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Visualization of plasma bubble accelerators using Frequency-Domain Shadowgraphy
High Energy Density Physics 6 (2010) 153–156
Contents lists available at ScienceDirect
High Energy Density Physics journal homepage: www.elsevier.com/locate/hedp
Visualization of plasma bubble accelerators using Frequency-Domain Shadowgraphy P. Dong a, *, S.A. Reed a, S.A. Yi a, S.Y. Kalmykov a, G. Shvets a, M.C. Downer a, N.H. Matlis b, W.P. Leemans b, C. McGuffey c, S.S. Bulanov c, V. Chvykov c, G. Kalintchenko c, K. Krushelnick c, A. Maksimchuk c, T. Matsuoka c, A.G.R. Thomas c, V. Yanovsky c a b c
Department of Physics, University of Texas at Austin, 1 University Station C1600, Austin, TX 78712-1081, USA Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA Center for Ultrafast Optical Science, University of Michigan, 2200 Bonisteel Blvd, Ann Arbor, MI 48109-2099, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 December 2009 Accepted 7 December 2009 Available online 16 December 2009
We report on generation of relativistic electron beams in the wake of a relativistically intense laser pulse traversing a 1.7 mm long atmospheric density helium gas jet. The plasma wake structure is recovered using a Frequency-Domain Holography (FDH) and Frequency-Domain Shadowgraphy (FDS). As the gas density changes, the accelerated electron beams show variations in cross-section area, divergence, total charge, and peak energy. FDH phase reconstruction shows discontinuities and large phase jumps due to plasma electrons blown out by the pump pulse, probe pulse refraction, and nonlinear propagation in plasma. However, FDS amplitude reconstruction shows bright spots that yield information about bubble formation and evolution. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Wakefield Laser Plasma Accelerator FDH
1. Introduction Table top plasma accelerators driven by intense ultrashort laser pulses have recently produced collimated electron bunches with hundreds of pC charge, a few percent energy spread, and central energy up to 1 GeV out of centimeter-long plasmas [1–3]. Large-scale particle-in-cell (PIC) simulations show that these high quality, quasi-monoenergetic electron bunches are associated with the formation of an electron density cavity, or bubble, with dimensions on the order of a plasma wavelength lp in the immediate wake of the drive laser pulse [4–6]. Strong electrostatic fields inside the bubble capture electrons from its surrounding electron sheath and accelerate them with exceptional uniformity to relativistic energy. Theoretical scalings [5] suggest that the favorable acceleration properties of this nonlinear bubble regime could help reach the energies in the TeV range provided that new plasma guiding technologies are developed [7]. However, direct observations of the plasma bubble structure have not been reported until now. As a consequence, planning and optimization of experiments had to rely primarily
* Corresponding author. Tel.: þ1 512 471 7251. E-mail address: [email protected] (P. Dong). 1574-1818/$ – see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.hedp.2009.12.003
on theoretical models and first-principle numerical simulations of nonlinear laser propagation, bubble formation and evolution, electron capture and acceleration, and electron propagation to a detector. In the interaction regimes with the plasma density and/or driving laser intensity well below the threshold for bubble formation, direct images of periodic laser wakefields were recently obtained using a frequency-domain holography (FDH) [8]. FDH is a single-shot interferometric technique in which a chirped probe pulse co-propagates with, and is phase modulated by, the laser-generated plasma structure. The probe then interferes with a chirped reference pulse at the detection plane of an imaging spectrometer. Fourier transformation of the recorded frequency-domain hologram reconstructs the plasma accelerator morphology. FDH images reveal variations in the accelerating structure as the initial parameters of laser and plasma change. The most remarkable feature resolved by means of FDH is the phase front curvature of the three-dimensional relativistic plasma wave, which reveals excellent agreement with a theory and numerical modelling. Higher densities and/or laser intensities enable formation of the electron density bubble. The highcontrast bubble structure causes strong refraction and focusing of the probe light. In addition, white light generated from pump pulse interferes with the probe pulse. These effects scramble the
154
P. Dong et al. / High Energy Density Physics 6 (2010) 153–156
phase information and preclude accurate reconstruction of the plasma wake morphology. In this regime, we modify the original FDH technique to reconstruct the probe pulse amplitude instead of the phase. We term this modified technique FrequencyDomain Shadowgraphy (FDS) because it infers the laser-induced plasma structure from changes in the probe amplitude caused by refraction. In this paper, we report on the evolution of electron beams properties caused by the variation of background plasma density. In the highest density case, single-shot images of laser driven bubbles obtained through FDS are correlated with the production of high quality electron beams.
