Laser–plasma accelerators deliver high-charge quasi-monoenergetic electron beams with properties of interest for many applications. Their angular divergence, limited to a few mrad, permits one to generate a small γ ray source for dense matter radiography, whereas their duration (few tens of fs) permits studies of major importance in the context of fast chemistry for example. In addition, injecting these electron beams into a longer plasma wave structure will extend their energy to the GeV range. A GeV laser-based accelerator scheme is presented; it consists of the acceleration of this electron beam into relativistic plasma waves driven by a laser. This compact approach (centimetres scale for the plasma, and tens of meters for the whole facility) will allow a miniaturization and cost reduction of future accelerators and derived X-ray free electron laser (XFEL) sources.
Particle accelerators are used in a tremendous variety of fields, ranging from medicine (for medical imaging and radiotherapy) to high-energy physics. Each progress of the beam parameters has permitted new discoveries and new applications. With conventional accelerators, based on the use of radio frequency accelerating structures, accelerating fields are limited to 50 MV m−1 due to material breakdown which occurs on the walls of the structure. As a consequence, high-energy accelerators tend to be expensive and large-scale infrastructures. A compact and economical approach will be beneficial for society and education. In this context, plasma-based accelerators (Tajima & Dawson 1979) are of great interest because of their ability to sustain extremely high-acceleration gradients, with peak values greater than 1 TV m−1 (Malka et al. 2002) achieved when the plasma wave amplitudes reach the nonlinear regime. Such high fields make plasma-based accelerators likely candidates for the next generation of compact accelerators.
The generation of stable accelerating structures (e.g. relativistic plasma waves) in plasmas has been demonstrated by different groups using laser beat wave or laser wakefield schemes. When the normalized vector potential associated with the laser field is not too high, these schemes can be reliable because of the linear nature of the laser interaction mechanisms with the plasma. The generation of intense accelerating fields in plasmas has been demonstrated in many experiments (Clayton et al. 1985; Kitagawa et al. 1992). Proof-of-principle experiments have shown the feasibility of externally injecting electrons from a conventional accelerator into the laser-driven plasma accelerating structure (Kitagawa et al. 1992; Everett et al. 1994; Amiranoff et al. 1998). However, the output beam quality has been poor: the electron energy distribution has had a 100% energy spread. The peak electric fields in these pioneering experiments were limited to the GV m−1 range, permitting electron energy gains of tens of MeV in the best case. The production of mono-energetic beams with this method puts stringent constraints on the injector: electrons have to be injected in a particular phase of the plasma wave, which implies injecting a sub-100 fs electron bunch. The technology for producing such short bunches containing a high charge does not exist yet.
However, electron beams can be generated directly from the plasma, without external injection. Until now, the most widespread method for producing electron beams from plasmas has relied on the self-modulated laser wakefield (SMLWF) accelerator. In the SMLWF accelerator, the laser pulse is longer than the plasma wavelength. Under the influence of the self-modulation instability, its envelope modulates at the plasma frequency and resonantly excites a plasma wave. When the plasma wave amplitude reaches the wavebreaking level, copious amounts of plasma background electrons are trapped in the plasma wave and accelerated.
To accelerate electrons at higher energy without energy spread, the duration of the injected electron bunch has to be shorter than the plasma period of the accelerating structure. Therefore to achieve high-quality beams from plasma-based accelerators one needs: (i) to produce a high quality and ultra short seed beam and (ii) to generate an accelerating structure in the plasma called relativistic plasma waves.
In this paper, we present the main results on high-quality quasi-monoenergetic electron beams produced with compact lasers. We demonstrate, on the basis of numerical simulation, that this electron beam can be injected into a plasma wave to be boosted to the GeV range. This shows that with current laser technology, a high-quality GeV electron beam can be obtained at lower cost and in a compact way.
2. Laser–plasma injector
(a) Maxwellian-like distribution
The first electron beam generated by a laser was observed in 1995 (Modena et al. 1995) using the Vulcan (20 terawatt (TW), 1 ps) laser. Plasma waves were excited by the laser in the SMLWF regime (Andreev et al. 1992; Antonsen & Mora 1992; Sprangle et al. 1992). The laser and plasma parameters for this regime were (i) a laser pulse with duration much greater than the plasma period and (ii) a laser power in excess of the critical power for relativistic self focusing. In the SMLWF, the growth of the plasma wave is amplified from an initial small level seed source, which itself depends on instabilities for its creation, therefore plasma wave characteristics can vary greatly from shot to shot. In the SMLWF regime, the plasma wave amplitude is limited to roughly 10% of the ambient density due to thermal loading of the plasma wave by hot background electrons (LeBlanc et al. 1996; Ting et al. 1996; Moore et al. 1997; Clayton et al. 1998), implying that the maximum energy to which electrons can be accelerated is not reached. In addition, in the SMLWF, the laser pulse interacts with several plasma wavelengths and, therefore, with electron bunches in these structures. This interaction reduces the electron beam quality.
