Ionization-induced electron injection was investigated experimentally by focusing a driving laser pulse with a maximum normalized potential of 1.2 at different positions along the plasma density profile inside a gas cell, filled with a gas mixture composed of 99%H2+1%N2. Changing the laser focus position relative to the gas cell entrance controls the accelerated electron bunch properties, such as the spectrum width, maximum energy, and accelerated charge. Simulations performed using the 3D particle-in-cell code WARP with a realistic density profile give results that are in good agreement with the experimental ones. The interest of this regime for optimizing the bunch charge in a selected energy window is discussed.

The mechanism of laser wakefield acceleration (LWFA) in a plasma1 can produce electric fields 3 orders of magnitude higher than in conventional RF accelerators. LWFA thus appears as a promising way to achieve compact relativistic electron sources. In this scheme, the plasma wave is excited by the ponderomotive force of a short intense laser pulse. At sufficiently high intensity gradient (typically achievable with an ultrashort laser pulse with intensity above 1019 W/cm2), plasma electrons are blown out of the laser axis behind the laser pulse. A cavity or “bubble” where only ions remain is created behind the laser pulse leading to strong transverse and longitudinal electrostatic fields. Plasma electrons can be trapped in this field and accelerated to high energy. This mechanism can occur continuously or several times over the plasma length as long as the laser intensity is high enough, which leads to accelerated electron bunches with a wide energy spread.

Several methods to increase the number of electrons and reduce the electron bunch energy spread have been proposed and tested such as the use of colliding pulses,2,3 density ramp injection,4,5 density transition injection,6,7 or ionization-induced injection.8–10 The mechanism of ionization-induced injection can be implemented simply by adding a small proportion of high-Z gas to the low-Z gas constituting the target medium. During the interaction with the intense laser pulse, the outer shell electrons of the high-Z gas are ionized in the front of the laser pulse and mostly contribute to the plasma wave, without being trapped. Electrons from the inner-shell of the high-Z atoms, having a much higher ionization threshold, are ionized closer to the intensity peak in a region where they can be more easily trapped by the plasma wave. This mechanism has shown its ability to increase the trapped charge11 and lower the transverse emittance of the electron bunches12 and is thus a promising candidate as an injector for multi-stage laser plasma accelerators. Although previous studies have used it in injector-accelerator experiments,13,14 a detailed specific study of the injection mechanism and the physics controlling the electron bunch properties in the experiments needed to be performed.

In this paper, the properties of electron bunches with energy in the range of 50–200 MeV, produced by ionization-induced injection using a single laser pulse focused in a gas cell target, are reported. The laser normalized vector potential and maximum plasma density are such that electron injection is dominated by ionization-induced injection, as shown in the previous work.11 The focal spot position was varied along the propagation axis to explore different injection conditions along the plasma density profile.

The use of gas cells has been shown to contribute to the stability of electron production15–18 as the gas confined in the cell is relatively homogeneous. Nevertheless, windows cannot be used to confine the gas on the intense short-pulse laser path, and density gradients are established due to gas leakage between the higher pressure volume of the gas cell and the low pressure chamber around it. Direct experimental measurement of these gradients is particularly difficult due to the small volume and large range of density to be probed. We have thus evaluated the gradients by their calculation through fluid simulations.

We performed experimental measurements of electron properties inside short gas cells, for which the focal plane position of the laser pulse was varied along the gradient. Experimental results were analyzed and compared with numerical modeling with the Particle-In-Cell (PIC) code WARP.19 It shows that the density profile and the focus position play a major role in the regime of intensity studied. The remaining of the paper is organized as follows: in Section II, the experimental set-up and parameters are described; Section III presents experimental results of the cell position scan and their analysis with the help of simulations; the influence of other parameters such as the cell length and laser energy on the bunch properties is discussed in Section IV.

