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Ultrarelativistic electron generation during the intense, ultrashort laser pulse interaction with clusters
Physics Letters A 363 (2007) 130–135 www.elsevier.com/locate/pla
Ultrarelativistic electron generation during the intense, ultrashort laser pulse interaction with clusters Y. Fukuda a , Y. Akahane a , M. Aoyama a , Y. Hayashi a , T. Homma a , N. Inoue a , M. Kando a , S. Kanazawa a , H. Kiriyama a , S. Kondo a , H. Kotaki a , S. Masuda a , M. Mori a , A. Yamazaki a , K. Yamakawa a , E.Yu. Echkina b , I.N. Inovenkov b , J. Koga a , S.V. Bulanov a,c,∗ a Kansai Photon Science Institute, Japan Atomic Energy Agency (JAEA), Kizu-cho, Kyoto 619-0215, Japan b Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia c A.M. Prokhorov General Physics Institute RAS, Vavilov street 38, Moscow 119991, Russia
Received 14 December 2006; accepted 18 December 2006 Available online 11 January 2007 Communicated by V.M. Agranovich
Abstract Using a cluster jet containing Ar clusters, collimated relativistic electrons up to 58 MeV with an electron charge of 2.1 nC were generated by a laser–cluster interaction. The resulting spectrum does not fit a Maxwellian distribution, but is well described by a two-temperature Maxwellian. Two-dimensional particle-in-cell simulations demonstrate an important role of clusters that the higher energy electrons are injected by the laser pulse interaction with the clusters and then they gain their energy during the direct acceleration by the laser pulse, while the lower energy electrons are accelerated by the wakefield being injected during the plasma wave breaking. © 2006 Elsevier B.V. All rights reserved. PACS: 52.38.Kd; 52.50.Jm; 52.35.Mw
1. Introduction Clusters, in addition to the properties common to both solids and gases, have their own specific properties. When a high intensity laser pulse interacts with a cluster target, the clusters absorb most of the incident laser energy, producing a high temperature “cluster plasma” which generates high-energy electrons and ions as well as bright X rays [1]. Moreover, the electron bunch expelled from the cluster oscillates under the action of the laser fields, emitting a high frequency ultrashort electromagnetic pulse due to collective nonlinear Thomson scattering [2] and high order harmonics generation [3]. Typically, as a result of supersonic gas expansion into vacuum, a multi-cluster cloud embedded in a low density background gas is produced [4] with the cluster size of the order * Corresponding author.
E-mail address: [email protected] (S.V. Bulanov). 0375-9601/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2006.12.061
of or less than the laser light wavelength, and the distance between the clusters substantially larger than the light wavelength. When such a cluster–gas target is irradiated by a high power laser pulse, its optical properties are expected to be new and intriguing in contrast to the interaction with a target comprising just clusters without the background gas. In the simplest case, we can see a counter-play of two competing effects. The first effect is the laser light incoherent scattering off individual clusters, which is expected to lead to the laser pulse spreading and energy attenuation. The second effect appears due to the change of the mean refractive index, which can result in selfguided laser pulse propagation as reported in Ref. [5]. In the latter case, the cluster–gas target can be an effective medium for electron acceleration. Electron acceleration in the laser wakefield is considered to be a promising candidate for a compact next-generation accelerator [6]. Following the experimental verifications of quasi-thermal relativistic electrons produced by the laser wakefield acceleration [7] and by the direct laser acceleration in
Y. Fukuda et al. / Physics Letters A 363 (2007) 130–135
a self-focusing channel [8], the recent demonstrations of quasimonoenergetic beams of relativistic electrons [9] have indicated a promising future in the development of compact sources for femtosecond X-rays [10] and terahertz radiation [11]. The success in obtaining the electron beam with quasi-monochromatic bunch energy spectrum is indeed a huge step forward, however, as realized in Ref. [9], the regime of electron injection via the transverse wake-wave breaking is not optimal from the point of view of the electron beam quality. Meanwhile, to the best of our knowledge, all studies of the electron acceleration via the laser plasma have been conducted with a gas target. Clusters in the gas jet, in addition to the above mentioned change of refractive index, can influence the laser pulse propagation and the wake plasma wave evolution, and then provide a unique injection of the electron bunch into the acceleration phase even below the wave breaking limit. In the present Letter, using a cluster–gas target containing Ar clusters, we present for the first time experimental results and supporting calculations of the generation of collimated relativistic electrons. The laser interaction with the cluster–gas plasma target has been simulated based on the two-dimensional particle-in-cell (2D-PIC) code, REMP [12]. We found that the ultrarelativistic electron generation from the cluster–gas target provides a unique realm of electron acceleration, since the clusters play an important role in producing a large quantity of high energy electrons. 2. Experimental setup The experiments were performed with the JAEA (Kyoto, Japan) Ti:sapphire laser system [13]. The laser delivered energies up to 406 mJ on target in 23-fs pulses centered at a wavelength of 800 nm with a 10 Hz repetition rate. A schematic diagram of experimental setup is shown in Fig. 1. In a vacuum target chamber, the laser pulses with linear polarization and the electric field parallel to the y axis were focused with a f/3.5 Aucoated off-axis parabolic mirror. The focus spot was a Gaussian
