laser-driven plasma-based accelerators: wakeﬁeld...

PHYSICS OF PLASMAS VOLUME 5, NUMBER 5 MAY 1998

Laser-driven plasma-based accelerators: Wakefield excitation, channelguiding, and laser triggered particle injection *

W. P. Leemans,†,a) P. Volfbeyn, K. Z. Guo, and S. ChattopadhyayErnest Orlando Lawrence Berkeley National Laboratory, University of California at Berkeley, Berkeley,California 94720

C. B. Schroeder, B. A. Shadwick, P. B. Lee, and J. S. WurteleUniversity of California at Berkeley, Berkeley, California 94720

E. EsareyNaval Research Laboratory, Washington, DC 20375-5320

~Received 18 November 1997; accepted 18 February 1998!

Plasma-based accelerators are discussed in which high-power short pulse lasers are the powersource, suitably tailored plasma structures provide guiding of the laser beam and support largeaccelerating gradients, and an optical scheme is used to produce time-synchronized ultrashortelectron bunches. From scaling laws laser requirements are obtained for development of compacthigh-energy accelerators. Simulation results of laser guiding and wakefield excitation in plasmachannels, as well as laser-based injection of particles into a plasma wake, are presented. Details ofthe experimental program at Lawrence Berkeley National Laboratory on laser guiding, laserwakefield-based accelerators, and laser triggered injection are given.@S1070-664X~98!96705-2#

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I. INTRODUCTION

As an alternative to rf linear accelerators~linacs!, laser-driven plasma-based accelerators1 are being studied at various universities and laboratories around the world.2 In anal-ogy with rf linacs, the plasma-based accelerator needconsist of an injector, an accelerating structure with longdinal electric fields that provides mode control for the accerating fields as well as guiding for the laser, and a suitalaser driver. The most significant differences between ladriven accelerators and rf accelerators are the two to thorders of magnitude larger longitudinal gradient and equsmaller wavelength of the accelerating fields. Wavelengon the order of 100mm are used in laser-driven acceleratocompared to several centimeters in rf linacs. In Sec. IIconcept of laser wakefield excitation is discussed and simscaling laws for the design of laser wakefield experimeare presented. Plasma channels are discussed as meaguiding a high-intensity laser pulse and wake excitation oextended distances. Simulation results from a numerical cmodeling the wakefield dynamics in a plasma channelpresented.

Production of electron beams with good pulse-to-puenergy stability and with low momentum spread using shwavelength structures places severe constraints on thechronization between the injected bunch and the wakefias well as on the bunch length. These requirements areyond the state-of-the-art performance of photocathodeguns. Novel schemes that rely on laser triggered injectionplasma electrons into plasma wakes have recently bproposed.3,4 These schemes are discussed in Sec. III, incling particle tracking simulations of laser injection. In Se

*Paper IWepT-1 Bull. Am. Phys. Soc.42, 1970~1997!.†Tutorial speaker.a!Electronic mail: [email protected]

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IV, recent progress will be presented of the experimenlaser wakefield accelerator program at Lawrence BerkeNational Laboratory~LBNL !. Section V is the conclusion.

II. LASER WAKEFIELD EXCITATION AND GUIDING

The laser driver in a plasma-based accelerator can econsist of a single large-amplitude pulse~so-called ‘‘laserwakefield accelerator,’’ LWFA1,5!, a train of pulses withfixed spacing~so-called ‘‘plasma beat wave acceleratorPBWA,1,6!, or a train of pulses with variable spacing anpulse widths~so-called ‘‘resonant laser plasma acceleratoRLPA7!. In the case of the LWFA, the laser pulse duratican either be matched to the plasma period~‘‘standard’’ re-gime! or be many plasma periods long~‘‘self-modulatedregime’’ 8 or ‘‘Raman forward scattering’’ regime9!. Scalinglaws for wakefield generation using standard LWFA in uform plasmas and in plasma channels are discussed nex

A. Uniform plasma

The laser driver will be assumed to have a pulse lencomparable to the plasma period, i.e.,vpt5kp. Heret isthe laser pulse width@full width at half-maximum~FWHM!#,vp5(4pn0e2/m)1/2 is the plasma frequency for an ambieplasma densityn0 , andk is a scaling factor of order unity.10

Also, m ande are the electron rest mass and charge, resptively. The normalized laser strengtha5eE'l/2pmc2, isrelated to the laser intensity,I , and powerP, at a wave-length,l, by

a>8.65310210l~mm!I 1/2~W/cm2!

