IONIZATION-INDUCED TRAPPING IN LASER-PLASMAACCELERATORS AND SYNCHROTRON RADIATION FROM THE

BETATRON OSCILLATION∗

M. Chen† , E. Esarey, C.G.R. Geddes, C.B. Schroeder, W.P. Leemans,LOASIS Program, LBNL, Berkeley, CA 94720, USA

E. Cormier-Michel, D.L. Bruhwiler, Tech-X Corporation, Boulder, CO 80303, USA

Abstract

Ionization injection into a laser wakefield accelerator isstudied by multi-dimensional particle-in-cell (PIC) simula-tions. To obtain low energy spread beams we use a shortregion of gas mixture (H+N) near the start of the stage totrap electrons, while the remainder of the stage uses pure Hand is injection-free. Effects of gas mix parameters, includ-ing concentration and length of the mixture region, on thefinal electron injection number and beam quality are stud-ied. Two dimensional PIC simulations show the injectedelectron beam has filament structures in the plane perpen-dicular to the laser polarization direction in early time andthis structure disappears later due to the betatron oscilla-tion of the electrons in the wakefield. Synchrotron radia-tion from the accelerated electrons is calculated by a postprocessing code - Virtual Detector for Synchrotron Radia-tion (VDSR).

INTRODUCTION

Laser-plasma accelerators are of great interest becauseof their ability to sustain extremely large accelerationgradients, enabling a compact accelerating structure [1].Recently GeV mono-energetic electron beams have beendemonstrated in experiments within centimetre scale [2, 3].To better use these accelerated beams, such as in an undu-lator for radiation sources, beam quality still needs to beimproved, especially the energy spread [4, 5, 6] and trans-verse emittance. To get high quality beams, in addition tothe acceleration process, the beam injection and trappingshould also be well controlled [7, 8]. Electron injectionin the laser wakefield has obtained great progress recentlyin experiments by using plasma density control [9, 10], ortrigged by multiple colliding laser pulses [8], or by ionizinghigh order electrons of the background ions [11, 12, 13]. Tofurther improve the beam quality, in this paper, we studythe last scheme in detail to understand the relationship be-tween the experimental conditions and the final beam qual-ity. Finally we also calculated the accelerated beam’s be-tatron radiation in the wakefield by a post processing code(VDSR).

∗Work supported by the U.S. Department of Energy under ContractNo. DE-AC02-05CH11231, the National Science Foundation, NationalNuclear Security Administration, NA-22, and by Tech-X Corporation.NERSC computational resources were used.

† Minchen@lbl.gov

IONIZATION INJECTION

Electrons to be trapped should have an initial energywhich is larger than a threshold which depends on the phaseposition of the electrons in the wake. Typically the wake-field has a phase velocity closed to the laser group velocityvg = (1 − ω2

p/ω20)c, where c is the light speed in vacuum,

ωp and ω0 are the plasma and laser frequency, respectively.In the ionization injection scheme, electrons of the innershell are ionized near the peak of the laser pulse, whichmakes their trapping threshold much lower than the pre-ionized back ground electrons which usually have negativelongitudinal momenta at this phase. From one dimensionalwakefield theory we know the trapping condition for ion-ized electrons is [14]:

Hi = 1− φ(ξi) ≤ Hs = γ⊥γ−1p − φmin, (1)

where ξi is the ionization phase position of the electronsin the wakefield, γp is the relativistic factor of the wake,φmin is the minimum potential of the wakefield, γ⊥ =√1 + p2⊥ =

√1 + a2⊥(ξi) and a⊥ = eA/mec

2 is thenormalized vector potential of the laser pulse. As we seeif φ(ξi) is large enough, the electrons born at ξi can betrapped by the wakefield. Ionization trapping can happenby using two crossing pulses [15] or by a single pulse go-ing through a neutral gas medium [11]. For a single pulsescheme, to reduce the beam energy spread, electron injec-tion should happen within a short region, otherwise en-ergy spread will increase due to the different accelerationlengths of the trapped electrons. Additionally, as we willsee, continuously electron injection makes beam load ef-fects severe, which reduces the final injection number.