2. Experimental setup Fig. 1 shows the experimental setup. We use the Ti:sapphire HERCULES laser system at the University of Michigan. Duration of the pulse with a central wavelength 800 nm is 30 femtoseconds (fs). The output power is 30 TW with less than 7% shot-to-shot energy fluctuation. Inside the experimental chamber, a 1-inch diameter aluminum mirror reflects the center portion of the 4inch diameter pump beam at 45 degrees to create reference and probe beams. The reflected beam is converted into two 400 nm probe pulses separated by 2 ps by passing through a 200 mm KDP crystal, a 0.5 inch BK7 glass and another 200 mm KDP crystal. After reflecting off a deformable mirror for wavefront correction and an optimum focal spot size of 8 mm, the pump pulse is recombined collinearly with the probe pulse using an 800 nm dielectric mirror. After passing through the mirror, the probe pulse is stretched to 1 ps. Both beams are focused by a 1-m focal length parabola onto the front edge of a 1.7 mm supersonic gas jet. After the gas jet, a 400 nm dielectric reflector blocks most of the pump beam and sends the probe beam into a telescope system which images the rear side of the gas jet onto the slit of an imaging spectrometer. An iris is inserted into the imaging system to block part of the white light and pump generated second harmonic pulse by taking advantage of the different focusing geometry of pump and probe pulse. A polarizer is also inserted to block the pump beam and transmit the probe beam. Electron beams are deflected by a 1 Tesla magnet onto a fluorescence screen where the electron spectrum is imaged by a CCD camera. A transverse Michelson interferometer outside the chamber measures the electron density. Thomson scattered light is also collected from the top of the gas jet to monitor the plasma column.
Fig. 1. The experimental setup. P – parabola; M8 – 800 nm dielectric mirror. M4 – 400 nm dielectric mirror; K – KDP crystal; G – glass to generate time delay between the probe and reference pulse; GJ – gas jet; I – iris; L – imaging lens; and PO – polarizer.
3. Relativistic electron beam generation Electron energy spectra are measured for electron densities in the range 0.2–3.2 1019 cm3. Moreover, position of the pump pulse focus has been varied from the entrance to the center of the gas jet. No accelerated electron has been detected at any plasma density when the laser was focused at the jet center. Focusing at the edge of the jet has been found optimal for the electron production. Relativistic electrons first appear at 1.6 1019 cm3 and are detectable at all higher densities; sample spectra are presented in Fig. 2. Electron beams with low divergence, low charge, wide almost flat-top energy spectrum with a sharp cutoff around 90 MeV are observed at ne z 1.7 1019 cm3. This regime is similar to the ‘‘forced wakefield’’ reported by Malka et al. [9]. One representative spectrum is shown in Fig. 2(a). As the density increases, the beam charge grows. Typical electron spectra observed around ne z 2.1 1019 cm3 show a broad peak centered at 50 MeV, and span up to w75 MeV. With higher charge, beam loading [10] effectively reduces the accelerating gradient and, hence, the peak electron energy. At ne ¼ 2.4 1019 cm3, electrons become poorly collimated. The energy spectrum displayed in Fig. 2(b) shows multiple sinusoidal tracks of electron beams. Since the oscillations are perpendicular to the pump polarization, these are not due to effect of the linearly polarized laser electric field. They are possibly caused by out-ofplane betatron oscillations due to asymmetric off-axis injection, which probably is driven by an asymmetric laser pulse intensity distribution [11,12]. Raising the density beyond ne ¼ 2.4 1019 cm3 results in a complete degradation of electron beam quality. The beam becomes strongly dispersed in the transverse direction. As is seen in Fig. 2(c), majority of electrons have energy below 30 MeV with a weak tail spanning up to 90 MeV. The features shown in Fig. 2(a)–(c) are consistently reproduced in almost every shot in the corresponding density ranges. Anomalies are quite infrequent (one shot out of ten). For instance, extremely well collimated monoenergetic electron beams with less than 1% energy spread were observed in several shots at densities ne a 2.9 1019 cm3. One such spectrum is shown in Fig. 2(d). Similar beams were observed in similar conditions by other groups [13–16]. The FDS diagnostic, which we discuss in the next Section,
