5
Science Motivation

5.1 INTRODUCTION TO THE INTENSITY ROADMAP OF OPPORTUNITIES AND DISCOVERY

This chapter and the next summarize the case for development and use of high-intensity lasers for research and applications. The impact of high-intensity laser technology on science is unusually strong and broad, spanning from the most basic questions of the cosmos to potential applications in medical therapy.

The primary motivation for high-intensity science is that it overturns the foundational assumption that the forces exerted by light are weak, and may therefore be treated as small perturbations to the forces that shape matter. The fields in a high intensity laser focus exert forces that are stronger than the physical systems they encounter—stronger than the chemical forces holding molecules and solids together; stronger than the coulomb fields that bind electrons in atoms; and ultimately stronger than the vacuum itself. This chapter introduces the scientific opportunities that are enabled by high intensity. Conclusion 1 is supported by the material here.

The high-intensity laser research opportunities described in this chapter cannot all be realized with only one type of large laser facility. Petawatt lasers configured to study particle acceleration are not optimized to excite or probe high density matter, for example. The facility location can also be important for some applications: A laser co-located with relativistic electron accelerators can enable science that would be difficult or impossible to explore with a stand-alone laser facility; large magnetic fields are needed to study some aspects in materials science.

In addition, auxiliary coherent sources such as high energy pulsed lasers or X-ray free-electron lasers (FELs) may be needed to study extreme conditions such as hot dense plasmas.

Figure 1.3 in the introductory chapter of this report, reproduced here for convenience, describes the regimes of extreme field physics associated with the historical development of technology for high peak power lasers. The threshold laser intensity for entrée to each regime is set by parameters that characterize the laser and physical system that describe the interaction. The dimensionless Keldysh parameter γ_k, for example, was an early measure of the level of extreme of a laser field that relates the electric field in the focused laser to the electric field binding an electron in an atom. It works out to the ratio of two rates: the laser angular frequency ω, and the bound electron’s tunneling rate in the intense field, Γ. The tunneling regime occurs for γ_K<1, which means that ionization occurs in less than

one optical cycle. For hydrogen this corresponds to peak electric fields of about 50 billion V/m, corresponding to laser intensities of ~0.3 PW/cm² at optical wavelengths. As Figure 1.3 in Chapter 1 shows, this is also the laser field corresponding to an atomic unit, where the laser field exceeds the coulomb field binding the electron to the proton, so that the standard atomic physics perturbation theory description of ionization due to absorption of multiple photons breaks down. See Appendix A for more information.

The Keldysh parameter can also be expressed as , where I.P. is the ionization potential of the atom, and U_P is the laser “ponderomotive potential,” the time averaged wiggle kinetic energy of a free electron in the oscillating field of the laser. U_P is proportional to I λ², where I is the laser intensity and λ is the laser wavelength. This is also shown in Figure 1.3, for laser wavelengths on the order of 0.8-1.0 microns, the most common wavelengths used for petawatt lasers.

Chirped-pulse amplification enabled a trend that continues today to advance the research frontier that can be accessed with higher peak laser fields and shorter pulses. One important consequence was the development of methods to study ionization on time scales shorter than a single optical cycle, termed “attosecond science.”¹ The current well-established model of strong-field ionization is based on sub-femtosecond motion of atomic electrons. Some of the important primary references to this model will be summarized briefly in Section 5.2, because this is part of the core underlying science in this field.

Shorter intense pulses from CPA lasers also led to more exploration of tabletop laser-driven coherent soft X-ray sources such as high harmonics or attosecond continuum radiation, with applications in science and technology. This will be discussed more fully in Chapter 5. The underlying science is field ionization of higher Z ions and nonlinear interactions of laser-driven electrons in plasmas.

CPA sources focused to intensities above ~10¹⁸W/cm² have ponderomotive potential energies that approach or exceed the rest energy of the electron. These relativistic laser field strengths enable a new regime of high-intensity physics. A dimensionless measure of the entrée to the relativistic regime is the normalized laser vector potential a = eA_o/mc, where e and m are the electron charge and mass, A_o is the laser vector potential (given here in SI units), and c is the speed of light.² The relationship between the laser intensity, the laser field, and the laser vector potential, is shown in Appendix A. For a∼1, an electron can be accelerated by the laser field to nearly the speed of light in a distance of the order of the laser wave-

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¹ P.M. Paul, E.S. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H.G. Muller, and P. Agostini, 2001, Observation of a train of attosecond pulses from high harmonic generation, Science 292(5522): 1689-1692.; M. Hentschel, R. Kienberger, Ch. Spielmann, G.A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, 2001, Attosecond metrology, Nature 414: 509-513.

² J.D. Jackson, 2001, Classical Electrodynamics, 3rd ed., Wiley, New York.

length (~ 1 µm). This intensity regime opens up the field of relativistic nonlinear optics, which includes applications in laser-driven particle acceleration³ and short wavelength radiation sources.⁴ Extreme fields can also arise as secondary sources from intense laser-matter interactions—in particular, as a consequence of bright relativistic electron and ion beams generated through laser-gas and laser-foil interactions. For example, giga-gauss scale magnetic fields have been generated by interaction of ~10²⁰ W/cm² laser pulses with thin foils.⁵

Finally, at the frontiers of intensity, one enters the quantum electrodynamics (QED) regime, where the vacuum itself becomes unstable and matter is created by light. The threshold laser field strength E₀ for entering this regime is the Schwinger field E_S, for which the work done on an electron-positron pair over one Compton wavelength is equal to their rest mass: eE_Sλ_C = 2mc². This occurs for E_S = 1.3 × 10¹⁸V/m, corresponding to intensity I_S = 2.3 × 10²⁹W/cm².⁶ This field is of sufficient strength to accelerate the virtual electrons and positrons that fleetingly appear from vacuum QED fluctuations At the same time, virtual electrons and positrons can mediate photon-photon interactions, which could continue to generate pairs in a cascade-like process.⁷

While this intensity level is not currently achievable, the QED regime may be accessed by colliding an ultra-relativistic electron beam from either a conventional laser accelerator or laser-driven wakefield accelerator with an extreme light infrastructure (ELI)-type laser. For interactions in a boosted frame of reference, the appropriate dimensionless parameter for entering the QED regime is χ = γE₀/E_S, where γ is the boosted frame’s Lorentz factor, reducing the required laser intensities in experiments involving particle accelerators.

In the electron’s frame, the laser’s intensity will undergo a relativistic boost, reducing the required laboratory-frame intensity. An alternate scheme, using a

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³ E. Esarey, C.B. Schroeder, and W.P. Leemans, 2009, Physics of laser-driven plasma-based electron accelerators, Rev. Mod. Phys. 81: 1229.

⁴ CORDE, 2015; S.V. Bulanov, N.M. Naumova, and F. Pegoraro, 1994, Interaction of an ultrashort, relativistically intense laser-pulse with an overdense plasma, Phys. Plasmas 1: 745.

⁵ A. Saemann, K. Eidmann, I.E. Golovkin, R.C. Mancini, E. Andersson, E. Förster, and K. Witte, 1999, Isochoric heating of solid aluminum by ultrashort laser pulses focused on a tamped target, Phys. Rev. Lett. 82: 4843.

⁶ J.A. Frenje, P.E. Grabowski, C.K. Li, F.H. Séguin, A.B. Zylstra, M. Gatu Johnson, R.D. Petrasso, V. Yu Glebov, and T.C. Sangster, 2015, Measurements of ion stopping around the Bragg peak in high-energy-density plasmas, Phys. Rev. Lett. 115: 205001; A. Di Piazza, C. Muller, K.Z. Hatsagortsyan, and C.H. Keitel, 2012, Extremely high-intensity laser interactions with fundamental quantum systems, Rev. Mod. Phys. 84: 1177.

⁷ W.P. Leemans, J. Daniels, A. Deshmukh, A.J. Gonsalves, A. Magana, H.S. Mao, D.S. Mittleberger, et al., 2013, BELLA lasers and operations, p. 1097 in Proceedings of PAC2013, Sept. 29-Oct. 4, Pasadena, Calif.

laser assist beam for extreme nonlinear four-wave mixing in vacuum, is depicted in Figure 5.1. This is discussed in Section 5.6.

The following sections discuss opportunities that follow this “extreme” intensity roadmap from the non-relativistic light-matter interaction into the realm of QED physics.

5.2 ULTRAFAST SPECTROSCOPY AND ATTOSECOND SCIENCE: THE ATOMIC UNIT OF INTENSITY 1-1000 PW/cm²

5.2.1 Extreme Nonlinear Optics: Interrogating the Electrons in Matter

Electron dynamics in atoms, molecules, plasmas, and condensed phase materials is a primary interest for physics, chemistry, and materials science. The principal means of study has always been spectroscopy. Sources based on extreme nonlinear optics using CPA lasers and gas targets have extended the range of spectroscopic tools to the vacuum ultraviolet spectral region.

A key nonlinear process that has enabled this extension is high harmonic generation (HHG), which occurs when a laser carrying an atomic unit of intensity interacts with a gas of atoms. Field ionization followed by field-driven recombination converts some of the laser light into a frequency comb of coherent extreme

ultraviolet (EUV) or soft X-ray radiation.⁸ HHG has become a powerful secondary table-top source of soft X-rays. The utility and full implications of the HHG process have continued to grow at an ever-increasing rate, which now span from electron and spin dynamics in atomic, molecular, and materials systems, to imaging with temporal resolution to make molecular movies, to high-precision spectroscopy. These applications are discussed more fully in Section 6.7.

5.2.2 The Attosecond Time Scale in Atoms and Molecules

In 2001, experimental observation of attosecond laser-induced phenomena was first reported.⁹ In these studies, an attosecond pulse or train of pulses were synthesized from a broadband high harmonic frequency comb created through intense laser-atom interactions. As of this writing, HHG from gases remains the most versatile demonstrated signature for attosecond electron-atom collisions. Current sources of laser-driven attosecond pulses and pulse trains made from these interactions have been demonstrated over 10-150 eV XUV photon energy range with 10⁸ to 10¹⁰ photons per pulse¹⁰ and 1-2 keV range with 10⁴ to 10⁵ photons per pulse.¹¹ The repetition rate of these sources is tied to the laser repetition rate and varies from ~10 Hz to 10 kHz, corresponding to ~µW average power. Current sources can drive linear absorption processes, but current pump-probe arrangements rely on a reference strong field, usually the fundamental femtosecond laser field, to initiate and drive nonlinear dynamics in matter.

Over the last decade, the worldwide activity in attosecond properties of matter has grown exponentially. However, current source parameters are limiting potential applications due to the poor conversion efficiency of laser light into attosecond soft X-ray pulses in coherently driven gases. Consequently, future opportunities will be significantly enhanced by novel sources such as X-ray FELs or sources that

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⁸ A. McPherson, G. Gibson, H. Jara, U. Johann, T.S. Luk, I.A. McIntyre, K. Boyer, and C.K. Rhodes, 1987, Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gasses, Journal of the Optical Society of America B 4: 595-601; M. Ferray, A. Lhuillier, X.F. Li, L.A. Lompre, G. Mainfray, and C. Manus, 1988, Multiple-harmonic conversion of 1064-Nm radiation in rare-gases, J. Phys. B 21: L31-L35; K.J. Schafer, B. Yang, L.F. DiMauro, and K.C. Kulander, 1993, Above threshold ionization beyond the high harmonic cutoff, Phys. Rev. Lett. 70: 1599-1602; P.B. Corkum, 1993, Plasma perspective on strong-field multiphoton ionization, Phys. Rev. Lett. 71: 1994-1997; M. Lewenstein, P. Balcou, M.Y. Ivanov, A. L’Huillier, and P.B. Corkum, 1994, Theory of high-harmonic generation by low-frequency laser fields, Phys. Rev. A 49: 2117-2132.

