Abstract DLA to the energy gain of the electrons

AbstractThedirect laser acceleration (DLA) of electrons in a laser wakefield accelerator(LWFA) operating in the forced or quasi-blowout regimes has been investigatedthrough experiment and simulation.  Whenthere is a significant overlap between the trapped electrons and the drivelaser in a LWFA cavity, the resulting electrons can gain energy from both theLWFA and the DLA mechanisms. Experimental work investigates the properties of the electron beamsproduced in a LWFA with ionization injection by dispersing those beams in the directionperpendicular to the laser polarization. These electron beams show certain spectral features that arecharacteristic of DLA.  Thesecharacteristic spectral features are reproduced in particle-in-cellsimulations, where particle tracking was used to elucidate the roles of LWFAand DLA to the energy gain of the electrons in this experimental regime and to demonstratethat such spectral features are definitive signatures of the presence of DLA inLWFA.

Introduction Asthe field of laser wakefield acceleration (LWFA) 1 matures, emphasis isshifting toward utilizing LWFA as a source of electron beams and x-rays forapplications.  There is an increasingemphasis on producing electron beams from LWFAs that can meet the stringentbeam requirements (narrow divergence, small emittance, narrow energy spread)necessary for use in staged plasma accelerators 2 and free electron lasers. Simultaneously,betatron x-rays from LWFA are being utilized for applications 3-7, whichplaces an emphasis on optimizing LWFA to produce these x-rays.  Even though these applications requireoptimization of different electron beam properties, all applications benefitfrom a more-complete understanding of the dynamics of electron energy gain inLWFA and how those dynamics affect properties such as electron beam energy, divergence,source size, shape, and energy spread.For therange of plasma densities (mid-1018 to a few 1019 cm-3)and laser pulse durations (35-45 femtoseconds full width at half maximum) thatare typically used in many current LWFA experiments in the forced orquasi-blowout regimes, the laser pulse length is on the order of the wake wavelength;therefore it may occupy the entire first bucket of the wake.  In such experiments, the wakefield structurehas a desirable transverse and longitudinal field structure for generating a self-injectedelectron bunch, but it also has the conditions needed for direct laseracceleration (DLA) 8, 9 if there is an overlap between the acceleratingelectrons and the transverse electric field of the laser pulse 10-16.

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  It is therefore important to understand therole that not only the longitudinal electric field of the wake, but also theother fields—namely, the transverse fields of the ion column and of the laseritself—play in determining the ultimate energy gained by the electrons.  In this paper, we show through experimentsdirect, observable signatures in the produced electron beams that indicate thatDLA makes a significant contribution to the electrons’ energy in LWFAs operatedin such a configuration. Three-dimensional (3D) particle-in-cell (PIC) simulations are usedto elucidate the energy dynamics that lead to this contribution.BackgroundInthe matched, self-guided 17 blowout regime of LWFA 18, an ultrashort,intense laser pulse propagates through either an underdense plasma or a neutralgas.  In the latter case, the leadingedge of the laser pulse ionizes the neutral gas, and the pondermotive force ofthe laser then expels the plasma electrons out and around the main body of thepulse.

On the femtosecond (fs) timescale of the laser, the more-massive ionsremain relatively immobile, so an ion column forms behind the drive laser. Theexpelled plasma electrons are drawn back to the laser axis by the Coulomb forceof the ion column, where they overshoot and oscillate about the axis andthereby set up a wake structure. The charge separation generated by this wakestructure produces a longitudinal electric field that is capable ofaccelerating electrons trapped in the wake at gradients > 1 GeV/cm. Thoseelectrons that are injected off-axis will undergo betatron oscillations inresponse to the linear transverse focusing force of the ions 19, 20.Electronscan become trapped in a LWFA by a variety of methods 21-31, but in the experimentsand simulations presented here, the ionization injection 32-34 technique isused. In this technique, the plasma is produced by the laser ionization of aneutral gas mixture comprised of a gas with a low ionization potential(commonly He or H2) doped with a gas with high ionization potential(commonly N2 or Ar).

  The lower-intensity front edge of the laserpulse ionizes the outer (typically L) shell electrons of the dopant gas alongwith all the electrons in the gas with a low ionization potential.  Because the inner (typically K) shellelectrons of the higher-Z atoms have a much higher ionization potential, theyare ionized only near the peak of the laser pulse within a fully formed wakeand are subsequently trapped without slipping all the way to the back of thewake.  Compared toself-trapping, this method of ionization injection permits trapping in a LWFAat reduced plasma densities and laser powers. Ina LWFA operating in the forced or quasi-blowout regime, the ion column acts asa very strong wiggler.  Trapped electronsthat are being accelerated by the wake undergo betatron oscillations inresponse to the transverse electric field of the ion column.