Fig. 2. False-color images of electron beam energy spectrum at different electron (b) 2.4 1019 cm3; (c) 2.7 1019 cm3; densities: (a) 1.7 1019 cm3; (d) 2.9 1019 cm3. The color intensity in the panel (a) is enhanced by a factor 3, and in panel (c) by a factor 2.
P. Dong et al. / High Energy Density Physics 6 (2010) 153–156
shows strong correlation of the electron beam generation and the presence of stable plasma bubble in this regime. The wide variety of electron beam properties provides a test bed for multi-dimensional PIC simulations. Importantly, even with nominally the same laser beam profile, energy, and backing pressure of the gas jet, the electron beam parameters fluctuate from shot to shot for densities above 2.1 1019 cm3, as is shown by error bars in Fig. 3. Therefore, an in situ measurement of the bubble structure becomes critically important. These measurements are discussed in the next Section. A theoretical scaling law predicts the peak electron energy as a function of electron density [5,17],
Emax ¼ 0:16mc2
cs P 2=3 nc 1=3 : r0 Prel ne
(1)
where m is the rest mass of electron, c is the speed of light in vacuum, s is the full width at half-maximum of the laser pulse in intensity, r0 is the laser spot size, P is the laser power, Prel ¼ 8.5 GW is the natural relativistic power unit, nc ¼ mu20/(4pe2) is the critical density. The equation is used for optimally matched laser spot size and duration at a given plasma density. However, as is seen in Fig. 3, predictions of Eq. (1) fit the experimental results reasonably well. The good agreement is due to the fact that self-focusing and compression of the pump pulse self-consistently adjust the pulse size to the optimal one. 4. FDH and FDS measurements The technique uses two 400 nm pulses that propagate through the gas jet collinearly with the pump pulse. The trailing probe pulse overlaps in time with the pump pulse and the wake. Thus the phase and amplitude of the probe are modulated by the plasma wake. By interfering the probe and reference beams in the frequency domain inside the spectrometer, we recover modified time-domain phase and amplitude of the probe pulse [8]. The data analysis involves a Fourier transformation of the electric field from frequency to time domain after the amplitude and phase information are obtained from the frequency-domain interference pattern. First a null shot with no gas jet is taken to measure background phase f0 between the probe and reference pulses and any other noise phase. In this experiment, the phase noise is about 0.1 radian. The procedure is then repeated with gas jet to retrieve the phase fdata. When combined with the separately measured chirp phase fchirp of the probe pulse, the total phase of the probe pulse f ¼ fdata þ fchirp þ f0 in frequency domain is obtained. The interference pattern of the probe and reference
electron max energy (MeV)
100 95 90
theory experiment
155
Fig. 4. Optical bullet (right) and corresponding monoenergetic electron beam (left) at ne ¼ 2.9 1019 cm3. Left panel: same as panel (d) of Fig. 2. Right panel: FDS image of the accelerating structure from the same shot (z is a time delay with respect to the driving pulse center, z ¼ 0). The optical bullet is pointed at by an arrow. The bright spot indicates strong focusing of the probe light by the plasma bubble. This feature is always observed together with the production of monoenergetic electron beam.