>6.82l~mm!A P~TW!

@r s~mm!#2, ~1!

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1616 Phys. Plasmas, Vol. 5, No. 5, May 1998 Leemans et al.

whereE' is the transverse electric field of the laser,c is thespeed of light in vacuum,r s is the laser spot size (E'

}e2r 2/r s2) and I 52P/(pr s

2). The laser pulse will generateplasma density modulation,dn, in a uniform plasma withdensity n0 according to the equation1,2,5,8,10 (]2/]z21kp

2)3(dn/n0)5(]2/]z2)(a2/2). Herez5z2ct and kp5vp /c.It is assumed thatr s is much larger than the plasma wavlength, i.e.,kp

2r s2@1, that the density modulation is sma

dn2/n02!1, and thata2!1. The required plasma density fo

optimum excitation in a uniform plasma has been calculafor various laser pulse shapes,10 and is given by

n0~cm23!5k2

•3.131021

t2~ fs!, ~2!

wherek depends on the laser pulse shape, e.g.,k50.75 for aGaussian laser pulse.10 The plasma wavelengthlp corre-sponding to the matched plasma density can be writtenlp~mm!50.6t~fs!/k. For example, the matched density for50 fs long Gaussian pulse is approximately 731017 cm23

and the plasma wavelength is about 40mm. The ratio ofplasma density to critical density ,nc ~the density for whichthe plasma frequency equals the laser frequency! for thiswavelength is only about 431024, and hence beam refraction issues are expected to play a minimal role in the progation through the plasma.11

The peak longitudinal electric field strengthEmax in onedimension~1D! is given by2,10

Emax~GeV/m!>9.743104S l0

r sD 2 kP~TW!

t~ fs!, ~3!

where it is assumed thata2 and thedn/n0 are both much lessthan unity.

For an accelerating distance limited to the diffractilength Ldiff5pZR5(pr s)

2/l, where ZR is the Rayleighlength of a Gaussian beam~i.e., no guiding! the maximumenergy gain of a test particle is2,10

DWdiff~MeV!5960kl0~mm!

t~ fs!P~TW!

>576l0~mm!

lp~mm!P~TW!, ~4!

which is independent of the laser spot size. As an examfor a laser producing 5 TW in 50 fs~i.e., 40 mm plasmawavelength! at a wavelength of 0.8mm, DWdiff557 MeV.Also, from Eq.~4!, the energy gain is inversely proportionto the number of laser wavelengths per plasma perHence, for constant laser power, the same energy gaiobtained in a standard LWFA using a 100 fs long pulse fra l51 mm laser as for a 1 pslong pulse from al510mmlaser. However, the amount of required laser energy willten times larger for the 10mm wavelength laser driver.

Assuming that diffraction of the laser pulse can be ovcome by guiding inside a plasma channel, and that the mmum distance of acceleration is limited to the dephaslength,Lp5lp

3/l2, the maximum energy gain is then2,10


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From Eq.~5!, it can be seen that the maximum energy gainindependent of the laser wavelength.

B. Modeling of laser wakefield dynamics in channels

To overcome the limitation on the acceleration distandue to laser beam diffraction, relativistic guiding2,12 andplasma channel guiding have been proposed.2,10,13–16

Self-guiding17,18 and channel guiding19 of laser pulses hasbeen demonstrated experimentally. In the absence oplasma wave,dn050, the general condition8 to relativisti-cally guide~i.e., r s5const! a long, axially uniform pulse in aplasma isP/Pc>12Dn/Dnc . In the limit Dnp5dn050, itcan be shown that the relativistic guiding of a long puoccurs when the laser power satisfiesP>Pc . For shortpulses the relativistic correction to the index of refractionexactly canceled by thedn/n0 of the excited plasma wakeOn the other hand, in the limitsP/Pc!1 anda2!1, it can beshown that a parabolic density channelDnp5Dnr2/r s

2 canguide a Gaussian laser pulse, provided that the channel dsatisfiesDn>Dnc , where Dnc5(pr er s