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with a diameter of 9.4 µm at 1/e2 , containing 60% of the total laser energy. Thus the laser peak intensity in vacuum was calculated to be 3.5 × 1019 W/cm2 , for which the corresponding normalized vector potential a0 = eA/m0 c2 is 4.1. A cluster–gas target was produced by expanding 60-bar Ar gas into vacuum using a pulsed valve connected with a special nozzle consisting of three truncated cones with different apex angles. The nozzle has the capability to produce the Ar clusters with an average diameter of 1.5 µm [4]. At the present experiment, the laser pulse contrast achieved, i.e., the ratio of the laser power at the maximum of the main femtosecond pulse to the prepulse, which precedes the main pulse by 10 ns, was C = 5 × 10−6 . Although the prepulse intensity is strong enough to ionize the Ar atoms in the clusters, the ionization and the expansion occur at the cluster peripheral region and the cluster core can be treated as frozen at this prepulse intensity of about 1013 W/cm2 [14]. Furthermore, since the rate of cluster decay is primarily determined by the number of atoms in the cluster [15], the micron-sized clusters can significantly reduce the cluster’s sensitivity to the laser prepulse, preclude low-density preplasma formation, and thus guarantee the direct interaction between the high-density cluster and the main fs pulse. The existence of a dense core region of the clusters was confirmed via analysis of the X-ray emissions from the Ar clusters in a separate experiment [16]. The position and timing of the nozzle were precisely adjusted so that the electron signal is maximized. As a result, the laser pulse under optimal conditions for electron acceleration was focused onto the edge of the gas jet, i.e. 1.5 mm downstream of the gas flow from the nozzle outlet and 1.3 mm off from the nozzle central axis, where the number densities of the micron-sized Ar clusters and the background Ar gas are estimated to be 2 × 107 cm−3 and 5.7 × 1018 cm−3 , respectively [4]. Thus the background gas plasma density is estimated to be 9.1 × 1019 cm−3 assuming that all the Ar atoms are ionized up a charge state of 16. The energy distribution of the electron beam generated from the laser–cluster interaction region was measured using a magnetic spectrometer, which has a dipole magnet and a 32-channel plastic scintillation array coupled with photomultipliers. Each scintillator was calibrated using a beta-decay source (90 Sr– 90 Y). At the entrance of the spectrometer, a collimator, made of a stack of polyethylene and lead, with an acceptance angle of 10 mrad was placed to increase energy resolution and to reduce the amount of X-rays hitting the scintillation array. By changing the magnetic field in the spectrometer from 0 to 1.1 T, it was possible to measure electron energy in the range up to 600 MeV with 10% resolution. Signals from the photomultipliers were taken with CAMAC charge-sensitive AD converters. 3. Experimental results
Fig. 1. (Color online.) A schematic diagram of experimental setup: (1) the off-axis parabolic mirror, (2) the laser beam, (3) the pulsed valve connected with a special nozzle, (4) the cluster–gas target, (5) the collimator, (6) the magnetic spectrometer, (7) the 32-channel plastic scintillation array coupled with photomultipliers, (8) the stack of imaging plates and aluminum plates.
The energy spectra of the electron beam measured with different magnetic field intensities are shown in Fig. 2. The data points were obtained by averaging over several tens of laser shots, and the error bars show the maximum and minimum limits. The solid line shows the detection threshold, which corre-
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Fig. 2. (Color online.) Energy spectrum obtained with different magnetic field intensities of 22.7 and 38.7 mT. The data points were obtained by averaging over several tens of laser shots, and the error bars show the maximum and minimum limits. The solid line shows the detection threshold which corresponds to the energy deposited by a relativistic electron entering each detector. The dotted and broken lines represent effective electron temperatures of 2.8 and 18.8 MeV, respectively, obtained from Maxwellian fittings.
sponds to the energy deposited by a relativistic electron entering each detector. We have confirmed that no signal was observed with the maximum magnetic field of 1.1 T. In this case, the spectrometer sweeps out the electron beam, but it has no influence on the propagation of X rays. We have also confirmed that when an aluminum shield of 5-mm thickness, which completely blocks off X rays, was installed in front of the scintillation array, weakened signals reduced by 60% were observed. These results lead us to the conclusion that the obtained spectrum is due to energetic electrons. High-energy electrons extending up to 58 MeV were observed. This is much greater than mc2 a02 /2 = 4.3 MeV (a0 = 4.1), the energy to which electrons initially at rest in vacuum are accelerated by the electromagnetic wave. The resulting spectrum does not fit a single Maxwellian distribution, but is fit well by a double-Maxwellian distribution with effective temperatures of 2.8 and 18.8 MeV for electrons below and above 30 MeV in energy, respectively. These results may indicate that electrons are accelerated by two different mechanisms. In order to measure the spatial distribution of the electron beam as a function of its energy, a stack with alternating layers of eight imaging plates (Fuji Film, BAS-SR) and eight 0.5-mm thick aluminum plates with a diameter of 80 mm, which was shielded with a 12-µm thick aluminum foil in order to block the laser light, was installed on the x (laser propagation) axis 177 mm away from the laser–cluster interaction region. The spatial distribution of the accelerated electrons was measured in the energy range from 0.25 to 5.5 MeV. The stopping energies and the errors are calculated with the EGS4 code including scattering effects on the electron beam propagation profile by the stacked Al plates and the imaging plates. Figs. 3(a) and 3(b) show typical images of the electron beam profiles, obtained by accumulating 100 laser shots. The beam divergence in the y and z directions with > 2.1 MeV electrons are 8.1 ± 0.2◦ and 7.4 ± 0.2◦ half-width at half maximum (HWHM), respectively, while those with > 5.5 MeV electrons are about 7.7 ± 0.6◦ and 5.6 ± 0.4◦ HWHM, respectively.
Fig. 3. (Color online.) Images of the electron beam profiles for electron energies > 2.1 MeV (a), and > 5.5 MeV (b), obtained by accumulating 100 laser shots.