beam also contains amplitude information. After the full reconstruction of the probe electric field in the frequency domain, Fourier transformation yields the electric field in the time domain. Here we examined both phase and amplitude of the probe in the time domain. The time-domain probe phase appears to be a poor diagnostic at these high gas densities. Strong refraction by high-contrast perturbations of the refractive index in the electron bubble scrambles the phase information in the radial direction. In addition, phase shifts exceeding 2p and strong phase discontinuities are present. By contrast, it appears that the amplitude yields a straightforward signature of the observed bubble structure. A bright spot (‘‘optical bullet’’ [18]) in the reconstructed probe amplitude, one example of which is shown in Fig. 4(b), is consistently observed together with the generation of high-energy electrons. The bullet is formed from the part of the probe light beam compressed and focused by the bubble. The transverse size of the bullet is about 13 mm, which is close to the pump spot size and theoretically calculated bubble size. Such optical bullets therefore appear to be a straightforward signature of the presence of plasma electron density bubbles. A detailed experimental and simulation study of optical bullet formation over a range of laser-plasma conditions has been submitted for publication [19]. 5. Conclusion Evolution of electron energy spectra due to the variation of background plasma density in the bubble regime of laser wakefield acceleration is presented. This study provides data for benchmarking PIC codes and theoretical scaling laws. Phase and amplitude reconstruction of the probe pulse using FDS is discussed. Formation of probe light bullets by focusing inside the plasma bubbles independently confirms bubble formation in conjunction with production of relativistic electrons. Acknowledgements
85 80
The work is supported by the US DoE grants DE-FG0207ER54945, DE-FG02-96ER40954, and DE-FG02-04ER41321, the NSF Physics Frontier Center FOCUS (grant PHY-011436) and NSF/ DNDO grant 0833499.
75 70 65 60
References
55 50 1.3
2.3 3.3 gas density (1019cm-3)
4.3
Fig. 3. Experimental data (squares with error bars) versus analytical prediction (dark gray line) of maximum electron energy.
[1] [2] [3] [4] [5] [6]
W.P. Leemans, B. Nagler, A.J. Gonsalves, et al., Nat. Phys. 2 (2006) 696. S. Karsch, J. Osterhoff, A. Popp, et al., New J. Phys. 9 (2007) 415. N.A.M. Hafz, T.M. Jeong, I.W. Choi, et al., Nat. Photon. 2 (2008) 571. A. Pukhov, J. Meyer-ter-Vehn, Appl. Phys. B 74 (2002) 355. W. Lu, M. Tzoufras, C. Joshi, et al., Phys. Rev. ST Accel. Beams 10 (2007) 061301. S. Kalmykov, S.A. Yi, V. Khudik, G. Shvets, Phys. Rev. Lett. 103 (2009) 135004.
156 [7] [8] [9] [10] [11]
P. Dong et al. / High Energy Density Physics 6 (2010) 153–156
C.B. Schroeder, E. Esarey, C.G.R. Geddes, et al., AIP Conf. Proc. 1086 (2009) 208. N.H. Matlis, S. Reed, S.S. Bulanov, et al., Nat. Phys. 2 (2006) 749. V. Malka, S. Fritzler, E. Lefebvre, et al., Science 298 (2002) 1596. M. Tsoufras, W. Lu, F.S. Tsung, et al., Phys. Plasmas 16 (2009) 056705. T. Matsuoka, C. McGuffey, C.M. Hungtington, et al., AIP Conf. Proc. 1086 (2009) 184. [12] Y. Glinec, J. Faure, A. Lifschitz, et al., Europhys. Lett. 81 (2008) 64001. [13] A. Maksimchuk, S. Reed, N. Naumova, et al., Appl. Phys. B 89 (2007) 201.
