Nonlinear interaction of intense laser pulses in plasmas

A Scalable, High-Efficiency, Low-Energy-Spread Laser Wakefield Accelerator Using a Tri-Plateau Plasma Channel

The emergence of multi-petawatt laser facilities is expected to push forward the maximum energy gain that can be achieved in a single stage of a laser wakefield acceleration (LWFA) to tens of giga-electron volts, which begs the question-is it likely to impact particle physics by providing a truly compact particle collider? Colliders have very stringent requirements on beam energy, acceleration efficiency, and beam quality. In this article, we propose an LWFA scheme that can for the first time simultaneously achieve hitherto unrealized acceleration efficiency from the laser to the electron beam of >20% and a sub-1% energy spread using a stepwise plasma structure and a nonlinearly chirped laser pulse. Three-dimensional high-fidelity simulations show that the nonlinear chirp can effectively mitigate the laser waveform distortion and lengthen the acceleration distance. This, combined with an interstage rephasing process in the stepwise plasma, can triple the beam energy gain compared to that in a uniform plasma for a fixed laser energy, thereby dramatically increasing the efficiency. A dynamic beam loading effect can almost perfectly cancel the energy chirp that arises during the acceleration, leading to the sub-percent energy spread. This scheme is highly scalable and can be applied to petawatt LWFA scenarios. Scaling laws are obtained, which suggest that electron beams with parameters relevant for a Higgs factory could be reached with the proposed high-efficiency, low-energy-spread scheme.

Self-compression of laser pulses induced by asymmetric self-phase modulation aided by backward Raman scattering in periodic density-modulated plasma

Here a mechanism for self-compression of laser pulses is presented, based on period density-modulated plasma. In this setup, two pump beams intersect at a small angle within the plasma. This interaction is facilitated by the ponderomotive ion mechanism, which causes a modulation in the density of plasma with long wavelengths and low amplitude. This modulation enhances the backward Raman scattering of the probe pulse. The trailing edge of the probe experiences greater energy loss, resulting in a steeper intensity gradient. This, in turn, induces an asymmetric self-phase modulation, which elevates the instantaneous frequency. It is notable that the laser in plasma exhibits opposite group velocity dispersion compared to traditional solid-state media. This unique property allows laser pulses to undergo dispersion compensation while broadening the spectrum, ultimately leading to self-compression. The 2D-PIC simulations demonstrate these phenomena, highlighting how period density-modulated plasma contributes to an asymmetric spectral distribution. The intricate interplay among self-phase modulation, group velocity, and backward Raman scattering results in the self-compressing of the laser pulse. Specifically, the pulses are compressed from their Fourier transform limit duration of 50 fs to a significantly reduced duration of 8 fs at plasma densities below 1/4 critical density, without the transverse self-focusing effects.

Energy-Conserving Theory of the Blowout Regime of Plasma Wakefield

We present a self-consistent theory of strongly nonlinear plasma wakefield (bubble or blowout regime of the wakefield) based on the energy conservation approach. Such wakefields are excited in plasmas by intense laser or particle beam drivers and are characterized by the expulsion of plasma electrons from the propagation axis of the driver. As a result, a spherical cavity devoid of electrons (called a "bubble") and surrounded by a thin sheath made of expelled electrons is formed behind the driver. In contrast to the previous theoretical model [W. Lu et al., Phys. Rev. Lett. 96, 165002 (2006)PRLTAO0031-900710.1103/PhysRevLett.96.165002], the presented theory satisfies the energy conservation law, does not require any external fitting parameters, and describes the bubble structure and the electromagnetic field it contains with much higher accuracy in a wide range of parameters. The obtained results are verified by 3D particle-in-cell simulations.