⁹ P.M. Paul, et al., 2001, Observation of a train of attosecond pulses; M. Hentschel, et al., 2001, Attosecond metrology.

¹⁰ Z. Chang, 2011, Fundamental of Attosecond Optics, CRC Press, Boca Raton.

¹¹ T. Popmintchev, M-C Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, et al., 2012, Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers, Science 336(6086): 1287-1291.

can scale to higher average and peak power, motivated by new optical laser drivers and paradigms for subcycle laser-matter response. In fact, the Extreme Light Infrastructure-Attosecond Light Pulse Source (ELI-ALPS) facility in Hungary is dedicated to pursuing this frontier. Figure 5.2 summarizes the history and future of ultrafast pulse generation driven by high-intensity lasers.

5.2.2.1 Attosecond Response of Matter Driven by High-Average Power Lasers

All stable matter is held together by electrons, whose mass (m=9 × 10^–31kg) and charge (e=-1.6 × 10^–19 c), along with Planck’s constant, lead to the quantum time scale of tens to hundreds of attoseconds for motion in a chemical or atomic bond. This motion cannot be directly observed using conventional experimental tools but can be studied using a powerful method where an electron is displaced with an attosecond pulse from a laser and then probed later to measure the change. High-intensity lasers are essential to produce these attosecond pulses. There are two current paths for expanding research using current attosecond generation and

detection methods and laser technology: (1) increase the number of photons per pulse by scaling the source geometry to higher laser pulse energy or (2) increase the number of pulses per second via larger average power drive lasers. The latter approach has several advantages including good data collection statistics with use of multiple simultaneous particle and photon diagnostics. Currently, 10 W average power drive lasers based on femtosecond titanium sapphire (Ti:Sapphire) amplifier architecture routinely operate at 1-10 kHz repetition rate. Maintaining a constant peak power, an increase in repetition rate to 100 kHz-1 MHz would require 1 kW drivers, thus increasing the attosecond source to nearly mW average power.

5.2.2.2 Attosecond Pulses from X-ray Free Electron Lasers

X-ray free-electron lasers (FELs), described in Chapter 2, have great potential for generating bright attosecond pulses, but controllable isolated attosecond pulses have not yet been reported.¹² There are several advantages of an X-ray FEL: the attosecond pulses can be generated in the soft and hard X-ray regime (0.1-10 keV), have high pulse energy (µJ), and produce high average power (1 watt). The X-ray FEL sources are national laboratory-scale facilities while current HHG sources are tabletop and more readily commercialized for broader use.

5.2.2.3 Sub-Attosecond Emission from Relativistic Plasmas

Extreme intensities in the relativistic regime (a>1) interacting with a solid target is a promising route for generating substantially brighter, harder X-rays (> 150 eV) with sub-attosecond (zeptosecond) duration. This technology could change the scope of ultrafast applications beyond current capabilities dramatically by reaching the nuclear time scale.

High harmonics radiation can be generated during relativistic laser-plasma interaction when the density scale-length is less than the laser wavelength.¹³ Under these conditions the laser’s electric field can couple efficiently to the critical den-

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¹² W. Helml, A.R. Maier, W. Schweinberger, I. Grguraš, P. Radcliffe, G. Doumy, C. Roedig, et al., 2014, Measuring the temporal structure of few-femtosecond free-electron laser X-ray pulses directly in the time domain, Nat Photon 8: 950–957; C. Feng, J. Chen, and Z. Zhao, 2012, Generating stable attosecond x-ray pulse trains with a mode-locked seeded free-electron laser, Phys. Rev. ST Accel. Beams 15: 080703; E. Prat and S. Reiche, 2015, Simple method to generate terawatt-attosecond x-ray free-electron-laser pulses, Phys. Rev. Lett. 114: 244801; J.D. Sadler, R. Nathvani, P. Oleśkiewicz, L.A. Ceurvorst, N. Ratan, M.F. Kasim, R.M.G.M. Trines, R. Bingham, and P.A. Norreys, 2015, Compression of x-ray free electron laser pulses to attosecond duration, Scientific Reports 5: 16755.

¹³ B. Dromey, M. Zepf, A. Gopal, K. Krushelnick, K. Lancaster, M.S. Wei, R. Clarke, et al., 2006, High harmonic generation in the relativistic limit, Nature Phys. 2: 456-459.

sity surface, which acts as a relativistic oscillating mirror,¹⁴ generating both odd and even harmonics. The coherent oscillation and the sharp density gradient of the mirror cause the entire spectrum to phase-lock. Theoretically this could produce a train of zeptosecond X-ray pulses phase-matched in a small solid angle.¹⁵ Furthermore, the large nonlinearity allows efficient coupling into the HHG comb. Researchers using the Vulcan laser facility in the UK have measured X-ray HHG extending to 3.3 Å (3.8 keV) from a high energy (> 200 J) petawatt-class laser-solid (CH-film) interaction.¹⁶

5.3 HIGH-INTENSITY PETAWATT LASER STUDIES OF HIGH ENERGY DENSITY SCIENCE, PLANETARY PHYSICS, AND ASTROPHYSICS

Laboratory-based experiments that create and explore extreme states of matter characterized by high density, temperature, and pressure—high energy density science—are the only terrestrial means for addressing issues relevant to the physics of planetary interiors, for example. High energy density science (HEDS) can be categorized as the study of warm dense matter (WDM) or hot dense matter (HDM), described in Figure 5.3.

The study of these regimes is also relevant for applications in energy and national security. This is discussed in Section 6.3.

Warm dense matter (WDM) is a regime that lies between traditional plasma physics, which applies to ionized matter at high thermal temperature and low density, and traditional condensed matter physics, which applies to thermally cold, dense matter. In the WDM regime of temperature/density space, neither condensed matter concepts of relatively cold near-degenerate Fermi gas metals apply, nor do the kinetic energy-dominated statistical physics models of plasmas. WDM occurs in the interior of planets like Jupiter and in laser-heated systems that start as a cold solid and end up as an ionized plasma, such as X-ray-driven inertial fusion. Here the average potential energy between charged particles can exceed their thermal energy.

Hot dense matter (HDM) occurs in stellar interiors, supernovae, and accretion discs. It also occurs in thermonuclear explosions or laser-driven inertial fusion experiments. Here, typical thermal energies can exceed inter-particle potential energies.

Researchers interested in exploring these physics regimes in the laboratory, either for astrophysics or for fusion or plasma physics, must create simultaneous conditions of high temperature and high density in a target and then view

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¹⁴ S.V. Bulanov, et al., 1994, Interaction of an ultrashort, relativistically intense laser-pulse.

¹⁵ G.D. Tsakiris, K. Eidmann, J. Meyer-ter-Vehn, and F. Krausz, 2006, Route to intense single attosecond pulses, New J. Phys. 8: 1-20.

¹⁶ B. Dromey, et al., 2006, High harmonic generation in the relativistic limit.

these conditions during the short time before radiation or collisional processes remove energy from the target, or the target distorts from mass flow. Transient high temperatures and densities imply the need for ultrafast, short wavelength probe beams.¹⁷ Ultrafast pulses of intense hard X-rays with photon energies of about 10 keV or greater can penetrate the plasma to reveal the conditions of its interior. X-ray scattering from these intense regions can accurately measure the plasma temperature and density using Thomson scattering from the plasma electrons; therefore, such X-ray sources are essential tools in all laboratories pursuing HEDS.

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¹⁷ R.W. Lee, 2007, High Energy Density Science at the Linac Coherent Light Source, Lawrence Livermore National Laboratory, UCRL-TR-236300.

The conditions for HEDS, in almost all laboratories where it is studied today, are produced by nanosecond pulsed lasers approaching 1 MJ per pulse, such as the Lawrence Livermore National Laboratory (LLNL) National Ignition (NIF) laser, the Rochester OMEGA laser, and the CEA Le Laser Mégajoule in France. The nanosecond-scale pulse duration for optimal heating is the set target size (~0.1-1 mm) divided by the plasma sound speed (~km/s). These are the highest energy lasers in the petawatt class, although their pulse durations are so long that generally they operate with sub-petawatt peak power. The requirement for nanosecond pulses means that these lasers do not employ CPA or aim for very broad bandwidth, two of the primary characteristics of ultrafast petawatt technology. Rather, they employ large aperture scaling with multiple arms of many stages of solid-state gain media in slabs on the order of 1 meter across and excited by very high energy flashlamps.

5.3.1 Planetary Physics and Astrophysics

For planetary physics, understanding the equation-of-state of extreme matter stands as a central challenge.¹⁸ The interiors of giant planets exist in a pressure/ temperature regime where accurate equation-of-state calculations are extremely difficult. Understanding chemistry under these extreme conditions is particularly challenging because molecules, atoms, and ions coexist in a fluid that is coupled by Coulomb interactions and is highly degenerate (free electrons governed by quantum and thermal effects). These strong interactions dominate in the steady-state interiors of giant planets such as Saturn and Jupiter and in brown dwarfs since their low mass never generates sustained thermonuclear fusion as in stars.

For astrophysics, laboratory experiments can provide important input data to models or help reveal the underlying mechanisms driving complex hydrodynamic processes. For instance, theoretical models of processes such as galaxy formation and stellar core collapse often rely on parameters not yet measured, such as the opacities that determine photon transport.¹⁹ Similarly, high-field magneto-hydrodynamics is conjectured to play a role in ultra-energetic cosmic ray generation²⁰—laser plasma studies can shed light on this process—while a focus on turbulence in shear flow can provide insight into momentum transport in plasmas and possibly explain how angular momentum is removed during matter accretion by black holes.²¹

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¹⁸ F.D. Stacey, 2005, High pressure equations of state and planetary interiors, Rep. Prog. Phys. 68: 341.

¹⁹ E. Bohm-Vitense, 1989, Introduction to Stellar Astrophysics, Vol. 1: Basic Stellar Observations and Data, Cambridge University Press, New York.

²⁰ K. Asano and P. Meszaros, 2016, Ultrahigh-energy cosmic ray production by turbulence in gamma-ray burst jets and cosmogenic neutrinos, Phys. Rev. D 94: 023005.

²¹ M. Hoshino, 2015, Angular momentum transport and particle acceleration during magnetorotational instability in a kinetic accretion disk, Phys. Rev. Lett. 114: 061101.

Extreme states of matter can be created using PW-class lasers over a wide range of photon energies. Currently, PW-class lasers operate at near-visible wavelengths and, depending on focusing, offer the highest on-target intensities. On the other hand, X-ray FELs are capable of producing more uniform heating since the low absorption cross section at short wavelength allows X-rays to penetrate compared to visible radiation. Uniform heating is critical to experiments that aim to measure equations-of-state.

Petawatt-class lasers (femtosecond pulses with <~1 kJ energy or nanosecond pulses with ~MJ energy (e.g., NIF, or in combination) are capable of heating samples to energy densities (pressure and temperature) much larger than other laboratory approaches such as gas guns and high explosives. Consequently, lasers can produce matter under reproducible conditions that, with rigorous scaling, are equivalent to those in large astrophysical systems, such as supernova, Herbig-Haro gas jets,²² or giant planets. They can also be used to probe these states either directly through absorption/scattering or indirectly by producing secondary probes such as X-rays, electrons, and protons or directly with X-ray FELs.

