Particle accelerators driven by the interaction of ultraintense and ultrashort laser pulses with a plasma 1 can generate accelerating electric fields of several hundred gigavolts per metre and deliver high-quality electron beams with low energy spread 2-5 , low emittance 6 and up to 1 GeV peak energy 7,8 . Moreover, it is expected they may soon be able to produce bursts of electrons shorter than those produced by conventional particle accelerators, down to femtosecond durations and less. Here we present wide-band spectral measurements of coherent transition radiation which we use for temporal characterization. Our analysis shows that the electron beam, produced using controlled optical injection 9 , contains a temporal feature that can be identified as a 15 pC, 1.4-1.8 fs electron bunch (root mean square) leading to a peak current of 3-4 kA depending on the bunch shape. We anticipate that these results will have a strong impact on emerging applications such as short-pulse and short-wavelength radiation sources 10,11 , and will benefit the realization of laboratory-scale free-electron lasers 12-14 .The ponderomotive force generated by the focused laser pulse is proportional to the gradient of the laser intensity. It pushes electrons out of regions of high intensity and separates them from the ions, thus creating a plasma wave that propagates in the wake of the laser pulse with a phase velocity close to c, the speed of light in vacuum. The characteristic length of the accelerating cavity that forms behind the driving laser pulse is the plasma wavelength λ p . In a typical laser wakefield acceleration experiment, λ p = 10-30 µm for plasma densities n e = 10 18 -10 19 cm −3 . The electric field changes along the length of the plasma wave, therefore, to generate an electron beam with low energy spread and low divergence, the electron bunch should reside within the focusing and accelerating phase of the wave, which has a length λ p /4. These heuristic arguments indicate that one would expect the bunch duration to be ultrashort, τ < λ p /4c ≈ 10 fs (refs 9,15). However, to the best of our knowledge, such short durations have not previously been directly measured.Traditional techniques to measure the electron bunch duration, such as streak cameras and radio-frequency sweeping cavities, do not have the temporal resolution required for femtosecond bunches. Therefore, we have employed a method in the frequency domain and measured the coherent transition radiation (CTR) that is emitted by the electron bunch as it passes through a thin metallic foil. CTR is an established particle beam diagnostic and has been used to diagnose micro-structures of picosecond-bunches 16,17 and for benchmarking simulations of femtosecond-bunch dynamics
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 ...
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