2.1. Electron beam generation in under dense plasmas

Electron beams can easily be generated by the breaking of relativistic plasma waves in an under dense plasma, where the plasma electron density is below the critical density, n_e < n_c, which limits the laser beam to propagate through matter. Due to the non-linear interaction that occurs at laser powers beyond some tens of TW, initially low-amplitude plasma waves can be very efficiently driven to wave breaking if the laser pulse length, cτ_L, is of the order of the plasma wavelength, λ_p, i.e., if the condition for classical wake field acceleration is not met. In this forced laser wake field (FLW) regime, a combination of laser beam self-focusing, front edge laser pulse steepening, and relativistic lengthening of the plasma wave wavelength can result in a forced growth of the wake field plasma wave (Malka et al., 2002; Najmudin et al., 2003). In the FLW regime the interaction of the bunch of accelerated electrons and the plasma wave with the laser is reduced, this can yield the highest known electron energy gains attainable today with laser plasma interactions.

Indeed the maximum energy in the FLW is significantly greater than in any other regime known so far, suggesting the growth of plasma waves with peak amplitudes greater then the initial plasma density. Interestingly, the plasma wake is mostly formed by a fast rising edge, and the back of the pulse has little interaction with the relativistic longitudinal oscillation of the plasma wave electrons. Graphically speaking, the relativistic laser plasma interaction occurs solely on one single plasma wave cycle, which is a subtle difference to other regimes. Indeed the increase of plasma wave wavelength due to relativistic effects means that the breaking and accelerating peak of the plasma wave sits behind most, if not all, of the laser pulse. Hence, its interaction and that of the accelerated electrons with the laser pulse is minimized, thus reducing possible undesirable emittance growth.

2.2. Proton beam generation in over dense plasmas

In contrast, proton beams are more efficiently generated in over dense plasmas, n_e > n_c. Even though the laser beam is prevented from propagating through this medium, its ponderomotive force nevertheless accelerates electrons in the plasma skin layer. These are electrons which can propagate through the target setting, up a space-charge field at the rear surface once they escape the plasma. Importantly, this space-charge field is quasi-static, i.e., protons which have a higher mass than electrons can respond to these fields, and can therefore be accelerated to high energies since these space-charge fields can exceed several TV/m as well.

The above mentioned optically induced particle sources currently have a Maxwellian-like energy distribution, they already have some interesting features like: (1) their accelerating field gradients are by 4 orders of magnitude higher than those attainable with today's standard techniques, which can indeed cut down the accelerating length significantly; (2) the required lasers are rather compact and cheap compared to current RF-structures; (3) no shielding for radioprotection is required up to the point where the laser creates a plasma on the target; and (4) the same laser can be used to generate electrons or protons simultaneously.

3.1. Experimental set-up

The very first experiment of the FLW regime was performed on the “salle jaune” laser at Laboratoire d'Optique Appliquée (LOA), operating at 10 Hz and a wavelength of 820 nm in the CPA mode. It delivered energies on target of 1 J in 30 fs, full width at half maximum (FWHM) linearly polarized pulses, the contrast ratio was better than 10⁻⁶ (Pittman et al. 2002). Using an f/18 off-axis parabolic mirror, the laser beam was focused onto the sharp edge of a 3 mm supersonic helium gas jet. The focal spot had a waist of 18 μm, this resulted in peak intensities of up to 3 × 10¹⁸ W/cm². The plasma period was chosen to vary between 25 and 14 fs by selecting initial electron densities, n_e, between 2 and 6 × 10¹⁹ cm⁻³, which was achieved by changing the backing pressure of the gas jet. Figure 1 shows the subsequently installed experimental set-up.

Experimental set-up at “salle jaune” laser. The laser beam was focused with an off-axis parabolic mirror (a) onto the edge of a 3 mm helium gas jet (b). The total number of generated electrons was determined with an Integrating Current Transformer (ICT) (c), which could be replaced with a secondary set-up for emittance measurements. The transmitted laser beam was analyzed with an optical spectrometer and recorded onto a CCD camera (d). A glass plate with a center hole separated the laser and electron beams non-destructively. The electron yield as a function of energy was determined with a spectrometer, which electrons could entered through a collimator (e) and measured with silicon barrier detectors (f). Lead walls shielded those from bremsstrahlung (g).

