2. PROTON IMAGING

Proton imaging employs proton beams as a diagnostic tool in a point-projection imaging scheme and provides the possibility of identifying electric fields in dense plasmas and laser-irradiated targets with unprecedented spatial and temporal resolution. The proton beams need not be monochromatic for this application. A broad spectrum can actually be advantageous, as it allows multiframe capability. The targets used for proton beam production are thin foils that act as the source of the proton beam as described in Borghesi et al. (2002a, 2003). The electromagnetic fields in a plasma between the source and the detector distort the geometrical propagation of the protons. In this way electric fields, slowly varying on the proton crossing time, can be detected with micron spatial resolution and their evolution can be followed on a picosecond time scale, as discussed in detail in Borghesi et al. (2003). This high temporal resolution makes laser-produced proton beams ideal to detect coherent field structures arising from the nonlinear plasma dynamics following intense, short pulse interactions. This is shown, for example, by the filamentary structures that are observed in the case of the ultraintense irradiation of a 150 μm glass microballoon. These filamentary structures are first seen a few picoseconds after the peak of the interaction pulse and have been interpreted as the growth, at the surface of the target, of an electromagnetic heat-flow instability (Haines, 1981) arising in the presence of two counterstreaming currents.

Proton probing was also used to investigate the field structures arising after the interaction of an ultraintense laser pulse with preformed plasmas. The main feature observed in the proton images was (Borghesi et al., 2002b) the onset of several bubblelike structures following closely the interaction. Analytical and numerical results (Bulanov et al., 1992, 1994, 1995, 1999; Sentoku et al., 1999; Esirkepov et al., 2002b; Lontano et al., 2003) show that slowly propagating, low-frequency, subcycle solitons can be generated in the interaction of ultrashort ultraintense laser pulses with underdense plasmas. The typical size of these structures is of the order of the collisionless electron skin depth d_e = c/ω_pe. Inside these solitons the electric and the magnetic fields oscillate synchronously with a frequency smaller than the plasma frequency ω_pe. In addition, an electrostatic field is present, arising from charge separation. These subcycle solitons expand radially on ion time scales and become almost quasineutral (Naumova et al., 2001). In this phase, initially separated solitons can merge and form a foam of plasma bubbles (Borghesi et al., 2002b).The residual electrostatic field inside these bubbles can deflect the trajectories of the protons in the beam. The resulting proton deflection pattern, interpreted in terms of the evolution of the laser-produced solitons, is consistent with the bubblelike structures observed in the plasma and allows us to measure both the bubble size and the electric field inside them (Borghesi et al., 2002b).

3. PROTON DRIVEN FAST IGNITION

In the model of the fast ignition of precompressed fusion targets by a beam of protons accelerated by the laser radiation (Bychenkov et al., 2001; Roth et al., 2001), a key element is the conversion of the energy of a petawatt laser pulse into a beam of fast ions that is used to ignite the target. This energy conversion occurs via the intermediate generation of strongly relativistic electrons that can accelerate the proton beam. In this scheme it is fundamental that the energy deposition inside the target be localized in space. In Roth et al. (2001), the beam was assumed to be monoenergetic. A recent investigation (Atzeni et al., 2002; Temporal et al., 2002) motivated by the fact that laser-induced proton sources in current experiments have broad energy spectra has examined how this energy spread may give rise to a substantial power deposition spread at the dense fuel. Proton beam requirements for DT fast ignition have then been studied using an analytical model and two-dimensional (2D) numerical radiation-hydro-nuclear simulations integrated with one-dimensional (1D) simulations of fuel compression. The simulations assume an exponential or Maxwellian velocity distribution of the protons. An important result is that the values of the ignition energy are characteristically higher than those estimated by Roth et al. (2001) by a factor of about 4.