Experiments were performed at the Lund Laser Centre (LLC), using a Ti:sapphire multi-terawatt laser system. Linearly polarized laser pulses, with duration τL=(37±3) fs full-width-at-half-maximum (fwhm), were focused using a 78 cm focal length off-axis parabola to a fwhm spot size of 17 μm. The laser wavefront was corrected using a deformable mirror to achieve a symmetrical circular distribution of energy in the transverse focal plane in vacuum. The laser envelope was close to the envelope of a Gaussian pulse and the measured Rayleigh length was zR1 mm. The laser energy on target was EL=(585±65) mJ and the resulting peak intensity in the focal plane was IL=(3.1±0.5)×1018W/cm2, which corresponds to a normalized vector potential of a0=(e/mec2)×(2IL/ε0ωL)1/2=1.2±0.1.

The target gas was contained in a variable length gas cell placed in the experimental vacuum chamber. The cell was made as a large diameter cylinder with replaceable entrance and exit faces, at the center of which 200 μm diameter holes were drilled to let the laser and electron bunches pass through. The thickness of the entrance and exit plates was 500 μm. A gas mixture composed of 99%H2+1%N2 was let in through an electrovalve opened 40 ms before the laser pulse. The stationary state plateau gas density in the cell was characterized prior to the experiment using interferometric measurements similar to the ones described in Ref. 20. Calculation of the profile with fluid simulations was performed using a transient turbulent sonic solver in OpenFOAM (sonicFoam).21 The normalized density profile ne/ne0 obtained from simulations is plotted as a function of the position along the laser propagation axis as a solid line in Fig. 1.

FIG. 1.

Normalized density profile for an inner cell length of Lcell=0.5 mm calculated with OpenFOAM (black solid line) and approximated density profile used in WARP simulations (red dotted line). The grey areas represent the entrance and exit plates. The colored circles are the in-vacuum focal plane positions of the laser pulse in the experimental study used for the numerical study.

FIG. 1.

Normalized density profile for an inner cell length of Lcell=0.5 mm calculated with OpenFOAM (black solid line) and approximated density profile used in WARP simulations (red dotted line). The grey areas represent the entrance and exit plates. The colored circles are the in-vacuum focal plane positions of the laser pulse in the experimental study used for the numerical study.

Close modal

The grey areas represent schematically the areas occupied by the walls of the gas cell; the laser is propagating from left to right. The density profile consists of a maximum in the inner part of the cell which length can be varied by moving the exit plate; on each side, sharp gradients at the transition with the plates are followed by smoother gradients in the vicinity of the holes, and sharp gradients outside the cell. The colored circles, labeled (a) to (d), represent the different positions of the focal plane in-vacuum relative to the gas cell, used to achieve results shown in Section III.

The focal plane is at a maximum distance of 1.4 mm from the 200 μm entry hole (in the case where it is located at 0.9 mm). In vacuum, the fwhm laser spot size at 1.4 mm from the focal plane is 41μm; in this case, all the detected laser energy is entering the gas cell. At the LLC facility, the laser pointing is actively stabilized to cancel drift of the laser spot in the focal plane, ensuring alignment of the gas cell to be optimized and stable over time of measurement duration. For the experimental results presented in this paper, the maximum electron number density in the cell was ne0=8.3×1018cm3, and the corresponding plasma frequency is ωp=1.6×1014 rad/s which leads to ωpτL6. The critical power for self-focusing associated to this density is PC = 3.6 TW, which gives a ratio of laser power to critical power PL/PC=(PL[GW]/17)×(ne/nc)4.1, where nc is the critical density. Self-focusing is thus expected to occur mainly in the area where the density is close to its maximum.

The generated electron bunches were characterized using a 12 cm-long magnetic dipole with a maximum field strength of 0.7 T and a LANEX screen imaged by a 16 bits CCD. The charge was calculated from LANEX images using published calibration factor22 and the lowest energy that could be measured was ∼50 MeV.

In this section, electron properties are presented for different positions of the focal plane relative to the entrance of the gas cell. Experimentally, the inner length of the cell was below 1 mm but was not known precisely. As the electron energy distribution is sensitive to the plasma length, measured electron spectra were compared with the results of simulations performed for several values of the plasma length. The best fit of experimental spectra was achieved for a cell length value of Lcell = 0.5 mm.