[14] R.C. Issac, G. Vieux, G.H. Welsh, et al., Proc. SPIE 7359 (2009) 735915-1. [15] S.M. Wiggins, M.P. Anania, E. Brunetti, et al., Proc. SPIE 7359 (2009) 735914-1. [16] J.G. Gallacher, M.P. Anania, E. Brunetti, et al., Phys. Plasmas 16 (2009) 093102. [17] B. Hidding, M. Geissler, G. Pretzler, et al., Phys. Plasmas 16 (2009) 043105. [18] Y.S. Kivshar, G.P. Agarwal, Optical Solitons: from Fibers to Photonic Crystals. Academic, San Diego, 2003. [19] P. Dong, S.A. Reed, S.A. Yi, et al., Phys. Rev. Lett., submitted for publication.
Contents lists available at ScienceDirect
High Energy Density Physics journal homepage: www.elsevier.com/locate/hedp
Visualization of plasma bubble accelerators using Frequency-Domain Shadowgraphy P. Dong a, *, S.A. Reed a, S.A. Yi a, S.Y. Kalmykov a, G. Shvets a, M.C. Downer a, N.H. Matlis b, W.P. Leemans b, C. McGuffey c, S.S. Bulanov c, V. Chvykov c, G. Kalintchenko c, K. Krushelnick c, A. Maksimchuk c, T. Matsuoka c, A.G.R. Thomas c, V. Yanovsky c a b c
Department of Physics, University of Texas at Austin, 1 University Station C1600, Austin, TX 78712-1081, USA Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA Center for Ultrafast Optical Science, University of Michigan, 2200 Bonisteel Blvd, Ann Arbor, MI 48109-2099, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 December 2009 Accepted 7 December 2009 Available online 16 December 2009
We report on generation of relativistic electron beams in the wake of a relativistically intense laser pulse traversing a 1.7 mm long atmospheric density helium gas jet. The plasma wake structure is recovered using a Frequency-Domain Holography (FDH) and Frequency-Domain Shadowgraphy (FDS). As the gas density changes, the accelerated electron beams show variations in cross-section area, divergence, total charge, and peak energy. FDH phase reconstruction shows discontinuities and large phase jumps due to plasma electrons blown out by the pump pulse, probe pulse refraction, and nonlinear propagation in plasma. However, FDS amplitude reconstruction shows bright spots that yield information about bubble formation and evolution. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Wakefield Laser Plasma Accelerator FDH
1. Introduction Table top plasma accelerators driven by intense ultrashort laser pulses have recently produced collimated electron bunches with hundreds of pC charge, a few percent energy spread, and central energy up to 1 GeV out of centimeter-long plasmas [1–3]. Large-scale particle-in-cell (PIC) simulations show that these high quality, quasi-monoenergetic electron bunches are associated with the formation of an electron density cavity, or bubble, with dimensions on the order of a plasma wavelength lp in the immediate wake of the drive laser pulse [4–6]. Strong electrostatic fields inside the bubble capture electrons from its surrounding electron sheath and accelerate them with exceptional uniformity to relativistic energy. Theoretical scalings [5] suggest that the favorable acceleration properties of this nonlinear bubble regime could help reach the energies in the TeV range provided that new plasma guiding technologies are developed [7]. However, direct observations of the plasma bubble structure have not been reported until now. As a consequence, planning and optimization of experiments had to rely primarily
* Corresponding author. Tel.: þ1 512 471 7251. E-mail address: [email protected] (P. Dong). 1574-1818/$ – see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.hedp.2009.12.003
