Nonlinear theory of nonparaxial laser pulse propagation in plasma channels

Spiral copropagation of two relativistic intense laser beams in a plasma channel

The copropagation of two relativistic intense laser beams with orthogonal polarization in a parabolic plasma channel is studied analytically and numerically. A set of coupled equations for the evolution of the laser spot sizes and transverse centroids are derived by use of the variational approach. It is shown that the centroids of the two beams can spiral and oscillate around each other along the channel axis, where the characteristic frequency is determined both by the laser and plasma parameters. The results are verified by direct numerical solution of the relativistic nonlinear Schrödinger equations for the laser envelopes as well as three-dimensional particle-in-cell simulations. In the case with two ultrashort laser pulses when laser wakefields are excited, it is shown that the two wake bubbles driven by the laser pulses can spiral and oscillate around each other in a way similar to the two pulses. This can be well controlled by adjusting the incidence angle and separation distance between the two laser pulses. Preliminary studies show that externally injected electron beams can follow the trajectories of the oscillating bubbles. Our studies suggest a new way to control the coupling of two intense lasers in plasma for various applications, such as electron acceleration and radiation generation.

Femtosecond Laser Fabrication of Curved Plasma Channels with Low Surface Roughness and High Circularity for Multistage Laser-Wakefield Accelerators

A multistage laser-wakefield accelerator with curved plasma channels was proposed to accelerate electrons to TeV energy levels. In this condition, the capillary is discharged to produce plasma channels. The channels will be used as waveguides to guide intense lasers to drive wakefields inside the channel. In this work, a curved plasma channel with low surface roughness and high circularity was fabricated by a femtosecond laser ablation method based on response surface methodology. The details of the fabrication and performance of the channel are introduced here. Experiments show that such a channel can be successfully used to guide lasers, and electrons with an energy of 0.7 GeV were achieved.

An optically multiplexed single-shot time-resolved probe of laser-plasma dynamics

We introduce a new approach to temporally resolve ultrafast micron-scale processes via the use of a multi-channel optical probe. We demonstrate that this technique enables highly precise time-resolved, two-dimensional spatial imaging of intense laser pulse propagation dynamics, plasma formation and laser beam filamentation within a single pulse over four distinct time frames. The design, development and optimization of the optical probe system is presented, as are representative experimental results from the first implementation of the multi-channel probe with a high-power laser pulse interaction with a helium gas jet target.

Electron acceleration by a radially-polarized laser pulse in a plasma micro-channel

Encouraged by recent advances in radially-polarized laser technology, simulations have been performed of electron acceleration by a tightly-focused, ultra-short pulse in a parabolic plasma micro-channel. Milli-joule laser pulses, generated at kHz repetition rates, are shown to produce electron bunches of MeV energy, pC charge, low emittance and low divergence. The pivotal role played by the channel length in controlling the process is demonstrated, and the roles of direct and wakefield acceleration are distinguished.

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.

Raman scattering of intense, short laser pulses in modulated plasmas

We examine the exponentiation of the Raman forward scattering instability in modulated plasma channels computationally and analytically. An evolution equation for the complex phases of the Raman scattered waves treating the spatial localization and discrete nature of the channel modes is derived. Simulations with WAKE [P. Mora and T. M. Antonsen Jr., Phys. Plasmas 4, 217 (1997)] verify the theory in the linear growth regime and provide insight into the nonlinear stage of the instability when cascading and pump depletion play a role. We find that the exponentiation in modulated channels depends on two factors: the increase in coupling due to the increased plasma wavenumber in the high-density regions of the channel and a decreased coupling due to the reduced longitudinal spatial coherence. For the parameters considered, simulations show that the finite extent of the pump pulse is more significant in determining the exponentiation than phase mixing due to the transverse variation of the channel. Both the theory and simulations confirm that modulated channels allow for the stable guiding of longer pulses than nonmodulated channels.

Nonlinear pulse propagation and phase velocity of laser-driven plasma waves

Laser evolution and plasma wave excitation by a relativistically intense short-pulse laser in underdense plasma are investigated in the broad pulse limit, including the effects of pulse steepening, frequency redshifting, and energy depletion. The nonlinear plasma wave phase velocity is shown to be significantly lower than the laser group velocity and further decreases as the pulse propagates owing to laser evolution. This lowers the thresholds for trapping and wave breaking and reduces the energy gain and efficiency of laser-plasma accelerators that use a uniform plasma profile.