Experimental results at different focus positions were then analyzed by comparison to quasi-three-dimensional, electromagnetic PIC simulations with the numerical code WARP, which uses a Fourier decomposition of the electromagnetic fields in the azimuthal direction with respect to the laser-propagation direction.23 Two Fourier modes were included in the simulations. A field ionization module based on the Ammosov-Delone-Krainov model was used to model ionization dynamics.24 The longitudinal profile calculated with OpenFOAM was used in the WARP simulations, with a maximum electron density of ne0=7.8×1018cm3, for a gas mixture of 99% of H2 and 1% of N2. The laser was linearly polarized. The driving laser parameters are a0=1.1, a spot size of 17 μm fwhm, and a duration of 40 fs. All simulations were carried out with 36 macroparticles per cell with a grid resolution of 1.25×λL/2π and 0.05×λL/2π in r- and z-directions, respectively.

In Figs. 2(a)–2(d) are displayed electron spectra, obtained from experimental data and from PIC simulation results, for different positions of the in-vacuum focal plane zf corresponding to the circles labeled (a) to (d) in Fig. 1. Only electrons with energy above ∼50 MeV could be detected experimentally and grey areas around the experimental spectra represent the uncertainty on the energy determination estimated from typical electron pointing fluctuations and divergence. We can observe for all focus positions a good agreement between experimental and simulation data. The electron spectrum shape is shown to be strongly dependent on the parameter zf. At zf=0.35 mm, the spectra exhibit a plateau up to ∼110 MeV and then a quasi-linear decrease up to ∼150 MeV. As the value of zf is increased, the extension of the plateau is reduced, and it vanishes at zf = 0.9 mm.

FIG. 2.

Electron spectra for different positions zf of the focal plane in vacuum (a) zf=0.35 mm, (b) zf = 0.15 mm, (c) zf = 0.65 mm, and (d): zf = 0.9 mm. Solid lines represent the experimental spectra (averaged over 2 shots), gray areas represent the experimental energy uncertainty, and dotted lines represent WARP simulation results for a maximum density in the cell of ne0=7.8×1018cm3 and an inner cell length of Lcell = 0.5 mm. Simulation spectra are normalized to the maximum value of the experimental spectrum for the position zf=0.35 mm.

FIG. 2.

Electron spectra for different positions zf of the focal plane in vacuum (a) zf=0.35 mm, (b) zf = 0.15 mm, (c) zf = 0.65 mm, and (d): zf = 0.9 mm. Solid lines represent the experimental spectra (averaged over 2 shots), gray areas represent the experimental energy uncertainty, and dotted lines represent WARP simulation results for a maximum density in the cell of ne0=7.8×1018cm3 and an inner cell length of Lcell = 0.5 mm. Simulation spectra are normalized to the maximum value of the experimental spectrum for the position zf=0.35 mm.

Close modal

Fig. 3 shows experimental and simulation results for (a) the total charge above 50 MeV, Qtot and (b) the maximum energy, Emax, of the electron bunch; crosses indicate experimental points for gas mixture and open circles with lines simulation results; Emax is defined as the energy above which the charge density becomes less than 10% of the maximum. The value of the charge obtained by simulations was normalized to the average of the experimental values at zf0.35 mm. Triangles in Fig. 3(a) are experimental results for pure H2 for similar ne (8.5×1018cm3) and Lcell (0.8 ± 0.5 mm, respectively). These data show that the addition of 1% N2 increases the accelerated charge by up to a factor of 10 for the range of parameters studied here, so that the injection of most electrons can be attributed to ionization-induced injection.

FIG. 3.

Simulation and experimental results comparison for charge and energy as a function of focal plane position, blue crosses are experimental data points, and red circles with solid line are simulation results: (a) Qtot: bunch charge for electrons with energy higher than 50 MeV; Blue triangles represent the experimental values of the charge obtained with pure hydrogen and (b) Emax: electron maximal energy.

FIG. 3.