Hydrodynamic Impacts of Short Laser Pulses on Plasmas

We determine conditions allowing for simplification of the description of the impact of a short and arbitrarily intense laser pulse onto a cold plasma at rest. If both the initial plasma density and pulse profile have plane symmetry, then suitable matched upper bounds on the maximum and the relative variations of the initial density, as well as on the intensity and duration of the pulse, ensure a strictly hydrodynamic evolution of the electron fluid without wave-breaking or vacuum-heating during its whole interaction with the pulse, while ions can be regarded as immobile. We use a recently developed fully relativistic plane model whereby the system of the Lorentz–Maxwell and continuity PDEs is reduced into a family of highly nonlinear but decoupled systems of non-autonomous Hamilton equations with one degree of freedom, the light-like coordinate ξ=ct−z instead of time t as an independent variable, and new a priori estimates (eased by use of a Liapunov function) of the solutions in terms of the input data (i.e., the initial density and pulse profile). If the laser spot radius R is finite and is not too small, the same conclusions hold for the part of the plasma close to the axis z→ of cylindrical symmetry. These results may help in drastically simplifying the study of extreme acceleration mechanisms of electrons.

Laser Wakefield Driven Generation of Isolated Carrier-Envelope-Phase Tunable Intense Subcycle Pulses

Sources of intense, ultrashort electromagnetic pulses enable applications such as attosecond pulse generation, control of electron motion in solids, and the observation of reaction dynamics at the electronic level. For such applications, both high intensity and carrier-envelope-phase (CEP) tunability are beneficial, yet hard to obtain with current methods. In this Letter, we present a new scheme for generation of isolated CEP tunable intense subcycle pulses with central frequencies that range from the midinfrared to the ultraviolet. It utilizes an intense laser pulse that drives a wake in a plasma, copropagating with a long-wavelength seed pulse. The moving electron density spike of the wake amplifies the seed and forms a subcycle pulse. Controlling the CEP of the seed pulse or the delay between driver and seed leads to CEP tunability, while frequency tunability can be achieved by adjusting the laser and plasma parameters. Our 2D and 3D particle-in-cell simulations predict laser-to-subcycle-pulse conversion efficiencies up to 1%, resulting in relativistically intense subcycle pulses.

Long propagating velocity-controlled Einstein's mirror for terahertz light conversion

We show that Einstein's relativistic mirror with long (hundreds of µm) propagation distance and controllable propagation velocity can be implemented in the form of a dense free carrier front generated by multiphoton absorption of tilted-pulse-front femtosecond laser pulses in a dielectric or semiconductor medium. The velocity control is achieved by varying the pulse front tilt angle. Simulations demonstrate that such fronts can serve as efficient Doppler-type converters of terahertz pulses. In particular, the pulse reflected from a front, generated by three-photon absorption of a Ti:sapphire laser in ZnS, can exhibit strong (up to more than an order of magnitude) pulse compression and spectrum broadening without a noticeable amplitude change. The proposed technique may be used to convert strong low-frequency terahertz pulses, generated by optical rectification of tilted-pulse-front laser pulses, to desirable temporal and spectral characteristics for a variety of applications.

THz Generation from Relativistic Plasmas Driven by Near- to Far-Infrared Laser Pulses

Terahertz pulse generation by ultraintense two-color laser fields ionizing gases with near- to far-infrared carrier wavelength is studied from particle-in-cell simulations. For a long pump wavelength (10.6  μm) promoting a large ratio of electron density over critical, photoionization is shown to catastrophically enhance the plasma wakefield, causing a net downshift in the optical spectrum and exciting THz fields with tens of GV/m amplitude in the laser direction. This emission is accompanied by coherent transition radiation (CTR) of comparable amplitude due to wakefield-driven electron acceleration. We analytically evaluate the fraction of CTR energy up to 30% of the total radiated emission including the particle self-field and numerically calibrate the efficiency of the matched blowout regime for electron densities varied over three orders of magnitude.

Pulse evolution and plasma-wave phase velocity in channel-guided laser-plasma accelerators

The self-consistent laser evolution of an intense, short-pulse laser exciting a plasma wave and propagating in a preformed plasma channel is investigated, including the effects of pulse steepening and energy depletion. In the weakly relativistic laser intensity regime, analytical expressions for the laser energy depletion, pulse self-steepening rate, laser intensity centroid velocity, and phase velocity of the plasma wave are derived and validated numerically.