With continued advances in modeling of planetary and astrophysical phenomena, one can anticipate that data from laboratory experiments will play an increasingly important role. Below the committee discusses some scientific and/or experimental issues relevant to planetary physics and astrophysics.

5.3.1.1 Giant Planets: Plasma Coupling and Degeneracy

Coupling in plasmas is typically characterized by a dimensionless parameter, Γ = (Ze)²/akT, where a is a characteristic separation distance between ions of charge state Ze. For Γ << 1, thermal effects dominate and the plasma is considered ideal. Strong coupling by Coulomb interactions occurs for Γ ≥ 1. Figure 5.3 shows that Jupiter and the brown dwarf Gliese 1229B, which are composed of H and He, are strongly coupled and highly degenerate. For Γ >> 1, the coupling becomes so strong that ions freeze into a crystal lattice. At high density and low temperature (kT < ε_F, the Fermi energy), the plasma becomes degenerate, e.g., right of the ε_F = kT line in Figure 5.3. Here Pauli exclusion plays a major role, through electron degeneracy, in determining the pressure. Hence the internal structure and the magnetic fields of giant planets are determined by knowledge of the equation-of-state at high pressures, 10¹¹ - 10¹³ pascal. Calculations based on first-principles theories are extremely difficult and inaccurate. Thus, PW-class laser experiments in this regime are a vital component in efforts to improve our understanding of planetary physics.

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²² Reipurth, B. and S. Heathcote, 1997, 50 years of Herbig-Haro research, pp. 3-18 in Herbig-Haro Flows and the Birth of Stars: Proceedings of the 182nd Symposium of the International Astronomical Union (B. Reipurth and C. Bertout, eds.), Springer, The Netherlands.

5.3.1.2 Dynamic Ramped Compression

PW-class lasers have demonstrated compression of a few terapascal (14-times the pressure in the earth center),²³ with dynamic ramp compression (DRC) of diamond to unprecedented densities of 12g/cm³.²⁴ The DRC method can produce extreme pressures that are much larger than using static methods, e.g., diamond anvil cells. In addition, DRC has advantages over other methods like light-gas guns or explosives since it can produce less dissipative heating, thus producing compression at lower temperature.²⁵ Sufficient control of these experiments is necessary to avoid shock compression. Consequently, these experiments are more aligned with the ambient environment of a planet’s interior.

Phase transitions play an important role in planetary physics and astrophysics, and this can also be studied using high-intensity lasers. For instance, understanding the high pressure phases of carbon is important since carbon is a major element of giant planets such as Uranus and Neptune.²⁶ PW-driven shock wave measurements of the diamond principal Hugoniot have been made at pressures between 6 and 19 Mbar using the Laboratory of Laser Energetics (LLE) OMEGA laser. The Hugoniot curve traces the path accessed by the laser-induced shock driven in the material. The results were in good agreement with published ab initio calculations and indicated that in the solid-liquid coexistence regime between 6 and 10 Mbar, the mixed phase may be slightly more dense than would be expected from a simple interpolation between liquid and solid Hugoniots.²⁷ (See Figure 5.4)

Near Jupiter’s surface (10¹¹ pascal and fraction of an electron volt), hydrogen exits in molecular form but it dissociates and ionizes deeper into the planet’s core (>10¹² pascal and few eV). This transition from insulator to conductor in the convective zone is believed to be responsible for Jupiter’s 10 to 15 gauss magnetic field. An open question is whether there is a sharp plasma phase transition. Experiments performed on the Nova laser at LLNL initially suggested that the transition was continuous,²⁸ and subsequent experiments unambiguously demonstrated that the transition from non-conducting molecular hydrogen to atomic metallic hydrogen at high pressure is a continuous transition. This suggests that the metallic region of Jupiter’s interior extends out to 90 percent of the radius of the planet and may

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²³ R.F. Smith, J.H. Eggert, R. Jeanloz, T.S. Duffy, D.G. Braun, J.R. Patterson, R.E. Rudd, et al., 2014, Ramp compression of diamond to five terapascals, Nature 511: 330-333.

²⁴ R.F. Smith, et al., 2014, Ramp compression.

²⁵ R.F. Smith, et al., 2014, Ramp compression.

²⁶ W.B. Hubbard, 1981, Interiors of the giant planets, Science 214(4517): 145-149.

²⁷ D.G. Hicks, T.R. Boehly, P.M. Celliers, D.K. Bradley, J.H. Eggert, R.S. McWilliams, R. Jeanloz, and G.W. Collins, 2008, High precision measurements of the diamond Hugoniot in and above the melt region, Phys. Rev. B 78: 174102.

²⁸ G.W. Collins, L.B. Da Silva, P. Celliers, and R. Cauble, 1998, Measurements of the equation of state of deuterium at the fluid insulator-metal transition, Science 281(5380): 1178-1181.

explain why the magnetic field of Jupiter is so much stronger than that of the other planets of our solar system.²⁹

A supernova (SN), the explosion of a star, is a spectacular event that can outshine a star’s entire host galaxy. Supernovae involve a broad range of physical processes across disparate areas of science such as nuclear physics, general relativity, and fluid mechanics. Type-II Supernovae—thought to occur as a result of gravitational collapse—pose a number of challenges to first principles models. Laboratory experiments exploring relevant hydrodynamic phenomena can improve our understanding of these complex astrophysical events.

It is believed that when an exploding star’s core collapses, an outward propagating shock is launched which reaches the star’s surface and leads to a burst of (optical) luminosity.³⁰ Theory indicates that 2D and 3D hydrodynamic effects play an important role in the rise of the luminosity burst—the observable detected by optical

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²⁹ P.M. Celliers, G.W. Collins, L.B. Da Silva, D.M. Gold, R. Cauble, R.J. Wallace, M.E. Foord, and B.A. Hammel, 2000, Shock-induced transformation of liquid deuterium into a metallic fluid, Phys Rev Lett. 84: 5564-5567.

³⁰ T. Shigeyama and K. Nomoto, 1990, Theoretical light curve of SN 1987A and mixing of hydrogen and nickel in the ejecta, Astrophys. J. 360: 242–256.

telescopes. The shock wave drives a stellar mixing process as an outward flow of heavy elements from the star’s core mixes with the hydrogen and helium that dominate at the star’s surface. While the Rayleigh-Taylor (RT) hydrodynamic instability is thought to play an important role in this hydrodynamic mixing,³¹ simulations of the RT instability have failed to explain SN observations.³² Given that unresolved hydrodynamic problems limit our understanding of supernovae, laboratory experiments that seek to observe the nonlinear hydrodynamics of this mixing process are well motivated. Experiments can test codes that simulate the nonlinear behavior to determine if any other physics, not present in the simulations, appears in the experiments.

Opacity measurements. The kinetic energy release in a typical supernova event is ~10⁴⁴ joules, with only a few percent of this energy emitted as visible radiation.³³ Since SN light detected by optical telescopes does not come from the exploding star’s core, where the energy is released, but rather from the star’s outer shell (photosphere), understanding the core-to-photosphere energy transport is very important to interpreting measured SN visible light curves. The transport of stellar matter and radiation is a complex and theoretically challenging hydrodynamic problem. Photon transport through a medium is characterized by the medium’s opacity, making opacity models particularly critical to modeling supernovae and other astrophysical phenomena such as the pulsing of Cepheid variable stars.³⁴ PW-class experiments enhance our understanding of variable stars by providing direct opacity measurements under astrophysically relevant conditions.

Relativistic plasmas and gamma-ray bursts. At sufficiently high energy density, relativistic plasma physics becomes important, and PW-class studies in this regime could provide information important to a number of astrophysical processes. Relativistic plasmas, for instance, are thought to be important to the origin of cosmic rays, beams of relativistic particles such as protons and atomic nuclei. The precise acceleration mechanisms are uncertain but shock fronts are thought to provide the acceleration, and it has been argued that cosmic rays could be produced along with gamma-ray bursts (GRBs).³⁵

Magnetic fields in astrophysics. Strong magnetic fields play an important role in a number of astrophysical processes such as solar flare generation and conver-

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³¹ W.D. Arnett, 1988, On the early behavior of supernova 1987A, Astrophys. J. 331: 377–387; D. Arnett, B. Fryxell, and E. Muller, 1989, Instabilities and nonradial motion in SN-1987A, Astrophys. J. Lett. 351: L63–L66.

³² P.G. Sutherland, 1990, Gamma-rays and x-rays from supernovae, p. 111 in Supernovae (A.G. Petschek, ed.), Springer-Verlag, New York.

³³ B.A. Remington, R.P. Drake, and D.D. Ryutov, 2006, Experimental astrophysics with high power lasers and Z pinches, Rev. Mod. Phys. 78: 755-807.

³⁴ E. Bohm-Vitense, 1989, Introduction to Stellar Astrophysics, Vol. 1.

³⁵ M.V. Medvedev and O.V. Zakutnyaya, 2009, Magnetic fields and cosmic rays in GRBs: a self-similar collisionless foreshock, The Astrophysical Journal 696: 2269–2274.

sion of stored stellar energy into either randomized (thermal) or directed (e.g., particle acceleration) kinetic energy.³⁶ PW-class studies of ultra-high magnetic field generation and interactions can address important questions such as whether magnetic fields affect cosmological structure formation and how strong magnetic fields originated in the universe.

5.3.2 Isochoric Heating and High Energy Density Plasmas

The study of the material properties of matter uniformly heated to extreme pressures is of interest for basic studies of strongly coupled plasmas, degenerate and non-degenerate warm dense matter, and the understanding of high density plasmas characteristic of inertial confinement fusion experiments and defense applications. Constant volume heating (isochoric heating) is desirable using intense ultrashort laser pulses,³⁷ as there is little material motion or expansion/compression during such pulses and uniform conditions can be subsequently probed. Such heater pulses can be from high-intensity ultrashort pulse lasers³⁸ or from X-ray FEL sources such as Linac Coherent Light Source (LCLS) or Flash,³⁹ or possibly a timed combination. The material and its electronic and structural properties can then be interrogated with auxiliary ultrashort particle and photon probe beams synchronized to the high-intensity ultrashort heater pulse. These probes can be secondary sources from the laser itself (such as laser accelerated electron bunches, laser-driven wakefield acceleration-driven betatron sources, or Compton scattering sources), or an X-ray FEL. Particle probes such as protons can image electric and magnetic fields internal to the material,⁴⁰ while high energy photon probes can generate radiographic images⁴¹ or reveal internal structure and dynamics through their coherent and incoherent scattering spectra.⁴²

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³⁶ M.V. Medvedev and A. Loeb, 1999, Generation of magnetic fields in the relativistic shock of gamma-ray burst sources, ApJ, 526: 697-706.

³⁷ R.R. Fäustlin, Th. Bornath, T. Döppner, S. Düsterer, E. Förster, C. Fortmann, S.H. Glenzer, et al., 2010, Observation of ultrafast nonequilibrium collective dynamics in warm dense hydrogen, Phys. Rev. Lett. 104: 125002.

³⁸ A. Saemann, et al., 1999, Isochoric heating of solid aluminum.

³⁹ R.R. Faustlin, et al., 2010, Observation of ultrafast nonequilibrium collective dynamics.