Simulation and experimental results comparison for charge and energy as a function of focal plane position, blue crosses are experimental data points, and red circles with solid line are simulation results: (a) Qtot: bunch charge for electrons with energy higher than 50 MeV; Blue triangles represent the experimental values of the charge obtained with pure hydrogen and (b) Emax: electron maximal energy.

Close modal

Simulation results and experimental data for gas mixture exhibit the same behavior. Experimental data show that both Emax and Qtot are increasing from zf0.6 mm to zf0.35 mm. zf=0.6 mm corresponds to a position of the focal plane in vacuum in front of the entrance of the cell, so that during the propagation, the laser diffracts significantly before the density is high enough for laser pulse self-focusing to occur; consequently, the maximum intensity is relatively low, leading to a low amplitude accelerating field. From zf0.6 mm to zf0.35 mm, the maximum energy is increasing, from zf=0.35 mm to zf = 0.15 mm it is nearly constant, and it decreases for zf larger than 0.15 mm. The reduction of the maximum energy for zf larger than 0.15 mm indicates a reduction of the accelerating length and/or of the accelerating field.

The evolution of the normalized vector potential a0 along the propagation axis, as given by PIC simulations, is plotted in Fig. 4 with the focal plane position as a parameter. The evolution of a0 is similar for the four cases corresponding to the spectra of Fig. 2. It shows that laser focusing and defocusing are in these cases dominated by the density profile. Indeed, a0 starts to increase around the same location for all cases which corresponds to the beginning of the laser self-focusing and decreases when the density is dropping. The variation of zf changes the maximum absolute values of a0, which are decreasing when zf is increased above zf = 0.15 mm.

FIG. 4.

Normalized vector potential obtained from WARP simulations along the propagation axis for different positions of the focal plane in vacuum. Solid lines represent the value of the normalized vector potential and vertical dashed lines indicate the start of injection in each case (for cases zf=0.35 mm and zf = 0.15, vertical lines are superimposed).

FIG. 4.

Normalized vector potential obtained from WARP simulations along the propagation axis for different positions of the focal plane in vacuum. Solid lines represent the value of the normalized vector potential and vertical dashed lines indicate the start of injection in each case (for cases zf=0.35 mm and zf = 0.15, vertical lines are superimposed).

Close modal

The locations where electron injection begins are indicated by vertical dashed lines in Fig. 4, and they are defined as the first locations at which electrons with an energy higher than 10 MeV are present. It can be seen that the beginning of injection occurs around the same value of a01.7±0.1 for all cases which is consistent with the ionization-induced trapping threshold given in Ref. 10 (in our case at the injection we have γp15 and kpLRMS2.1, where γp is the Lorentz factor of the plasma wave, kp its wave number, and LRMS the longitudinal root-mean-square laser pulse length). As zf is increased above 1.15 mm, this value of a0 is reached after a longer propagation distance; injection then starts later and the acceleration length is reduced as the plasma length is constant.

In the simulation, we also observe that the largest maximum longitudinal electric field of the wake is obtained for zf = 0.15 mm. Therefore, a shift of zf away from zf = 0.15 mm leads to a reduction of the length available to inject and accelerate electrons and of the amplitude of the electric field responsible for the trapping and acceleration processes. The consequence is that both the charge and the maximum energy of accelerated electrons are reduced when zf is shifted away from zf = 0.15 mm, as observed in Fig. 3. These results show that a change of the laser focal plane position along the density profile allows control of the position of injection, and subsequently the accelerated charge and energy distribution.

In addition to the focus position, in the regime of interest for an injector, other parameters, such as the plasma density and length, and the laser strength, have a significant role in determining the accelerated charge and the energy of the electron bunch. In this section, we examine the influence of these parameters on the total charge and in a limited energy range suitable for an injector. The energy window 60–70 MeV is of interest as it contains a significant charge for all parameter sets. Table I summarizes the parameters of 4 different cases that were studied experimentally.

TABLE I.

Parameters of 4 different cases for comparison of accelerated charge in experiments; ne is the maximum value of the plateau, and the non-linear dephasing length Lφ is evaluated for this density.

