The extraordinary ability of space-charge waves in plasmas to accelerate charged particles at gradients that are orders of magnitude greater than in current accelerators has been well documented. We develop a phenomenological framework for laser wakefield acceleration (LWFA) in the 3D nonlinear regime, in which the plasma electrons are expelled by the radiation pressure of a short pulse laser, leading to nearly complete blowout. Our theory provides a recipe for designing a LWFA for given laser and plasma parameters and estimates the number and the energy of the accelerated electrons whether self-injected or externally injected. These formulas apply for self-guided as well as externally guided pulses (e.g. by plasma channels). We demonstrate our results by presenting a sample particle-in-cell (PIC) simulation of a 30 fs, 200 TW laser interacting with a 0.75 cm long plasma with density 1:5 10 18 cm ÿ3 to produce an ultrashort (10 fs) monoenergetic bunch of self-injected electrons at 1.5 GeV with 0.3 nC of charge. For future higher-energy accelerator applications, we propose a parameter space, which is distinct from that described by Gordienko and Pukhov [Phys. Plasmas 12, 043109 (2005)] in that it involves lower plasma densities and wider spot sizes while keeping the intensity relatively constant. We find that this helps increase the output electron beam energy while keeping the efficiency high.

A nonlinear kinetic theory for multidimensional plasma wave wakes with phase velocities near the speed of light is presented. This theory is appropriate for describing plasma wakes excited in the so-called blowout regime by either electron beams or laser pulses where the plasma electrons move predominantly in the transverse direction. The theory assumes that all electrons within a blowout radius are completely expelled. These radially expelled electrons form a narrow sheath just beyond the blowout radius which is surrounded by a region which responds weakly (linearly). This assumption is reasonable when the spot size of the electron beam and laser are substantially less than the blowout radius. By using this theory one can predict the wakefield amplitudes and blowout radius in terms of the electron beam or laser beam parameters, as well as predict the nonlinear modifications to the wake’s wavelength and wave form. For the laser case, the laser spot size must also be properly matched in order for a narrow sheath to form. The requirements for forming a spherical wave form, i.e., “bubble,” are also discussed. The theory is also used to show when linear fluid theory breaks down and how this leads to a saturation of the logarithmic divergence in the linear Green’s function.

A theory that describes how to load negative charge into a nonlinear, three-dimensional plasma wakefield is presented. In this regime, a laser or an electron beam blows out the plasma electrons and creates a nearly spherical ion channel, which is modified by the presence of the beam load. Analytical solutions for the fields and the shape of the ion channel are derived. It is shown that very high beam-loading efficiency can be achieved, while the energy spread of the bunch is conserved. The theoretical results are verified with the particle-in-cell code OSIRIS.

An analytical theory for the interaction of an electron bunch with a nonlinear plasma wave is developed to make it possible to design efficient laser- and/or beam-driven accelerators that generate high quality monoenergetic electron beams. This theory shows how to choose the charge, the shape, and the placing of the bunch so that the conversion efficiency from the fields of the bubble to the accelerating electrons reaches nearly 100% and the beam quality is optimized. For intense drivers the nonlinear wake is described by the shape of the bubble and beam loading arises when the radial space-charge force of the beam acts back on the electron sheath surrounding the ion channel. The modification of the wake due to the presence of flat-top electron bunches is studied and it is shown that the energy spread of an externally injected flat-top electron bunch can be kept low. The bunch profile that leads to zero energy spread is also derived.

The dynamics of plasma electrons in the focus of a petawatt laser beam are studied via measurements of their x-ray synchrotron radiation. With increasing laser intensity, a forward directed beam of x-rays extending to 50 keV is observed. The measured x-rays are well described in the synchrotron asymptotic limit of electrons oscillating in a plasma channel. The critical energy of the measured synchrotron spectrum is found to scale as the maxwellian temperature of the simultaneously measured electron spectra. At low laser intensity transverse oscillations are negligible as the electrons are predominantly accelerated axially by the laser generated wakefield. At high laser intensity, electrons are directly accelerated by the laser and enter a highly radiative regime with up to 5% of their energy turned into x-rays. PACS numbers: Valid PACS appear hereThe advent of high power lasers has led to rapid progress in the field of plasma based particle acceleration [1]. In particular, the measurement of monoenergetic electron beams from wakefields generated by short lasers [2] has stimulated great interest in producing such beams and understanding their dynamics. One potential use for these compact sources of energetic particles is as a driver for novel light sources. Laser-accelerated electrons could be injected into a magnetic undulator realizing a compact tunable-energy femtosecond x-ray source synchronized to the laser. A laser-based x-ray source could be downsized further, using the self-generated magnetic and electrostatic fields of the plasma channel as a miniature undulator [3]. For electron beams of sufficiently high quality, an ion channel laser analogous to conventional free electron lasers may be feasible [4]. X-rays can also be produced in intense laser-plasma interactions by nonlinear Thomson scattering [5].Relativistic electron beams have also been measured from interactions at very high laser intensities, where electrons gain energy directly from the laser [6]. At high intensity, the ponderomotive force of the laser can expel plasma electrons leaving a positively charged ion channel. Electrons inside the channel experience a net focusing force due to the space charge and undergo oscillation at the betatron frequency ω β = ω p / √ 2γ z0 , where ω p is the plasma frequency and γ z0 is the Lorentz factor associated with the electrons motion along the plasma channel. Electrons resonant with the laser frequency can gain energy from the transverse electric field of the laser, which can be directed into longitudinal momentum through the v × B force [7]. Accelerating charges radiate electromagnetic radiation. For small betatron strength parameters a β = γ z0 r β ω β /c 1 (undulator limit), the spectrum of the radiation will be narrowly peaked about the resonant fre-is the Doppler factor and α is the angle between the direction of observation and the direction of γ z0 [8]. This highlights the interdependency of spectral and angular distributions. As a β → 1, emitted radiation also appears at harmonics of the resonant...