⁴⁰ C.K. Li, F.H. Séguin, J.A. Frenje, J.R. Rygg, R.D. Petrasso, R.P.J. Town, P.A. Amendt, et al., 2006, Measuring E and B fields in laser-produced plasmas with monoenergetic proton radiography, Phys. Rev. Lett. 97: 135003.

⁴¹ F.J. Marshall, P.W. McKenty, J.A. Delettrez, R. Epstein, J.P. Knauer, V.A. Smalyuk, J.A. Frenje, et al., 2009, Plasma-density determination from x-ray radiography of laser-driven spherical implosions, Physics Review Letters 102(18): 185004.

⁴² S.H. Glenzer and R. Redmer, 2009, X-ray Thomson scattering in high energy density plasmas, Rev. Mod. Phys. 81: 1625.

Isochorically-heated material can remain at near-solid density when heated by an intense short pulse⁴³ or can be strongly compressed to many times solid density by separate, longer duration laser pulses after which it is strongly heated by a short pulse.⁴⁴ Isochoric heating can also be accomplished using ultrashort charged particle beams driven by primary ultrashort intense laser pulses. Figure 5.3 shows the states of matter plotted versus density and temperature. One area of application of well-characterized isochorically heated matter is studying their interaction with high energy ions, including α-particles (helium nuclei).⁴⁵ A useful measurable parameter describing the interaction is the α-particle stopping power. This has application to heating of laboratory and solar/astrophysical fusion plasmas and will inform use of high energy ions as probes and as therapeutic interaction beams.⁴⁶ The short pulse α-particle beam will be produced from laser solid interaction, and the dense target can be generated with a portion of the same beam.

Another area is fundamental—the material properties of dense hydrogen and deuterium plasmas, the most basic of materials. Aside from its relevance to theoretical models of condensed matter physics in extreme conditions, the study of dense hydrogen is directly relevant to an understanding of planetary interiors and stars (as discussed in Sec 5.3.3) and fusion plasmas.⁴⁷ Intense heating using a combination of laser pulses can generate hydrogenic plasmas at variable density and temperature, allowing exploration of various phases and their electronic and structural properties, potentially including the long sought after metallic hydrogen state.⁴⁸ Such targets can be probed, for example, using short LCLS X-ray pulses to measure density, temperature, conductivity, ion-ion correlations, structure factors, and transport coefficients using both collective scattering (coherent Thomson scattering) from density structures and scattering from individual electrons (incoherent Thomson scattering, transitioning to Compton scattering for high energy probe photons),⁴⁹ as well as supplemented by older shock-based diagnostics such

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⁴³ Y. Ping, D. Hanson, I. Koslow, T. Ogitsu, D. Prendergast, E. Schwegler, G. Collins, and A. Ng, 2006, Broadband dielectric function of nonequilibrium warm dense gold, Phys. Rev. Lett. 96: 255003.

⁴⁴ S.H. Glenzer and A.J. Mackinnon, 2015, New Science Opportunities enabled by Petawatt-class Lasers at LCLS-II, SLAC National Accelerator Laboratory, Menlo Park, Calif.

⁴⁵ J.A. Frenje, et al., 2015, Measurements of ion stopping around the Bragg peak.

⁴⁶ C.K. Li, et al., 2006, Measuring E and B fields in laser-produced plasmas; J.A. Frenje, et al., 2015, Measurements of ion stopping around the Bragg peak; S.V. Bulanov and V.S. Khoroshkov, 2002, Feasibility of using laser ion accelerators in proton therapy, Plasma Physics Reports 28(5): 453-456.

⁴⁷ K. Falk, 2015, “Warm Dense Matter,” presented at ELI Summer School, Sept. 21-25, Bucharest, Romania.

⁴⁸ E. Conover, 2016, The pressure is on to make metallic hydrogen, Science News 190(4): 18.

⁴⁹ S.H. Glenzer and R. Redmer, 2009, X-ray Thomson scattering.

as interferometry of and pyrometry of induced shock fronts.⁵⁰ The shortness of the available probes driven by the laser itself and from X-ray FELs can enable time resolution in such measurements, making possible the tracking of electron-ion equilibration, the evolution of electron degeneracy, and the assessment of the applicability of equation-of-state models.

Laser plasma backlighters have most often been used as probes in these experiments. Their primary limitations, even those driven by petawatt lasers, are that they have insufficient brightness and time resolution. Since they are incoherent point sources, their total useful flux depends on the solid angle of the X-ray shadow from the backlighter source that is cast by the target on an area detector illuminated by the X-rays. On the other hand, X-ray FELs are far brighter, have transverse coherence, and are directional. In addition, with pulse durations well under 100 fs, they are an effective probe with sufficient time resolution to view the HED transient state. For this reason, the co-location of ultrashort high-intensity lasers and X-ray FELs is particularly advantageous for such experiments.

5.3.3 Science That Combines X-ray Free-Electron Lasers, High Energy Electron Accelerators, and Petawatt-Class Lasers

X-ray FELs are high-intensity light sources of a special nature that can be used for unique science tasks related to their short wavelength (see Chapters 1 and 2, Section 5.2, and Section 5.7). In addition to this, conventional petawatt lasers can carry out many research applications when combined with X-ray FELs. This topic has always been one of the main science drivers for X-ray FELs. Early conceptions of this new regime of high-intensity physics are described in LCLS:The First Experiments.⁵¹ Further workshops over the past 15 years have continued to develop this theme. Petawatt lasers now exist at SACLA, and they are already in the advanced planning stage at LCLS and European X-ray FEL.⁵²

Here the committee summarizes one compelling science case for the study of High Energy Density Science. The high-energy nanosecond Nd:glass lasers used in most HEDS research are large billion-dollar-class stand-alone facilities. None is located in the vicinity of the half-dozen or so hard X-ray FELs, which are also of billion-dollar class. Instead, HEDS lasers such as NIF and OMEGA employ auxiliary

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⁵⁰ K. Falk, E.J. Gamboa, G. Kagan, D.S. Montgomery, B. Srinivasan, P. Tzeferacos, and J. F. Benage, 2014, Equation of state measurements of warm dense carbon using laser-driven shock and release technique, Phys. Rev. Lett. 112(15): 155003.

⁵¹ Stanford Linear Accelerator Center (SLAC), 2003, LCLS: The First Experiments, http://slac.stanford.edu/pubs/slacreports/reports03/slac-r-611.pdf.

⁵² S.H. Glenzer and A.J. Mackinnon, 2015, New Science Opportunities; M. Nakatsutsumi and Th. Tschentscher, 2013, Conceptual Design Report: Scientific Instrument HED, European X-Ray Free-Electron Laser Facility GmbH, Hamburg, Germany.

high-intensity short laser pulse-driven plasmas which act as sources of X-rays to backlight the HED plasmas of interest. The backlighter drive lasers are optimized to produce very high temperature plasmas that generate hard X-rays. This can be a femtosecond PW-class laser source, and X-ray backlighters of this type have been discussed in Chapter 3.

X-rays from FELs are employed in these experiments either to view the conditions created by conventional high-intensity lasers or to create the extreme conditions themselves.⁵³ These are “single-shot” experiments, and therefore require the high X-ray flux delivered only by X-ray FEL, which are about one thousand times shorter (less than 100 fs) and one million times more energetic (millijoules of energy) than the largest synchrotron sources.

5.4 PETAWATT LASER-DRIVEN PARTICLE ACCELERATORS

5.4.1 Particle Acceleration and Particle Physics

Particle accelerators driven by intense, short pulse lasers are in development for the purpose of a new technology of ultra-high gradient devices that occupy a much smaller footprint than conventional machines. A primary limitation of conventional charged particle accelerators for particle physics and higher intensity sources is their size and the associated costs of large conventional machines. Smaller and lower cost laser-driven acceleration solutions are therefore valuable.⁵⁴ High particle energy, high beam intensity and brightness, and high efficiency are important goals of this research. Laser-driven accelerators will enable applications for discovery science in particle physics and other basic sciences, as well as applications in medical physics and compact light source development. To set the scale, electron accelerators at >10 GeV and proton accelerators at >100 MeV will demand lasers of PW-peak power, high repetition rate, high average power, and high efficiency. The research and development of laser-driven accelerators is intimately tied to the technological development of ultrafast PW-class lasers.

Particle accelerators of higher energy and higher luminosity⁵⁵ are required to advance the frontiers of particle physics. The highest center-of-mass energy (CME) for searching for new particles and probing for new fundamental interactions are

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⁵³ S. H. Glenzer et al., “Matter under Extreme Conditions Experiments at the Linac Coherent Light Source,” Journal of Physics B: Atomic, Molecular and Optical Physics 49, no. 9 (2016): 092001, doi:10.1088/0953-4075/49/9/092001.

⁵⁴ England, “Dielectric Laser Accelerators,” Rev Mod Phys. 86, 1337 (2014); and The Economist, “Small Really is Beautiful,” Oct. 19, 2014.

⁵⁵ In particle physics, luminosity measures the ability of a particle accelerator to produce the required number of interactions and is the proportionality factor between the number of events per second and the collision cross section, and has units of cm^–2 s^–1.

provided by intersecting particle storage rings, which collide two intense beams of particles. Currently, the Large Hadron Collider (LHC) (i.e., proton-proton beams) at CERN is the state of the art in this field. The aim of the LHC is to allow physicists to test the predictions of different theories of particle physics, including measuring the properties of the Higgs boson (awarded the 2013 Nobel Prize in Physics)⁵⁶ and searching for the large family of new particles predicted by supersymmetric theories,⁵⁷ as well as other unsolved questions about fundamental particles. Increasing the CME in the next generation collider using current accelerator structures is a challenge due to the unfavorable technical scaling with size (the LHC tunnel is already 17 miles in circumference) and economics (the LHC cost $4.75 billion to construct and costs $1 billion per year to operate).⁵⁸ At dawn of the new millennium, Figure 5.5 shows that these challenges have greatly reduced the projections in achieving higher CME for colliders.⁵⁹

To go beyond the current state of the art, the high energy physics Particle Physics Project Prioritization Panel (P5) report recommended a greatly expanded accelerator research and development program that would emphasize the ability to build very high-energy accelerators (larger acceleration gradients) beyond the High-Luminosity LHC and International Linear Collider at dramatically lower cost.⁶⁰ PW laser-driven acceleration is one concept under consideration.

The technical requirements for colliders are extreme, and development of a future high energy collider is the most challenging and long-term application of laser-driven particle accelerators. Conventional charged particle accelerators have already enabled the development of coherent and incoherent high energy photon sources having application to basic science, engineering, and medicine. Laser-driven high-energy accelerators make possible a new generation of such light sources on a much more compact scale (meter scale), including FELs and Thomson scattering sources producing high-energy X-rays. Early experiments have already demonstrated some of these sources.⁶¹ The compact scale of these laser-driven sources will facilitate their wide application. The high energy charged particles from laser-driven accelerators can also be employed for medical imaging,

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⁵⁶ CERN, “The Higgs Boson,” https://home.cern/topics/higgs-boson, accessed February 9, 2017.

⁵⁷ CERN, “United Forces,” http://home.cern/about/physics/unified-forces, accessed February 9, 2017.

⁵⁸ A. Knapp, 2012, “How Much Does It Cost To Find A Higgs Boson?” Forbes Magazine, July 5.

⁵⁹ M. Tigner, 2001, Does accelerator-based particle physics have a future? Phys. Today 54(1): 36.