Case No.Case 1Case 2Case 3Case 4
ne (1018 cm−38.3 9.5 8.5 9.3 
Lcell (mm) 0.5 0.7 10 
Lcell (Lφ0.9 1.5 18.5 10.5 
Lφ (mm) 0.56 0.46 0.54 0.48 
zf (mm) 0.9 −0.25 −0.25 −0.5 
Case No.Case 1Case 2Case 3Case 4
ne (1018 cm−38.3 9.5 8.5 9.3 
Lcell (mm) 0.5 0.7 10 
Lcell (Lφ0.9 1.5 18.5 10.5 
Lφ (mm) 0.56 0.46 0.54 0.48 
zf (mm) 0.9 −0.25 −0.25 −0.5 

The laser vector potential is a0=1.2 and the corresponding values of the total charge, Qtot (blue bars), and of the charge in the [60–70 MeV] energy range, Q[6070MeV] (red bars), for these 4 cases are plotted in Fig. 5(a). For all cases, the selected value of zf corresponds to the focal position maximizing the charge in the 60–70 MeV energy range. Case 1 is extracted from the study presented in Section III (i.e., zf = 0.9 mm). We then compare three other sets of parameters to case 1. We first increase the density (case 2) keeping the cell length in the same range and observe a strong increase on both Qtot and Q[6070MeV]: Qtot is increased by a factor of 12 and Q[6070MeV] by a factor of 5. Then, we increase the length at a similar density (case 3), and we can observe a significant increase for Qtot but a decrease for Q[6070MeV]. Finally, we increase both the density and the cell length (case 4) and observe an increase for both Qtot and Q[6070MeV].

FIG. 5.

Experimental cases comparison. (a) Total charge Qtot (blue bars) and charge in the 60–70 MeV energy range Q[6070MeV] (red bars) for parameters of cases 1 to 4 listed in Table I. (b) Corresponding energy spectra.

FIG. 5.

Experimental cases comparison. (a) Total charge Qtot (blue bars) and charge in the 60–70 MeV energy range Q[6070MeV] (red bars) for parameters of cases 1 to 4 listed in Table I. (b) Corresponding energy spectra.

Close modal

To further understand this behavior, we plotted the electron spectra for cases 1–4 in Fig. 5(b). Compared with case 1 (solid black line), case 2 (solid blue line) exhibits a higher charge density over the whole spectrum and extends to higher electron energy. For case 2, as the density is higher, the laser self-focuses earlier in the profile, leading to higher charge and higher accelerating field amplitude. The length for case 3 is much longer than the dephasing length and the ionization-induced injection process is in this case continuous which explains the broad spectrum observed in Fig. 5(b) (solid red line). Both the dephasing length and the depletion length at this density (ne08.3×1018cm3,LD2.3mm, and Lφ0.6 mm (Ref. 25)) are larger than the cell length of case 1; therefore, an increase in length compared with case 1 leads to an increase of Emax as seen in Fig. 5(b) for case 3. For case 4, density and length are both increased, leading to an increase of accelerated charge (similar to case 2) and energy spectrum broadening (similar to case 3). In comparison with case 2, case 4 presents a lower high energy charge density which is probably due to the dephasing effect. The comparison of these 4 cases shows that the charge in the range of 60–70 MeV is maximized for larger ne0, although for the set of parameters studied it reaches only 25% of the total measured charge at a value around 8 pC.

The effect of a0 variations was studied numerically using WARP simulations, as the laser energy could not be increased in the experiment. In Fig. 6 are plotted Qtot and Q[6070MeV] and the associated spectra at ne0=7.8×1018cm3 and zf = 0.65 mm and for different values of a0 indicated on the horizontal axis. Qtot and Q[6070MeV] are normalized to the same value as in Fig. 3(a) to be comparable to experimental values in pC and the spectra are normalized to the same value as in Fig. 2 to be comparable to experimental spectra in pC/MeV. Fig. 6(a) shows that an increase of a0 from 1.1 to 2 multiplies Qtot by 13.7 and Q[6070MeV] by 8.3. In Fig. 6(b), we observe that the spectra exhibit higher charge density over all the spectrum for higher a0 and a higher Emax. We also observe a peak appearing around 50 MeV for a0=2 which can be of interest for an injector at this energy.

