Spontaneous radiation emitted from relativistic electrons undergoing betatron motion in a plasma focusing channel is analyzed and applications to plasma wakefield accelerator experiments and to the ion channel laser (ICL) are discussed. Important similarities and differences between a free electron laser (FEL) and an ICL are delineated. It is shown that the frequency of spontaneous radiation is a strong function of the betatron strength parameter a β , which plays a similar role to that of the wiggler strength parameter in a conventional FEL. For a β > ∼ 1, radiation is emitted in numerous harmonics.Furthermore, a β is proportional to the amplitude of the betatron orbit, which varies for every electron in the beam. The radiation spectrum emitted from an electron beam is calculated by averaging the single electron spectrum over the electron distribution. This leads to a frequency broadening of the radiation spectrum, which places serious limits on the possibility of realizing an ICL.03.65. 02.60.Cb, Typeset using REVT E X 1

Electron self-injection into an evolving plasma bubble: Quasi-monoenergetic laser-plasma acceleration in the blowout regime" (2011 An electron density bubble driven in a rarefied uniform plasma by a slowly evolving laser pulse goes through periods of adiabatically slow expansions and contractions. Bubble expansion causes robust self-injection of initially quiescent plasma electrons, whereas stabilization and contraction terminate self-injection thus limiting injected charge; concomitant phase space rotation reduces the bunch energy spread. In regimes relevant to experiments with hundred terawatt-to petawatt-class lasers, bubble dynamics and, hence, the self-injection process are governed primarily by the driver evolution. Collective transverse fields of the trapped electron bunch reduce the accelerating gradient and slow down phase space rotation. Bubble expansion followed by stabilization and contraction suppresses the low-energy background and creates a collimated quasi-monoenergetic electron bunch long before dephasing. Nonlinear evolution of the laser pulse (spot size oscillations, self-compression, and front steepening) can also cause continuous self-injection, resulting in a large dark current, degrading the electron beam quality.

Common time-explicit numerical methods for kinetic simulations of plasmas in the lowcollisions limit fall into two classes of algorithms: momentum conserving [also known as Particle-In-Cell (PIC)] and energy conserving. Each has certain drawbacks. The PIC algorithm does not conserve total energy, which may lead to spurious numerical heating (grid heating). Its overall accuracy is at most second due to the nature of the force interpolation between grid and particle position. Energy-conserving algorithms do not exhibit grid heating, but because their formulation uses potentials, computationally undesirable matrix inversions may be necessary. In addition, compared to PIC algorithms for the same accuracy, these algorithms have higher numerical noise due to the restricted choice of particle shapes. Here we formulate time-explicit, finite-size particle algorithms using particular reductions of the particle distribution function. These reductions are used in two variational principles, a Lagrangian-based and a Hamiltonian-based in conjunction with a non-canonical Poisson bracket. The Lagrangian formulations here generalize previous such formulations. The Hamiltonian formulation is presented here for the first time. Many drawbacks of the two classes of particle methods are mitigated. For example, restrictions on particle shapes are relaxed in energy conserving algorithms, which allows to decrease the numerical noise in these methods. The Hamiltonian formulation of particle algorithms is done in terms of fields instead of potentials, thus avoiding solving Poisson's equation. An algorithm that conserves both energy and momentum is presented. Other features of the algorithms include a natural way to perform coordinate transformations, the use of various time integrating methods, and the ability to increase the overall accuracy beyond second order, including all generalizations. For simplicity, we restrict our discussion to one-dimensional, non-relativistic, unmagnetized, electrostatic plasmas.

Recent experiments with 100 terawatt-class, sub-50 femtosecond laser pulses show that electrons self-injected into a laser-driven electron density bubble can be accelerated above 0.5 gigaelectronvolt energy in a sub-centimetrelength rarefied plasma. To reach this energy range, electrons must ultimately outrun the bubble and exit the accelerating phase; this, however, does not ensure high beam quality. Wake excitation increases the laser pulse bandwidth by red-shifting its head, keeping the tail unshifted. Anomalous group velocity dispersion of radiation in plasma slows down the red-shifted head, compressing the pulse into a few-cycle-long piston of relativistic intensity. Pulse transformation into a piston causes continuous expansion of the bubble, trapping copious numbers of unwanted electrons (dark current) and producing a poorly collimated, polychromatic energy tail, completely dominating the electron spectrum at the dephasing limit. The process of piston formation can be mitigated by using a broad-bandwidth (corresponding to a few-cycle transform-limited duration), negatively chirped pulse. Initial blue-shift of the pulse leading edge compensates for the nonlinear frequency red-shift and delays the piston formation, thus significantly suppressing the dark current, making 3 the electron rest mass, n 0 is the background electron density and e is the electron charge. Even with the Lorentz factor γ g approaching 100, the bubble is a 'slow' structure capable of capturing and accelerating initially quiescent electrons of the ambient plasma [22,23,[45][46][47]. Optical diagnostics directly correlate the generation of a collimated electron beam with bubble formation [48][49][50][51][52]. While other (e.g. all-optical) injection schemes are currently being explored [53][54][55][56][57], electron self-injection has its own advantages: it greatly reduces the technical complexity of the experiment, preserving flexibility in parameters and enabling a single-stage acceleration of nano-Coulomb (nC) charge [23,47].Accelerated electrons eventually outrun the slow bubble. They exit the accelerating phase within a time intervalis the bubble radius and k p = ω pe /c. In strongly rarefied plasmas, where γ g k p R b , dephasing takes many Rayleigh lengths 5 . Propagation of the pulse over this distance relies on a combination of relativistic and ponderomotive self-guiding [58][59][60]. Upon entering the plasma, the pulse, with P P cr and duration τ L < 2π/ω pe , self-focuses until full electron cavitation is achieved, and the charge-separation force balances the radial ponderomotive force; the pulse is then guided until depletion (here, P cr = 16.2γ 2 g GW is the critical power for relativistic self-focusing [61]). As this force balance is approached, the bubble size oscillates, causing electron injection during a brief time interval. A QME electron bunch thus forms early [45,62,63]. However, transient dynamics before the onset of self-guiding [23], as well as laser evolution during self-guiding [5,7,22,23,[63][64][65], may cause ...