⁶⁰ Particle Physics Project Prioritization Panel, 2014, Building for Discovery: Strategic Plan for US Particle Physics in the Global Context, https://science.energy.gov/~/media/hep/hepap/pdf/May-2014/FINAL_P5_Report_Interactive_060214.pdf.

⁶¹ V. Malka, J. Faure, Y.A. Gauduel, E. Lefebvre, A. Rousse, and K.T. Phuoc, 2008, Principles and applications of compact laser–plasma accelerators, Nat. Phys. 4: 447-453; E. Esarey, et al., 2009, Physics of laser-driven plasma-based electron accelerators.

radionuclide production, and cancer therapy. Of particular use for cancer therapy are high energy proton beams, which have a well-defined stopping distance (Bragg peak) in human tissue, thus reducing collateral tissue damage. Currently, proton cancer therapy is performed at large and expensive cyclotron facilities, making laser-driven sources especially desirable.

Several techniques for laser-driven electron acceleration are under investigation. The most successful method, demonstrating the highest energy and beam quality, uses laser-driven plasmas as the acceleration medium. This scheme is called “laser-driven wakefield acceleration” (LWFA) and uses the large longitudinal electrostatic field of a laser-driven plasma wave to effect the acceleration. Two other schemes using short pulse lasers, well behind LWFA in development, will not be discussed in detail here. One uses quasi-phase matching in corrugated plasma guiding structures of the propagating optical laser field to the electrons, directly accelerating them,⁶² and is called direct laser acceleration (DLA). The other scheme is non-plasma based and uses micron-scale dielectric structures driven by optical lasers.⁶³ As this method is also reliant on direct acceleration by the laser, it is also referred to as DLA, where the first letter can signify “dielectric” or “direct.”

5.4.2 Laser-Driven Plasma Wakefield Acceleration

LWFA is realized by using an intense, ultrafast laser pulse to produce a ponderomotive force to drive a plasma wave. The plasma wave is created as the laser pulse propagates in subcritical density plasma generated in a gas jet or in a plasma discharge, using high-intensity optical guiding using pre-formed plasmas⁶⁴ or self-guiding.⁶⁵ The enormous axial electrostatic field of the plasma wave, which propagates with the group velocity of the laser pulse, can accelerate electrons externally injected or self-injected from the plasma background by wave-breaking or ionization injection.⁶⁶ Relativistic electrons injected with the proper phase can be accelerated and focused by the wakefield. Figure 5.6 illustrates a LWFA.

The energy gain of the accelerated particles is limited by depletion of the energy of the laser pulse and dephasing as the accelerated electrons advance from

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⁶² A.G. York, B.D. Layer, J.P. Palastro, T.M. Antonsen, and H.M. Milchberg, 2008, Ultrahigh-intensity optical slow-wave structure for direct laser electron acceleration, J. Opt. Soc. Am. B 25 (7): B137-B146.

⁶³ R.J. England, R.J. Noble, K. Bane, D.H. Dowell, C-K Ng, J.E. Spencer, S. Tantawi, et al., 2014, Dielectric laser accelerators, Rev. Mod. Phys. 86(4): 1337.

⁶⁴ C.G. Durfee and H.M. Milchberg, 1993, Light pipe for high intensity laser pulses, Phys. Rev. Lett. 71: 2409; Erlich, 1996.

⁶⁵ E. Esarey, et al., 2009, Physics of laser-driven plasma-based electron accelerators.

⁶⁶ V. Malka, et al., 2008, Principles and applications of compact laser–plasma accelerators; E. Esarey, et al., 2009, Physics of laser-driven plasma-based electron accelerators.

an accelerating to a decelerating bucket in the plasma wave. Both of these limitations point to the need for high energy/intensity lasers: high energy pulses counterbalance depletion and drive large amplitude plasma waves over long propagation distances especially at low plasma densities where dephasing is minimized. Using a PW-class laser, the Berkeley Lab Laser Accelerator facility at Lawrence Berkeley National Laboratory has reported a record 4.2 GeV electron beam in single 10 cm plasma channel, with 10 GeV in 1-meter appearing feasible.⁶⁷

Achieving even higher beam energies requires a “staging” of many laser-plasma acceleration modules in order to mitigate depletion and dephasing. Acceleration

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⁶⁷ W.P. Leemans, A.J. Gonsalves, H-S. Mao, K. Nakamura, C. Benedetti, C.B. Schroeder, Cs. Tóth, et al., 2014, Multi-GeV electron beams from capillary-discharge-guided subpetawatt laser pulses in the self-trapping regime, PRL 113(24): 245002.

to beam energies above 1 TeV would require more than 100 acceleration stages. Staging places stringent requirements on the quality of the accelerated beam, as well as demanding a mechanism for introducing new laser pulses between stages. Despite the challenges, staging has been recently demonstrated at the ~100 MeV level in a proof-of-principle experiment.⁶⁸

The concept of an electron-positron collider based on the LWFA technique is schematically illustrated in Figure 5.7. Electrons are injected into the first stage of the electron acceleration arm where they are accelerated to 10 GeV by the wakefield driven by a laser pulse. From the first stage, the accelerated electrons will enter the next acceleration stage. A new laser pulse is introduced between stages. In this example, the electron arm consists of 100 10-GeV stages, bringing the electron beam to an energy at collision of 1 TeV. A single LWFA stage is used to produce positrons to be injected into the positron acceleration arm. The positron arm also consists of 100 acceleration stages.

In order to achieve the necessary luminosity demanded by the high energy physics community, an electron-positron collider would require a repetition rate of 15 kHz. Energy efficiency from wall plug to beam of 10 percent would lead to a total power of 100 stages of 100 MW (one arm). Additional key accelerator and laser parameters can be found in Leemans (2010).⁶⁹ Nonetheless, the laser requirements are very challenging and beyond current state of the art, thus necessitating advances in PW-class laser technology. The primary mission of the Extreme Light Infrastrucutre-Nuclear Physics (ELI-NP) project in Prague is to push this frontier.

The laser requirements for LWFA-driven X-ray FEL are not as stringent as for colliders.⁷⁰ A single acceleration stage of 10 GeV, or less, could provide a compact source to power an FEL producing femtosecond X-rays for basic science applications. Multiple 10-GeV stages would provide X-rays at higher energies than current FELs. Low repetition rates could provide high-peak brightness light for user experiments; however, large-scale user facilities requiring high-average brightness would require high repetition rate, e.g., PW peak power pulses at 1 kHz beyond the current state of the art. Since the X-ray FEL requirements are less demanding than collider requirements, a LWFA-driven FEL could be a stepping stone in the development of an LWFA-based collider or as an ultimate goal of development of the LWFA technique.

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⁶⁸ S. Steinke, J. van Tilborg, C. Benedetti, C.G.R. Geddes, C.B. Schroeder, J. Daniels, K.K. Swanson, et al., 2016, Multistage coupling of independent laser-plasma accelerators, Nature 530: 190.

⁶⁹ W.P. Leemans, 2010, White Paper of the ICFA-ICUIL Joint Task Force—High Power Laser Technology for Accelerators, http://icfa-bd.kek.jp/WhitePaper_final.pdf.

⁷⁰ V. Malka, et al., 2008, Principles and applications of compact laser–plasma accelerators.

5.5 INTENSE LASER-DRIVEN PARTICLE SOURCES OF ENERGETIC PHOTONS, NEUTRONS, AND POSITRONS

The generation of short, high flux pulses of energetic photons, neutrons, and positrons by intense laser interaction with matter offers new and unique opportunities in scientific, engineering, and medical imaging. Applications in materials processing and in radiography both call for intense and bright sources of X-rays, positrons, protons, and neutrons that can be supplied by intense lasers. Laser-driven sources can replace much larger facilities such as cyclotrons, synchrotrons, and nuclear reactors if more compact or portable sources of energetic photons or particles are needed. Laser-driven sources can also provide higher source brightness and shorter pulse duration than conventional particle facilities.

The LWFA schemes described in Section 5.4.2 provide a route using electrons to drive secondary processes, e.g., X-ray FEL. However, other intense short pulse laser-driven processes enable generation of high energy protons, neutrons, positrons, and photons. For cases where compact or portable sources of energetic photons or particles are needed irrespective of pulse duration, laser-driven sources may replace much larger facilities such as cyclotrons, synchrotrons, and nuclear reactors. When high source brightness and short pulse duration are also needed, PW-driven sources are unique, and there is no other conventional facility to match them, except for X-ray FEL sources of coherent ultrafast X-rays.

5.5.1 Photon Sources

There are currently four main intense laser-based approaches for X-ray and γ-ray generation.

Relativistic Thomson backscattering of intense laser pulses from relativistic e-beams. An intense laser pulse counter-propagating with respect to a relativistic (γ>> 1) electron bunch can backscatter. The backscattered radiation, in the direction of the electron beam, has a maximum X-ray energy of ħω_X =4γ²ħω_L. Thus, the laser frequency is γ²-boosted into the X-ray regime. The electron beam can originate either from a conventional accelerator, such as a linear accelerator, or in an all-optical configuration from a laser-driven accelerator, such as a LWFA. Photon energies can range from keV to MeV.⁷¹ Assuming an all-optical system, a range of laser energies will be appropriate, depending on the desired backscattered photon energy. For >1 MeV photons, γ > ~200 (or ~100 MeV e-beams) are needed. For this purpose, a 10 TW laser system is sufficient. Higher energy lasers could increase the number of backscattered photons while maintaining constant intensity.

Betatron radiation from laser-accelerated electrons. As LWFA electrons propagate through the plasma, they transversely oscillate about the plasma ion column and emit forward-directed X-rays with a high degree of transverse coherence.⁷² Photons are typically generated in the tens of keV range.

Directing laser-plasma accelerated electron bunches into a high-Z dense material to produce short pulses of bright, forward directed γ-rays via bremsstrahlung radiation.⁷³ Photon energies are typically > 1MeV, depending on the energy of the laser accelerated electrons.

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⁷¹ K. Khrennikov, J. Wenz, A. Buck, J. Xu, M. Heigoldt, L. Veisz, and S. Karsch, 2015, Tunable all-optical quasimonochromatic Thomson x-ray source in the nonlinear regime, PRL 114(19): 195003.

⁷² S. Corde, K. Ta Phuoc, G. Lambert, R. Fitour, V. Malka, A. Rousse, A. Beck, and E. Lefebvre, 2013, Femtosecond x rays from laser-plasma accelerators, Rev. Mod. Phys. 85(1).

⁷³ Y. Glinec, J. Faure, L. Le Dain, S. Darbon, T. Hosokai, J.J. Santos, E. Lefebvre, et al., 2005, High-resolution x-ray radiography produced by a laser-plasma driven electron source, PRL 94(2): 025003.

Both betatron and plasma sources can operate in a limited way with laser powers as low as 10 TW, but higher powers lead to increased photon numbers.

Short-wavelength high harmonics from laser-driven relativistic mirrors. When a laser pulse with normalized vector potential a>1 interacts with a sharp solid density interface, its ponderomotive pressure drives an oscillating relativistic mirror in the induced plasma.⁷⁴ This leads to generation of a spatially and temporally coherent beam of odd and even high harmonics into the specular reflection direction of the driving pulse, with as much as ~10^–6 efficiency per harmonic. Succsessful operation relies on pulses with extremely high contrast ratios as defined in Appendix A1. The need to maintain a sharp initial interface puts severe limits (< 10^–11) on the prepulse level, demanding pre-pulse mitigation using complex and intrinsically low repetition rate plasma mirrors.

