Naval Research Laboratory Plasma Physics Division

An overview is given of the physics issues relevant to the plasma wakefield accelerator, the plasma beat-wave accelerator, the laser wakefield accelerator, including the self-modulated regime, and wakefield accelerators driven by multiple electron or laser pulses. Basic properties of linear and nonlinear plasma waves are discussed, as well as the trapping and acceleration of electrons in the plasma wave. Formulas are presented for the accelerating field and the energy gain in the various accelerator configurations. The propagation of the drive electron or laser beams is discussed, including limitations imposed by key instabilities and methods for optically guiding laser pulses. Recent experimental results are summarized.

A nonlinear theory of intense laser-plasma interactions is developed and used to describe relativistic optical guiding, coherent harmonic radiation production, and nonlinear plasma wakefield generation. Relativistic optical guiding is found to be ineffective in preventing the leading portion (\ensuremath{\le} a plasma wavelength) of a laser pulse from diffracting. Coherent harmonic generation is found to be most efficient for short laser pulses. Optical guiding and harmonic generation may be enhanced by the presence of large amplitude plasma wakefields. These phenomena may be important in laser-driven plasma accelerators, x-ray sources, and fusion schemes.

Several features of intense, short-pulse (/spl lsim/1 ps) laser propagation in gases undergoing ionization and in plasmas are reviewed, discussed, and analyzed. The wave equations for laser pulse propagation in a gas undergoing ionization and in a plasma are derived. The source-dependent expansion method is discussed, which is a general method for solving the paraxial wave equation with nonlinear source terms. In gases, the propagation of high-power (near the critical power) laser pulses is considered including the effects of diffraction, nonlinear self-focusing, ionization, and plasma generation. Self-guided solutions and the stability of these solutions are discussed. In plasmas, optical guiding by relativistic effects, ponderomotive effects, and preformed density channels is considered. The self consistent plasma response is discussed, including plasma wave effects and instabilities such as self-modulation. Recent experiments on the guiding of laser pulses in gases and in plasmas are briefly summarized.

A two-dimensional, axisymmetric, relativistic fluid model describing the propagation of intense laser pulses in plasmas is formulated and numerically evaluated. Relativistic guiding is ineffective in preventing the diffractive spreading of short laser pulses and long pulses become modulated due to relativistic and wake-field effects. Laser pulses can be propagated over many Rayleigh lengths by use of a performed plasma density channel or by tailoring the pulse profile. Ultrahigh axial electric fields can be generated behind the laser pulse.

An injector and accelerator is analyzed that uses three collinear laser pulses in a plasma: an intense pump pulse, which generates a large wake field $(\ensuremath{\ge}20\mathrm{GV}/\mathrm{m})$, and two counterpropagating injection pulses. When the injection pulses collide, a slow phase velocity beat wave is generated that injects electrons into the fast wake field for acceleration. Particle tracking simulations in 1D with injection pulse intensities near ${10}^{17}\mathrm{W}/\mathrm{cm}{}^{2}$ indicate the production of relativistic electrons with bunch durations as short as 3 fs, energy spreads as small as 0.3%, and densities as high as ${10}^{18}\mathrm{cm}{}^{\ensuremath{-}3}$.