2)21 is the criticaldepth,14 and r e5e2/mec

2 is the classical electron radius.Previous theoretical studies of plasma wakes in chan

have considered either stepfunction transverse densityfiles, for which there is an exact expression for the wake,alternatively, parabolic profiles. The drive pulse propagattheory is simpler for a parabolic profile, but until now thwake calculation has been made, assuming the densitydient is weak. Hollow channels, while perhaps difficultrealize in the laboratory, have many desirable propertiesacceleration,10,14–16 such as~up to ordervp

2/v2! a trans-versely uniform accelerating field and linear focusing forcPlasma channel profile control is therefore a key issue: bthe transverse profile of the wakefield structure left bylaser pulse and the damping of the wakefields in timeindeed determined by the shape of the plasma channel. Nwe discuss theoretical efforts on modeling the excitationplasma wakes in channels, and in Sec. IV we discuss expmental progress on characterizing plasma channel profile

As part of an ongoing program of developing efficienumerical tools for designing plasma-based acceleratorsvelopment is underway of a code20 for simulating wakefieldgeneration and laser propagation in a plasma channel, wthe plasma electrons are modeled as a cold, nonrelativfluid. Although fluid codes cannot account for trappparticles21 or wave breaking,22 as well as other purely kineticeffects, they have the advantage that one has control ovedetailed physics involved.

In the fluid code the plasma is described by a densfield, n, and velocity field,v. Newton’s second law and conservation of mass yield the equations

]v

]t1v–“v5

q

m S E1v

c3BD ,

]n

]t1“–~nv!50, ~6!

where the electric and magnetic fields are coupled toplasma through Maxwell’s equations:


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1617Phys. Plasmas, Vol. 5, No. 5, May 1998 Leemans et al.

FIG. 1. Equilibrium plasma density used in the computations. The horizontal axis is in unitskpx and the vertical axis is plasma density normalized to ambidensityn0.

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whereni is the fixed background ion density. These equtions are linearized about an equilibrium electron densityn0 .Note that although nonuniform equilibria are hydrodynamcally unstable, experiments operate on a much shorter tscale than hydrodynamic instability. The linear systemthen further simplified by transforming to a frame comovinwith the laser pulse and assuming the system is nonevolvi.e., all quantities depend only uponj5z2ct and r' . Byadopting slab geometry, we reduce this to a one-dimensio~1D! time-dependent problem, withj taking the role of thetime-like variable. Under these assumptions, the equatidescribing the wakefields~E andB! in the region behind thelaser pulse are given by

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These equations present a boundary-value problemx~the remaining transverse dimension! and an initial-valueproblem inj ~the distance from the laser pulse!. While ourpreliminary code is based on a reduced set of fluid equati@Eq. ~8!#, we have obtained some interesting results thatlustrate the utility of fluid models. In particular, for nonunform equilibrium plasma density~for example, see Fig. 1!,we observe dissipation of the wakefields and a related23 fine-scale spatial structure in the electric and magnetic fields. Tdynamics of a wakefield in a nonuniform plasma are shoin Fig. 2. Initially, as seen in Fig. 3, the various plasma fiel

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FIG. 2. Longitudinal plasma electric field structure in a narrow channel~see Fig. 1! showing the dynamics of the wake in the region behind the laser pu
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FIG. 3. Transverse cross section of the fields atj/vp052.88. The horizontal axis is in unitskpx and the vertical axis is dimensionless field amplitu~arbitrary units!.

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and densities are slowly varying in space with scale lengcomparable to the scale of the equilibrium density profile.this system evolves, the large longitudinal electric field dsipates. The energy associated with this field is transferreboth the transverse electric field and the transverse veloof the electrons in the plasma walls. In the region whereequilibrium density is varying, the fields, as well as the traverse current density and the perturbed plasma densityvelop fine-scale spatial structure with significant amplituFor example, atj/vp0'30, the longitudinal electric field hadissipated to approximately 30% of its initial value and a fispatial structure, with wave numberk'30kp , is clearly evi-dent~see Fig. 4!. These results are in close agreement witLaplace transform analysis,24 which yields the damping rateand oscillation frequency of the channel mode. The traverse current density develops an increasing amounshear,“v, confined to the region wheredvp /dxÞ0, i.e., the