Gas Length and Concentration Effects

To study the effect of the gas conditions on the final elec-tron beam we did particle-in-cell simulations by use of theionization included in the VLPL code [16]. To save compu-tational time we use electrons (instead of Hydrogen atoms)and Nitrogen atoms as the background plasma. The nor-malized electron density ne = 0.001 nc (initial free elec-tron density plus Nitrogen density times 5) is made uniformthroughout the plasma after a ramp region (20 λ0 long)in the beginning of the plasma to avoid boundary injec-tion, where nc = 1.7 × 1021/cm3 is the critical densityfor a laser of 800nm wavelength (λ0 = 800 nm). We

Proceedings of 2011 Particle Accelerator Conference, New York, NY, USA MOP159

Advanced Concepts and Future Directions 1

(b)

(c) (d)

(a)

Figure 1: (a) Trapped electron number vs the length ofthe mixed gas traversed by laser pulse. (b) Trapped num-ber evolution vs the laser propagation distance. Here themixed gas length is fixed to be 1000λ0. (c) Evolution ofenergy spread and injected electron number along with themixed gas length. (d) Dependence of energy spread andfinal electron injection number on the concentration of Ni-trogen. Here the mixed gas length is 200λ0.

fixed our laser intensity to be a = 2.0 and Full Width atHalf Maximum (FWHM) to be LFWHM = 14.89 T0 withT0 = 2.67 fs the laser period. To study the mixed gaslength effect on the final beam quality we also fixed theNitrogen concentration to be 1%. Figure 1 (a) shows thetrapped electron number evolution with mixed gas length.The trapped electron number here is calculated by thecriterion of Eq. 1. As we see, when the mixed gas isshort, the trapped electron number linearly increases withlength. However, number trapped saturates later and thendecreases if the mixed gas length becomes longer. The rea-son is that the newly injected electrons make the beam load-ing effect stronger, and some of the trapped particles arelost due to this effect. If we fix the mixed gas length at theoptimum length (1000 λ0 here) we keep the injection num-ber at the maximum as Fig. 1 (b) shows. Fig. 1 (c) showsthe simulation results of the mixed gas length effects on thebeam quality. As we see, for the trapped number, the resultsare the same as those we get from Eq. 1. Within the re-gion where the trapped number linearly increases with themixed gas length, the energy spread is also almost linearlyincreasing. To get a high quality beam one should henceuse as short a mixed gas as possible. Figure 1 (d) showsthe concentration effect on the beam quality. In these sim-ulations we fixed the mixed gas length to be 200 λ0 butchanged the Nitrogen concentration. As we see the injec-tion number also shows the linear scaling at lower concen-tration and then saturates. The energy spread at first weaklydepends on the concentration then increases linearly withit. This gives us some hint on the parameter selection, asone can use a relatively high concentration and short mixedgas to get the same charge and lower energy spread beam.

Figure 2: Transverse spatial structures of the acceleratedelectron beam when a S-polarized laser pulse (a) or a P-polarized laser pulse (b) is used. The acceleration lengthhere is 94λ0. Typical trajectories of the injected electronsin the simulations corresponding to the S-polarized laserpulse (c) and the P-polarized laser pulse (d) cases, respec-tively.

Multi Dimensional Effects

To study multi dimensional effects on the beam structureand reduce simulation time we conducted two dimensionalsimulations with different laser polarization directions. Thelaser pulse parameters are: a = 2.0, LFWHM = 14.89 T0,focus at 75 λ0 from the simulation box boundary, the spotsize is WFWHM = 17.66 λ0, and the uniform plasma den-sity is ne = 0.001 nc, the mixed gas length is 20 λ0. Inthe first simulation the laser polarization is out of the sim-ulation plane (S-polarization) and in the second the polar-ization is parallel to the simulation plane (P-Polarization).Phase-space electron beam structures of these two casesat an early acceleration time are shown in Fig. 2 (a) and(b). As we see, in the S-polarization case the electronbeam shows a filament structure (or a hollow structure).In the simulation we found when the acceleration distanceis small these filaments appear and merge periodically. Fi-nally, these structures disappear when the electrons’ energyis higher. We show some typical electron trajectories inFig. 2(c) and (d) corresponding to the two cases, respec-tively. As we see, in the S-polarization case electrons showregular betatron oscillation and they are almost in phase atthe earlier time. The period of the oscillation is the beta-tron wavelength 2πc/ωβ =

√2γλp, where γ is the rela-

tivistic factor of the electron beam and λp is the plasmawavelength. Over long acceleration length, the differenceof the betatron phase increases which makes the betatrontrajectories mix, so the filament structures disappear. Onthe contrary, in the P-polarization case the electrons’ tra-jectories are initially not in phase due to the effect of thelaser electric field in the same plane. Correspondingly thebeam shows a normal transverse profile and its size gradu-ally reduces due to the energy increase.