  Therefore, if a LWFA is configured such thatsome of the trapped electrons undergo betatron oscillations in the plane ofpolarization of the laser’s electric field, the transverse field of the drivelaser can give the electrons additional transverse momentum.  This transverse momentum can then beconverted to longitudinal momentum via the vx B force.  Thus, the DLA mechanism 8, 9 can accelerateelectrons by this coupling of the transverse field of the laser through thebetatron motion of the electrons.  As aresult, there is a potential for those electrons to be accelerated by the DLAmechanisms in addition to the LWFA mechanism in a LWFA where the drive laseroverlaps the trapped electrons 10-16. It has been noted that DLA is the inverse ofthe ion channel laser mechanism 35.

  DLA in LWFA is also similar to inverse freeelectron laser (IFEL) acceleration 36, 37, except that the static magneticundulator used in an IFEL is replaced by the transverse electric field of theions in DLA and the resonance condition need not be strictly obeyed as in theIFEL 11, 13-14.  In principle, theresonance condition for DLA is similar to that for an IFEL 38; i.e., in anideal situation, the laser pulse overtakes the electrons by one wavelength perbetatron oscillation once the electrons come into resonance with thefundamental (N=1) harmonic, where the electrons are bunched on alaser-wavelength scale 8, 39-42.  However,unlike in an IFEL, sustained resonance for DLA is more difficult to designbecause in the latter case, the normalized undulator strength K >> 1 andthe energy and betatron frequency of the electrons as well as the laserproperties are continuously and rapidly changing 11, 13, 14.  The condition for energy gain from the DLAmechanism is typically expressed using the one-dimensional resonance conditionfor a single electron 8, 9                                                        (1)whereN is an integer indicating the harmonic of the betatron frequency ??  =                                                                         (2) is the velocity of the electron in thelongitudinal direction, and v? and ?0 are the phasevelocity and frequency, respectively, of the electromagnetic wave (i.e.

,laser).  Essentially, this resonancecondition means that in order for an electron to gain energy from DLA, aharmonic of the betatron frequency  must equal the Doppler-shifted laser frequency witnessed by the electron 8, 9, 11, 13, 14.  It is well known that in LWFAs, especiallythose not in the ideal blowout regime 18, the properties of the drive laser,including  and , evolve throughout the accelerationdistance.  Furthermore,as electrons are accelerated in a LWFA, their longitudinal momentum, andtherefore , increases, and their betatronfrequency is expected to fall as ?-1/2 as seen in Equation 2.  Despite these evolving quantities, electronsthat are being accelerated in a LWFA are able to gain significant energy fromDLA because the quantities evolve together such that a quasi-resonance is setup and the electrons are in a phase where they gain energy from the DLAmechanism for more than one-half of each betatron cycle 11, 13, 14.Todetermine if a LWFA is operating in a regime where DLA is expected to contributeto the energy gain of the electrons, the LWFA can be characterized using theratio of the laser pulse length ?laser relative to the nonlinearplasma wavelength ?wake.  This ratio can be represented by thedimensionless pulse length parameter 13, 14Tp= c?laser/?wake = ?p?laser/(2?a01/2)                                  (3)If the laser pulse length c?laseris equal to the a0-dependent length of the first bucket 18 ?wake ?  then Tp= 1.  Here, kp = ?p/c,and a0 is the normalized vector potential a0 = eE0/mc?0? 8.

6 x 10-10 ??m, where I0 is the laser intensity and ?is the wavelength of the laser. In the case where Tp is 0.5 orless, the laser does not overlap the trapped electrons in the LWFA while theyare being accelerated; those electrons gain energy purely from the longitudinalwakefield 10, 13, 14.

When Tp reaches 0.6 or more, the laser pulsewill overlap the trapped electrons, and DLA can play a role in the accelerationof those electrons 10, 13, 14. A Tp> 1 indicates a significant overlap between the transverse laser field andthe trapped electrons 13, 14.Experimental Methods and ResultsInthis section, we show definitive experimental evidence of the presence of DLAin nonlinear LWFAs where the laser pulse overlaps the trapped electrons.  We first demonstrate that the electron beamsare indeed interacting with the drive laser when there is an overlap betweenthe laser and trapped electrons, as might be expected in a DLA-assisted LWFAexperiment.  We then show that thetransverse structure of the dispersed electron beams exhibits characteristicfeatures that are indicative of DLA as an additional accelerationmechanism.