4. ONCOLOGICAL PROTON THERAPY

The use of protons in radiotherapy for cancer treatment (Khoroshkov & Minakova, 1998; Amaldi, 2001; Kraft, 2001; Goiten et al., 2002) has several advantages: (1) The proton beam scattering on the atomic electrons is weak and thus there is less irradiation of healthy tissues in the vicinity of the tumor; (2) the slowing down length for a proton with given energy is fixed, which avoids undesirable irradiation of healthy tissues at the rear side of the tumor; and (3) the well-localized maximum of the proton energy losses in matter (the Bragg peak) leads to a substantial increase of the irradiation dose in the vicinity of the proton stopping point. However the construction and operation costs of hospital-based proton therapy centers remain comparatively higher (Bulanov et al., 2002b, 2002c) than those of the most expensive conventional beam therapy plants designed for radiation therapy. An attractive possibility for reducing such costs is to use ultrashort, ultraintense laser pulses to produce the proton beams. In this scheme, the laser radiation is delivered to the target, where its energy is converted into the energy of fast protons. In this approach, the central accelerator, the channels through which the fast protons are transported, and most of the gantry, which provides multidirectional irradiation of a lying patient, is no longer required.

The basic parameters required for a proton beam to be used for medical applications can easily be reached with present accelerator technology. The proton beam intensity must be in the 10¹⁰ to 5 × 10¹⁰ protons per second range, the maximum proton energy must be in the 230 to 250 MeV range. For laser accelerators, the most demanding conditions are the requirement for a highly monoenergetic proton beam with ΔE/E = 10⁻² and the system duty factor, that is, the fraction of the time during which the proton beam can be used, which is important in determining the economical feasibility of the use of a laser accelerator. Indeed the main physical challenge is to devise a method of producing proton beams of sufficiently high quality in terms of energy resolution to ensure that a substantially high and homogeneous dose is delivered to the tumor while sparing neighboring healthy tissues. In the following, we discuss a possible method of achieving such high quality proton beams by using short laser pulses and a target made of a layer of heavy ions followed by a thin proton layer with a transverse size smaller than the pulse waist. Double layer targets were shown experimentally in Badziak et al. (2001, 2002) to provide a considerable increase in energies and current of protons produced.

5. HIGH QUALITY PROTON BEAMS

In this layered target scheme (Bulanov et al., 2002a, 2002b, 2002c; Esirkepov et al., 2002a), a foil is used as the target and its rear surface is coated with a thin and transversally narrow hydrogen layer, as shown schematically in Figure 1. An ultrashort, ultraintense laser pulse irradiates the target: The heavy atoms are partly ionized and most of the resulting free electrons abandon the foil. This leads to a large electric field due to charge separation. Heavy ions with a large mass-to-charge ratio remain at rest whereas the protons in the coating are accelerated. If the proton coating is thin and has a transverse size smaller that the diameter of the focal spot of the laser pulse, this scheme provides a controlled acceleration of protons.

Two-layer target. The rear side of the foil of heavy ions is coated with a thin hydrogen layer.

The electrons escaping the heavy ion foil under the action of the ponderomotive pressure of the laser radiation give rise to a quasistatic electric field caused by the unneutralized electric charge. This field is localized in a finite region with dimensions comparable to the transverse dimension of the laser pulse. In this initial stage, the protons are accelerated by this electric field before the heavy ions of the first layer start to move. If the total number of protons is small in comparison with the number of electrons that have escaped from the target, the effect of the electric field of the protons on their dynamics can be neglected. In this case the proton acceleration can be described in the approximation of test particles moving in an assigned electric field and the expression for the particle energy spectrum N(E) is given by the continuity equation for the particle flux in phase space as

where n₀(x₀) is the initial proton density, x₀ is their initial position, and |dE/dx₀| is calculated at x₀ = x₀(E). Equation (1) holds in a 1D approximation, justified in the case where the transverse size of the proton layer is smaller than the pulse waist, and shows that a proton beam with a small energy spread can be obtained using a thin proton layer with a small thickness δx₀, in which case the energy spread of the proton beam is proportional to the layer width δx₀. The characteristic value of the particle energy E at the end of the acceleration region can be estimated, for laser pulses of sufficiently high intensities, by assuming that all the electrons produced by ionization in the focal spot on the target escape from it. In this situation, the electric field near the proton layer is equal to E₀ = 2πn_iZ_iel, where n_i is the heavy ion density inside the target, Z_ie their charge, and l is target thickness. Taking the longitudinal dimension of the acceleration region of the order of the diameter 2R* of the focal spot, we obtain

Here, we have assumed that the energy of the electrons accelerated by the laser field is of the order of, or higher than, the energy required to overcome the attractive (positive) electric field in the acceleration region.