5.5.2 Neutron Sources

Three intense laser-based generation schemes for neutrons are currently under investigation.

The first method is laser-accelerated proton collisions with nuclei and generation of neutrons via the (p,n) reaction in low-Z foil targets, such as Be.⁷⁵ Such neutron beams can be used as passive or active material probes, including hidden contraband materials.

A second method under study is generation of bremsstrahlung γ-rays from stopping of laser-accelerated electron beams in high-Z targets followed by neutron-emitting (γ n) decay of photo-activated nuclei.⁷⁶

A third method creates neutrons from nuclear DD-fusion of D₂ clusters irradiated by intense laser pulses.⁷⁷ Here, fusion is induced by collisions of keV energy deuterium nuclei from cluster plasma explosions in a laser-heated gas of D₂ clusters.

None of these techniques generates femtosecond neutron pulses—the duration is limited by the non-relativistic neutron velocities to their target, as well as transit time of the initiating γ-rays or protons traversing the converter target. How to generate ultrashort neutron pulses is still an open question with important potential applications such as time-resolved neutron diffraction.

The typical laser systems used in neutron generation experiments are large; for example, one study used the Los Alamos Trident laser with ~100 J in a sub--

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⁷⁴ B. Dromey, et al., 2006, High harmonic generation in the relativistic limit.

⁷⁵ M. Roth, D. Jung, K. Falk, N. Guler, O. Deppert, M. Devlin, A. Favalli, et al., 2013, Bright laser-driven neutron source based on the relativistic transparency of solids, PRL 110(4): 044802.

⁷⁶ I. Pomerantz, E. McCary, A.R. Meadows, A. Arefiev, A.C. Bernstein, C. Chester, J. Cortez, et al., 2014, Ultrashort pulsed neutron source, PRL 113(18): 184801.

⁷⁷ T. Ditmire, J. Zweiback, V.P. Yanovsky, T.E. Cowan, G. Hays, and K.B. Wharton, 1999, Nuclear fusion from explosions of femtosecond laser-heated deuterium clusters, Nature 398: 489-492.

picosecond pulse.⁷⁸ This is motivated by the low conversion efficiency of laser energy to accelerated protons or to gamma rays.

5.5.3 Positron Sources

Intense laser plasma interactions can generate positrons via two leading processes:

1. Bethe-Heitler process. Laser accelerated electrons produce γ-rays from bremsstrahlung in a high-Z converter foil, and a γ-ray of energy greater than 1.022 MeV undergoes pair production in the foil to generate an electron and a positron.⁷⁹ This process dominates in thick, high-Z targets (such as Pb).
2. The trident process. Laser accelerated electrons collide directly with the target Au foil nuclei, yielding e⁻–e⁺ pair production from electron–nucleus collisions.⁸⁰ This process dominates in thinner foils.

Positron generation can occur with lasers of a few TW, but generation of large numbers or high densities of positrons can require hundreds of TW.⁸¹

Particle beams have scientific applications that will be discussed in the remainder of this chapter. They are also useful in some medical and security applications, which are discussed in Chapter 6.

5.6 HIGH-INTENSITY, ULTRAFAST LASERS FOR NUCLEAR PHYSICS

5.6.1 Introduction

High power PW-class lasers can enable the production of high energy charged particles, γ-rays, and neutrons, with peak flux orders of magnitude higher than possible with conventional accelerators. These high flux beams interacting with a PW-laser can probe a new regime of nuclear physics, which can lead to practical

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⁷⁸ M. Roth, Bright laser-driven neutron source based on the relativistic transparency of solids, op.cit.

⁷⁹ C. Gahn, G.D. Tsakiris, G. Pretzler, K.J. Witte, C. Delfin, C.G. Wahlström, and D. Habs, 2000, Generating positrons with femtosecond laser pulses, App. Phys. Lett. 77(17): 2662-2664.

⁸⁰ H.C. Scott, C. Wilks, J.D. Bonlie, E.P. Liang, J. Myatt, D.F. Price, D.D. Meyerhofer, and P. Beiersdorfer, 2009, Relativistic positron creation using ultraintense short pulse lasers, PRL 102(10): 105001.

⁸¹ Hui Chen et al., “Relativistic Positron Creation Using Ultraintense Short Pulse Lasers,” Physical Review Letters 102, no. 10 (March 11, 2009): 105001, doi:10.1103/PhysRevLett.102.105001.

applications in nuclear and material science.⁸² The thrust of the ELI-NP facility, under construction in Bucharest, Romania, is based on investigations of laser-induced nuclear reactions. The aim is to achieve a better understanding of nuclear properties, nuclear reaction rates in laser plasmas, and the development of novel characterization methods based on nuclear techniques. In addition to their discovery science role, these facilities will produce nuclear reactions for many non-science applications, including energy and security. The ELI-NP infrastructure will support two synchronized 10 PW lasers for conducting ultrafast particle-light interaction studies at intensities of 10²⁴ W/cm². See the ELI-NP website for more details.⁸³

5.6.2 High Power Laser Systems for Nuclear Physics

High power laser systems enable numerous scientific opportunities. For instance, fission-fusion experiments using ion beams generated by high-intensity lasers illuminating thin metal production targets enable nuclear physics experiments aimed at understanding how the elements are made in the cosmos. They will also enable studies of strong-field quantum chromodynamics and of laser-gamma interactions.

5.6.3 γ-ray Beam Systems for Nuclear Physics

γ-ray beam systems enable a number of types of experimental studies of nuclear physics, particularly of nuclear structure and nucleosynthesis. γ-ray beams are made by scattering a laser beam off an electron beam; through the incoherent Compton scattering process, energy from the scattered electron is transferred to the scattered photon. The energy of the scattered photon depends upon the energy of the electron beam, the scattering angle, and the wavelength of the laser beam. Typically, γ-ray energies in the MeV range are used for nuclear structure studies or to induce nuclear reactions for other applications. For example, an ultra-short burst of γ-rays, together with high energy protons, can be used, through either [γ,n] and [p,n] reactions, to create short-lived radioisotopes for ultrafast photonuclear studies. This could offer an alternate approach to conventional accelerators for isotope production for clinical medical and materials applications.

5.6.4 Applications Beyond Nuclear Physics

The laser-based facilities and techniques developed for the study of nuclear physics could also be used in many other future applications, some of which are

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⁸² F. Negoita, M. Roth, P.G. Thirolf, S. Tudisco, F. Hannachi, S. Moustaizis, I. Pomerantz, et al., 2016, Laser driven nuclear physics at ELI-NP, Romanian Reports in Physics 68: S37–S144.

⁸³ Extreme Light Infrastructure-Nuclear-Physics, http://www.eli-np.ro/, accessed February 9, 2017.

outlined here. In most of these applications, high γ-ray beam intensity shortens the time to scan the object.

Energy applications: High power laser systems enable testing of new materials for use in the extreme environments of fusion and fission energy applications. Nuclear resonance fluorescence (NRF) with gamma beams can be used to identify isotopes in radioactive waste.

Medical applications: High energy particle- and photo-induced nuclear transitions can be used to produce radioisotopes for medical applications with gamma beam systems. The cost effectiveness of high-intensity laser isotope production methods for medical applications is uncertain.

Security applications: NRF with γ-ray beams can be used to search containers for nuclear material and explosives.

Materials applications: High power laser systems enable testing of materials for use in extreme environments. They enable study of new materials for use in components of accelerators, such as high power targets and beam collimators. They also enable testing materials for space science, simulating the radiation environment of space missions, and they make possible studies of effects of radiation on biological systems.

Computed tomography (CT): CT can be performed with γ-ray beams—for instance, for non-destructive inspection of objects.

5.7 EXTREME INTENSITY: TOWARD AND BEYOND THE SCHWINGER LIMIT OF 10¹⁴ PW/cm²

5.7.1 Introduction

Elementary particle interactions can be studied in new ways using the extreme fields of focused petawatt-class lasers, where the strength of the laser field can exceed the dielectric breakdown strength of the vacuum, known as the Schwinger limit, thereby providing an exotic form of particle production that cannot be studied without petawatt-class lasers. These laser beams can distort the properties of the vacuum, probing its properties such as vacuum birefringence. Laser fields can also be controlled to minimize (or eliminate) particle collisions, allowing nonlinear processes to be studied with precision.

QED studies with petawatt lasers must be pursued at facilities that have co-located relativistic particle accelerators in order to achieve the highest effective fields, because the laser intensity in the center of momentum frame scales as γ², where γ is the Lorentz factor of Special Relativity. Conventional RF accelerators such as those at the Stanford Linear Accelerator Center (SLAC) routinely operate at γ² ~ 10⁹ and have achieved values of γ² approaching 10¹⁰, a 10-billion-fold

enhancement in the laser intensity as viewed in the particle rest frame. For large γ, even a moderately intense laser field can, in the rest frame of the relativistic particle, become an ultra-intense laser field.

The general science case for fundamental particle physics with intense lasers can be traced back to the remarkable success of QED in regimes where perturbation theory is valid, that is, for particle scattering experiments, high resolution Lamb shift or Rydberg measurements, and trap- or ring-based measurements of the anomalous magnetic moments of fermions. Calculations using covariant perturbation expansions have been used to compare experimental results to fundamental interaction theories. Intense lasers have the potential to create field strengths significantly exceeding the range of applicability of perturbation theory, giving rise to new effects, including many-body relativistic vacuum physics and possibly a hint of physics beyond the Standard Model.

The physics case for QED experiments using intense lasers has two general justifications. First, many basic QED processes have not yet been observed or have not been observed in sufficiently clean experiments to allow for detailed comparison with QED predictions. Second, many extensions of the standard model predict as yet unobserved particles/fields. If such particles exist, they typically modify the vacuum polarizability and can therefore have observable consequences on QED processes. Therefore, measurement of fundamental QED processes can, when carefully compared to theory, constitute a search for physics beyond the standard model.

5.7.2 The Schwinger Limit

The Schwinger limit is the laser intensity where the vacuum becomes unstable to the production of electron-positron pairs. It can be calculated within QED but can be estimated accurately using simple ideas based on the uncertainty principle.^84–88

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⁸⁴ Sebastian Meuren, Christoph H. Keitel, and Antonino Di Piazza, “Semiclassical Picture for Electron-Positron Photoproduction in Strong Laser Fields,” Physical Review D 93, no. 8 (April 21, 2016): 085028, doi:10.1103/PhysRevD.93.085028.

⁸⁸ Sebastian Meuren et al., “High-Energy Recollision Processes of Laser-Generated Electron-Positron Pairs,” Physical Review Letters 114, no. 14 (April 9, 2015): 143201, doi:10.1103/ PhysRevLett.114.143201.

The quantum vacuum contains virtual relativistic matter-antimatter pairs that exist for times consistent with quantum uncertainty: Δt ≤ ħ/2mc². Even for the lightest particles, electrons and positrons, this is an exceedingly short time, equal to 0.5α² atomic units of time, or about 0.7 zeptoseconds (0.7×10⁻²¹ s). During their brief existence, these charged particles can interact with an applied laser field E. The maximum work the field can impart to an electron-positron pair is therefore on the order of 2EcΔt ≈ Eλ_C, where λ_C = h/mc is the Compton wavelength. The vacuum becomes unstable at the Schwinger field E_s when this work exceeds the rest mass of the particle pair, E_sλ_C > ~2mc². Above this threshold field (intensity), laser energy is efficiently converted to matter-antimatter pairs. This corresponds to E_s> 1.3×10¹⁶ V/cm, or I_s > 2.3×10²⁹ W/cm², the Schwinger intensity.