Pulse shaping during Raman-seed amplification for short laser pulses

Raman-seed pulse amplification in a one-dimensional backscattering geometry is investigated with the help of numerical simulations and analytical estimates. The significant dependence of the initial amplification on the pulse form is revisited on the basis of a three-wave interaction as well as a kinetic Vlasov model. It is shown how the short duration of the input seed pulse influences its subsequent behavior, depending on plasma density and pump strength. The evolution during a "start-up period," which has been observed earlier, can be explained analytically. In the nonlinear (pump depletion) regime, the pulse generated in the start-up period will be further amplified and may evolve into a self-similar π-pulse solution. The Vlasov code predicts algebraic growth in time of the seed amplitude, similar to the findings based on self-similar solutions of the three-wave-interaction model. An initially very narrow pulse is shown to grow more slowly than an initially broad one.

Complete temporal characterization of asymmetric pulse compression in a laser wakefield

We present complete experimental characterization of the temporal shape of an intense ultrashort 200-TW laser pulse driving a laser wakefield. The phase of the pulse was uniquely measured by using (second-order) frequency-resolved optical gating. The pulses are asymmetrically compressed and exhibit a positive chirp consistent with the expected asymmetric self-phase-modulation due to photon acceleration or deceleration in a relativistic plasma wave. The measured pulse duration decreases linearly with increasing length and density of the plasma, in quantitative agreement with the intensity-dependent group velocity variation in the plasma wave.

Single-cycle strong terahertz pulse generation from a vacuum-plasma interface driven by intense laser pulses

Single-cycle strong terahertz pulses can be generated by irradiating ultrashort intense laser pulses onto a tenuous plasma slab. At the plasma surface, laser ponderomotive force accelerates electrons and induces net currents, which radiate terahertz pulses. Our theoretical model suggests that if tau_{L}>2pi/omega_{p}, with tau_{L} as the laser-pulse duration and omega_{p} as the plasma frequency, the emission frequency is around tau_{L};{-1}. On the other hand, the emission frequency is around omega_{p}/2pi if tau_{L}<2pi/omega_{p}. Our numerical simulations support the theoretical model, showing that such a terahertz source is capable of providing megawatt power, field strengths of MV/cm, and broad frequency tunability.

Magnetowave induced plasma wakefield acceleration for ultrahigh energy cosmic rays

Magnetowave induced plasma wakefield acceleration (MPWA) in a relativistic astrophysical outflow has been proposed as a viable mechanism for the acceleration of cosmic particles to ultrahigh energies. Here we present simulation results that clearly demonstrate the viability of this mechanism for the first time. We invoke the high frequency and high speed whistler mode for the driving pulse. The plasma wakefield obtained in the simulations compares favorably with our newly developed relativistic theory of the MPWA. We show that, under appropriate conditions, the plasma wakefield maintains very high coherence and can sustain high-gradient acceleration over hundreds of plasma skin depths. Invoking active galactic nuclei as the site, we show that MPWA production of ultrahigh energy cosmic rays beyond ZeV (10{21} eV) is possible.

All-optical suppression of relativistic self-focusing of laser beams in plasmas

It is demonstrated that a catastrophic relativistic self-focusing (RSF) of a high-power laser pulse can be prevented all-optically by a second, much weaker, copropagating pulse. RSF suppression occurs when the difference frequency of the pulses slightly exceeds the electron plasma frequency. The mutual defocusing is caused by the three-dimensional electron density perturbation driven by the laser beat wave slightly above the plasma resonance. A bienvelope model describing the early stage of the mutual defocusing is derived and analyzed. Later stages, characterized by the presence of a strong electromagnetic cascade, are investigated numerically. Stable propagation of the laser pulse with weakly varying spot size and peak amplitude over several Rayleigh lengths is predicted.

Electro-optic shocks from ultraintense laser-plasma interactions

Second harmonic radiation in the form of an electro-optic shock is produced in the blowout regime of a laser wakefield in a plasma. The shock is produced by the interaction between the laser field and the electron sheath surrounding the electron cavitation region. Because the sheath is thin, phase matching is unimportant, and the radiated energy grows secularly with the interaction length. The angle of emission is given by the Cherenkov angle associated with the ratio of the second harmonic phase velocity to the fundamental phase velocity. The shock formation is investigated in three dimensions via analysis and particle-in-cell simulations.