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channel walls. The net current in the wall is significanreduced due to this highly sheared velocity~and current! dis-tribution, leading to a much reduced longitudinal field oaxis. Although the present code does not include the nonear termv.“v, the qualitative aspect of the field distributiois believed to be accurately modeled, for sufficiently sminitial fields ~i.e., a!1!. Modifications to this behavior dueto nonlinear effects will be reported in a future paper.20

Recent work has also concentrated on understandhow the driving laser pulse evolves as it propagates throa uniform plasma and through a channel.25 From simple one-dimensional scaling laws, laser wavelength reddeningpulse length shortening are qualitatively described. Odimensional self-consistent equations that provide a detadescription of the laser pulse evolution for the case of progation in a uniform plasma, have been extended to treatcase of laser pulse propagation in a hollow channel.25 The

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FIG. 4. Transverse cross section of the fields atj/vp0529.92. The horizontal axis is in unitskpx and the vertical axis is dimensionless field amplitu~arbitrary units!.

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coupling between the plasma and the laser pulse was calated using energy conservation and a simple methodinferring the plasma wake characteristics from measuremof changes in phase and amplitude of the driving laser pwas obtained. The implications of the changes in laser pproperties on pump depletion, and hence efficiency, of lawakefield accelerators are being studied theoretically.

III. LASER INJECTION

As discussed in the Sec. I, the generation of electbunches with stable energy and low momentum spread uplasma structures with a characteristic scale length onorder of a few tens ofmm, requires femtosecond electrobunches to be generated with femtosecond synchronizawith respect to the plasma wake. All-optical methods habeen proposed for injection into a standard LWFA usingfirst laser pulse to generate the wakefield~i.e., plasma oscil-lation! and a second to locally dephase electrons that tcan get trapped in the plasma wake.3 Recently, a scheme habeen proposed4 that relies on the use of three collinear laspulses: an intense laser pulse~denoted by subscript 0! thatgenerates a large wakefield (.20 GV/m), and two counter-propagating injection pulses~denoted by subscript 1 andfor forward and backward, respectively!. This ‘‘colliding’’laser pulse scheme for laser triggered injection of electrondiscussed next. The frequency, wave number, and normized intensity of the three pulses are denoted byv i , ki , andai ( i 50,1,2), respectively. Figure 5 shows the profiles ofpump lasera0 , the wake potentialf, and the forwarda1

injection pulse, all of which are stationary in thec5kp(z2vp0t) frame, and the backward injection pulsea2 thatmoves to the left, wherevp0'c is the phase velocity of thewake. Furthermore,v15v02Dv, v25v0 , and v0@Dv@vp are assumed, such thatk252k0 andk1'k0 . When theinjection pulses collide~some distance behind the pump! inthe plasma wake of the pump laser, they generate a sphase velocity ponderomotive beat wave. This beat wavecause electrons, undergoing a plasma oscillation causea0 , to acquire a momentum and phase change sufficientrapping.

FIG. 5. Profiles of the pump lasera0 , the wakef, and the forwarda1

injection pulse, all of which are stationary in thec5kp(z2vp0t) frame, andthe backward injection pulsea2 that moves to the left at'2c.


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In the 1-D limit (kpr s@1), the equations of motion of anelectron in the longitudinal, electrostatic plasma wa@f(c)5f0 cosc# and the electromagnetic fields of the coliding laser pulses (aW 5ai@ x sinci1y cosci#) is given by

dz

dt5bz ,

d~gbz!

dt5

]f

] z2

1

2g

]a2

] z,

dg

dt5bz

]f

] z1

1

2g

]a2

]t.

~9!

Herea25a121a2

212a1a2 cos(c12c2) is the ponderomotivepotential produced by the beating of the two colliding pulsandc i5ki(z2bf ict)1w i the phase of the electromagnetfield with phase velocitybf ic5v i /ki . Temporal and spatiacoordinates have been normalized with respect tovp andkp ,respectively, and potentials have been normalized withspect to the rest mass energy of the electron. Also, the pand counterpropagating laser pulses are assumed to havposite polarization, such thataW 0•aW 250.

Equation~9! is solved numerically and the particles aloaded with a uniform distribution in phase, wherec j is thephase of thej th electron on an untrapped wake orbit, with

bz j5bf2@11f~c j !#Abf

2 211@11f~c j !#2

b021@11f~c j !#

2 . ~10!