5.7.3 Vacuum Polarization: Matter from Light

There are many closely related processes for producing matter from light. A listing of these is given below.

5.7.3.1 Schwinger Critical Field Exceeded in Laser Collisions with Relativistic Electrons

In its current configuration, the SLAC linear accelerator in Menlo Park, California, operates as three 1-km linear accelerators, two of which are capable of producing ~ 15GeV electrons (γ = 30,000). If one of these relativistic electron beams collides with a focused laser with peak intensity in the range of 10²¹W/cm², this is sufficient to exceed the Schwinger limit by more than an order of magnitude and produce copious amounts of matter in the laser focus (Figure 5.8). The committee stresses that this field will not be achieved at ELI, since none of the ELI sites is collocated with a GeV-scale linear accelerator, and without it the laser must supply 1 billion times more intensity, e.g., 1 Exawatt focused to a 20 nm focal spot.

5.7.3.2 Cascade Processes

The presence of a single fermion, or even a single high energy photon to initiate pair formation, is expected to make a significant difference and can lead to a cascade in very general circumstances. For intensities above ~3×10²³ W/cm², the number of pairs produced by photon-induced pair production rises steeply. These pairs are accelerated and generate additional photons and pairs. At ~ 10²⁴ W/cm², the laser power is predicted to be divided roughly equally between photons and electron-positron pairs, each with energy ~80 MeV, independent of the number of electrons initially in the interaction region. Complete conversion of laser energy to photons and pairs implies the production of 4×10¹⁰ pairs per Joule of laser energy. There are many calculations covering variations of geometry and polarization.⁸⁹

5.7.3.3 Linear Breit-Wheeler Process (Basic and Stimulated)

The Breit-Wheeler (BW) process is represented by a perturbative Feynman graph describing two photons colliding to produce an e-e+ pair (Figure 5.9).

Since the energy of the e-e+ pair is ~1 MeV, the photons are nominally gamma rays, but in principle these could be made using nonlinear laser-matter interactions with a petawatt-class laser. These gammas must collide at a nonzero crossing angle to satisfy momentum conservation. Breit and Wheeler calculated that the cross section for this process was of order r_e², where r_e = e²/mc² is the classical electron radius. This simple process has never been directly observed by colliding two real gamma ray beams. Subsequent calculations identified resonances in the BW cross section that increase the cross section by several orders of magnitude and are associated with the so-called stimulated BW process.⁹⁰

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⁸⁹ C.P. Ridgers, C.S. Brady, R. Duclous, J.G. Kirk, K. Bennett, T.D. Arber, A.P.L. Robinson, and A.R. Bell, 2012, Dense electron-positron plasmas and ultraintense γ rays from laser-irradiated solids, Phys Rev Letters 108(16): 165006; A.R. Bell and J.G. Kirk, 2008, Possibility of prolific pair production with high-power lasers, Phys Rev Letters 101(20): 200403.

⁹⁰ Cheng, Hung, Er-Cheng Tsai, and Xiquan Zhu. “Delbrück Scattering.” Physical Review D 26, no. 4 (August 15, 1982): 908–21. doi:10.1103/PhysRevD.26.908.

5.7.3.4 Multiphoton Breit-Wheeler Process

The multiphoton Breit-Wheeler process refers to a BW process whereby one of the gammas is replaced by several lower energy photons (Figure 5.10).

The multiphoton BW process was observed in the E144 experiment at SLAC which studied the collision of a 46.6 GeV electron beam with terawatt 527 nm laser pulses.⁹¹ The effective intensity in the rest frame of the electron beam was below the Schwinger intensity but in the regime to see nonlinear QED effects. Roughly 100 positrons were detected and attributed to the cooperative interaction of laser photons with a backscattered Compton gamma ray.

5.7.3.5 Spin Polarization

Pair production by a high-energy photon and a strong laser field show differences between boson and fermion pair production in an oscillating electric field and also show that the existence of a fermionic (bosonic) particle in the initial state leads to suppression (enhancement) of the pair-production probability due to the different quantum statistics. This has been discussed extensively.⁹²

5.7.3.6 Breit-Wheeler with Short Pulses

The BW process can be modified by finite pulse duration and is also predicted to be sensitive to the carrier-envelope relative phase. Again, none of these subtle effects has been observed.⁹³

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⁹¹ D.L. Burke, R.C. Field, G. Horton-Smith, J.E. Spencer, D. Walz, S.C. Berridge, W.M. Bugg, et al., 1997, Positron production in multiphoton light-by-light scattering, Phys. Rev. Lett. 79(9): 1626.

⁹² Tsai (1993); D.Y. Ivanov, G.L. Kotkin, and V.G. Serbo, 2005, Complete description of polarization effects in e + e– pair productionby a photon in the field of a strong laser wave, Eur. Phys. J. C 40: 27; Popov (1972); Krekora, Su, and Grobe, 2004; Cheng et al., 2009; Wagner et al., 2010a,b.

⁹³ A.I. Titov, B. Kampfer, H. Takabe, and A. Hosaka, 2013, Breit-Wheeler process in very short electromagnetic pulses, Physical Review A 87(4): 042106.

5.7.3.7 Hohlraum Breit-Wheeler

Large numbers of BW pairs per laser shot are predicted using a laser-accelerated particle beam to produce gammas, which then interact with thermal radiation made by a laser-heated hohlraum.⁹⁴

5.7.3.8 Delbrück Scattering

Delbrück scattering (DS) is the deflection (coherent elastic scattering) of high-energy photons in the Coulomb field of nuclei and is a consequence of vacuum polarization.^95,96 The electrons/positrons of the vacuum are capable of producing coherent-elastic photon scattering because the recoil momentum during absorption and emission of the photon is transferred to the total atom while the electrons remain in their state of negative energy. Delbrück scattering is therefore analogous to atomic Rayleigh scattering except that in the latter case, the electrons are bound in the electron cloud of the atom.

5.7.3.9 Trident Process

The trident process refers to e-e+ pair production via a collision between one or more real photons and a virtual photon that is provided by a strong field, typically that of a heavy nucleus. This process is inefficient, producing ~10^–4 positrons for each fast electron.⁹⁷

5.7.3.10 Muon and Pion Pairs

Muons and pions are heavier than electrons (207 and 273 times, respectively) so that their production via a Schwinger tunneling mechanism is unachievable with foreseeable lasers and electron accelerators. (The Schwinger critical field for muon/anti-muon production is~ 5.6×10²⁴ V/cm). However, muons are easy to detect and to differentiate from electrons, so novel mechanisms for muon pair production that are related to the collective copious production of e+e- pairs may

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⁹⁴ O. J. Pike, F. Mackenroth, E.G. Hill, S.J. Rose, 2014, A photon–photon collider in a vacuum hohlraum, Nature Photonics 8: 434–436.

⁹⁵ Cheng, Hung, Er-Cheng Tsai, and Xiquan Zhu. “Delbrück Scattering.” Physical Review D 26, no. 4 (August 15, 1982): 908–21. doi:10.1103/PhysRevD.26.908.

⁹⁶ Koga, James K., and Takehito Hayakawa. “Possible Precise Measurement of Delbrück Scattering Using Polarized Photon Beams.” Physical Review Letters 118, no. 20 (May 17, 2017): 204801. doi:10.1103/PhysRevLett.118.204801.

⁹⁷ Hu, Huayu. “Complete QED Theory of Multiphoton Trident Pair Production in Strong Laser Fields.” Physical Review Letters 105, no. 8 (2010). doi:10.1103/PhysRevLett.105.080401.

be studied with great sensitivity, and there are several different types of proposals for muons from laser-generated e+e- plasmas.^98,99 Muon and pion pairs have also been predicted to arise from a collision between an X-ray laser beam and a relativistic nuclear beam.¹⁰⁰

5.7.4 Nonlinear Thomson and Compton Scattering

An electron driven by an electromagnetic field emits radiation in a scattering process termed Thomson scattering when quantum effects such as photon recoil are negligible and Compton scattering when they are not. Multiphoton versions of these processes correspond to events where more than one photon is scattered.

Thomson and Compton scattering have been theoretically considered many times in the literature. One recent description of multiphoton Compton scattering accounted for the electron and photon polarizations,¹⁰¹ while others have evaluated the effects of finite, even ultrashort, pulse duration on multiphoton Thomson and Compton scattering.¹⁰² For this latter consideration, the main differences with respect to the monochromatic case are a broadening of the lines, corresponding to the emitted frequencies, and the appearance of sub-peaks, due to interference between emission from the front and back ends of the laser pulse. Similarly, Thomson and Compton scattering have been shown to exhibit observable effects of the relative carrier envelope phase.¹⁰³

From an experimental perspective, Bula et al. (1996) reported observation of multiphoton Compton scatter for the first time in an experiment involving a collision between a relativistic (46.6 GeV) electron beam and visible (527 nm) laser

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⁹⁸ M. Yu. Kuchiev, “Production of High-Energy Particles in Laser and Coulomb Fields and the <span Class,” Physical Review Letters 99, no. 13 (2007), doi:10.1103/PhysRevLett.99.130404.

⁹⁹ Carsten Müller, Karen Z. Hatsagortsyan, and Christoph H. Keitel, “Particle Physics with a Laser-Driven Positronium Atom,” Physics Letters B 659, no. 1 (January 17, 2008): 209–13, doi:10.1016/j. physletb.2007.11.002.

¹⁰⁰ I. Kuznetsova, D. Habs, and J. Rafelski, 2008, Pion and muon production in e–, e+, γ plasma, Physical Review D - Particles, Fields, Gravitation and Cosmology 78(1): 014027; Thoma, (2009a, 2009b); A.I. Titov, B. Kämpfer, and H. Takabe, 2009, Dimuon production by laser-wakefield accelerated electrons, Phys. Rev. ST Accel. Beams 12(11): 111301;Bychenkov et al. (2001); C. Müller, C. Deneke, and C.H. Keitel, 2008, Muon-pair creation by two x-ray laser photons in the field of an atomic nucleus, Phys. Rev. Lett. 101(6): 060402; Muller, Deneke et al., 2009; Dadi and Muller (2011).

¹⁰¹ Ivanov, G.L. Kotkin, and V.G. Serbo, 2005, Complete description of polarization effects in e + epair production.

¹⁰² M. Boca and V. Florescu, 2009, Nonlinear Compton scattering with a laser pulse, Phys. Rev. A 80(5): 053403.

¹⁰³ K. Krajewska, and J. Z. Kamiński, 2012, Breit-Wheeler process in intense short laser pulses, Phys. Rev. A 86: 052104.

photons focused to an intensity, in the electron rest frame, of ~10¹⁸ W/cm².¹⁰⁴ Four-photon Compton scattering was observed indirectly via a nonlinear energy shift in the spectrum of the outgoing electrons. More recently, multiphoton Thomson scattering of laser radiation in the X-ray domain was reported¹⁰⁵ as was anomalous X-ray Compton scattering.¹⁰⁶ In this latter paper, 9 keV X-rays interacting with a Be target produced a single higher-energy photon redshifted from the second harmonic. The anomalous redshift was attributed to scattering from X-ray excited states produced via the interaction of the intense X-ray beam (4×10²⁰ W/cm²) with the solid Be target.

Since high-energy photons can be emitted via Thomson and Compton scattering, these processes have been of interest for producing short wavelength radiation. The main advantages of these sources compared, for instance, to synchrotron sources, are their compactness, wide tunability, short pulse durations (femtosecond or shorter), and the potential for high brightness. Applications based on these advantages are considered in Chapter 6.