Monoenergetic electronic beam production using dual collinear laser pulses

The production of monoenergetic electron beams by two copropagating ultrashort laser pulses is investigated both by experiment and using particle-in-cell simulations. By proper timing between guiding and driver pulses, a high-amplitude plasma wave is generated and sustained for longer than is possible with either of the laser pulses individually, due to plasma waveguiding of the driver by the guiding pulse. The growth of the plasma wave is inferred by the measurement of monoenergetic electron beams with low divergence that are not measured by using either of the pulses individually. This scheme can be easily implemented and may allow more control of the interaction than is available to the single pulse scheme.

Single-cycle powerful megawatt to gigawatt terahertz pulse radiated from a wavelength-scale plasma oscillator

We propose a scheme to generate single-cycle powerful terahertz (THz) pulses by ultrashort intense laser pulses obliquely incident on an underdense plasma slab of a few THz wavelengths in thickness. THz waves are radiated from a transient net current driven by the laser ponderomotive force in the plasma slab. Analysis and particle-in-cell simulations show that such a THz source is capable of providing power of megawatts to gigawatts, field strength of MV/cm-GV/cm, and broad tunability range, which is potentially useful for nonlinear and high-field THz science and applications.

Monoenergetic beams of relativistic electrons from intense laser-plasma interactions

High-power lasers that fit into a university-scale laboratory can now reach focused intensities of more than 10(19) W cm(-2) at high repetition rates. Such lasers are capable of producing beams of energetic electrons, protons and gamma-rays. Relativistic electrons are generated through the breaking of large-amplitude relativistic plasma waves created in the wake of the laser pulse as it propagates through a plasma, or through a direct interaction between the laser field and the electrons in the plasma. However, the electron beams produced from previous laser-plasma experiments have a large energy spread, limiting their use for potential applications. Here we report high-resolution energy measurements of the electron beams produced from intense laser-plasma interactions, showing that--under particular plasma conditions--it is possible to generate beams of relativistic electrons with low divergence and a small energy spread (less than three per cent). The monoenergetic features were observed in the electron energy spectrum for plasma densities just above a threshold required for breaking of the plasma wave. These features were observed consistently in the electron spectrum, although the energy of the beam was observed to vary from shot to shot. If the issue of energy reproducibility can be addressed, it should be possible to generate ultrashort monoenergetic electron bunches of tunable energy, holding great promise for the future development of 'table-top' particle accelerators.

Electron acceleration in an ultraintense-laser-illuminated capillary

An ultraintense laser injected a 10 J of power at 1.053 microm in 0.5 ps into a glass capillary of 1 cm long and 60 microm in diameter and accelerated plasma electrons to 100 MeV. One- and two-dimensional particle codes describe wakefields with 10 GV/m gradient excited behind the laser pulse, which are guided by a plasma density channel far beyond the Rayleigh range. The blueshift of the laser spectrum supports that a plasma of 10(16) cm(-3) is inside the capillary. A bump at the high energy tail suggests the electron trapping in the wakefield.

Propagation of intense short laser pulses in the atmosphere

The propagation of short, intense laser pulses in the atmosphere is investigated theoretically and numerically. A set of three-dimensional (3D), nonlinear propagation equations is derived, which includes the effects of dispersion, nonlinear self-focusing, stimulated molecular Raman scattering, multiphoton and tunneling ionization, energy depletion due to ionization, relativistic focusing, and ponderomotively excited plasma wakefields. The instantaneous frequency spread along a laser pulse in air, which develops due to various nonlinear effects, is analyzed and discussed. Coupled equations for the power, spot size, and electron density are derived for an intense ionizing laser pulse. From these equations we obtain an equilibrium for a single optical-plasma filament, which involves a balancing between diffraction, nonlinear self-focusing, and plasma defocusing. The equilibrium is shown to require a specific distribution of power along the filament. It is found that in the presence of ionization a self-guided optical filament is not realizable. A method for generating a remote spark in the atmosphere is proposed, which utilizes the dispersive and nonlinear properties of air to cause a low-intensity chirped laser pulse to compress both longitudinally and transversely. For optimally chosen parameters, we find that the transverse and longitudinal focal lengths can be made to coincide, resulting in rapid intensity increase, ionization, and white light generation in a localized region far from the source. Coupled equations for the laser spot size and pulse duration are derived, which can describe the focusing and compression process in the low-intensity regime. More general examples involving beam focusing, compression, ionization, and white light generation near the focal region are studied by numerically solving the full set of 3D, nonlinear propagation equations.