Herebz j is chosen such that the electrons are at rest priothe wake generation, i.e., 15g j (12bfb j )2f(c j ) andbf5vp0 /c. As an example, Fig. 6 shows the orbit in phaspace~gb,c! of a single particle in the plasma wake wit~solid curve! and without~dashed curve! the colliding pulses.The simulation parameters weref50.7, a15a250.5, lp

540mm, l05l250.8mm, l150.9mm, and laser pulselengthsL15L2510mm. As can be seen from Fig. 6, theffect of the beating of the colliding pulses is to causemomentum and phase shift across the plasma wake setrix from an untrapped to a trapped orbit. Figures 7~a!–7~d!show the electron energy versus the phase in the wake~dots!,before, during, and after the laser pulses collide, withseparatrix that distinguishes the trapped and untrappedgions superimposed~a dashed line!.

Particle tracking simulations in 1D4 and 3D26 indicatethat the production of high-current electron bunches as s

FIG. 6. Orbit in phase space~gb,c! of a single particle in the plasma wakwith ~solid curve! and without ~dashed curve! the colliding pulses. Thesimulation parameters weref50.7, a15a250.5, lp540mm, l05l2

50.8mm, l150.9mm, and laser pulse lengthsL15L2510mm.



FIG. 7. Snapshot in time of the particle energy before~a!, during ~b!, and after~c!, ~d! the overlap of the laser pulses. Superimposed~dashed line! is theseparatrix from the plasma wake. Particles inside the separatrix are trapped and accelerated.

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as 3 fs, with a mean energy on the order of 25 MeV annormalized energy spread of 0.3% are possible after anceleration distance of 1.5 mm, using injection laser puintensities on the order of 1017 W/cm2. The number oftrapped electrons in a plasma with a density of31017 cm23 is on the order of 106, with a normalized emit-tance on the order of 1 mm mrad. Detailed parametric stuof the beam dynamics in one and three dimensions arederway to completely characterize the longitudinal and traverse phase space properties of the trapped elecbunches.26

IV. LWFA LASER SYSTEM AND CHANNELINTERFEROMETRY RESULTS

As discussed in Sec. II, the standard LWFA schemequires a laser system that is capable of generating high ppower ~TW! short (,100 fs) laser pulses with a duratiomatched to the plasma period. Second, overcoming difftion of the laser pulse by relying on channel guiding, i.increasing the acceleration distance, requires a multi-pslaser pulse for plasma channel generation.19 Third, time-synchronized pulses are needed for diagnosing channelmation and for probing wakefield characteristics. Andnally, a laser triggered injection scheme relies on near persynchronization between the drive laser pulse and thecolliding laser pulses. Furthermore, the production ofelectron beam with an average beam current comparabstandard rf technology demands all these laser pulses tgenerated at a high repetition rate~10 Hz or more!. Next, wewill discuss a multiterawatt laser system that is being builLawrence Berkeley National Laboratory~LBNL !, with theunique design feature that such perfectly time-synchronipulses with different time structure and energy are produfrom a single master oscillator laser. We also present reresults on time-resolved studies of laser-produced pla


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channels. As discussed in Sec. II, knowledge of the plaschannel transverse profile is essential in determiningcharacteristics of the wakefield profiles.

A. Laser system

The laser system starts with a Kerr lens mode lockTi:Al 2O3 oscillator, lasing at about 0.8mm ~‘‘red’’ beam!,which produces a 90 MHz train of pulses with an averapower of about 0.25 W. The spectral bandwidth~and hencepulse length! is controllable from about 10–60 nm with aintracavity slit. The oscillator pulses are first stretched bsingle grating~1200 g/mm groove density! all-reflective op-tics stretcher to a length of up to 300 ps, controllable throuthe bandwidth of the injected oscillator pulses. The stretcpulses are amplified in a regenerative amplifier, whichpumped with a 1 kHz intracavity doubled Nd:YLF laser. Thoutput of the amplifier is split into two beams, with onbeam~about 5% energy! being sent to the built in compressor and the remaining 1.2–1.5 mJ sent to a two-pass prealifier. The compressed beam is frequency doubled~400 nm‘‘blue’’ beam! and is used as the probe beam for the plasinterferometry diagnostic, which will be described below.