5.7.5 Radiation Reaction

Radiation reaction (RR) refers to the damping/friction experienced by a charged particle arising from the electromagnetic field the particle itself has radiated. RR becomes important when the momentum change due to the electron radiation competes with the Lorentz force of the laser. In the regime a>>1 but χ=γE₀/E_s <<1, the electron trajectory can be significantly affected by cumulative emission of photons, each of which causes a recoil negligible compared to the Lorentz force and the electron energy. As the laser field E₀ increases to χ~1 into the quantum-dominated regime, the recoil can be a sizeable fraction of the electron energy.¹⁰⁷

While high intensity (>10²⁴ W/cm²) is typically required before RR effects become important, observable effects have been predicted at lower intensity (>10²² W/cm²). Simulations, for instance, show that the predicted angular width of radiation emitted in laser/electron collisions changes significantly if RR effects

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¹⁰⁴ C. Bula, K.T. McDonald, E.J. Prebys, C. Bamber, S. Boege, T. Kotseroglou, A.C. Melissinos, et al., 1996, Observation of nonlinear effects in Compton scattering, Phys. Rev. Lett. 76(17): 3116.

¹⁰⁵ M. Babzien, I.B. Zvi, K. Kusche, I.V. Pavlishin, I.V. Pogorelsky, D.P. Siddons, V. Yakimenko, et al., 2006, Observation of the second harmonic in Thomson scattering from relativistic electrons, Phys. Rev. Lett. 96(5): 054802.

¹⁰⁶ M. Fuchs, M. Trigo, J. Chen, S. Ghimire, S. Shwartz, M. Kozina, M. Jiang, T. Henighan, C. Bray, G. Ndabashimiye, P. H. Bucksbaum, Y. Feng, S. Herrmann, G. A. Carini, J. Pines, P. Hart, C. Kenney, S. Guillet, S. Boutet, G. J. Williams, M. Messerschmidt, M. M. Seibert, S. Moeller, J. B. Hastings, and D. A. Reis, 2015, Anomalous nonlinear X-ray Compton scattering, Nature Physics 11: 964–970.

¹⁰⁷ Extremely high-intensity laser interactions with fundamental quantum systems, A. Di Piazza, C. Muller, K. Z. Hatsagortsyan, and C. H. Keitel, Rev. Mod. Phys., 84, 1177-1228 (2012).

are included: a 10 degree angular change is predicted for an optical intensity of 5×10²² W/cm² and an initial electron energy of 40 MeV.¹⁰⁸ Similarly, another investigation found that self-field effects induce peculiar electron spin dynamics.¹⁰⁹ More generally, quantum mechanical calculations indicate that RR effects primarily modify the spectrum of radiation emitted by a charged particle as follows: the photon yield is increased at low photon energies and decreased at high photon energies so that there is an overall shift of photon spectrum to low energy.¹¹⁰

From an applications perspective, when a relativistic electron beam collides with a sufficiently intense laser pulse, RR effects can strongly alter the beam dynamics. Classical calculations indicate that RR has a beneficial effect on an electron beam, predicting that the laser interaction tends to reduce the beam’s energy spread. However, when quantum effects become important, RR induces the opposite effect and the electron beam energy spread increases upon interacting with a laser pulse. The intrinsic stochasticity of photon emission, which becomes important in the quantum regime, is identified as the underlying mechanism for the increased energy spread.¹¹¹ Beam cooling is important, for instance, for accelerator and FEL applications.

In a related paper, Capdessus et al. find that stochastic electron motion in combined laser and plasma (electrostatic) fields strongly affects the spectrum of radiation generated by accelerated electrons during high-intensity laser plasma interaction. This is explained as a collective effect occurring for laser intensities above 10²² W/cm² and plasma densities more than 10 times the critical density. The authors suggest that their findings may be important for laboratory modeling of radiation-dominated relativistic astrophysical events and that they can be tested in experiments with solid hydrogen and deuterium targets.¹¹²

With regard to applications in e-e+ production, a theoretical investigation concluded that RR effects inhibit the development of an e-e+ cascade, a process theorized to produce a high density e-e+ plasma.¹¹³

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¹⁰⁸ A. Di Piazza, K.Z. Hatsagortsyan, and C.H. Keitel, 2009, Strong signatures of radiation reaction below the radiation-dominated regime, Phys. Rev. Lett. 102(25): 254802.

¹⁰⁹ S. Meuren and A. Di Piazza, 2011, Quantum electron self-interaction in a strong laser field, Phys. Rev. Lett. 107(26): 260401.

¹¹⁰ Cheng, Hung, Er-Cheng Tsai, and Xiquan Zhu. “Delbrück Scattering.” Physical Review D 26, no. 4 (August 15, 1982): 908–21. doi:10.1103/PhysRevD.26.908; A. Di Piazza, K.Z. Hatsagortsyan, and C.H. Keitel, 2009, “Strong signatures of radiation reaction.”

¹¹¹ N. Neitz, “Stochasticity Effects in Quantum Radiation Reaction,” Physical Review Letters 111, no. 5 (2013), doi:10.1103/PhysRevLett.111.054802.

¹¹² R. Capdessus, E. d’Humières, and V.T. Tikhonchuk, 2013, Investigation of collective electron effects in radiation production, Phys. Rev. Letters 110(21): 215003.

¹¹³ I.V. Sokolov, N.M. Naumova, J.A. Nees, and G.A. Mourou, 2010, Pair creation in QED-strong pulsed laser fields interacting with electron beams, Phys. Rev. Lett. 105(19): 195005.

5.7.6 Vacuum Polarization: Elastic Light Scattering

Classically, photons (transverse EM fields) do not interact with one another; a fact reflected in the linearity of the Maxwell equations. However, the underlying quantum nature of the vacuum implies a nonzero vacuum polarizability that enables photon-photon interactions. Photons can, for instance, fluctuate into e-e+ pairs, which can in turn directly interact with one another.

5.7.6.1 Vacuum Birefringence

One way to observe vacuum polarization effects is to detect their influence on the polarization properties of a probe electromagnetic beam. Within the framework of QED, the vacuum can be a birefringent medium due to the presence of a “background” electromagnetic field. This field will in general polarize the vacuum and in doing so introduce a preferred vacuum direction. This nonisotropic vacuum polarization amounts to vacuum birefringence and can lead to observable effects on a probe laser beam, rotating its polarization axis and/or inducing ellipticity. Calculations indicate that a linearly polarized X-ray beam co-propagating with an intense laser will emerge elliptically polarized.¹¹⁴

5.7.6.2 Light-Light Scattering in the X-ray Regime

Recently, a search for light-light scattering in the X-ray regime was performed using the SACLA X-ray FEL. A signal, photons scattered elastically along the boost axis of the two-photon system, was not observed. Owing to high background counts, the inferred upper limit on the cross section for light-light scattering was well above the predicted QED value. Improvements to the X-ray FEL beams are expected to increase the experimental sensitivity close to the QED predicted signal level.¹¹⁵

5.7.7 Beyond the Standard Model

5.7.7.1 Light Scattering Through a Wall Experiments

Light scattering through a wall (LSW) experiments search for hidden sector particles, such as Axions, Axion-like particles (ALPs), and paraphotons, by searching for transmission of (real) photons through barriers that are effectively impenetrable within the Standard Model. The particles of interest are weakly interacting;

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¹¹⁴ T. Heinzl, B. Liesfeld, K.-U. Amthor, H. Schwoerer, R. Sauerbrey, and A. Wipf, 2006, On the observation of vacuum birefringence, Opt.Commun. 267(2): 318-321.

¹¹⁵ T. Inadaa, T. Yamajia, S. Adachia, T. Nambab, S. Asaia, T. Kobayashib, K. Tamasaku, et al., 2014, Search for photon–photon elastic scattering in the X-ray region, Physics Letters B 732: 356-359.

in particular, they are typically assumed to have zero electric charge. Transmission may occur as real photons transform into hidden sector particles that propagate through the barrier and then oscillate back into real photons to be detected on the other side of the barrier.

Magnetic fields are used to drive Axion/ALP oscillation, while magnetic fields are typically not used in paraphoton searches. LSW experiments have been performed in optical and X-ray regimes since these different spectral regions are optimized for particles of different mass and/or photon coupling strength.

Since the oscillation probability for Axions/ALPs scales with magnetic field strength, the highest practical field strength is desirable. While searches to date have used static fields in the few Tesla range, high-intensity lasers have been considered for LSW experiments owing to their very high peak magnetic fields (~ 6.5×10⁵ T at 10²² W/cm²). The small space-time footprint of an intense laser pulse, compared to a CW-laser/static-magnetic-field configuration, works against high-intensity experiments, reducing the advantage associated with high peak fields. Still, initial analysis of high power (~ 1 PW) LSW experiments suggests that they should be competitive with CW-laser/static-field experiments.¹¹⁶

5.7.7.2 Minicharged Particle Experiments

In addition to electrically neutral BSM particles such as axions, yet unobserved particles with nonzero charge may also exist. These particles could either be very heavy and therefore appropriate for large-scale accelerator experiments, or they could be light and weakly charged, so-called minicharged particles, well suited for laser-based searches.¹¹⁷

Vacuum nonlinearities associated with minicharged particles may be observable in a strong external laser field, modifying the vacuum birefringence effects expected within the Standard Model (i.e., deviations from QED predictions would be observed).¹¹⁸ Analysis indicates that strong field vacuum birefringence experiments could significantly improve existing experimental constraints on minicharged particles in the mass range below 0.1 eV.¹¹⁹

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¹¹⁶ J.T. Mendoca, 2007, Axion excitation by intense laser fields, Europhysics Letters 79(2).

¹¹⁷ H. Gies, 2009, Strong laser fields as a probe for fundamental physics, Eur. Phys. J. D 55: 311–317.

¹¹⁸ Gies, H., J. Jaeckel, and A. Ringwald, Polarized light propagating in a magnetic field as a probe of millicharged fermions, Phys. Rev. Lett. 97, 140402 (2006).

¹¹⁹ Ibid.

5.7.7.3 Quantum Electrodynamics Experiments

Beyond the specific minicharged particle predictions mentioned above, there is a rather broad array of weakly interacting particles predicted by various extensions of the Standard Model.¹²⁰ Generally speaking, the existence of additional particles modifies the vacuum polarizability, leading in principle to observable consequences in a range of QED processes. While only a modest number of specific experimental predictions exists at present, theoretical guidance for observing signatures of BSM physics in QED experiments can be expected to grow as experimental approaches both diversify and mature.

5.7.7.4 Unruh Radiation

Intense lasers can rapidly accelerate electrons and it has been suggested that high-intensity lasers could achieve accelerations comparable to those experienced in the vicinity of a black hole.¹²¹ Such rapidly accelerated electrons are expected to emit Unruh radiation. This may be useful in exploring as yet unresolved issues associated with the Hawking radiation predicted to arise near a black hole event horizon.

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¹²⁰ Asimina Arvanitaki, Savas Dimopoulos, Sergei Dubovsky, Nemanja Kaloper, and John March-Russell, Phys. Rev. D 81, 123530 (2010).

¹²¹ Pisin Chen, “Accelerating Plasma Mirrors to Investigate the Black Hole Information Loss Paradox,” Physical Review Letters 118, no. 4 (2017), doi:10.1103/PhysRevLett.118.045001.