MOP159 Proceedings of 2011 Particle Accelerator Conference, New York, NY, USA

2 Advanced Concepts and Future Directions

BETATRON RADIATION

When the electrons make betatron oscillations in thewakefield, they emit radiation. This gives a new kind oflaser plasma based radiation source [17, 18]. To calculatesuch radiation a parallel C++ code named Virtual Detectorfor Synchrotron Radiation (VDSR) is made. The radiationintensity distribution is calculated according to the follow-ing equation:

d2I

dωdΩ=

e2ω2

4π2c

∑

j

∣∣∣∣

∫ ∞

−∞�n× (�n× �βj)e

iω[t−�n·�r(t)/c]dt∣∣∣∣

2

,

(2)where �n is the unit vector pointing to the detector pixel,�βj and �rj are the normalized velocity and spatial coordi-nates of the jth electron. VDSR reads the electrons’ tra-jectories from the PIC simulation and then calculates everyelectron’s radiation according to their trajectories and sumsthem incoherently [19].

Radiation has been modeled from a colliding pulse in-jection simulation using the VORPAL code [20, 21]. Thedriving laser parameters are the same as our ionizationinjection case, however the plasma is composed of pre-ionized electrons with the density of 0.001 nc. The in-jection is caused by a colliding pulse whose intensity isa1 = 0.3 and duration is LFWHM = 3.75 T0 � 10 fs.Figure 3 (a,b) shows the radiation distribution of the tracedelectrons. 1000 particles are used to represent the 1 pCelectron beam. The statistical information of these parti-cles are shown in Fig. 3 (c) and (d), in which the spreadof the transverse position and longitudinal momenta areshown. The radiation is calculated after a total accelerationlength of about 1.12 mm. The electron beam’s center en-ergy there is about 100MeV and the transverse radius sizeis about 0.75λ0 = 0.6 μm. If we think of the wakefield as ahollow bubble structure, the betatron strength parameter isaβ = γrkβ = π

√2γr/λp � 1.0, where the average value

of < γ >= 100 has been used. According to betatron ra-diation theory the peak radiation frequency on axis shouldbe at h̄ωc = 2γ2h̄ωβ/(1 + γ2θ2 + a2β/2) [17]. If we use< γ >= 100 and h̄ωβ = h̄ωp/

√2 < γ > � 0.00347 eV,

the radiation peak is at h̄ωc � 45eV when θ = 0o. Aswe can see this value is close to the on axis peak photonenergy in our simulation [See Fig. 3 (a) at θ = 0o]. Theangularly integrated spectrum shows the radiation peak isat the photon energy of about 90 eV. This means the higherenergy radiation is not exactly on axis. However most ofthe radiation is still within 10mrad ∼ 1/ < γ >.

SUMMARY

In summary, ionization injection and betatron radiationwere studied by multi dimensional PIC simulations. Mixedgas length and concentration effects on the ionized injectedbeam quality were shown. To get a high quality beam, us-ing high concentration and short mixed gas is better thanusing low concentration and long mixed gas. In a low

01

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x

(c)

X−ray photon energy [keV]

Ang

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rad]

X-ray distribution [photons/sr/0.1%BW]

0.05 0.15 0.25 0.35 0.45

5

15

25

35

0.5

1

1.5

2

2.5x 10

5

(a)0.05 0.15 0.25 0.35 0.45

0

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X−r

ay s

pect

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[pho

tons

/0.1

%B

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X−ray photon energy [keV]

(b)

200 400 600 800 1000 1200 1400 <z>

0 50 100 150 200 <pz>0

510pz

(d)

1520

rms

rms

Figure 3: (a) Radiation angular and energy distribution. (b)Angularly integrated radiation spectrum distribution. Evo-lution of the spread of the transverse position (c) and thespread of the longitudinal momenta (d) of the traced elec-trons.

energy beam, electron filaments have been observed inthe plane perpendicular to the laser polarization. Electronbeam betatron radiation was also calculated by a post pro-cessing code, and the calculated results fit the betatron ra-diation theory well.

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