Raman forward scattering and self-modulation of laser pulses in tapered plasma channels

The propagation of intense laser pulses with durations longer than the plasma period through tapered plasma channels is investigated theoretically and numerically. General propagation equations are presented and reduced partial differential equations that separately describe the forward Raman (FR) and self-modulation (SM) instabilities in a nonuniform plasma are derived. Local dispersion relations for FR and SM instabilities are used to analyze the detuning process arising from a longitudinal density gradient. Full-scale numerical fluid simulations indicate parameters that favorably excite either the FR or SM instability. The suppression of the FR instability and the enhancement of the SM instability in a tapered channel in which the density increases longitudinally is demonstrated. For a pulse undergoing a self-modulation instability, calculations show that the phase velocity of the wakefield in an untapered channel can be significantly slower than the pulse group velocity. Simulations indicate that this wake slippage can be forestalled through the use of a tapered channel.

Trapping, compression, and acceleration of an electron bunch in the nonlinear laser wakefield

A scheme of laser wakefield acceleration, when a relatively rare and long bunch of nonrelativistic or weakly relativistic electrons is initially in front of the laser pulse, is suggested and considered. The motion of test electrons is studied both in the one-dimensional (1D) case (1D wakefield) and in the case of three-dimensional laser wakefield excited in a plasma channel. It is shown that for definite parameters of the problem the bunch can be trapped, effectively compressed both in longitudinal and transverse directions, and accelerated to ultra-relativistic energies in the region of first accelerating maximum of the wakefield. The accelerated bunch has sizes much less than the plasma wavelength and relatively small energy spread.

Steady ion momentum in nonlinear plasma waves

The analysis of a one-dimensional two-fluid hydrodynamic model with relativistic electrons and nonrelativistic ions shows that the propagation of a nonlinear plasma wave is accompanied by a steady currentless plasma drift. Ions, due to their larger mass, appear to be the main carriers of the average momentum of the plasma wave. Two examples of nonlinear plasma waves generated by moving sources (short laser pulses and electron bunches) are analyzed to show details of the energy and momentum conservation laws.

Harmonic generation of ultraintense laser pulses in underdense plasma

We propose a nonlinear theory of the generation of harmonic radiation from the interaction of ultraintense laser beams with plasma. The harmonic generation is related to the transition of the laser-plasma equilibrium state. By taking into account correlations among sidebands, we study many sidebands comprehensively. The harmonic generation is viewed as a redistribution of laser field over different frequencies because of the requirement of system stability. We introduce a system parameter S that is related to the sideband intensity spectrum and self-consistently calculate the value of S. Our numerical experiments reveal that the variations of controllable system parameters, plasma density, and laser peak intensity have a great effect on S.

Observation of the second-harmonic generation from relativistically quivering electrons in exciting laser wakefield

The second-harmonic emission generated by the spatially asymmetric quivering electrons caused by the ponderomotive force was studied. The intensity of the second harmonic was proportional to the focused intensity of the pump pulse with the power of 1.8. This intensity dependence can be explained by the relativistic effect of the quivering electrons.