In order to obtain information about the opening cone of the generated electron beam as a function of its energy, a secondary detector was implemented. This consisted of a stack of radiochromic film (RCF) to visualize, and copper pieces of various thicknesses to stop the electron beam. To avoid illumination of the RCF by the laser, this stack was completely shielded with aluminium wrapping. It was placed on the laser beam axis behind the center of the gas jet nozzle. The emittance of an electron beam is usually normalized to the usual relativistic electron parameters. As the energy spectrum of the electron source generated in this experiment is expected to be broad, the single electron energies need to be dispersed. This was achieved by implementing a secondary magnet, which was installed directly behind the gas jet nozzle. Electrons could enter this non-focusing magnet through two different stainless steel collimators. These collimators served to obtain a reasonable energy resolution while taking into account the opening cone as well as the halo of the electron beam. Since the emittance can be seen as the area of the electron divergence distribution as a function of position within the beam envelope, the electron beam envelope was partially masked, solely permitting single electron beamlets at a defined position to pass through these holes. This arrangement is known as a “pepper-pot” (Yamazaki et al., 1992). Here, lead plates of varying thicknesses were implemented, which were sufficient to stop electrons at the regarded energy bins. These masks were fixed directly next to the magnet and were displaced vertically. The electron beam passing through these holes was visualized at various distances behind the mask with RCF, which has a spatial resolution below 10 μm, and which was scanned with the same resolution directly after the experiment. To avoid illumination of the RCF by the laser beam it was shielded with aluminium wrapping correcting afterward the scattering of electrons within this wrapping.

3.2. Results

The resulting electron spectrum for a neutral plasma electron density, n_e, of 2.5 × 10¹⁹ cm⁻³ is shown in Figure 2. Although it is possible to fit to the lower energy electrons a relativistic Maxwell-Jüttner distribution, which results in an electron temperature of (18 ± 1) MeV for electrons of less than 130 MeV, this description is not adequate to describe the higher energy electrons. A significant number of electrons exists in a “hot tail” that extends beyond 200 MeV. Measurements with the ICT showed that the total beam charge was (5 ± 1) nC. As can be seen in Figure 3, the higher the energy of electrons within this electron bunch, the better the collimation.

Electron energy spectra for 2.5 × 1019 cm−3 electron density and a laser irradiance of 3 × 1018 W/cm2. An effective longitudinal electron temperature of (18 ± 1) MeV can be derived for electrons of less than 130 MeV (continuous line).

FWHM of the angular distribution of the electron beam as measured with RCF and copper stack.

Numerical simulations of this experiment indicated that during this relativistic laser plasma interaction accelerating fields of around 1.4 TV/m were induced when wave breaking occurred. As for this experiment, the laser pulse duration was of the order of the plasma wavelength, one might conjecture that only a single electron bunch is accelerated, with a bunch duration of the order of tens of fs. This was also verified numerically as the plasma wave generated in this experiment suffered strong wave breaking and accelerated electrons up to 200 MeV, it is also rapidly damped after its first accelerating extremum. As a result these simulations showed that there is little or no wave breaking for the plasma wave oscillations behind the first extremum, so that the hot electron population is localized in space. Importantly, only in the first plasma wave wavelength electrons are accelerated above 50 MeV and the duration of this 50-plus MeV bunch at the exit of the plasma extends over less than 20 μm, which corresponds to a pulse duration of 67 fs (Fritzler et al., 2003a).

Figure 4 shows the experimentally determined emittance of this electron beam as a function of its energy. Interestingly, the normalized vertical emittance was found to be as low as (2.7 ± 0.9) π mm mrad for (54 ± 1) MeV electrons. It is clear that this emittance does indeed cope with today's standards in accelerator physics—in particular combined with its very short pulse length (Fritzler et al., 2003b).

Normalized vertical emittance λn,x as a function of electron energy.

3.3. Applications and outlook

Conventional accelerators typically provide energetic electron bunches with pulse duration in the ps order and an energy resolution of less than 10⁻³. To achieve these performances, such devices are precisely designed and, hence, for a fixed electron energy only. Even though this high energy resolution is not met in the FLWF scheme, it enables to select an arbitrary energy bin out of the entire spectrum of up to 200 MeV at low emittances and with sub-ps pulse lengths over a wide range of electron energies. However, the convolution of the measured electron yield and its angular distribution shows that the bunch charge of high energy electrons does not compare so far to accelerators' that typically operate at several pC and even nC. Additionally, peak electron currents of about 10 A for 45 MeV electrons is not competitive, even though the quantity is favored by the ultra short bunches. However, simulations for a 12 J, 33 fs laser pulse interacting with an under dense plasma suggest that a large beam charge increase could be obtained in an improved mode of the FLW regime, where the laser pulse propagates inside a solitary plasma cavity (Pukhov & Meyer-ter-Vehn, 2002). In this case, the distribution of the accelerated electrons is no longer Maxwellian but shows a clear peak with charges as high as, say, 5 nC at (300 ± 25) MeV. Up to now, this “broken wave” regime cannot be experimentally verified, since such challenging laser systems do not currently exist. Nevertheless, they are already today an issue for laser development.