These results show that the low-energy electrons were accelerated in a broader cone in the forward direction, whereas the high-energy electrons were more collimated in the z direction, which is perpendicular to the laser polarization axis. Assuming that the electron beam spot, r0 , at the focus is the same as that of the laser and the average beam divergence is 7.2◦ (HWHM), the emittance is estimated to be 0.4π mm mrad, where no spacecharge effects are included in this calculation. From the imaging plate shown in Fig. 3(a), the electric charge of accelerated electrons with energy larger than 2.1 MeV is estimated to be 2.1 nC (1.3 × 1010 particles) per shot. In order to confirm that the clusters in the gas jet were responsible for the electron acceleration, a large laser prepulse (> 1016 W/cm2 ) was intentionally introduced before the main pulse so that the clusters in the gas jet could be completely destroyed before the arrival of the main pulse. In the second case the laser beam was focused into a 60-bar He gas target (plasma density = 8.5 × 1018 cm−3 ) using the same special nozzle, where no clusters could be produced because of the weak van der Waals force. In both cases, no electrons above 1 MeV were observed. 4. Results of 2D-PIC simulations We performed 2D-PIC simulations of the laser pulse interaction with the cluster–gas plasma target corresponding to the parameters of our experiment in order to elucidate the role of clusters in the electron acceleration. We use a two-dimensional version of the fully relativistic PIC simulation code REMP, which self-consistently solves Maxwell’s equations along with the particle equations of motion [12]. The system size is 450λ0 in the x (laser propagation) direction and 45λ0 in the y (transverse) direction with the number of the mesh steps equal to 4500 × 450 and the total number of quasiparticles of about 107 . We assume that the incident on-target laser pulse waist is 8λ0 , its length is 12λ0 , and the laser intensity corresponds to the dimensionless amplitude a0 = 4.1. The pulse is linearly polarized with the electric field parallel to the y axis. The background electron density is chosen to be equal to n = 2.5 × 10−3 ncr , where ncr = me ω2 /4πe2 , which corresponds to the density n = 5 × 1018 cm−3 for a laser with λ0 = 0.8 µm. The charge
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Fig. 4. (a) Electron phase plane, (x, px ), (b) the electron energy spectrum, and (c) the electron density distribution in the x, y plane at t = 255 × (2π/ω0 ) for a laser pulse interacting with the cluster–gas plasma target. The arrows indicate the place where the laser pulse is.
to mass ratio, ZA/mi = 2/5, is approximately the same as for Ar atoms ionized up to a charge state of 16. The plasma density is set to be lower than the above estimated density of the background Ar gas because for higher density we did not observe efficient electron acceleration. The background density decrease can be caused by the laser prepulse effect, which heats the gas and makes the plasma to expand outwards from the laser pulse axis. Embedded in the underdense plasma, clusters are distributed randomly with a mean distance between them of the order of 10λ0 . The plasma density inside the cluster is equal to ncl = 25ncr , and the cluster diameter is 0.3λ0 = 0.24 µm. We point out that the chosen cluster size is about six times smaller than the estimated initial diameter, because, as mentioned above, the peripheral region of the cluster can be ionized and evaporated by the irradiation of the 10−6 -level prepulse, and the clusters shrink in size before the interaction with the main fs pulse. Figs. 4(a) and 4(b) show the electron phase plane, (x, px ), and the electron energy spectrum at t = 255 × (2π/ω0 ), respectively, for the laser pulse interacting with the cluster–gas plasma target with the above described parameters. We see that the electron energy spectrum reproduces well the observed spectra shown in Fig. 2. It can be approximated by a two-temperature distribution with maximal electron energy equal to 61 MeV. The electrons with the energy below and above 30 MeV have an effective temperature approximately equal to 3 and 20 MeV, respectively. The important finding is that as seen in Fig. 4(a) the most intense peak at x = 240 exactly corresponds to the place where the laser pulse is. This means that the electrons located at x = 240 are inside the laser pulse, i.e. these electrons gain their energy due to the direct acceleration by the laser pulse propagating in the plasma. The high energy electrons with energies 30 < ε < 60 MeV shown in Fig. 4(b) come only from these electrons. The rather broad peak around x = 215 corresponds to the place where the acceleration phase of the first cycle of the wakefield is. That means the electrons with energies
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Fig. 5. The same as in Fig. 4, at t = 437.5×(2π/ω0 ) for a laser pulse interacting with an underdense plasma slab without clusters. The arrows indicate the place where the laser pulse is.
below 30 MeV are accelerated by the wakefield. In Fig. 4(c) we can see the electron density distribution in the x, y plane at t = 255 × (2π/ω0 ), which clearly shows a distorsion of the wake wave caused by the laser pulse and wake wave interaction with the clusters. On the other hand, Figs. 5(a) and 5(b) show the electron phase plane, (x, px ), and the electron energy spectrum at t = 437.5 × (2π/ω0 ), respectively, for the laser pulse interacting with an underdense plasma slab without clusters, which corresponds to the standard regime of the wake wave generation clearly seen in Fig. 5(c) where the electron density distribution in the x, y plane at t = 437.5 × (2π/ω0 ) is presented. This case has led to completely different phenomena; as shown in Fig. 5(a), there are no electrons at the place x = 415 where the laser pulse is, and monoenergetic electron bunch formation at x = 405 with an energy of 49 MeV occurred. The monoenergetic electron bunch seen at x = 405 was trapped in the first cycle of the wakefield due to the transverse wave breaking [17] in the self-injection regime similar to that observed in Refs. [9]. Furthermore, when the laser pulse interacts with a randomly distributed cluster cloud only (no background gas plasma), the electron acceleration was not efficient; the energy is just of the order of 4 to 5 MeV (not shown here). This energy is almost equal to mc2 a02 /2 = 4.3 MeV (a0 = 4.1) which is the energy electrons initially at rest in vacuum obtain via acceleration by the electromagnetic wave. This means that the interplay between the cluster plasma and the background gas plasma is essential to produce the high energy electrons. We note that the background electrons undergo essentially different quiver motion from the electrons inside the cluster, because in a collisionless system the particle response to the periodic laser field can be expressed by a formula composed of terms connected not only with the frequency of the laser pulse, but also with the local plasma frequency which is different inside and outside of the cluster. The simulation results demonstrate that the clusters embedded in the background gas play an important role in producing the high energy electrons, which could be injected into the laser
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the relativistically strong electromagnetic wave (see Ref. [18]):
γph = 1 + a02 (ω0 /ωpe ). In our case for n = 2.5 × 10−3 ncr and a0 = 4.1 we find that γph ≈ 80. Using the dependence of the longitudinal electron momentum on the transverse, p⊥,0 , and longitudinal, px,0 , components, we find that under the assumption p⊥,0 = 0, the experimentally observed maximum electron energy 58 MeV requires that the electrons be injected with an initial energy of the order of 3.8 MeV. Such an injection energy can be achieved at the stage when the electron is expelled from the clusters, and it corresponds to the maximal quiver momentum, pinj ≈ max{2a0 , a02 /2}. 5. Summary Fig. 6. Longitudinal electron momentum versus p⊥,0 and px,0 for a0 = 4.1.