on theoretical models and first-principle numerical simulations of nonlinear laser propagation, bubble formation and evolution, electron capture and acceleration, and electron propagation to a detector. In the interaction regimes with the plasma density and/or driving laser intensity well below the threshold for bubble formation, direct images of periodic laser wakefields were recently obtained using a frequency-domain holography (FDH) [8]. FDH is a single-shot interferometric technique in which a chirped probe pulse co-propagates with, and is phase modulated by, the laser-generated plasma structure. The probe then interferes with a chirped reference pulse at the detection plane of an imaging spectrometer. Fourier transformation of the recorded frequency-domain hologram reconstructs the plasma accelerator morphology. FDH images reveal variations in the accelerating structure as the initial parameters of laser and plasma change. The most remarkable feature resolved by means of FDH is the phase front curvature of the three-dimensional relativistic plasma wave, which reveals excellent agreement with a theory and numerical modelling. Higher densities and/or laser intensities enable formation of the electron density bubble. The highcontrast bubble structure causes strong refraction and focusing of the probe light. In addition, white light generated from pump pulse interferes with the probe pulse. These effects scramble the
154
P. Dong et al. / High Energy Density Physics 6 (2010) 153–156
phase information and preclude accurate reconstruction of the plasma wake morphology. In this regime, we modify the original FDH technique to reconstruct the probe pulse amplitude instead of the phase. We term this modified technique FrequencyDomain Shadowgraphy (FDS) because it infers the laser-induced plasma structure from changes in the probe amplitude caused by refraction. In this paper, we report on the evolution of electron beams properties caused by the variation of background plasma density. In the highest density case, single-shot images of laser driven bubbles obtained through FDS are correlated with the production of high quality electron beams.
2. Experimental setup Fig. 1 shows the experimental setup. We use the Ti:sapphire HERCULES laser system at the University of Michigan. Duration of the pulse with a central wavelength 800 nm is 30 femtoseconds (fs). The output power is 30 TW with less than 7% shot-to-shot energy fluctuation. Inside the experimental chamber, a 1-inch diameter aluminum mirror reflects the center portion of the 4inch diameter pump beam at 45 degrees to create reference and probe beams. The reflected beam is converted into two 400 nm probe pulses separated by 2 ps by passing through a 200 mm KDP crystal, a 0.5 inch BK7 glass and another 200 mm KDP crystal. After reflecting off a deformable mirror for wavefront correction and an optimum focal spot size of 8 mm, the pump pulse is recombined collinearly with the probe pulse using an 800 nm dielectric mirror. After passing through the mirror, the probe pulse is stretched to 1 ps. Both beams are focused by a 1-m focal length parabola onto the front edge of a 1.7 mm supersonic gas jet. After the gas jet, a 400 nm dielectric reflector blocks most of the pump beam and sends the probe beam into a telescope system which images the rear side of the gas jet onto the slit of an imaging spectrometer. An iris is inserted into the imaging system to block part of the white light and pump generated second harmonic pulse by taking advantage of the different focusing geometry of pump and probe pulse. A polarizer is also inserted to block the pump beam and transmit the probe beam. Electron beams are deflected by a 1 Tesla magnet onto a fluorescence screen where the electron spectrum is imaged by a CCD camera. A transverse Michelson interferometer outside the chamber measures the electron density. Thomson scattered light is also collected from the top of the gas jet to monitor the plasma column.
Fig. 1. The experimental setup. P – parabola; M8 – 800 nm dielectric mirror. M4 – 400 nm dielectric mirror; K – KDP crystal; G – glass to generate time delay between the probe and reference pulse; GJ – gas jet; I – iris; L – imaging lens; and PO – polarizer.