Inverse free electron lasers and laser wakefield acceleration driven by CO2 lasers

The staged electron laser acceleration (STELLA) experiment demonstrated staging between two laser-driven devices, high trapping efficiency of microbunches within the accelerating field and narrow energy spread during laser acceleration. These are important for practical laser-driven accelerators. STELLA used inverse free electron lasers, which were chosen primarily for convenience. Nevertheless, the STELLA approach can be applied to other laser acceleration methods, in particular, laser-driven plasma accelerators. STELLA is now conducting experiments on laser wakefield acceleration (LWFA). Two novel LWFA approaches are being investigated. In the first one, called pseudo-resonant LWFA, a laser pulse enters a low-density plasma where nonlinear laser/plasma interactions cause the laser pulse shape to steepen, thereby creating strong wakefields. A witness e-beam pulse probes the wakefields. The second one, called seeded self-modulated LWFA, involves sending a seed e-beam pulse into the plasma to initiate wakefield formation. These wakefields are amplified by a laser pulse following shortly after the seed pulse. A second e-beam pulse (witness) follows the seed pulse to probe the wakefields. These LWFA experiments will also be the first ones driven by a CO(2) laser beam.

Relativistic channeling by intense laser pulse in overdense plasmas

Channeling in overdense plasma by relativistic laser pulse is investigated. The critical laser power needed to maintain a plasma channel as well as the mode profiles of the electromagnetic fields in the channel cross section are obtained analytically. A scaling law showing that the critical power is proportional to the square of the background plasma density is found.

Asymmetric self-phase modulation and compression of short laser pulses in plasma channels

A relativistically intense femtosecond laser pulse propagating in a plasma channel undergoes dramatic photon deceleration while propagating a distance on the order of a dephasing length. The deceleration of photons is localized to the back of the pulse and is accompanied by compression and explosive growth of the ponderomotive potential. Fully explicit particle-in-cell simulations are applied to the problem and are compared with ponderomotive guiding center simulations. A numerical Wigner transform is used to examine local frequency shifts within the pulse and to suggest an experimental diagnostic of plasma waves inside a capillary.

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.

Propagation of short intense laser pulses in gas-filled capillaries

The guided laser pulse propagation and wake-field generation are studied in a wide (in comparison with the laser spot size) gas-filled capillary with an on-axis gas density depletion, which can be produced by a rapid spin of the capillary around its axis or by radially propagating shock waves generated in a piezoceramic tube. A single equation for the wake-field potential, which describes the fully relativistic plasma response in the presence of optical field ionization (OFI) of a gas, is derived and used to demonstrate a guided propagation of a short intense laser pulse over many Rayleigh lengths in a leaky plasma channel produced by the pulse due to OFI in the capillary filled with a radially inhomogeneous gas. The efficient generation of a regular wake field over long distances suitable for the laser wake-field accelerators is shown.

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 of laser wakefield acceleration of an ultrashort electron bunch

The dynamics of the acceleration of a short electron bunch in a strong plasma wave excited by a laser pulse in a plasma channel is studied both analytically and numerically in slab geometry. In our simulations, a fully nonlinear, relativistic hydrodynamic description for the plasma wave is combined with particle-in-cell methods for the description of the bunch. Collective self-interactions within the bunch are fully taken into account. The existence of adiabatic invariants of motion is shown to have important implications for the final beam quality. Similar to the one-dimensional case, the natural evolution of the bunch is shown to lead, under proper initial conditions, to a minimum in the relative energy spread.

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.

Generation of fast electrons by breaking of a laser-induced plasma wave

A one-dimensional model for fast electron generation by an intense, nonevolving laser pulse propagating through an underdense plasma has been developed. Plasma wave breaking is considered to be the dominant mechanism behind this process, and wave breaking both in front of and behind the laser pulse is discussed. Fast electrons emerge as a short bunch, and the electrostatic field of this bunch is shown to limit self-consistently the amount of generated fast electrons.

Compressing and focusing a short laser pulse by a thin plasma lens

We consider the possibility of using a thin plasma slab as an optical element to both focus and compress an intense laser pulse. By thin we mean that the focal length is larger than the lens thickness. We derive analytic formulas for the spot size and pulse length evolution of a short laser pulse propagating through a thin uniform plasma lens. The formulas are compared to simulation results from two types of particle-in-cell code. The simulations give a greater final spot size and a shorter focal length than the analytic formulas. The difference arises from spherical aberrations in the lens which lead to the generation of higher-order vacuum Gaussian modes. The simulations also show that Raman side scattering can develop. A thin lens experiment could provide unequivocal evidence of relativistic self-focusing.

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.