 ns and corresponding measured density profiles along the blue line in Fig. 2(b), respectively. The delay is defined as the time separation between the falling edges of the probe and the main pulses. The main laser spots are labelled by the red circles in Fig. 2(a) and the initial position of the CH foils is marked by the red columns in Fig. 2(c). Two dark regions in Fig. 2 are owing to that the density gradient is much higher and the probing light is refracted out of the collective optical system. At 1 ns, the fringes near the target surface are shifted due to two plasmas expanding. The fringes in the middle are still straight. This indicates that both of
plasma streams meet each other but no shockwaves form. At 2 ns, the fringes in the middle become discontinuous. The width of this density jump region is about 150 mm. At 3 ns, two plasma streams continue to propagate after collision and then penetrate through each other. The fringes in the middle are shifted less, illustrating the interaction between streams becoming weak. At 5 ns, there are some filamentous structures appeared in the middle region caused by some plasma instability. At 9 ns, a density jump region appears again. Fig. 2(f) shows the density profiles obtained by using Abel inversion of the measured interferograms. The horizontal coordinate represents the distance between CH foils. The longitudinal coordinate represents the electron density. An obvious density jump arises in the regions from 2350 mm to 2500 mm. This abrupt density change indicates that there is the formation of shock and the width of shock is about 150 mm. The electron density of the plasmas in the interaction region is about 1019 cm3. The expansion velocity is 1.1 108 cm/s calculated by irradiating only a target with one bunches of four laser pulses. Using the formula for the mean free paths [14],
Fig. 2. Panels (a)e(f) are the interferograms obtained at delay times of 1 ns, 2 ns, 3 ns, 5 ns, 9 ns and corresponding measured density profiles along the blue line in Fig. 2(b), respectively. Red circles in (a) represent the laser focal spots. The green boxes in (b) and (e) indicate the density jump regions. The red columns in (c) represent the initial position of the targets. The green box in (d) indicates the filamentous structures. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
D.W. Yuan et al. / High Energy Density Physics 9 (2013) 239e242
lii ¼
m2i v412 4pe4 Z 4 nLnL
12
where n is the ion density, v12 is the relative plasma expanding velocity, Z is the ionization state of plasma, mi is the ion mass, e is the elementary electric charge and LnL12 is Coulomb logarithm. In our experiment, n ¼ 1019 cm3, Z ¼ 6, LnL12 ¼ 6; v12 ¼ 2.2 108 cm/s, mi ¼ 20.04 1027 kg, e ¼ 1.6 1019 C, the low limit of lii is estimated to be 110 cm. Since the width of the measured density jump is much shorter than lii, the interaction between plasma streams at 2 ns and 3 ns in our experiment is believed to be collisionless. Previous works with particle-in-cell (PIC) simulations [15,16] show that the electrostatic instability (ESI), which is driven by the large difference between the electron temperature and ion temperature, can excite the collisionless shockwaves in counterstreaming plasmas. We have carried out hydrodynamical simulations with the same conditions of our experiment. The electron and ion temperatures are obtained by 2D radiative-hydrodynamics simulations with XRL2D codes, which is a two temperature model. In this model, the evolution of electron temperature and ion temperature are not the same. The results show that the electron temperature is much higher than ion temperature before two plasma streams colliding. Moreover, the larger the distance between plasma and the surface of CH target, the larger the ratio of the electron temperature to ion temperature. Fig. 3 shows the distribution of the ratio of the electron temperature to ion temperature at 2.5 ns. The X-axis represents the distance from the CH target surface and the Y-axis represents the position along the target surface. From Fig. 3 we can see the large difference between the electron and ion temperatures, particularly at the plasma edge. Such differences may induce the shockwave observed at 2 ns due to the electrostatic interaction between the two plasmas. According to the previous PIC simulations [17,18], electromagnetic Weibel-type instability (WBI) beside ESI could be also excited during the interaction between two counter-streaming plasmas. The growth rate of ESI grows up much quicker than that of WBI at the early stage. Therefore, ESI plays a major role in the interaction between plasma streams at the beginning. Meanwhile, ESI could produce an electric field heating the ion, and reduce the difference between electron and ion temperature. This will result in
Fig. 3. Distribution of the electron to ion temperature ratio at 2.5 ns, obtained with the hydrodynamics code. The X-axis represents the distance from the CH target surface and the Y-axis represents the position along the target surface. The scale on the right stands for the ratio of the electron temperature to ion temperature.