The three-pass preamplifier Ti:Al2O3 crystal~1 cm diam,1.5 cm long!, pumped by typically 380 mJ of 532 nm radiation from a commercial Q-switched, frequency doublNd:YAG laser operating at 10 Hz, produces about 45–50per pulse. The pump fluence in the preamplifier is ab3.2 J/cm2. The pulses are then amplified in a 212 pass mainamplifier. The main amplifier crystal~1.5 cm diam, 1.5 cmlong! is pumped from both sides with 9 mm beams containg up to 1 J energy~per side! in a 7–8 ns long pulse at 53nm. The 532 nm radiation is produced by a frequendoubled Nd:YAG laser system that consists of an oscillatoamplifier Q-switched laser that generates a 1.2 J flatmode that is relay imaged on the input of two amplifier armeach having two amplifier heads. The.2 J output per arm is


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frequency doubled and relay imaged onto the Ti:Al2O3 tomaintain a flat top pump profile. At the present time, usintotal of 1.8 J pump beam, we have produced about 400after passing the amplifier crystal twice.

About 60% of the pulse energy is directed towardsingle grating, folded vacuum compressor to produce abo100–120 mJ pulse in 70–75 fs measured using a frequeresolved optical grating system~FROG!.27 This short pulsewill be used for wake excitation experiments. Calculatioindicate that gain saturation in the Ti:Al2O3 crystal after twopasses is expected to be minimal and therefore cause nonificant spectral distortion. The remaining pulse enedouble passes the main amplifier again, resulting in anergy of 400–500 mJ. This long pulse is used for the prodtion of channels.19 Optical delay lines have been implemented to ensure proper timing between the terawatt puthe long pulse and the blue probe pulse.

B. Interferometry of laser-produced plasma channels

The measurement of density profiles in laser-produplasma channels through interferometry28 has shown that therequired density profile can indeed be achieved for guidof laser pulses over distances long compared to the Rayllength.19 Here, we report recent results on plasma productand the interferometric measurement of plasma density

FIG. 8. Two-dimensional interferogram and phase shift profile obtainedpropagating a 400 nm wavelength probe beam transversely throuplasma, immediately after~a!, ~b! and 500 ps after ionization~c!, ~d!. Theplasma was produced in a static fill of N2 by a laser pulse~10 mJ in 150 ps,1014 W/cm2!.


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files using the compressed and uncompressed regeneramplifier and preamplifier output. The goal of these expements is to gain a detailed understanding of the channelmation and its control through the laser pulse parameter

A Mach–Zehnder-type interferometer with a measurspatial resolution of 4mm was used to measure the linintegrated laser-produced plasma density. This interferoeter measures the relative spatial phase shift betweenblue ~400 nm! 50 fs pulses: one propagating through plasand the other one propagating through air. Figure 8 showtwo-dimensional interferogram and phase shift profile otained by propagating the probe beam through a plasmaduced with an uncompressed pulse~10 mJ energy, 150 ps! inN2, immediately after laser ionization has occurred~a!, ~b!and about 500 ps later~c!, ~d!. The laser beam was focusedown with an F/4 spherical lens to a 7mm diam spot in air,yielding a peak intensity of 1014 W/cm2. Phase retrieval ofthe interferogram was done with a spectral frequencymodulation algorithm29 and plasma density versus positiowas obtained with a robust Abel inversion technique.30 Bydelaying the blue beam in time with the ionizing beaplasma expansion, and channel formation was observedseen in Fig. 9~a!. From the rate of expansion@Fig. 9~b!# wehave inferred an ion acoustic speed of 63106 cm/s.28,31 Wefind that the average ionization degree is about 3, resultina plasma temperature of about 65 eV. The expansionfound to evolve ast1/2, as expected from theory.31 From the

ya

FIG. 9. ~a! Plasma density profiles obtained through Abel inversion ofline profile through the phase shift contours@Figs. 8~b!, 8~d!# at the positionsmarked by the arrows.~b! Plasma size, obtained from laser interferogramversus the probe beam delay time. The plasma was produced by focuslaser beam~10 mJ energy in 150 ps! into a static fill of N2 gas at a pressureof 380 Torr. The data is in good agreement with at1/2 dependence~solidcurve!, as expected from theory.30