Using a shorter laser pulse (30 fs) with a power exceeding the critical power for self focusing and a low-density plasma for which the plasma period is close to the laser pulse duration, a highly nonlinear regime, called the forced laser wakefield (FLWF), has been demonstrated. Through a combination of front-edge pulse sharpening, optical compression and relativistic increase of the plasma wave wavelength, a large amplitude plasma wave can grow in the FLWF. In this regime, the lack of instabilities in the interaction results in a lower plasma temperature allowing a plasma wave amplitude with a much higher value, approaching the cold wavebreaking limit (Akhiezer & Polovin 1956), , to develop, where Emax is the maximum electric field associated with the relativistic plasma wave, , and γp is the Lorentz factor associated with the plasma wave phase velocity, which for sufficiently under dense plasmas is approximately , the square root of the ratio of critical density to plasma density. The corresponding electric field value has been computed to be 1.4 TV m−1, close to these theoretical values. Also, due to the relativistic steepening of the plasma wave and optical compression of the laser, the accelerating plasma wave density spikes, and thus most of the trapped and accelerated electrons sit behind the laser pulse. This means that in the FLWF regime the effect of direct laser acceleration (DLA) is greatly reduced. DLA has been shown to be a possible accelerating mechanism in long pulse high-intensity interactions (Gahn et al. 1999; Pukhov et al. 1999), but it is associated with transverse momentum gain for the accelerated electrons, which can result in undesirable emittance growth. In the FLWF, the electrons interact primarily with the focusing and accelerating fields of the plasma wave and this can result in greatly improved beam emittances. Electron energy distribution and emittance measurements (Fritlzer et al. 2004) have indeed demonstrated that this new regime is suitable for improvement of electron beam parameters.
The use of these ultra short and collimated electron beams has already allowed significant progress to be made in fields such as material science and chemistry. For material science the collimation of an electron beam can be used to generate an extremely small γ ray source. A proof of principle experiment has been done at LOA, using a tantalum foil of 2.5 mm thickness as a γ convertor. The thickness has been selected by minimizing the γ source size, while keeping a high flux (Glinec et al. 2005). Image analysis indicates that the γ source size is less than 400 μm in diameter, which is a few times smaller than existing γ sources produced by conventional radiography accelerators. The second property of interest for new applications is the shortness of the electron bunch. This property has been used in order to study fast radiolysis for chemistry. The dynamics of solvated aqueous solutions excited by ionizing radiation (here the electron beam) has been investigated for the first time in the sub picosecond regime using a laser–plasma accelerator. Another major advantage of this approach is the perfect synchronization between the electron beam (used as a pump beam) and part of the laser beam (used as a probe beam) for this pump-probe experiment (Brozek-Pluska et al. 2005).
An advantage of the short laser pulse is the energy requirement: lower laser energy is needed to obtain high peak intensities. Thus, the thermal load on the amplifiers is greatly reduced and these systems can operate at much higher repetition rate (typically 10 Hz). These ultra short lasers are perfectly suited for applications. More importantly, it has been demonstrated that the interaction of shorter laser pulses (few tens of fs) with underdense plasma produced higher quality monoenergetic electron beams (Faure et al. 2004; Geddes et al. 2004; Mangles et al. 2004) with very low emittance value.
(b) Monoenergetic electron beam
(i) Experimental set-up
The experiment was performed using a titanium doped sapphire (Ti : Sa) laser (Strickland & Mourou 1985) of the ‘salle jaune’ operating at 10 Hz and a wavelength λL of 820 nm in the chirped-pulse amplification (CPA) mode (Pittman et al. 2002). The laser delivered energies of up to 1 J on target in 30 fs full width at half maximum (FWHM) pulses, with a linear polarization. To avoid refraction induced by ionization processes (Decker et al. 1996) the laser beam was focused with an f/18 off-axis parabolic mirror onto the edge of a 3 mm diameter supersonic helium gas jet. The optimized (Semushin & Malka 2001) neutral density profile jet was characterized by interferometry (Malka et al. 2000) and found to be uniform. The laser distribution at full energy in the focal plane was a Gaussian with a waist w0 of 18 μm containing 50% of the total laser energy. This produces vacuum focused intensities IL on the order of 4×1018 W cm−2, for which the corresponding normalized vector potential is 1.4.