pulse when they are expelled from the clusters by the laser pulse field. They then gain their energy during the direct acceleration by the laser pulse. In order to analyze the observed direct electron acceleration, we take into account that the phase velocity of the electromagnetic wave propagating in an underdense plasma, vph , is larger than the speed of light in vacuum, i.e. βph = vph /c > 1. We note that the physical mechanism of the direct acceleration in plasmas is similar to the well-known direct acceleration in vacuum with the difference in the value of the phase velocity of the laser pulse. The Hamiltonian for the electron interacting with the electromagnetic wave given by its vector potential a = a(X)ey can be cast in the form 2 H = 1 + p⊥,0 − a(X) + px2 − βph px = h0 , (1) which is constant, H = h0 . HereX is an independent variable:
2 + p2 − β p X = x − βph t , the constant h0 = 1 + p⊥,0 ph x,0 is x,0 determined by the initial values of the transverse and longitudinal components of the electron momentum: p⊥,0 and px,0 . We use here normalized variables, where the momentum is normalized by me c, the phase velocity is measured in units of c, and the vector potential is normalized by me c2 /e. From the Hamiltonian (1) conservation, we can find the longitudinal electron momentum h0 βph 2 1 + [p⊥,0 − a(X)]2 − h20 βph h0 − 2 . + px = 2 2 βph − 1 βph − 1 βph − 1 (2)
The electron energy equals ε = me c2 (h0 + βph px ). In the 2 /(β 2 − 1) + h2 [p 2 limit h20 βph ⊥,0 − a(X)] , we have px ≈ ph 0 2 /(β 2 − 1) + {[p⊥,0 − a(X)]2 − h20 }/(2βph h0 ), and for h20 βph ph h20 [p⊥,0 − a(X)]2 the longitudinal momentum is px ≈ 2 − 1. Fig. 6 shows the longitudinal elec[p⊥,0 − a(X)]/ βph tron momentum versus the initial transverse, p⊥,0 , and longitudinal, px,0 , components of the electron momentum for dimensionless amplitude of the laser pulse equal to 4.1. In this
2 − 1, was calcase the gamma factor, defined as γph = βph culated according to the expression for the phase velocity of
Relativistic electrons up to 58 MeV with an electron charge of 2.1 nC were generated by the interaction of intense laser pulses with an Ar cluster–gas target at the laser intensity of 3.5 × 1019 W/cm2 . The resulting energy spectrum distinctly shows two populations of fast electrons, which indicates two mechanisms of the electron acceleration. With 2D-PIC simulations, we found that the high energy electrons are injected when they are expelled from the clusters by the laser pulse field. They then gain their energy during the direct acceleration by the laser pulse, whose phase velocity in the underdense plasma is larger than the speed of light in vacuum, while the lower energy electrons are accelerated by the wakefield having been injected during the plasma wave breaking. We have demonstrated that the cluster–gas target provides a unique electron injection realm for the ultrarelativistic electron generation which is not governed by the wake-wave breaking, and has the potential to provide a new electron injection process for monoenergetic electron beam generation. Acknowledgements This work was supported by the Grant-in-Aid for Scientific Research on Specially Promoted Research (15002013) by MEXT. The authors acknowledge T. Tajima, Y. Kishimoto, K. Nakajima, and T. Kimura for fruitful discussions, as well as T.Zh. Esirkepov for providing the PIC code. References [1] A. McPherson, et al., Nature (London) 370 (1994) 631; T. Ditmire, et al., Nature (London) 386 (1997) 54; M. Lezius, et al., Phys. Rev. Lett. 80 (1998) 261; T. Ditmire, et al., Nature (London) 398 (1999) 489; V. Kumarappan, M. Krishnamurthy, D. Mathur, Phys. Rev. Lett. 87 (2001) 085005; V.P. Krainov, M.B. Smirnov, Phys. Rep. 370 (2002) 237; Y. Fukuda, et al., Phys. Rev. A 67 (2003) 061201; K.Y. Kim, et al., Phys. Rev. Lett. 90 (2003) 023401. [2] S.V. Bulanov, et al., Plasma Phys. Rep. 30 (2004) 196. [3] V.P. Krainov, Phys. Rev. E 68 (2003) 027401; M.V. Fomyts’kyi, et al., Phys. Plasmas 11 (2004) 3349. [4] A.S. Boldarev, et al., Rev. Sci. Instrum. 77 (2006) 083112. [5] I. Alexeev, et al., Phys. Rev. Lett. 90 (2003) 103402; V. Kumarappan, et al., Phys. Rev. Lett. 94 (2005) 205004. [6] T. Tajima, J.M. Dawson, Phys. Rev. Lett. 43 (1979) 267.