241
the electrostatic interaction between the plasmas to become weak with time. This process agrees with experimental results at 3 ns, at which the fringes in the interaction region are shifted less. Fig. 4 shows a shadowgraph taken at 5 ns [The corresponding interferogram shown in Fig. 2(d)]. The filamentous structures are much clear in the shadowgraph. The length of the filaments is about 550 mm. The filaments observed are not well understood till now. There are some instabilities inducing filamentary structures, such as electrostatic instability (ESI), electromagnetic Weibel-type instability (WBI), RayleigheTaylor instability (RTI) and so on. According to the theoretical simulations [17,18], the length of filaments excited by the WBI is larger than that caused by the ESI, moreover, larger than the plasma wavelength, i.e., LESI < l < LWBI, where L is the length of the filamentous structures. The wavelength, l ¼ c=upe ¼ cð4pne0 e2 =me Þ1=2 , where ne is the electron density, and c is the light speed, is estimated to be 2 mm. It is smaller than the length of the filaments (w550 mm). This may indicates that the filaments are not caused by ESI. Simulations show that WBI induced filaments can be generated only when the flow velocity [18] or the shock velocity is extremely high [19]. Such high velocity may be reached only on NIF laser facility. As for RTI, it is an instability of an interface between two fluids of different densities, which occurs when the lighter fluid is pushing the heavier fluid [20]. In our experiments, the two target foils were irradiated by the identical laser pulses with basically same energy, durations, and focal spots, so the parameters (density, temperature and pressure) of the two plasmas should be symmetrical. Therefore, the filaments are also not caused by the RTI. Understanding the filamentous structures observed in our experiment needs to further experimental and theoretical investigation. In addition, we observed the interaction for a nonsymmetrical laser driven condition in the experiment. The right CH foil was heated by four laser beams with a focal spot of 350 mm FWHM, while the left CH foil heated by three laser beams with a focal spot of 150 mm FWHM at a delay time of 1.5 ns. Fig. 5(a) and (b) shows the interferogram and the shadowgraph at 2 ns after the three laser beams heating on the left target. The expansion velocity of plasma from the left target is about 1.1 108 cm/s, the right one about 0.8 108 cm/s. The width of interaction region is about 500 mm. The electron density is 1019 cm3. The mean free path is about 59 cm using the above formula. It is smaller than the width of interaction
Fig. 4. (a) Shadowgraph obtained at delay time of 5 ns. (b) Post-processed shadowgraph at the same delay time to reduce the noise. The green boxes in (a) and (b) show the region where the filaments are induced. The length of the filaments is about 550 mm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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D.W. Yuan et al. / High Energy Density Physics 9 (2013) 239e242
Fig. 5. (a) The interferogram obtained at delay time of 1.5 ns. The red columns represent the position of the CH foils. The green circles represent the laser focal spots. The pink circle represents the left plasma edge at delay time 2 ns and the yellow circle represents the right plasma edge at delay time 3.5 ns. The width of interaction region is about 500 mm. (b) The shadowgraph at the same delay time. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
region. Therefore, the interaction is also collisionless. Note that the structures are mushroom-like, instead of filaments. 4. Conclusion The interaction between two counter-streaming laser-produced, low-density, non-relativistic plasmas is investigated by using the SG-II laser beams to irradiate double-foil targets. During the interaction density jump and filamentous structures are observed. The structures are probably due to collisionless mechanisms. However, understanding the jump and the filamentous structures observed in our experiment needs further experimental and theoretical investigations. Acknowledgements This work is supported by the National Nature Science Foundation of China (Grant Nos. 11135012 and 10925421). The authors thank the staff of SG-II laser facility for operating the laser and target area. References [1] R.Z. Sagdeev, Cooperative phenomena and shock waves in collisionless plasmas, Rev. Plasma Phys. 4 (1966) 23. [2] A.R. Bell, S.G. Lucek, Cosmic ray acceleration in pulsar-driven supernova remnants: the effect of scattering, Mon. Not. R. Astron. Soc. 283 (1996) 1083e1088. [3] R.D. Blandford, J.P. Ostriker, Particle acceleration by astrophysical shocks, Astrophys. J. Lett. 221 (1978) L29. [4] W.I. Axford, E. Leer, J.F. McKenzie, The structure of cosmic ray shocks, Astron. Astrophys. 111 (1982) 317e325. [5] J.M. Dawson, On the production of plasma by giant pulse lasers, Phys. Fluids 7 (1964) 981.
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