Another interesting feature of such sub-ps electron bunches showed an experiment on ultra-fast radiation chemistry. In this pump-probe experiment such a sub-ps electron bunch was propagating through a suprasil cell containing pure liquid water. Importantly, radiolytic events induced by electrons today only well-known on ns time scales, have been studied for the first time in the sub-ps regime at LOA (Gauduel et al., 2004) will potential impact for modern oncology.

4.1. Experimental set-up

Here, the laser with an on target energy of up to 840 mJ and an FWHM duration of 40 fs was focused using a f/3 off-axis parabolic mirror. The focal waist was 4 μm, this resulted in peak intensities of up to 6 × 10¹⁹ W/cm². For these impulsions, the laser contrast ratio was, again, found to be of the order of 10⁻⁶. In this experiment the target were 6 μm thick aluminium foils.

The energy, yield as well as the opening cone of generated protons were determined with CR-39 nuclear track detectors, which were partially covered with aluminium foils of varying thicknesses, which served also as energy filters.

4.2. Results

Figure 5 shows the measured proton energy distribution. Clearly, the energy of this beam reaches 10 MeV. As can be seen in Figure 6, the proton beam is more collimated at higher energy. NB, that recently only proton beams of up to 1.5 MeV have been reported with similar short pulse and high repetition rate lasers. Interestingly, these measurements are in qualitative agreement with kinetic simulations, which again demonstrate numerically the generation of accelerating fields beyond some TV/m at the space-charge field induced on the rear surface of the target. The regular variations, followed by an abrupt cut-off at the maximum energy and the smooth transverse variations of the accelerating field fully reproduce the experimental findings.

Proton energy spectra at a laser irradiance of 6 × 1019 W/cm2 for a 6 μm aluminium target. The arrow indicate the minimum number of protons, which results of the saturation of the detectors.

FWHM of the proton beams shown in Figure 5.

4.3. Applications

Even though the energy spectrum of this proton beam has a broad Maxwellian-like distribution, it can nevertheless be interesting for the generation of Positron Emission Tomography (PET) radio-isotopes since its energy is greater than the Q-value, i.e., the threshold of the corresponding (p,n) reactions. Since the Q-values for most prominent isotopes, ¹¹B and ¹⁸O, are 2.8 and 2.4 MeV, respectively, this laser produced proton beam might therefore represent an alternative method for PET isotope production than it is pursued today. Naturally, this possibility favors all of the above mentioned benefits of relativistic laser plasma interactions. Calculating the expected PET isotopes activity after an irradiation time of 30 min and a repetition rate of 1 kHz, which is indeed feasible in the very near future, activities of the order of 1 GBq can be obtained for ¹¹B and ¹⁸O, which are required in order to separate the tracer from the inactive carrier with fast chemistry techniques. Interestingly, numerical simulations indicate that a modest increase in laser intensity to 8 × 10¹⁹ W/cm² can result in even more protons at higher energies and can lead to a sevenfold increase in ¹⁸F activity (Fritzler et al., 2003c). This favorable intensity scaling is supported by recent experimental observations at 5 × 10²⁰ W/cm² which measured 3 MBq of ¹¹C, more than one order of magnitude greater than what was obtained at 5 × 10¹⁹ W/cm² with the same experimental set-up.

Another very interesting challenge concerns the use of optically induced proton beams for proton-therapy. Some groups already started to investigate this approach on the basis of numerical simulations, and have shown that implementing a PW laser with a pulse duration of 30 fs, and a repetition rate of 10 Hz will indeed meet the requirements for this purpose (Fourkal et al., 2002), as the dose the delivery delivered with such an adjustable proton beam spectrum within the therapeutic window (in between 60 and 200 MeV) is already expected to be beyond some few Gy/min. Importantly this approach would provide a double benefit:

1. As high-intensity lasers can generate very large accelerating fields, the acceleration length and hence the size and weight of the facility is tremendously reduced, allowing a possible installation inside standard radiotherapy departments. This significantly reduces the costs and provides larger accessibility.
2. As the main beam in this “accelerator” is just a laser beam, while proton generation only occurs at the end, one could also expect to considerably reduce the size and weight of the gantries and the radiation shielding.

The development of such a laser will permit to confirm the benefit of this approach, to investigate the shot-to-shot study reproducibility of the generated proton beam as well as the optimization of the laser and the target parameters (contrast, focal spot, thickness, etc…) (Malka et al., 2004).