  Theexperiments presented in this paper were conducted at UCLA using an 815-nmTi:Sapphire laser with a fixed pulse length ?laser of 45 ± 5 fs fullwidth at half maximum of intensity and a spot size w0 of 6.7?m.  The laser was run with powers P upto 10 TW, which correspond to an a­0 up to 2.6.  An f/6 off-axis parabola (OAP) system focusedthe main laser pulse at the entrance of a variable-length (0.

1-2 mm) gas cell 43,44 as shown in Figure 1.  Thegas cell was filled with a 95% He/5% N2 neutral gas mixture using apulsed solenoid valve.  The gas mixturewas used so that ionization injection 32 could be used to both inject chargeearly into the wake and increase the amount of trapped charge.  Theplasma density was measured on every shot using a Michelson interferometer andwas varied by changing the gas pressure 43, 44.  The produced electron beams were dispersed inenergy with a 0.92 tesla (T) dipole magnet onto a plastic scintillator or a LANEXscreen and recorded using a PI-MAX intensified CCD camera.  This electron spectrometer could be rotatedby 900 so that the electron beam could be dispersed parallel to ororthogonal to the linear laser polarization 13, 14.  Figure 1: Experimentalsetup.

  The thick red line shows the main laser pulsebeing focused by the f/6 OAP system at the entrance of the gas cell.  The laser is linearly polarized in the planeof the page. The thin red line shows the probe for the Michelsoninterferometer.  A typical interferogramis shown.

  The electrons are dispersed bythe 0.92 T dipole magnet onto a scintillator or a LANEX and imaged by a PI-MAX3 camera.  The dipole magnet and screencould be rotated by 900 so that the electron beams could bedispersed parallel or orthogonal to the laser polarization.  The dipole magnet typically was located 3.2cm downstream from the gas cell, and the distance from the end of the magnet tothe screen was 7.0 cm.

  A typical measuredelectron spectrum is shown.Because the energy gain from DLA relies onthe coupling between the transverse laser field and the betatron motion of theelectrons, the first observable signature of an interactionbetween the laser and the trapped electrons in a LWFA is that the undispersedelectron beam should be elliptical in the direction of the laser polarization 45.The white ellipses in Figure2(a)are fits to the 50% contour of the undispersed electron beams from 10consecutive shots where the laser had horizontal, linear polarization and avacuum a0 of ~1.5.  The plasmadensity was ~1.7 x 1019 cm-3, which yields a Tpvalue of ~1.3, and the gas cell length was 900 ?m.  The fits show a strong ellipticity in thedirection of the laser polarization with an average measured half-width athalf-maximum (HWHM) divergence of 12.

2 mrad. In contrast, the average measured HWHM divergence in the perpendiculardirection was 5.6 mrad.

  The direction ofthe linear polarization of the drive laser was then rotated 900using a thin (1 mm) quartz half wave plate for high-laser-energyapplications.  The ellipticity of theundispersed electron beams rotated with the laser polarization, as shown in Figure2(b),which indicates that the trapped electrons’ transverse momentum is beingenhanced in the polarization plane.  Withthe vertical laser polarization, the average measured HWHM divergence in thedirection of the laser polarization was 13.0 mrad, and the average measuredHWHM divergence in the perpendicular direction was 6.5 mrad.  Therefore, under the laser-plasma parametersdescribed above, the measured divergence of undispersed electron beamsemanating from the LWFA shows ellipticity that is correlated to thepolarization of the laser pulse.  This correlationdemonstrates that the electrons are indeed interacting with the drive laser.

AlthoughDLA is expected to preferentially increase the divergence of the electron beamin the plane of the laser polarization, the observed ellipticity in thedivergence of the undispersed electron beams in Figure2 initself is not definitive proof that DLA is present in the LWFA 13.  Rather, because the energy gain from DLA relies on the couplingbetween the transverse laser field and the betatron motion of the electrons, asignature of this transverse coupling must be present in the energy gain of theelectrons to demonstrate the presence of DLA in LWFAFigure 2: (a, b)  Fits (white ellipses) to the 50% contour ofundispersed electron beams from a series of 9 and 10, respectively, consecutivelaser shots when using horizontal and vertical, respectively, linear laser polarization.  (Inset) Typical undispersed electron beam from data shown in (a) with 50%contour points marked by the black crosses and the fit to that point marked bythe white ellipse.