A comprehensive theory is developed to describe the nonlinear Thomson scattering of intense laser fields from beams and plasmas. This theory is valid for linearly or circularly polarized incident laser fields of arbitrary intensities and for electrons of arbitrary energies. Explicit expressions for the intensity distributions of the scattered radiation are calculated and numerically evaluated. The space-charge electrostatic potential, which is important in high-density plasmas and prevents the axial drift of electrons, is included self-consistently. Various properties of the scattered radiation are examined, including the linewidth, angular distribution, and the behavior of the radiation spectra at ultrahigh intensities. Nonideal effects, such as electron-energy spread and beam emittance, are discussed. A laser synchrotron source (LSS), based on nonlinear Thomson scattering, may provide a practical method for generating tunable, near-monochromatic, well-collimated, short-pulse x rays in a compact, relatively inexpensive source. Two examples of possible LSS configurations are presented: an electron-beam LSS generating hard (30-keV, 0.4-\AA{}) x rays and a plasma LSS generating soft (0.3-keV, 40-\AA{}) x rays. These LSS configurations are capable of generating ultrashort (\ensuremath{\sim}1-ps) x-ray pulses with high peak flux (\ensuremath{\gtrsim}${10}^{21}$ photons/s) and brightness [\ensuremath{\gtrsim}${10}^{19}$ photons /(s ${\mathrm{mm}}^{2}$ ${\mathrm{mrad}}^{2}$), 0.1% bandwidth].

This article reviews the state-of-the-art in high-power microwave source research. It begins with a discussion of the concepts involved in coherent microwave generation. The main varieties of microwave tubes are classified into three groups, according to the fundamental radiation mechanism involved: Cherenkov, transition, or bremsstrahlung radiation. This is followed by a brief discussion of some of the technical fundamentals of high-power microwave sources, including power supplies and electron guns. Finally, the history and recent developments of both high-peak power and high-average power sources are reviewed in the context of four main areas of application: (1) plasma resonance heating and current drive; (2) rf acceleration of charged particles; (3) radar and communications systems; and (4) high-peak power sources for weapons-effect simulation and exploratory development.

A nonlinear one-dimensional theory is developed that describes some important aspects of intense laser-plasma interactions. The self-consistent laser-plasma analysis includes nonlinear plasma wake-field generation, relativistic optical guiding, coherent harmonic radiation production, as well as other related phenomena. Relativistic optical guiding is found to be most effective for long laser pulses having slow rise times. Short laser pulses are shown to be weakly guided. Coherent harmonic generation using a linearly polarized laser is found to be most efficient for short laser pulses and can be enhanced by the presence of large amplitude plasma wake fields. Aspects of particle acceleration by laser pulses as well as possible methods for upshifting the frequency of laser pulses are also discussed.

Several features of vacuum laser acceleration are reviewed, analyzed, and discussed, including electron acceleration by two crossed laser beams and acceleration by a higher-order Gaussian beam. In addition, the vacuum beat wave accelerator (VBWA) concept is proposed and analyzed. It is shown that acceleration by two crossed beams is correctly described by the Lawson-Woodward (LW) theorem, i.e., no net energy gain results for a relativistic electron interacting with the laser fields over an infinite interaction distance. Finite net energy gains can be obtained by placing optical components near the laser focus to limit the interaction region. The specific case of a higher-order Gaussian beam reflected by a mirror placed near focus is analyzed in detail. It is shown that the damage threshold of the mirror is severely limiting, i.e., substantial energy gains require very high electron injection energies. The VBWA, which uses two copropagating laser beams of different frequencies, relies on nonlinear ponderomotive forces, thus violating the assumptions of the LW theorem. Single-particle simulations confirm that substantial energy gains are possible and that optical components are not needed near the focal region.

Experimental demonstration of optical guiding of a high intensity $(>{10}^{16}\mathrm{W}/{\mathrm{cm}}^{2})$ laser pulse in a 1 cm long cylindrical plasma channel formed by a slow capillary discharge is presented. Optical guiding in a curved plasma $(\mathrm{radius}\mathrm{of}\mathrm{curvature}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}10\mathrm{cm})$ is also demonstrated. It is shown experimentally that the guiding mechanism is insensitive to laser intensity over a wide range $(\ensuremath{\sim}{10}^{8}--{10}^{16}\mathrm{W}/{\mathrm{cm}}^{2})$. Results show guiding over $\ensuremath{\simeq}11$ vacuum diffraction lengths in both straight and curved channels, in agreement with theory and simulation.