3. Relativistic electron beam generation Electron energy spectra are measured for electron densities in the range 0.2–3.2 1019 cm3. Moreover, position of the pump pulse focus has been varied from the entrance to the center of the gas jet. No accelerated electron has been detected at any plasma density when the laser was focused at the jet center. Focusing at the edge of the jet has been found optimal for the electron production. Relativistic electrons first appear at 1.6 1019 cm3 and are detectable at all higher densities; sample spectra are presented in Fig. 2. Electron beams with low divergence, low charge, wide almost flat-top energy spectrum with a sharp cutoff around 90 MeV are observed at ne z 1.7 1019 cm3. This regime is similar to the ‘‘forced wakefield’’ reported by Malka et al. [9]. One representative spectrum is shown in Fig. 2(a). As the density increases, the beam charge grows. Typical electron spectra observed around ne z 2.1 1019 cm3 show a broad peak centered at 50 MeV, and span up to w75 MeV. With higher charge, beam loading [10] effectively reduces the accelerating gradient and, hence, the peak electron energy. At ne ¼ 2.4 1019 cm3, electrons become poorly collimated. The energy spectrum displayed in Fig. 2(b) shows multiple sinusoidal tracks of electron beams. Since the oscillations are perpendicular to the pump polarization, these are not due to effect of the linearly polarized laser electric field. They are possibly caused by out-ofplane betatron oscillations due to asymmetric off-axis injection, which probably is driven by an asymmetric laser pulse intensity distribution [11,12]. Raising the density beyond ne ¼ 2.4 1019 cm3 results in a complete degradation of electron beam quality. The beam becomes strongly dispersed in the transverse direction. As is seen in Fig. 2(c), majority of electrons have energy below 30 MeV with a weak tail spanning up to 90 MeV. The features shown in Fig. 2(a)–(c) are consistently reproduced in almost every shot in the corresponding density ranges. Anomalies are quite infrequent (one shot out of ten). For instance, extremely well collimated monoenergetic electron beams with less than 1% energy spread were observed in several shots at densities ne a 2.9 1019 cm3. One such spectrum is shown in Fig. 2(d). Similar beams were observed in similar conditions by other groups [13–16]. The FDS diagnostic, which we discuss in the next Section,
Fig. 2. False-color images of electron beam energy spectrum at different electron (b) 2.4 1019 cm3; (c) 2.7 1019 cm3; densities: (a) 1.7 1019 cm3; (d) 2.9 1019 cm3. The color intensity in the panel (a) is enhanced by a factor 3, and in panel (c) by a factor 2.
P. Dong et al. / High Energy Density Physics 6 (2010) 153–156
shows strong correlation of the electron beam generation and the presence of stable plasma bubble in this regime. The wide variety of electron beam properties provides a test bed for multi-dimensional PIC simulations. Importantly, even with nominally the same laser beam profile, energy, and backing pressure of the gas jet, the electron beam parameters fluctuate from shot to shot for densities above 2.1 1019 cm3, as is shown by error bars in Fig. 3. Therefore, an in situ measurement of the bubble structure becomes critically important. These measurements are discussed in the next Section. A theoretical scaling law predicts the peak electron energy as a function of electron density [5,17],
Emax ¼ 0:16mc2
cs P 2=3 nc 1=3 : r0 Prel ne
(1)
where m is the rest mass of electron, c is the speed of light in vacuum, s is the full width at half-maximum of the laser pulse in intensity, r0 is the laser spot size, P is the laser power, Prel ¼ 8.5 GW is the natural relativistic power unit, nc ¼ mu20/(4pe2) is the critical density. The equation is used for optimally matched laser spot size and duration at a given plasma density. However, as is seen in Fig. 3, predictions of Eq. (1) fit the experimental results reasonably well. The good agreement is due to the fact that self-focusing and compression of the pump pulse self-consistently adjust the pulse size to the optimal one. 4. FDH and FDS measurements The technique uses two 400 nm pulses that propagate through the gas jet collinearly with the pump pulse. The trailing probe pulse overlaps in time with the pump pulse and the wake. Thus the phase and amplitude of the probe are modulated by the plasma wake. By interfering the probe and reference beams in the frequency domain inside the spectrometer, we recover modified time-domain phase and amplitude of the probe pulse [8]. The data analysis involves a Fourier transformation of the electric field from frequency to time domain after the amplitude and phase information are obtained from the frequency-domain interference pattern. First a null shot with no gas jet is taken to measure background phase f0 between the probe and reference pulses and any other noise phase. In this experiment, the phase noise is about 0.1 radian. The procedure is then repeated with gas jet to retrieve the phase fdata. When combined with the separately measured chirp phase fchirp of the probe pulse, the total phase of the probe pulse f ¼ fdata þ fchirp þ f0 in frequency domain is obtained. The interference pattern of the probe and reference
electron max energy (MeV)
100 95 90
theory experiment
155
Fig. 4. Optical bullet (right) and corresponding monoenergetic electron beam (left) at ne ¼ 2.9 1019 cm3. Left panel: same as panel (d) of Fig. 2. Right panel: FDS image of the accelerating structure from the same shot (z is a time delay with respect to the driving pulse center, z ¼ 0). The optical bullet is pointed at by an arrow. The bright spot indicates strong focusing of the probe light by the plasma bubble. This feature is always observed together with the production of monoenergetic electron beam.