Simulations of a hydrogen-filled capillary discharge waveguide

A one-dimensional dissipative magnetohydrodynamics code is used to investigate the discharge dynamics of a waveguide for high-intensity laser pulses: the gas-filled capillary discharge waveguide. Simulations are performed for the conditions of a recent experimental measurement of the electron density profile in hydrogen-filled capillaries [D. J. Spence et al., Phys. Rev. E 63, 015401 (R) (2001)], and are found to be in good agreement with those results. The evolution of the discharge in this device is found to be substantially different to that found in Z-pinch capillary discharges, owing to the fact that the plasma pressure is always much higher than the magnetic pressure. Three stages of the capillary discharge are identified. During the last of these the distribution of plasma inside the capillary is determined by the balance between ohmic heating, and cooling due to electron heat conduction. A simple analytical model of the discharge during the final stage is presented, and shown to be in good agreement with the magnetohydrodynamic simulations.

Long plasma channels generated by femtosecond laser pulses

Generation of a long plasma channel by femtosecond laser pulses is investigated. The results show that the balance between the nonlinear self-focusing of the laser beam and plasma defocusing forms a long plasma channel, which guides the laser beam to propagate a long distance in air. This phenomenon can be used to trigger lightning.

Bulk-to-surface-wave self-conversion in optically induced ionization processes

Nonlinear time evolution of a p-polarized wave mode with inhomogeneous transverse structure producing tunnel ionization of a gas is investigated by numerical simulation and theoretical analysis. A phenomenon of trapping of electromagnetic radiation via its adiabatic conversion into surface waves guided by the field-created plasma structure is found out numerically. This process is accompanied by significant frequency downshifting of the electromagnetic radiation. The underlying physical mechanism is explained using a simple theoretical model. The described phenomena may play significant role in the self-channeling and frequency tuning of intense (approximately 10(14)-10(18) W/cm(2)) laser pulses in dense gases.

Wakefield generation and GeV acceleration in tapered plasma channels

To achieve multi-GeV electron energies in the laser wakefield accelerator (LWFA), it is necessary to propagate an intense laser pulse long distances in a plasma without disruption. One of the purposes of this paper is to evaluate the stability properties of intense laser pulses propagating extended distances (many tens of Rayleigh ranges) in plasma channels. A three-dimensional envelope equation for the laser field is derived that includes nonparaxial effects such as group velocity dispersion, as well as wakefield and relativistic nonlinearities. It is shown that in the broad beam, short pulse limit the nonlinear terms in the wave equation that lead to Raman and modulation instabilities cancel. This cancellation can result in pulse propagation over extended distances, limited only by dispersion. Since relativistic focusing is not effective for short pulses, the plasma channel provides the guiding necessary for long distance propagation. Long pulses (greater than several plasma wavelengths), on the other hand, experience substantial modification due to Raman and modulation instabilities. For both short and long pulses the seed for instability growth is inherently determined by the pulse shape and not by background noise. These results would indicate that the self-modulated LWFA is not the optimal configuration for achieving high energies. The standard LWFA, although having smaller accelerating fields, can provide acceleration for longer distances. It is shown that by increasing the plasma density as a function of distance, the phase velocity of the accelerating field behind the laser pulse can be made equal to the speed of light. Thus electron dephasing in the accelerating wakefield can be avoided and energy gain increased by spatially tapering the plasma channel. Depending on the tapering gradient, this luminous wakefield phase velocity is obtained several plasma wavelengths behind the laser pulse. Simulations of laser pulses propagating in a tapered plasma channel are presented. Experimental techniques for generating a tapered density in a capillary discharge are described and an example of a GeV channel guided standard LWFA is presented.

Simulation and design of stable channel-guided laser wakefield accelerators

Most laser wakefield accelerator (LWFA) experiments to date have operated in the self-modulated (SM) regime and have been self-guided. A channel-guided LWFA operating in the standard or resonant regime is expected to offer the possibility of high electron energy gain and high accelerating gradients without the instabilities and poor electron beam quality associated with the SM regime. Plasma channels such as those produced by a capillary discharge have demonstrated guiding of intense laser pulses over distances of several centimeters. Optimizing the performance in a resonant LWFA constrains the on-axis plasma density in the channel to a relatively narrow range. A scaling model is presented that quantifies resonant LFWA performance in terms of the maximum accelerating gradient, dephasing length, and dephasing-limited energy gain. These performance quantities are expressed in terms of laser and channel experimental parameters, clearly illustrating some of the tradeoffs in the choice of parameters. The predicted energy gain in this model is generally lower than that indicated by simpler scaling models. Simulations agree well with the scaling model in both low and high plasma density regimes. Simulations of a channel-guided, self-modulated LWFA are also presented. Compared with the resonant LWFA regime, the requirements on laser and channel parameters in the SM regime are easier to achieve, and a channel-guided SM-LWFA is likely to be less unstable than a self-guided SM-LWFA.