Instead of measuring the electron energy spectra using a few diodes, we have chosen a new compact spectrometer consisting of a 0.45 t, 5 cm long permanent magnet and a LANEX phosphor screen. Doing so, we were able to measure, in a single shot, whole spectra on a 16-bit charged coupled device (CCD) camera. Since we do not use a collimator, the vertical direction on the LANEX screen corresponds to the angular aperture of the electron beam. The LANEX screen was protected by a 100 μm thick aluminium foil in order to avoid direct exposure to the laser light. For deconvolution of the images obtained with the LANEX screen, electron deviation in the magnetic field has been considered as well as the electron stopping power inside the LANEX screen. The location of the integrating current transformer (after the magnet), allows the measurement of the charge of electrons with energies greater than 100 MeV. A schematic description and a picture of the inside of the vacuum chamber are presented in figure 1.
The electron beam distribution obtained in the optimum condition, i.e. when the laser interacts with a plasma density of ne=6×1018cm−3 is shown in figure 2. The distribution is significantly different from measurements done in previous experiments at lower or higher density. One must notice the quasi-monoenergetic component peaked at 170 MeV, which dominates the distribution. The resolution is limited by the electron beam aperture and by the dispersing power of the magnet. The resolution was respectively 32 and 12 MeV for 170 and 100 MeV energies. Above 200 MeV, the resolution quickly degrades.
The charge contained in this bunch can be inferred using the integrating current transformer: the whole beam contains 2±0.5 nC and the charge at 170±20 MeV is 0.5±0.2 nC. The electron beam energy was estimated to be close to 100 mJ, which corresponds to almost 10% of the laser energy. At lower density, the peak energy is at approximately the same position even if the number of electrons is reduced by a factor of 10, whereas at higher density, the peak energy decreases and vanishes progressively into the Maxwellian distribution.
(ii) The bubble regime
Such quasi-monoenergetic electron distribution has been predicted in the pioneering work of Pukhov & Meyer-Ter-Vehn (2002). Using a three-dimensional PIC code (Pukhov 1999), it was shown that in a new regime (the so-called ‘bubble regime’), electron injection can be somewhat controlled. In addition, in this regime, the electron energy distribution exhibits peaked distributions. The plasma density was close to the experimental one, whereas the laser energy was significantly higher (12 J). To reach this regime, with the laser and plasma parameters of the experiment, one needs to account for the effect of relativistic self focusing which increases the laser peak intensity to a level corresponding to this regime. The laser ponderomotive force expels the plasma electrons radially and longitudinal and leaves a spherical cavity behind. The electron density just behind the bubble increases before the trapping process starts. This injection is well located in space, thus giving an electron beam with a transverse dimension smaller than the initial laser waist and a duration shorter than the laser pulse. The normalized transverse emittance of the beam was computed to be close to 4π mm mrad, which is quite competitive with the best conventional accelerators. Simulations also show that the electron bunch duration is about 30 fs. Since the electron distribution is quasi-monoenergetic, the bunch can stay short upon propagation.
Recent PIC simulations, with parameters corresponding to our experiment, have shown that we are at the dawn of this regime: the laser forms a very nonlinear wakefield with strong cavitation. The measured electron distribution and its evolution with the plasma densities are in good agreement with three-dimensional PIC simulations (Malka et al. 2005).
3. Towards the GeV range
Two scenarios are envisaged for accelerating electrons to GeV energies. The first one is the natural extension of the FLWF experiments presented above. It consists in raising the laser power from 100 TW to some petawatts (PW) keeping similar values for the pulse waist radius and duration. Numerical simulations have shown that in this strongly nonlinear ‘bubble’ regime, GeV energies can be attained in a single stage with acceleration lengths of some millimetres (Pukhov et al. 2004; Tsung et al. 2004). As an example, PIC simulations predict that electrons of 1.5±0.3 GeV can be obtained with a 96 J–4 PW laser pulse (a0=40, τL=20 fs) and an acceleration distance of 0.8 mm.
