Attosecond Electron Bunches N. Naumova, 1, * I. Sokolov, 2 J. Nees, 1 A. Maksimchuk, 1 V. Yanovsky, 1 and G. Mourou 1 1 Center for Ultrafast Optical Science and FOCUS Center, University of Michigan, Ann Arbor, Michigan 48109, USA 2 Space Physics Research Laboratory, University of Michigan, Ann Arbor, Michigan 48109, USA (Received 21 April 2004; published 4 November 2004) Electron bunches of attosecond duration may coherently interact with laser beams. We show how p-polarized ultraintense laser pulses interacting with sharp boundaries of overdense plasmas can produce such bunches. Particle-in-cell simulations demonstrate attosecond bunch generation during pulse propagation through a thin channel or in the course of grazing incidence on a plasma layer. In the plasma, due to the self-intersection of electron trajectories, electron concentration is abruptly peaked. A group of counterstream electrons is pushed away from the plasma through nulls in the electromagnetic field, having inherited a peaked electron density distribution and forming relativistic ultrashort bunches in vacuum. DOI: 10.1103/PhysRevLett.93.195003 PACS numbers: 52.38.Kd, 52.27.Ny, 52.65.Rr The attosecond temporal domain is of interest, not only for studies of atomic and molecular dynamics [1], but also for the generation of high fields and coherent x rays. We have previously shown how electromagnetic pulses of attosecond duration can be formed by a laser pulse that self-organizes its own reflection from an overdense plasma [2]. In that work, the short interaction length imposed by the overdense plasma fostered fine structure in the resulting radiation. Indeed, this effect is so efficient that it could be applied to bring us close to the critical field, which bears electron-positron pairs from vacuum, because the attosecond pulses could, in principle, be focused to a much smaller spot [3]. Experimentally, with the reduction of the focal volume of the laser pulse [4], a highly relativistic intensity of 10 22 W=cm 2 has been achieved [5], with 0:8-m 30-fs laser pulses focused to a 0:8-m diameter spot. Here we demonstrate that a relativistically strong (a 0  eE 0 =m e ! 0 c> 1) tightly fo- cused short laser pulse can, interacting with an overdense plasma, generate electron bunches of attosecond duration. These bunches could be applied to plasma wakefield acceleration, attosecond electron diffraction and micros- copy, and, via Thomson scattering, to coherent x-ray production and radiography. Laser-plasma interactions that drive electrons in over- dense plasmas have been extensively investigated theo- retically and experimentally (see the review in Ref. [6]). Recently electron jets have been directly observed in experiments during the interaction of p-polarized laser pulses with solid targets [7], and indirect evidence for the same effect (jetlike x-ray emission) has been obtained with s-polarized laser pulses [8] as well. Collimated elec- tron jets for both polarizations have been observed in simulations of overdense plasma [9–11]. Evidence of ul- trashort electron bunches has been found experimentally at the rear surface of thick solid targets [12]. The electron ejection was assigned to either vacuum or j  B heating mechanisms [13,14], and their collimation to self- generated quasistatic magnetic fields [15]; however, the details of electron bunching were not given by these authors. In this Letter we discuss the conditions that are re- quired for efficient backward Thomson scattering and we demonstrate in detail, with the help of particle-in-cell (PIC) simulations, how overdense plasmas, reflecting rel- ativistically intense tightly focused ultrashort pulses, be- come sources of freely propagating attosecond electron bunches. We also show the high conversion efficiency of grazing incidence p-polarized laser pulses impinging on overdense plasmas to attosecond electron bunches and attosecond electromagnetic pulses. Let us consider an electron beam interacting with a powerful electromagnetic wave. Among different kinds of interaction is Thomson scattering, which can convert the powerful laser wave to a highly collimated x-ray beam [16]. Straightforward estimates result in the evident considerations, that the efficiency of this interaction cru- cially depends on the ability to form the said electron beam into electron bunches, and that, for this interaction to be coherent, the bunch thickness, d, in the direction of the electron propagation should be much less than the wavelength, , of the electromagnetic wave (i.e., their duration should be in the attosecond range for 0:8-m light). In order to discuss the efficiency of Thomson scattering in more detail, let us establish a theoretical framework to show how the electron bunch duration influences the scattering efficiency. Consider a single electron slab mov- ing with a positive velocity V> 0 in the laboratory frame K. Assuming the electron bunch thickness to be d 0 in the K 0 frame, in which the bunch is at rest, in the K frame, the thickness becomes: d  d 0 =, where  1  V 2 =c 2  1=2 . The seed pulse, with frequency ! in the K frame, counterpropagates with respect to the electron bunch. In the K 0 frame, the Doppler shifted frequency equals ! 0  !1  V=c both for seed and reflected waves. In the K frame, the reflected wave frequency is larger due to the double Doppler effect: ! refl  !1  V=c 2  2  4! 2 . VOLUME 93, NUMBER 19 PHYSICAL REVIEW LETTERS week ending 5 NOVEMBER 2004 195003-1 0031-9007= 04=93(19)=195003(4)$22.50  2004 The American Physical Society 195003-1