beam also contains amplitude information. After the full reconstruction of the probe electric field in the frequency domain, Fourier transformation yields the electric field in the time domain. Here we examined both phase and amplitude of the probe in the time domain. The time-domain probe phase appears to be a poor diagnostic at these high gas densities. Strong refraction by high-contrast perturbations of the refractive index in the electron bubble scrambles the phase information in the radial direction. In addition, phase shifts exceeding 2p and strong phase discontinuities are present. By contrast, it appears that the amplitude yields a straightforward signature of the observed bubble structure. A bright spot (‘‘optical bullet’’ [18]) in the reconstructed probe amplitude, one example of which is shown in Fig. 4(b), is consistently observed together with the generation of high-energy electrons. The bullet is formed from the part of the probe light beam compressed and focused by the bubble. The transverse size of the bullet is about 13 mm, which is close to the pump spot size and theoretically calculated bubble size. Such optical bullets therefore appear to be a straightforward signature of the presence of plasma electron density bubbles. A detailed experimental and simulation study of optical bullet formation over a range of laser-plasma conditions has been submitted for publication [19]. 5. Conclusion Evolution of electron energy spectra due to the variation of background plasma density in the bubble regime of laser wakefield acceleration is presented. This study provides data for benchmarking PIC codes and theoretical scaling laws. Phase and amplitude reconstruction of the probe pulse using FDS is discussed. Formation of probe light bullets by focusing inside the plasma bubbles independently confirms bubble formation in conjunction with production of relativistic electrons. Acknowledgements
85 80
The work is supported by the US DoE grants DE-FG0207ER54945, DE-FG02-96ER40954, and DE-FG02-04ER41321, the NSF Physics Frontier Center FOCUS (grant PHY-011436) and NSF/ DNDO grant 0833499.
75 70 65 60
References
55 50 1.3
2.3 3.3 gas density (1019cm-3)
4.3
Fig. 3. Experimental data (squares with error bars) versus analytical prediction (dark gray line) of maximum electron energy.
[1] [2] [3] [4] [5] [6]
W.P. Leemans, B. Nagler, A.J. Gonsalves, et al., Nat. Phys. 2 (2006) 696. S. Karsch, J. Osterhoff, A. Popp, et al., New J. Phys. 9 (2007) 415. N.A.M. Hafz, T.M. Jeong, I.W. Choi, et al., Nat. Photon. 2 (2008) 571. A. Pukhov, J. Meyer-ter-Vehn, Appl. Phys. B 74 (2002) 355. W. Lu, M. Tzoufras, C. Joshi, et al., Phys. Rev. ST Accel. Beams 10 (2007) 061301. S. Kalmykov, S.A. Yi, V. Khudik, G. Shvets, Phys. Rev. Lett. 103 (2009) 135004.
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P. Dong et al. / High Energy Density Physics 6 (2010) 153–156
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