A systematic experimental study of annular aluminum-wire Z-pinches on a 20-TW electrical generator shows that the measured spatial characteristics and emitted x-ray power agree more closely with rad-hydro simulations when large numbers of wires are used. The measured x-ray power increases first slowly and then rapidly with decreasing interwire gap spacing. Simulations suggested that this increase reflects the transition from implosion of individual wire plasmas to one of an azimuthally symmetric plasma shell. In the plasma-shell regime, x-ray powers of 40 TW are achieved.

Intense, ultrashort laser pulses propagating in the atmosphere have been observed to emit sub-THz electromagnetic pulses (EMPS). The purpose of this paper is to analyze EMP generation from the interaction of ultrashort laser pulses with air and with dielectric surfaces and to determine the efficiency of conversion of laser energy to EMP energy. In our self-consistent model the laser pulse partially ionizes the medium, forms a plasma filament, and through the ponderomotive forces associated with the laser pulse, drives plasma currents which are the source of the EMP. The propagating laser pulse evolves under the influence of diffraction, Kerr focusing, plasma defocusing, and energy depletion due to electron collisions and ionization. Collective effects and recombination processes are also included in the model. The duration of the EMP in air, at a fixed point, is found to be a few hundred femtoseconds, i.e., on the order of the laser pulse duration plus the electron collision time. For steady state laser pulse propagation the flux of EMP energy is nonradiative and axially directed. Radiative EMP energy is present only for nonsteady state or transient laser pulse propagation. The analysis also considers the generation of EMP on the surface of a dielectric on which an ultrashort laser pulse is incident. For typical laser parameters, the power and energy conversion efficiency from laser radiation to EMP radiation in both air and from dielectric surfaces is found to be extremely small, < 10(-8). Results of full-scale, self-consistent, numerical simulations of atmospheric and dielectric surface EMP generation are presented. A recent experiment on atmospheric EMP generation is also simulated.

An envelope equation describing laser pulse self-focusing and optical guiding in plasmas is derived and is used to analyze self-modulation. Included is the plasma wave generated by the pulse front, which leads to periodic focusing, radial energy transport, and laser envelope modulation. The onset criterion and growth rates are calculated and compared to simulations using the envelope equation and a nonlinear fluid code. For a long square pulse, onset of strong self-modulation occurs at one-half the power needed for optical guiding.

In this paper we discuss some of the important issues pertaining to laser acceleration in vacuum, neutral gases, and plasmas. The limitations of laser vacuum acceleration as they relate to electron slippage, laser diffraction, material damage, and electron aperture effects, are discussed. An inverse Cherenkov laser acceleration configuration is presented in which a laser beam is self-guided in a partially ionized gas. Optical self-guiding is the result of a balance between the nonlinear self-focusing properties of neutral gases and the diffraction effects of ionization. The stability of self-guided beams is analyzed and discussed. In addition, aspects of the laser wakefield accelerator are presented and laser-driven accelerator experiments are briefly discussed.

Soft x-ray 3p\ensuremath{\rightarrow}3s lasing in neonlike germanium (${\mathrm{Ge}}^{22+}$) and copper (${\mathrm{Cu}}^{19+}$) in the wavelength interval of 195 to 285 A\r{} is observed for the first time, with gain coefficients ranging from 1.7 to 4.1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, the higher gain with germanium. The lasing plasmas are produced by focusing a driving laser beam (\ensuremath{\lambda}=1.05 \ensuremath{\mu}m, 2-ns FWHM) into an 18-mm-long line onto thin films and slab targets. The measured J=0 to 1 gain coefficients are comparable to those of the J=2 to 1 transitions. The measured wavelengths of the six lasing lines compared favorably with recent calculations.