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[7] K. Nakajima, et al., Phys. Rev. Lett. 74 (1995) 4428; A. Modena, et al., Nature (London) 337 (1995) 606; V. Malka, et al., Science 298 (2002) 1596. [8] C. Gahn, et al., Phys. Rev. Lett. 83 (1999) 4772. [9] S.P.D. Mangles, et al., Nature (London) 431 (2004) 535; C.G.R. Geddens, et al., Nature (London) 431 (2004) 538; J. Faure, et al., Nature (London) 431 (2004) 541; E. Miura, et al., Appl. Phys. Lett. 86 (2005) 251501; A. Yamazaki, et al., Phys. Plasmas 12 (2005) 093101; T. Hosokai, et al., Phys. Rev. E 73 (2006) 036407; M. Mori, et al., Phys. Lett. A 356 (2006) 146; W.P. Leemans, et al., Nature Phys. 2 (2006) 696. [10] W.P. Leemans, et al., IEEE J. Quantum Electron. 33 (1997) 1879;
K. Ta Phuoc, et al., Phys. Rev. Lett. 91 (2003) 195001. W.P. Leemans, et al., Phys. Rev. Lett. 91 (2003) 074802. T.Zh. Esirkepov, Comput. Phys. Commun. 135 (2001) 144. K. Yamakawa, et al., Opt. Lett. 23 (1998) 1468. M.B. Smirnov, et al., JETP 98 (2004) 1123. T. Ditmire, et al., Phys. Rev. A 53 (1996) 3379. J. Abdallah Jr., et al., Phys. Rev. A 68 (2003) 063201. S.V. Bulanov, et al., Phys. Rev. Lett. 78 (1997) 4205; T.V. Liseikina, et al., Phys. Rev. E 60 (1999) 5991; A. Pukhov, J. Meyer-ter-Vehn, Appl. Phys. B 74 (2002) 355. [18] A.I. Akhiezer, R.V. Polovin, Sov. Phys. JETP 3 (1956) 696. [11] [12] [13] [14] [15] [16] [17]
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Ultrarelativistic electron generation during the intense, ultrashort laser pulse interaction with clusters Y. Fukuda a , Y. Akahane a , M. Aoyama a , Y. Hayashi a , T. Homma a , N. Inoue a , M. Kando a , S. Kanazawa a , H. Kiriyama a , S. Kondo a , H. Kotaki a , S. Masuda a , M. Mori a , A. Yamazaki a , K. Yamakawa a , E.Yu. Echkina b , I.N. Inovenkov b , J. Koga a , S.V. Bulanov a,c,∗ a Kansai Photon Science Institute, Japan Atomic Energy Agency (JAEA), Kizu-cho, Kyoto 619-0215, Japan b Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia c A.M. Prokhorov General Physics Institute RAS, Vavilov street 38, Moscow 119991, Russia
Received 14 December 2006; accepted 18 December 2006 Available online 11 January 2007 Communicated by V.M. Agranovich
Abstract Using a cluster jet containing Ar clusters, collimated relativistic electrons up to 58 MeV with an electron charge of 2.1 nC were generated by a laser–cluster interaction. The resulting spectrum does not fit a Maxwellian distribution, but is well described by a two-temperature Maxwellian. Two-dimensional particle-in-cell simulations demonstrate an important role of clusters that the higher energy electrons are injected by the laser pulse interaction with the clusters and then they gain their energy during the direct acceleration by the laser pulse, while the lower energy electrons are accelerated by the wakefield being injected during the plasma wave breaking. © 2006 Elsevier B.V. All rights reserved. PACS: 52.38.Kd; 52.50.Jm; 52.35.Mw
1. Introduction Clusters, in addition to the properties common to both solids and gases, have their own specific properties. When a high intensity laser pulse interacts with a cluster target, the clusters absorb most of the incident laser energy, producing a high temperature “cluster plasma” which generates high-energy electrons and ions as well as bright X rays [1]. Moreover, the electron bunch expelled from the cluster oscillates under the action of the laser fields, emitting a high frequency ultrashort electromagnetic pulse due to collective nonlinear Thomson scattering [2] and high order harmonics generation [3]. Typically, as a result of supersonic gas expansion into vacuum, a multi-cluster cloud embedded in a low density background gas is produced [4] with the cluster size of the order * Corresponding author.
E-mail address: [email protected] (S.V. Bulanov). 0375-9601/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2006.12.061
of or less than the laser light wavelength, and the distance between the clusters substantially larger than the light wavelength. When such a cluster–gas target is irradiated by a high power laser pulse, its optical properties are expected to be new and intriguing in contrast to the interaction with a target comprising just clusters without the background gas. In the simplest case, we can see a counter-play of two competing effects. The first effect is the laser light incoherent scattering off individual clusters, which is expected to lead to the laser pulse spreading and energy attenuation. The second effect appears due to the change of the mean refractive index, which can result in selfguided laser pulse propagation as reported in Ref. [5]. In the latter case, the cluster–gas target can be an effective medium for electron acceleration. Electron acceleration in the laser wakefield is considered to be a promising candidate for a compact next-generation accelerator [6]. Following the experimental verifications of quasi-thermal relativistic electrons produced by the laser wakefield acceleration [7] and by the direct laser acceleration in
Y. Fukuda et al. / Physics Letters A 363 (2007) 130–135
a self-focusing channel [8], the recent demonstrations of quasimonoenergetic beams of relativistic electrons [9] have indicated a promising future in the development of compact sources for femtosecond X-rays [10] and terahertz radiation [11]. The success in obtaining the electron beam with quasi-monochromatic bunch energy spectrum is indeed a huge step forward, however, as realized in Ref. [9], the regime of electron injection via the transverse wake-wave breaking is not optimal from the point of view of the electron beam quality. Meanwhile, to the best of our knowledge, all studies of the electron acceleration via the laser plasma have been conducted with a gas target. Clusters in the gas jet, in addition to the above mentioned change of refractive index, can influence the laser pulse propagation and the wake plasma wave evolution, and then provide a unique injection of the electron bunch into the acceleration phase even below the wave breaking limit. In the present Letter, using a cluster–gas target containing Ar clusters, we present for the first time experimental results and supporting calculations of the generation of collimated relativistic electrons. The laser interaction with the cluster–gas plasma target has been simulated based on the two-dimensional particle-in-cell (2D-PIC) code, REMP [12]. We found that the ultrarelativistic electron generation from the cluster–gas target provides a unique realm of electron acceleration, since the clusters play an important role in producing a large quantity of high energy electrons. 2. Experimental setup The experiments were performed with the JAEA (Kyoto, Japan) Ti:sapphire laser system [13]. The laser delivered energies up to 406 mJ on target in 23-fs pulses centered at a wavelength of 800 nm with a 10 Hz repetition rate. A schematic diagram of experimental setup is shown in Fig. 1. In a vacuum target chamber, the laser pulses with linear polarization and the electric field parallel to the y axis were focused with a f/3.5 Aucoated off-axis parabolic mirror. The focus spot was a Gaussian
