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.

Wakefield Generation and GeV Acceleration in Tapered Plasma Channels

Self-injection in a laser-plasma wakefield accelerator is usually achieved by increasing the laser intensity until the threshold for injection is exceeded. Alternatively, the velocity of the bubble accelerating structure can be controlled using plasma density ramps, reducing the electron velocity required for injection. We present a model describing self-injection in the short-bunch regime for arbitrary changes in the plasma density. We derive the threshold condition for injection due to a plasma density gradient, which is confirmed using particle-in-cell simulations that demonstrate injection of subfemtosecond bunches. It is shown that the bunch charge, bunch length, and separation of bunches in a bunch train can be controlled by tailoring the plasma density profile.

https://link.aps.org/pdf/10.1103/PhysRevLett.119.044801

Towards Attosecond High-Energy Electron Bunches: Controlling Self-Injection in Laser-Wakefield Accelerators Through Plasma-Density Modulation.

Plasma density gradients in a gas jet were used to control the wake phase velocity and trapping threshold in a laser wakefield accelerator, producing stable electron bunches with longitudinal and transverse momentum spreads more than ten times lower than in previous experiments (0.17 and 0.02 MeV/c FWHM, respectively) and with central momenta of 0.76 +- 0.02 MeV/c. Transition radiation measurements combined with simulations indicated that the bunches can be used as a wakefield accelerator injector to produce stable beams with 0.2 MeV/c-class momentum spread at high energies.

/pdf/plasma-density-gradient-injection-of-low-absolute-momentum-5d67un6wl8.pdf

Plasma density gradient injection of low absolute momentum spread electron bunches - eScholarship

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.

/pdf/nonlinear-pulse-propagation-and-phase-velocity-of-laser-p39ymn5ns6.pdf

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

Charged (nano)particles confined in electrodynamic traps can evolve into strongly correlated Coulomb systems, which are the subject of current investigation. Exciting physical phenomena associated to Coulomb systems have been reported such as autowave generation, phase transitions, system self-locking at the ends of the linear Paul trap, self-organization in layers, or pattern formation and scaling. The dynamics of ordered structures consisting of highly nonideal similarly charged nanoparticles, with coupling parameter of the order $\Gamma = 10^8$ is investigated. This approach enables us to study the interaction of nanoparticle structures in presence and in absence of the neutralizing plasma background, as well as to investigate various types of phenomena and physical forces these structures experience. Applications of electrodynamic levitation for mass spectrometry, including containment and study of single aerosols and nanoparticles are reviewed, with an emphasis on state of the art experiments and techniques, as well as future trends. Late experimental data suggest that inelastic scattering can be successfully applied to the detection of biological particles such as pollen, bacteria, aerosols, traces of explosives or synthetic polymers. Brownian dynamics is used to characterize charged particle evolution in time and thus identify regions of stable trapping. An analytical model is used to explain the experimental results. Numerical simulations take into account the stochastic forces of random collisions with neutral particles, the viscosity of the gas medium, the regular forces produced by the a.c. trapping voltage, and the gravitational force. We show that microparticle dynamics is characterized by a stochastic Langevin differential equation. Laser plasma acceleration of charged particles is also discussed.

The physics and applications of strongly coupled plasmas levitated in electrodynamic traps

The effect of bubble shape in laser-plasma electron acceleration was investigated. We showed the general existence of an ellipsoid bubble. The electromagnetic field in this bubble and its dependence on bubble shape were determined through theory. The electron-trapping cross-section for different bubble aspect ratios was studied in detail. When the shape of the bubble was close to spherical, the trapping cross-section reached to the maximum. When the bubble deviated from a spherical shape, the cross-section decreased until electron injection no longer occurred. These results were confirmed by particle-in-cell simulation.

Dependence of electron trapping on bubble geometry in laser-plasma wakefield acceleration

The electromagnetic field in the electron “bubble” regime for ultra-intense laser wakefield acceleration was solved using the d'Alembert equations. Ignoring the residual electrons, we assume an ellipsoidal bubble forms under ideal conditions, with bubble velocity equal to the speed of light in vacuum. The general solution for bubble shape and electromagnetic field were obtained. The results were confirmed in 2.5D PIC (particle-in-cell) simulations. Moreover, slopes for the longitudinal electric field of larger than 0.5 were found in these simulations. With spherical bubbles, this slope is always smaller than or equal to 0.5. This behavior validates the ellipsoid assumption.

Bubble shape and electromagnetic field in the nonlinear regime for laser wakefield acceleration

It is well known that if electrons are externally injected into a density upramp, then their dephasing lengths will be extended greatly, and thus these electrons will gain more energy. However, we find that a density upramp can also be used to control the beam's collimation and the emittance that occurs by self-injection in the gradient. When electrons self-inject into the wakefield in a density gradient, an electron filtering mechanism is found to occur in the injection process. Electrons with high transverse velocities are scattered and only electrons with high longitudinal to transverse velocity ratios can be candidate electrons for self-injection. This causes the trapped electrons to be more highly collimated. In addition, the injection occurs near the axis, which causes the accelerated electron beam to have reduced emittance. An ultra-collimated electron beam with an angle spread of ∼1° and emittance of ∼0.01 mm mrad is generated by a 2.5-dimensional particle-in-cell (2.5-D PIC) simulation.

Electron self-injection into the phase of a wake excited by a driver laser in a nonuniform density target

The bubble structure generated by laser-plasma interactions changes in size depending on the local plasma density. The self-injection electrons' position with respect to wakefield can be controlled by tailoring the longitudinal plasma density. A regime to enhance the energy of the wakefield accelerated electrons and to improve the beam quality is proposed and achieved using layered plasmas with increasing densities. Both the wakefield size and the electron bunch duration are significantly contracted in this regime. The electrons remain in the strong acceleration phase of the wakefield, while their energy spread decreases because of their tight spatial distribution. An electron beam of 0.5 GeV with less than 1% energy spread is obtained through 2.5D particle-in-cell simulations.

Controllable high-quality electron beam generation by phase slippage effect in layered targets

The bubble structure generated by laser and plasma interactions changes in size depending on the local plasma density. The self injection electrons position with respect to wakefield can be controlled by tailoring the longitudinal plasma density. A regime to enhance the energy of the wakefield accelerated electrons and improve the beam quality is proposed and achieved using layered plasmas with increasing densities. Both the wakefield size and the electron bunch duration are significantly contracted in this regime. The electrons remain in the strong acceleration phase of the wakefield while their energy spread decreases because of their tight spatial distribution. An electron beam of 0.5GeV with less than 0.01 energy spread is obtained through 2.5D PIC simulations.

S. Huang

Papers

Dependence of electron trapping on bubble geometry in laser-plasma wakefield acceleration

Bubble shape and electromagnetic field in the nonlinear regime for laser wakefield acceleration

Electron self-injection into the phase of a wake excited by a driver laser in a nonuniform density target

Controllable high-quality electron beam generation by phase slippage effect in layered targets

Controllable high-quality electron beam generation by phase slippage effect in layered targets