Stable laser-pulse propagation in plasma channels for GeV electron acceleration

To achieve multi-GeV electron energies in the laser wakefield accelerator (LWFA) it is necessary to propagate an intense laser pulse long distances in plasma without disruption. A 3D envelope equation for a laser pulse in a tapered plasma channel is derived, which includes wakefields and relativistic and nonparaxial effects, such as finite pulse length and group velocity dispersion. It is shown that electron energies of approximately GeV in a plasma-channel LWFA can be achieved by using short pulses where the forward Raman and modulation nonlinearities tend to cancel. Further energy gain can be achieved by tapering the plasma density to reduce electron dephasing.

Generation of one-cycle laser pulses by use of high-amplitude plasma waves

The dynamics of a short laser pulse located in the density trough of a background plasma wave is investigated and a scheme is proposed to compress the pulse duration by use of a high-amplitude plasma wave. The threshold amplitude of the plasma wave, at which the compressing effect just balances the dispersive spreading of the laser pulse, is estimated for certain pulse profiles. Numerical simulations are conducted with particle-in-cell codes, where a pump pulse is used to generate a high-amplitude plasma wave and a signal pulse copropagates behind. It is shown that the signal pulse can be compressed by the plasma wave from ten laser cycles to about one cycle within a millimeter in tenuous plasma only a few percent of the critical density.

Relativistic focusing and ponderomotive channeling of intense laser beams

The ponderomotive force associated with an intense laser beam expels electrons radially and can lead to cavitation in plasma. Relativistic effects as well as ponderomotive expulsion of electrons modify the refractive index. An envelope equation for the laser spot size is derived, using the source-dependent expansion method with Laguerre-Gaussian eigenfunctions, and reduced to quadrature. The envelope equation is valid for arbitrary laser intensity within the long pulse, quasistatic approximation and neglects instabilities. Solutions of the envelope equation are discussed in terms of an effective potential for the laser spot size. An analytical expression for the effective potential is given. For laser powers exceeding the critical power for relativistic self-focusing the analysis indicates that a significant contraction of the spot size and a corresponding increase in intensity is possible.

Laser pulse modulation instabilities in plasma channels

In this paper the modulational instability associated with propagation of intense laser pulses in a partially stripped, preformed plasma channel is analyzed. In general, modulation instabilities are caused by the interplay between (anomalous) group velocity dispersion and self-phase modulation. The analysis is based on a systematic approach that includes finite-perturbation-length effects, nonlinearities, group velocity dispersion, and transverse effects. To properly include the radial variation of both the laser field and plasma channel, the source-dependent expansion method for analyzing the wave equation is employed. Matched equilibria for a laser beam propagating in a plasma channel are obtained and analyzed. Modulation of a uniform (matched) laser beam equilibrium in a plasma channel leads to a coupled pair of differential equations for the perturbed spot size and laser field amplitude. A general dispersion relation is derived and solved. Surface plots of the spatial growth rate as a function of laser beam power and the modulation wave number are presented.

Excitation of nonlinear two-dimensional wake waves in radially nonuniform plasma

It is shown that an undesirable curvature of the wave front of a two-dimensional nonlinear wake wave, excited in uniform plasma by a relativistic charged bunch or laser pulse, may be compensated by radial change of the equilibrium plasma density.

Propagation of intense, ultrashort laser pulses in plasmas

We have investigated the propagation of terawatt-power laser pulses in gases. The spatial distribution of focused radiation is modified by refraction that results from the spatially inhomogeneous refractive index of the plasma generated by high field ionization. We observe Thomson scattering, stimulated Raman scattering, and large wavelength shifting of the laser light.