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with a diameter of 9.4 µm at 1/e2 , containing 60% of the total laser energy. Thus the laser peak intensity in vacuum was calculated to be 3.5 × 1019 W/cm2 , for which the corresponding normalized vector potential a0 = eA/m0 c2 is 4.1. A cluster–gas target was produced by expanding 60-bar Ar gas into vacuum using a pulsed valve connected with a special nozzle consisting of three truncated cones with different apex angles. The nozzle has the capability to produce the Ar clusters with an average diameter of 1.5 µm [4]. At the present experiment, the laser pulse contrast achieved, i.e., the ratio of the laser power at the maximum of the main femtosecond pulse to the prepulse, which precedes the main pulse by 10 ns, was C = 5 × 10−6 . Although the prepulse intensity is strong enough to ionize the Ar atoms in the clusters, the ionization and the expansion occur at the cluster peripheral region and the cluster core can be treated as frozen at this prepulse intensity of about 1013 W/cm2 [14]. Furthermore, since the rate of cluster decay is primarily determined by the number of atoms in the cluster [15], the micron-sized clusters can significantly reduce the cluster’s sensitivity to the laser prepulse, preclude low-density preplasma formation, and thus guarantee the direct interaction between the high-density cluster and the main fs pulse. The existence of a dense core region of the clusters was confirmed via analysis of the X-ray emissions from the Ar clusters in a separate experiment [16]. The position and timing of the nozzle were precisely adjusted so that the electron signal is maximized. As a result, the laser pulse under optimal conditions for electron acceleration was focused onto the edge of the gas jet, i.e. 1.5 mm downstream of the gas flow from the nozzle outlet and 1.3 mm off from the nozzle central axis, where the number densities of the micron-sized Ar clusters and the background Ar gas are estimated to be 2 × 107 cm−3 and 5.7 × 1018 cm−3 , respectively [4]. Thus the background gas plasma density is estimated to be 9.1 × 1019 cm−3 assuming that all the Ar atoms are ionized up a charge state of 16. The energy distribution of the electron beam generated from the laser–cluster interaction region was measured using a magnetic spectrometer, which has a dipole magnet and a 32-channel plastic scintillation array coupled with photomultipliers. Each scintillator was calibrated using a beta-decay source (90 Sr– 90 Y). At the entrance of the spectrometer, a collimator, made of a stack of polyethylene and lead, with an acceptance angle of 10 mrad was placed to increase energy resolution and to reduce the amount of X-rays hitting the scintillation array. By changing the magnetic field in the spectrometer from 0 to 1.1 T, it was possible to measure electron energy in the range up to 600 MeV with 10% resolution. Signals from the photomultipliers were taken with CAMAC charge-sensitive AD converters. 3. Experimental results
Fig. 1. (Color online.) A schematic diagram of experimental setup: (1) the off-axis parabolic mirror, (2) the laser beam, (3) the pulsed valve connected with a special nozzle, (4) the cluster–gas target, (5) the collimator, (6) the magnetic spectrometer, (7) the 32-channel plastic scintillation array coupled with photomultipliers, (8) the stack of imaging plates and aluminum plates.
The energy spectra of the electron beam measured with different magnetic field intensities are shown in Fig. 2. The data points were obtained by averaging over several tens of laser shots, and the error bars show the maximum and minimum limits. The solid line shows the detection threshold, which corre-
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Fig. 2. (Color online.) Energy spectrum obtained with different magnetic field intensities of 22.7 and 38.7 mT. The data points were obtained by averaging over several tens of laser shots, and the error bars show the maximum and minimum limits. The solid line shows the detection threshold which corresponds to the energy deposited by a relativistic electron entering each detector. The dotted and broken lines represent effective electron temperatures of 2.8 and 18.8 MeV, respectively, obtained from Maxwellian fittings.
sponds to the energy deposited by a relativistic electron entering each detector. We have confirmed that no signal was observed with the maximum magnetic field of 1.1 T. In this case, the spectrometer sweeps out the electron beam, but it has no influence on the propagation of X rays. We have also confirmed that when an aluminum shield of 5-mm thickness, which completely blocks off X rays, was installed in front of the scintillation array, weakened signals reduced by 60% were observed. These results lead us to the conclusion that the obtained spectrum is due to energetic electrons. High-energy electrons extending up to 58 MeV were observed. This is much greater than mc2 a02 /2 = 4.3 MeV (a0 = 4.1), the energy to which electrons initially at rest in vacuum are accelerated by the electromagnetic wave. The resulting spectrum does not fit a single Maxwellian distribution, but is fit well by a double-Maxwellian distribution with effective temperatures of 2.8 and 18.8 MeV for electrons below and above 30 MeV in energy, respectively. These results may indicate that electrons are accelerated by two different mechanisms. In order to measure the spatial distribution of the electron beam as a function of its energy, a stack with alternating layers of eight imaging plates (Fuji Film, BAS-SR) and eight 0.5-mm thick aluminum plates with a diameter of 80 mm, which was shielded with a 12-µm thick aluminum foil in order to block the laser light, was installed on the x (laser propagation) axis 177 mm away from the laser–cluster interaction region. The spatial distribution of the accelerated electrons was measured in the energy range from 0.25 to 5.5 MeV. The stopping energies and the errors are calculated with the EGS4 code including scattering effects on the electron beam propagation profile by the stacked Al plates and the imaging plates. Figs. 3(a) and 3(b) show typical images of the electron beam profiles, obtained by accumulating 100 laser shots. The beam divergence in the y and z directions with > 2.1 MeV electrons are 8.1 ± 0.2◦ and 7.4 ± 0.2◦ half-width at half maximum (HWHM), respectively, while those with > 5.5 MeV electrons are about 7.7 ± 0.6◦ and 5.6 ± 0.4◦ HWHM, respectively.