FIG. 6.

(a) Simulated electron bunches total charge Qtot (blue bars) and charge in the 60–70 MeV energy range Q[6070MeV] (red bars) and (b) associated electron energy distribution for different values of a0. Normalization is the same as in Fig. 3.

FIG. 6.

(a) Simulated electron bunches total charge Qtot (blue bars) and charge in the 60–70 MeV energy range Q[6070MeV] (red bars) and (b) associated electron energy distribution for different values of a0. Normalization is the same as in Fig. 3.

Close modal

Fig. 7 presents the evolutions of a0 along the propagation axis and the beginning of injection for the different cases. For all simulation results, injection is observed when ϕ=ϕiϕmin1, where ϕi is the normalized electrostatic potential of the plasma wave (ϕ=eΦ/mec2) at the position of creation of electrons ionized from N5+ and N6+ and ϕmin its first minimum. To satisfy this condition at a density lower than ne0, i.e., to drive a similar amplitude plasma wave at lower density, the laser amplitude must be higher.26 For a value in-vacuum of a0=2, the laser power is high enough for self-focusing to occur in the entry gradient. In this case, injection is observed at ne0.4×ne0 when a01.9. It thus shows that increasing the initial value of a0 and keeping zf constant lead to injection earlier during the propagation.

FIG. 7.

Evolution of a0 along the propagation axis for different values of a0 in vacuum. Solid lines represent the value of the normalized vector potential and dashed lines indicate the start of injection in each case.

FIG. 7.

Evolution of a0 along the propagation axis for different values of a0 in vacuum. Solid lines represent the value of the normalized vector potential and dashed lines indicate the start of injection in each case.

Close modal

For a0=1.5 and 2, we observe significant injection of hydrogen electrons although their contribution to the spectrum is smaller than the contributions of electrons coming from ionized N5+ and N6+. Indeed, electrons from hydrogen represent ∼9% and ∼17% of the total charge in case of an initial a0 of 1.5 and 2, respectively. We also observe that the maximum longitudinal electric field is ∼1.9 and ∼2.7 times higher for a0=1.5 and a0=2, respectively. Both effects, earlier injection and the excitation of larger amplitude electric fields over a longer distance, contribute to produce higher charge and electron bunches with higher energy.

In conclusion, we showed that the position of the laser focal plane along the density profile of a gas cell plays a major role in triggering the ionization-induced injection of electrons and controlling acceleration processes, and therefore on determining the properties of generated electron bunches. Especially, we showed that the focal plane position relative to the cell entrance changes the maximum value of a0, which has an impact on the longitudinal position of injection and electrostatic fields magnitude. By changing the focal plane position, the electron bunch charge and energy distribution can be tuned, either to optimize the electron bunch total charge or the charge in a given energy range, for example, 60–70 MeV optimized to 41% of the total measured charge for the case of Fig. 2(d) (case 1). For this case, the focal plane in vacuum is located in the exit density gradient (zf = 0.9 mm) and a0=1.1, simulation results show a distribution centered at ∼68 MeV. The charge in the 60–70 MeV range can be increased by a factor of 5 by increasing the density (case 2). When a0 is increased from 1.1 to 2, simulations predict 13.6 times higher charge electron bunch exhibiting a peaked distribution at ∼50 MeV.

Authors acknowledge the use of the computing facility clusters GMPCS of the LUMAT federation (FR LUMAT 2764). This work was supported by the Triangle de la Physique under Contract No 2012-032TELISA. Authors also acknowledge the support of the Swedish Research Council, the Knut and Alice Wallenberg Foundation, the Swedish Foundation for Strategic Research, Laserlab-Europe/CHARPAC, and EuCARD2/ANAC2 (Grant Agreements Nos. 284464 and 312453, EC's 7th Framework Programme). This work was supported in part by the Director, Office of Science, Office of High Energy Physics, U.S. Dept. of Energy under Contract No. DE-AC02-05CH11231.

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