In the second scenario, an electron bunch of some MeV created in a first stage is injected into the wakefield of a moderate amplitude laser (a0≃1) and accelerated over distances of some centimetres (Reitsma et al. 2000; Gorbunov & Kalmykov 2005; Gordon et al. 2005). The weakly nonlinear nature of the interaction in this second scheme could give stable operation conditions, avoiding wave breaking, strong self focusing and the onset of microscopic instabilities (such as filamentation, two-stream, etc.). Therefore, operating in this regime gives larger flexibility and better control over the beam properties.
In this second regime, monochromatic beams can be produced in two ways. In the first one, injected bunches have energies close to the threshold for trapping in the radial focusing region, typically 1–2 MeV (Lifschitz et al. 2005). Bunch lengths can be as large as the plasma length λp, and the final spectrum is insensitive to the injection phase. On the other hand, the bunch charge is limited to a few hundred pC due to focusing constrains. The second approach consists of injecting highly relativistic and ultrashort bunches (Lb≪λp). In this case, injection phase must be accurately tuned, but larger charges are allowed. As we showed in the previous section, laser wakefield acceleration has allowed the production of low emittance, monochromatic and ultrashort electron bunches. These bunches are ideally suited for injecting into the weakly nonlinear wakefield, thus the complete accelerator will be based on laser–plasma interaction.
We have performed numerical simulations of the acceleration of short bunches using the code WAKE (Mora & Antonsen 1997). In order to limit laser energy, pulses are guided through a plasma channel. Radial density profile is parabolic, and given by(3.1)Electron bunch parameters are: duration 30 fs, energy 170±20 MeV and angular divergence 10 mrad. Small energy spectral widths are obtained when the accelerating field varies little along the bunch length. Therefore, plasma density must be low enough to allow the fulfilment of the condition Lb/λp≪1. Energy spectra for Lb/λp=0.11 (n0=1.7×1017 cm−3) and selected channel lengths are shown in figure 3. We use a conservative value for the channel depth, Δn=2n0. We set the channel radius to rch=29 μm, close to the critical value (Sprangle et al. 1992). Narrower and steeper channels could be used to guide the pulse, although the formation of such channels requires further investigation. The vacuum spot radius is 32 μm, a value larger than the matched radius. Simulations for different radii show that perfect matching is not necessary to obtain good guiding and high-quality beams. Laser intensity is 4.8×1018 W cm−2, corresponding to normalized amplitude a0=1.5, energy 6.4 J and power of 80 TW. Bunches are injected into the second wake period, with the tail at the maximum of longitudinal electric field. As can be seen, a 4 cm channel is enough to produce GeV electrons. The distribution is relatively monochromatic with an energy spread of roughly 20% at 4 cm.
The final angular divergence of 10 mrad is close to the injection one. Although the initial radial velocity distribution is not matched, there is not significant degradation of emittance.
A smaller energy spread can be obtained by further reducing the plasma density. For n0=8.6×1016 cm−3, that corresponds to Lb/λp=0.064 as can be seen in figure 4. In this simulation, we used the same value for Δn/n0 as in the previous one, Δn/n0=2. To confine the pulse, both the channel radius and the pulse spot must be larger. We set w0=46 μm and rch=41 μm. The laser energy is 11 J, whereas the power is 140 TW. On the other hand, lower plasma density implies weaker electric field (the wake electric field is roughly proportional to ), and therefore larger acceleration paths are needed. To reach 1 GeV, the channel length should be 8 cm, twice that of the previous case.
In conclusion, quasi-monoenergetic electron beams generated by ultra short lasers have suitable properties for a two stage laser–plasma accelerator. On the basis of numerical simulations, it appears that high-charge 1 GeV electron beams with low-energy spreads can be produced in a very compact way. Importantly, the beam quality is preserved as well as the very short bunch duration. In the future, we will consider the beam loading effect due to the interaction of the electron with the plasma medium.
The bunch duration (sub-30 fs), along with the present improvement of the charge (nC) and the quality of the electron beam at 1 GeV (monoenergetic spectrum, low divergence) reinforce the major relevance of plasma-based accelerators for the production of X-rays in the XFEL concept. Such a demonstration will be fruitful for future laser–plasma accelerators based on a multi-stage approach.
The authors acknowledge useful conversations with E. Levebfre, P. Mora and A. Pukhov. We acknowledge the support of the European Community Research Infrastructure Activity under the FP6 Structuring the European Research Area program (CARE, contract number RII3-CT-2003-506395).
One contribution of 15 to a Discussion Meeting Issue ‘Laser-driven particle accelerators: new sources of energetic particles and radiation’.
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