Fig. 3. (Color online.) Images of the electron beam profiles for electron energies > 2.1 MeV (a), and > 5.5 MeV (b), obtained by accumulating 100 laser shots.
These results show that the low-energy electrons were accelerated in a broader cone in the forward direction, whereas the high-energy electrons were more collimated in the z direction, which is perpendicular to the laser polarization axis. Assuming that the electron beam spot, r0 , at the focus is the same as that of the laser and the average beam divergence is 7.2◦ (HWHM), the emittance is estimated to be 0.4π mm mrad, where no spacecharge effects are included in this calculation. From the imaging plate shown in Fig. 3(a), the electric charge of accelerated electrons with energy larger than 2.1 MeV is estimated to be 2.1 nC (1.3 × 1010 particles) per shot. In order to confirm that the clusters in the gas jet were responsible for the electron acceleration, a large laser prepulse (> 1016 W/cm2 ) was intentionally introduced before the main pulse so that the clusters in the gas jet could be completely destroyed before the arrival of the main pulse. In the second case the laser beam was focused into a 60-bar He gas target (plasma density = 8.5 × 1018 cm−3 ) using the same special nozzle, where no clusters could be produced because of the weak van der Waals force. In both cases, no electrons above 1 MeV were observed. 4. Results of 2D-PIC simulations We performed 2D-PIC simulations of the laser pulse interaction with the cluster–gas plasma target corresponding to the parameters of our experiment in order to elucidate the role of clusters in the electron acceleration. We use a two-dimensional version of the fully relativistic PIC simulation code REMP, which self-consistently solves Maxwell’s equations along with the particle equations of motion [12]. The system size is 450λ0 in the x (laser propagation) direction and 45λ0 in the y (transverse) direction with the number of the mesh steps equal to 4500 × 450 and the total number of quasiparticles of about 107 . We assume that the incident on-target laser pulse waist is 8λ0 , its length is 12λ0 , and the laser intensity corresponds to the dimensionless amplitude a0 = 4.1. The pulse is linearly polarized with the electric field parallel to the y axis. The background electron density is chosen to be equal to n = 2.5 × 10−3 ncr , where ncr = me ω2 /4πe2 , which corresponds to the density n = 5 × 1018 cm−3 for a laser with λ0 = 0.8 µm. The charge
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Fig. 4. (a) Electron phase plane, (x, px ), (b) the electron energy spectrum, and (c) the electron density distribution in the x, y plane at t = 255 × (2π/ω0 ) for a laser pulse interacting with the cluster–gas plasma target. The arrows indicate the place where the laser pulse is.
to mass ratio, ZA/mi = 2/5, is approximately the same as for Ar atoms ionized up to a charge state of 16. The plasma density is set to be lower than the above estimated density of the background Ar gas because for higher density we did not observe efficient electron acceleration. The background density decrease can be caused by the laser prepulse effect, which heats the gas and makes the plasma to expand outwards from the laser pulse axis. Embedded in the underdense plasma, clusters are distributed randomly with a mean distance between them of the order of 10λ0 . The plasma density inside the cluster is equal to ncl = 25ncr , and the cluster diameter is 0.3λ0 = 0.24 µm. We point out that the chosen cluster size is about six times smaller than the estimated initial diameter, because, as mentioned above, the peripheral region of the cluster can be ionized and evaporated by the irradiation of the 10−6 -level prepulse, and the clusters shrink in size before the interaction with the main fs pulse. Figs. 4(a) and 4(b) show the electron phase plane, (x, px ), and the electron energy spectrum at t = 255 × (2π/ω0 ), respectively, for the laser pulse interacting with the cluster–gas plasma target with the above described parameters. We see that the electron energy spectrum reproduces well the observed spectra shown in Fig. 2. It can be approximated by a two-temperature distribution with maximal electron energy equal to 61 MeV. The electrons with the energy below and above 30 MeV have an effective temperature approximately equal to 3 and 20 MeV, respectively. The important finding is that as seen in Fig. 4(a) the most intense peak at x = 240 exactly corresponds to the place where the laser pulse is. This means that the electrons located at x = 240 are inside the laser pulse, i.e. these electrons gain their energy due to the direct acceleration by the laser pulse propagating in the plasma. The high energy electrons with energies 30 < ε < 60 MeV shown in Fig. 4(b) come only from these electrons. The rather broad peak around x = 215 corresponds to the place where the acceleration phase of the first cycle of the wakefield is. That means the electrons with energies
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Fig. 5. The same as in Fig. 4, at t = 437.5×(2π/ω0 ) for a laser pulse interacting with an underdense plasma slab without clusters. The arrows indicate the place where the laser pulse is.
below 30 MeV are accelerated by the wakefield. In Fig. 4(c) we can see the electron density distribution in the x, y plane at t = 255 × (2π/ω0 ), which clearly shows a distorsion of the wake wave caused by the laser pulse and wake wave interaction with the clusters. On the other hand, Figs. 5(a) and 5(b) show the electron phase plane, (x, px ), and the electron energy spectrum at t = 437.5 × (2π/ω0 ), respectively, for the laser pulse interacting with an underdense plasma slab without clusters, which corresponds to the standard regime of the wake wave generation clearly seen in Fig. 5(c) where the electron density distribution in the x, y plane at t = 437.5 × (2π/ω0 ) is presented. This case has led to completely different phenomena; as shown in Fig. 5(a), there are no electrons at the place x = 415 where the laser pulse is, and monoenergetic electron bunch formation at x = 405 with an energy of 49 MeV occurred. The monoenergetic electron bunch seen at x = 405 was trapped in the first cycle of the wakefield due to the transverse wave breaking [17] in the self-injection regime similar to that observed in Refs. [9]. Furthermore, when the laser pulse interacts with a randomly distributed cluster cloud only (no background gas plasma), the electron acceleration was not efficient; the energy is just of the order of 4 to 5 MeV (not shown here). This energy is almost equal to mc2 a02 /2 = 4.3 MeV (a0 = 4.1) which is the energy electrons initially at rest in vacuum obtain via acceleration by the electromagnetic wave. This means that the interplay between the cluster plasma and the background gas plasma is essential to produce the high energy electrons. We note that the background electrons undergo essentially different quiver motion from the electrons inside the cluster, because in a collisionless system the particle response to the periodic laser field can be expressed by a formula composed of terms connected not only with the frequency of the laser pulse, but also with the local plasma frequency which is different inside and outside of the cluster. The simulation results demonstrate that the clusters embedded in the background gas play an important role in producing the high energy electrons, which could be injected into the laser
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the relativistically strong electromagnetic wave (see Ref. [18]):
γph = 1 + a02 (ω0 /ωpe ). In our case for n = 2.5 × 10−3 ncr and a0 = 4.1 we find that γph ≈ 80. Using the dependence of the longitudinal electron momentum on the transverse, p⊥,0 , and longitudinal, px,0 , components, we find that under the assumption p⊥,0 = 0, the experimentally observed maximum electron energy 58 MeV requires that the electrons be injected with an initial energy of the order of 3.8 MeV. Such an injection energy can be achieved at the stage when the electron is expelled from the clusters, and it corresponds to the maximal quiver momentum, pinj ≈ max{2a0 , a02 /2}. 5. Summary Fig. 6. Longitudinal electron momentum versus p⊥,0 and px,0 for a0 = 4.1.