The trapping and acceleration of a test electron in a nonlinear plasma wave is analyzed in one dimension using Hamiltonian dynamics. The plasma wave is described by a nonlinear, cold fluid model. The maximum energy gain and the minimum energy required for trapping of the test electron are determined. The separatrix is plotted for several values of plasma wave amplitude. In the large wave amplitude limit, the maximum energy of a trapped electron scales as 2γ2pE2z, where γp is the relativistic factor associated with plasma wave phase velocity and Ez is the electric field amplitude of the nonlinear plasma wave. This is in contrast to the well-known results for a sinusoidal wave, in which the maximum energy scales as 4γ2pEz. As the nonlinear plasma wave approaches wavebreaking, the maximum energy is given by γmax→4γ3p−3γp, where γmax is the relativistic factor of the trapped electron.

The nonlinear interaction of ultraintense laser pulses with electron beams and plasmas is rich in a wide variety of new phenomena. Advances in laser science have made possible compact terawatt lasers capable of generating subpicosecond pulses at ultrahigh powers (≥1 TW) and intensities (≥1018 W/cm2). These ultrahigh intensities result in highly relativistic nonlinear electron dynamics. This paper briefly addresses a number of phenomena including (i) laser excitation of large-amplitude plasma waves (wake fields), (ii) relativistic optical guiding of laser pulses in plasmas, (iii) optical guiding by preformed plasma channels, (iv) laser frequency amplification by ionization fronts and plasma waves, (v) relativistic harmonic generation, (vi) stimulated backscattering from plasmas and electron beams, (vii) nonlinear Thomson scattering from plasmas and electron beams, and (viii) cooling of electron beams by intense lasers. Potential applications of these effects are also discussed.

A compact laser synchrotron source (LSS) is proposed as a means of generating tunable, narrow bandwidth, ultra-short pulses of hard x rays. The LSS is based on the Thomson backscattering of intense laser radiation from a counterstreaming electron beam. Advances in both compact ultra-intense solid-state lasers and high brightness electron accelerators make the LSS an attractive compact source of high brightness pulsed x rays, particularly at photon energies beyond ∼30 keV. The x-ray wavelength is λ[Å]=650 λ0[μm]/Eb2[MeV], where λ0 is the laser wavelength and Eb is the electron beam energy. For Eb=72 MeV and λ0=1 μm, x rays at λ=0.12 Å (100 keV) are generated. The spectral flux, brightness, bandwidth, and pulse structure are analyzed. In the absence of filtering, the spectral bandwidth in the LSS is typically ≲1% and is limited by electron beam emittance and energy spread. Two configurations of the LSS are discussed, one providing high peak power and the other moderate average power x rays. Using present day technology, the LSS can generate picosecond pulses of x rays consisting of ≳109 photons/pulse with a peak brightness of ≳1020 photons/s mm2 mrad2 (0.1% BW) and photon energies ranging from 50 to 1200 keV.

An alternative configuration of the laser wake-field accelerator is proposed in which enhanced acceleration is achieved via resonant self-modulation of the laser pulse. This requires laser power in excess of the critical power for relativistic guiding and a plasma wavelength short compared to the laser pulse length. Relativistic and density wake effects strongly modulate the laser pulse at the plasma wavelength, resonantly exciting the plasma wave and leading to enhanced acceleration.

A linearly polarized, ultraintense laser field induces transverse plasma currents which are highly relativistic and nonlinear, resulting in the generation of coherent harmonic radiation in the forward direction (i.e., copropagating with the incident laser field). A nonlinear cold fluid model, valid for ultrahigh intensities, is formulated and used to analyze relativistic harmonic generation. The plasma density response is included self-consistently and is shown to significantly reduce the current driving the harmonic radiation. Phase detuning severely limits the growth of the harmonic radiation. The effects of diffraction are considered in the mildly relativistic limit. No third-harmonic signal emerges from a uniform plasma of near-infinite extent. A finite third-harmonic signal requires the use of a semi-infinite or finite slab plasma. For an initially uniform plasma, no second-harmonic radiation is generated. Generation of even harmonics requires transverse gradients in the initial plasma density profile.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>