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discussion in Sec. IV B, such a channel is capable of guida laser pulse. Integration of the obtained three-dimensiodensity profiles indicates that there is an increase of ab10%–20% of the total number of electrons, in agreemwith hydrodynamic simulations that indicate continuing clisional ionization as the shock wave expands outwaChannel formation over longer lengths~0.5 cm–1 cm! as afunction of laser parameters is currently being studied igasjet to avoid ionization induced refraction,11 associatedwith the use of a static fill. These experiments aim atoptimization of the channel shape through control ofamount of laser heat deposition~i.e., inverse brehmsstrahung!, with the goal of guiding the high-intensity ultrashopulses in channels and the excitation of plasma wakesproperties suitable for acceleration of particles.32 Experimen-tally measured profiles will be used to calculate expecwakefield profiles as discussed in Sec. II.

V. CONCLUSION

Scaling laws have been presented for designing laguiding and wakefield excitation experiments. From a 1analysis, energy gain in a standard LWFA without changuiding is shown to be proportional to the laser power athe ratio of laser to plasma wavelengths, i.e., inversely pportional to the number of laser periods per plasma perThrough the dependence on laser energy, however, showavelength lasers, capable of producing ultrashort puand hence ultrahigh peak powers, are favored. In the casa channel guided LWFA, the energy gain is proportionalthe ratio of laser intensity and plasma density, which isdependent of the laser wavelength.

Simulation results from a fluid-based code on the lawake dynamics in channels have been presented. Suchcodes have the advantage over particle-in-cell~PIC! codesthrough the control of the detailed physics used in the moand through the computational speed, which is a direct aioptimization of experiments, with quick turnaround time. Fnonuniform equilibrium plasma density, we observe dissition of the wakefields and a related fine-scale spatial stture in the electric and magnetic fields.

The effect of the plasma on the laser pulse evolution iuniform plasma and a channel has also been studied. Fsimple one-dimensional scaling laws, laser wavelength rdening and pulse length shortening have been qualitatidescribed.

We have also discussed a novel scheme for particlejection into plasma wakes based on a colliding laser puscheme. Simulations indicate that the physical mechanfor the particle trapping is a momentum and phase kcaused by the ponderomotive beat wave potential of thecounterpropagating, colliding laser pulses. Particle tracksimulations in one dimension further indicate that productof high-current electron bunches as short as 3 fs, with a menergy on the order of 25 MeV and a normalized enespread of 0.3% are possible after an acceleration distanc1.5 mm, using injection laser pulse intensities on the orde1017 W/cm2.


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Finally, progress on the experimental program at LBNhas been presented. A multiterawatt laser system, whiccapable of producing perfectly time-synchronized lapulses with different pulse lengths and energies is neacompletion. Time-resolved interferometric studies on plaschannel production for the guiding of high-intensity laspulses are underway. Laser ionization and heating of plashas been observed, leading to plasma density channelaser-produced plasmas. The present experiments arecentrating on control of the plasma channel propertieslaser-ionized gas jets, through laser pulse length and enand on the propagation of laser pulses with intensities onorder of 1018 W/cm2. Experimentally measured plasmchannel profiles will be used in the fluid codes to predwakefield profiles excited by propagating a short intenseser through the channel.

Last, laser injection using the colliding laser pulscheme will be studied experimentally. A second Ti:Al2O3

amplifier chain is planned to increase the available lapower to the 10 TW level, and a double focusing magnespectrometer and femtosecond electron bunch measusystem are being designed for measuring the energy strum and electron bunch length, respectively.33

ACKNOWLEDGMENTS

We would like to acknowledge useful discussions wMax Zolotorev on the laser injection scheme and beam dnostics and the technical contributions from Leon Archabault and Jim Dougherty. We would also like to acknowedge Earl Marmar for making the Abel inversion algorithavailable, and assistance on laser safety from K. Barat.

This work is supported by the Director, Office of EnergResearch, Office of High Energy and Nuclear Physics, Dsion of High Energy Physics, of the U.S. Dept. of Enerunder Contract No. DE-AC-03-76SF0098.

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laser-driven plasma-based accelerators: wakeﬁeld...

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