pulse when they are expelled from the clusters by the laser pulse field. They then gain their energy during the direct acceleration by the laser pulse. In order to analyze the observed direct electron acceleration, we take into account that the phase velocity of the electromagnetic wave propagating in an underdense plasma, vph , is larger than the speed of light in vacuum, i.e. βph = vph /c > 1. We note that the physical mechanism of the direct acceleration in plasmas is similar to the well-known direct acceleration in vacuum with the difference in the value of the phase velocity of the laser pulse. The Hamiltonian for the electron interacting with the electromagnetic wave given by its vector potential a = a(X)ey can be cast in the form 2 H = 1 + p⊥,0 − a(X) + px2 − βph px = h0 , (1) which is constant, H = h0 . HereX is an independent variable:
2 + p2 − β p X = x − βph t , the constant h0 = 1 + p⊥,0 ph x,0 is x,0 determined by the initial values of the transverse and longitudinal components of the electron momentum: p⊥,0 and px,0 . We use here normalized variables, where the momentum is normalized by me c, the phase velocity is measured in units of c, and the vector potential is normalized by me c2 /e. From the Hamiltonian (1) conservation, we can find the longitudinal electron momentum h0 βph 2 1 + [p⊥,0 − a(X)]2 − h20 βph h0 − 2 . + px = 2 2 βph − 1 βph − 1 βph − 1 (2)
The electron energy equals ε = me c2 (h0 + βph px ). In the 2 /(β 2 − 1) + h2 [p 2 limit h20 βph ⊥,0 − a(X)] , we have px ≈ ph 0 2 /(β 2 − 1) + {[p⊥,0 − a(X)]2 − h20 }/(2βph h0 ), and for h20 βph ph h20 [p⊥,0 − a(X)]2 the longitudinal momentum is px ≈ 2 − 1. Fig. 6 shows the longitudinal elec[p⊥,0 − a(X)]/ βph tron momentum versus the initial transverse, p⊥,0 , and longitudinal, px,0 , components of the electron momentum for dimensionless amplitude of the laser pulse equal to 4.1. In this
2 − 1, was calcase the gamma factor, defined as γph = βph culated according to the expression for the phase velocity of
Relativistic electrons up to 58 MeV with an electron charge of 2.1 nC were generated by the interaction of intense laser pulses with an Ar cluster–gas target at the laser intensity of 3.5 × 1019 W/cm2 . The resulting energy spectrum distinctly shows two populations of fast electrons, which indicates two mechanisms of the electron acceleration. With 2D-PIC simulations, we found that the high energy electrons are injected when they are expelled from the clusters by the laser pulse field. They then gain their energy during the direct acceleration by the laser pulse, whose phase velocity in the underdense plasma is larger than the speed of light in vacuum, while the lower energy electrons are accelerated by the wakefield having been injected during the plasma wave breaking. We have demonstrated that the cluster–gas target provides a unique electron injection realm for the ultrarelativistic electron generation which is not governed by the wake-wave breaking, and has the potential to provide a new electron injection process for monoenergetic electron beam generation. Acknowledgements This work was supported by the Grant-in-Aid for Scientific Research on Specially Promoted Research (15002013) by MEXT. The authors acknowledge T. Tajima, Y. Kishimoto, K. Nakajima, and T. Kimura for fruitful discussions, as well as T.Zh. Esirkepov for providing the PIC code. References [1] A. McPherson, et al., Nature (London) 370 (1994) 631; T. Ditmire, et al., Nature (London) 386 (1997) 54; M. Lezius, et al., Phys. Rev. Lett. 80 (1998) 261; T. Ditmire, et al., Nature (London) 398 (1999) 489; V. Kumarappan, M. Krishnamurthy, D. Mathur, Phys. Rev. Lett. 87 (2001) 085005; V.P. Krainov, M.B. Smirnov, Phys. Rep. 370 (2002) 237; Y. Fukuda, et al., Phys. Rev. A 67 (2003) 061201; K.Y. Kim, et al., Phys. Rev. Lett. 90 (2003) 023401. [2] S.V. Bulanov, et al., Plasma Phys. Rep. 30 (2004) 196. [3] V.P. Krainov, Phys. Rev. E 68 (2003) 027401; M.V. Fomyts’kyi, et al., Phys. Plasmas 11 (2004) 3349. [4] A.S. Boldarev, et al., Rev. Sci. Instrum. 77 (2006) 083112. [5] I. Alexeev, et al., Phys. Rev. Lett. 90 (2003) 103402; V. Kumarappan, et al., Phys. Rev. Lett. 94 (2005) 205004. [6] T. Tajima, J.M. Dawson, Phys. Rev. Lett. 43 (1979) 267.
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