These simple analytical considerations are supported by more detailed numerical analyses (Esirkepov et al., 2002a; Bulanov et al., 2002a, 2002b, 2002c) that take into account the nonlinear kinetic processes that occur during the interaction of an ultraintense laser pulse with a target and that extend the results obtained above to 2D and three-dimensional (3D) geometries. Here, we report recent results obtained in 3D simulations (Esirkepov et al., 2002a; Bulanov et al., 2002a) using a numerical model of the proton acceleration in the two-layer target where an ultrashort laser pulse, without a prepulse or pedestal, impinges on a preformed plasma slab. These results were obtained using the relativistic electro-magnetic particle–mesh (REMP) code (Esirkepov, 2001), which is designed so as to reduce the numerical effect of plasma heating as well as other nonphysical effects peculiar to the PIC method. In these simulations, the plasma consists of particles of three species: heavy ions and electrons in the first layer and protons and electrons in the second. The proton-to-electron mass ratio is m_p /m_e = 1836, and the mass-to-charge ratio of the heavy ions (gold) is m_i /(m_eZ_i) = 195.4 × 1836/2. The electron density of the gold layer corresponds to ω_pe /ω = 3, where ω is the laser frequency, and the density in the hydrogen layer corresponds to ω_pe /ω = 0.53. The gold layer is 0.5λ thick and 10λ wide, the hydrogen layer is 0.03 λ thick and 5λ wide. The total number of electrons in the gold plasma layer is approximately 2000 times larger than that in the hydrogen layer. The pulse dimensionless amplitude, a₀ = 30, corresponds to an intensity of 10²¹ W/cm². The laser pulse was assumed to be trapezoidal with a sharp leading head and a short plateau (growth − plateau decrease = 3λ, 2λ, 10λ). The transverse profile of the pulse is 12λ wide and is constant over 10λ. The computation region was chosen to be 80 × 32 × 32 λ³ and the spatial mesh consisted of 2560 × 1024 × 1024 cells. The total number of particles varied from 62 × 10⁶ to 820 × 10⁶. The calculations were carried out on 64 processors at the NECSX-5 parallel supercomputer at Osaka University.

Figure 2 shows the energy spectra of the protons and of the heavy ions at the normalized time t = 80. The protons have been accelerated to an energy of about 63 MeV. The relative width of the proton energy spectrum is 5%. The energy spectrum of heavy ions is broad, with maximum energy around 37 MeV, which corresponds to an energy per nucleon of about 0.2 MeV, much smaller than the proton energy. The angular distribution of the protons and of the heavy ions (not shown here) indicates that the proton layer moves in the direction of propagation of the laser pulse, while the heavy ions move not only in the direction of the pulse but also in the opposite direction, as is characteristic of the Coulomb explosion.

Energy spectra of protons (left) and of heavy ions (right) at time t = 80 laser periods.

Proton beams with larger maximum energies have been obtained in the 2D PIC simulations in an electron proton plasma presented by Fourkal et al. (2002) using pulses with lengths ranging from 14 to 65 fs, with 0.8 μm wavelength and intensity of 1.9 × 10²¹ W/cm². The laser pulse was chosen to be normally incident on an underdense plasma slab (preplasma) 7 μm long, followed by a thin dense plasma slab 0.4 μm thick with (ω_pe /ω)² = 30. It was shown that, by tailoring the geometry of the high-density plasma target as well as by optimizing the laser and plasma parameters, proton beams can be produced with maximum energy ranging from of 147 MeV, for a 14 fs pulse, to 308 MeV, for a 49 fs laser pulse, and a broad energy profile with a cutoff at around 150 MeV and 308 MeV, respectively, and broad angular spectra. Contrary to the results presented in the first part of this section, no effort is made by Fourkal et al. (2002) to obtain a beam with a narrow energy spectrum. For oncological applications, such a beam requires a particle selection system that can be used for the reformation of the proton energy spectrum needed for a given tumor treatment.