Tunable high-energy ion source via oblique laser pulse incidence on a double-layer target
T. Morita, T. Zh. Esirkepov, S. V. Bulanov, J. Koga, M. Yamagiwa
TTunable high-energy ion source via oblique laser pulse incidence on a double-layertarget
T. Morita, T. Zh. Esirkepov, S. V. Bulanov, J. Koga, and M. Yamagiwa
Japan Atomic Energy Agency, 8-1 Umemidai, Kizugawa, Kyoto 619-0215, Japan
The laser-driven acceleration of high quality proton beams from a double-layer target, comprisedof a high-Z ion layer and a thin disk of hydrogen, is investigated with three-dimensional particle-in-cell simulations in the case of oblique incidence of a laser pulse. It is shown that the protonbeam energy reaches its maximum at a certain incidence angle of the laser pulse, where it can bemuch greater than the energy at normal incidence. The proton beam propagates at some angle withrespect to the target surface normal, as determined by the proton energy and the incidence angle.
PACS numbers: 52.38.Kd, 29.25.Ni, 52.65.RrKeywords: Ion acceleration, monoenergetic ion beams, laser plasma interaction, Particle-in-Cell simulation
The method of charged particle acceleration by usinglaser light is very attractive, since the acceleration rateis much higher and the facility size can be substantiallysmaller than standard accelerators. Ion acceleration dur-ing the high intensity electromagnetic wave interactionwith plasmas was proposed more than 50 years ago [1].Currently, ion acceleration experiments using high powerlasers close to petawatt levels are going on all over theworld [2]. Laser driven fast ions are considered in regardto applications ranging from hadron therapy [3], fast ig-nition of thermonuclear targets [4], production of PETsources [5], conversion of radioactive waste [6], a laser-driven heavy ion collider [7], injectors for standard accel-erators [8], and proton radiography [9] to proton dumpfacilities for neutrino oscillation studies [10] (see Refs.[11] and literature quoted therein).The typical energy spectrum of laser accelerated par-ticles from unoptimized targets is thermal-like, with acut-off at a maximum energy. On the other hand, al-most all the above mentioned applications require highquality proton beams, i.e. beams with sufficiently smallenergy spread ∆ E / E (cid:28)
1. As suggested in Ref. [12],such a required beam of laser accelerated ions can beobtained using a double-layer target, which consists ofhigh-Z atoms and a thin coating of low-Z atoms. Exten-sive computer simulations of this target were performedin Refs. [13] and [14], where multi-parametric particle-in-cell (PIC) simulations were used to optimize the laser-driven proton acceleration by choosing appropriate laserand target conditions. The feasibility of the double-layertarget scheme was demonstrated experimentally with mi-crostructured targets in Ref. [15]. The effects of targetshaping on the laser-driven ion acceleration were also re-ported in Refs. [16]. Previously, the double-layer tar-get scheme for high and controllable quality ion accel-eration has been mostly studied in the configuration ofnormal incidence of the laser pulse on the target. How-ever, the case of oblique incidence provides an additionalparameter for manipulation of the fast ion energy, theemittance, energy spectrum and the proton beam prop-agation direction. As is well known, the energy transfer from a p-polarized obliquely incidence electromagneticwave to the electron energy via the so-called ”vacuumheating” mechanism [17] depends on the incidence an-gle and is substantially higher than for normal incidence.A stronger electron heating results in a stronger electricfield generation due to the electric charge separation ef-fect, which in turn leads to more efficient ion acceleration.In this Letter, we study the dependence of the ionbeam energy and quality on the laser incidence angle. Weuse an idealized model, in which a Gaussian p-polarizedlaser pulse is incident on a double-layer target of colli-sionless plasmas. The simulations are performed witha three-dimensional massively parallel electro magneticcode, based on the PIC method [18]. The number of gridcells is equal to 2800 × ×
720 along the x , y , and z axes. The total number of quasi-particles equals 7 × .The size of the simulation box is 100 λ × . λ × . λ ,where λ is the laser wavelength. The boundary condi-tions for the particles and for the fields are periodic in thetransverse ( y , z ) direction and absorbing at the bound-aries of the computation box along the x axis. Here thelaser wavelength determines the transformation from di-mensionless to dimensional quantities and vice versa. Be-low, the dimensional quantities are given for λ = 0 . µ m;the spatial coordinates are normalized to λ and the timeis measured in the laser period, 2 π/ω .The Gaussian laser pulse with the dimensionless ampli-tude a = eE /m e ωc = 30, which corresponds to the laserpeak intensity 2 × W/cm , is 8 λ long in the propa-gation direction and it is focused to a spot with size 6 λ (FWHM). The oblique incidence of the laser pulse is re-alized by tilting the target around the z − axis, Fig. 1(d),while the laser pulse propagates along the x − axis. Bothlayers of the double-layer target are shaped as disks. Thefirst, gold, layer has a diameter 10 λ and thickness 0 . λ .The second, hydrogen, layer is narrower and thinner; itsdiameter is 5 λ and thickness is 0 . λ . The electron den-sity inside the gold layer is n e = 1 . × cm − ; insidethe proton layer it is n e = 5 × cm − .Figure 1 shows the proton beam acceleration for twocases of normal and oblique incidence. For the present a r X i v : . [ phy s i c s . p l a s m - ph ] S e p FIG. 1: Proton acceleration driven by the laser pulse withnormal (a,b) and oblique (c,d) incidence. (a,c): Electric fieldmagnitude (isosurface for value a = 2) at t=10; half of thebox is removed to reveal the internal structure. (b,d): Dis-tribution of gold ions (blue), electrons (yellow), and protons(light blue) at t=80. The laser pulse incidence angle in (c,d)is θ = 30 o . simulation parameters, the target is partially transpar-ent for the electromagnetic wave (due to the relativistictransparency effect), which, according to Refs. [13] and[14], corresponds to an optimal condition of the ion accel-eration. In the case of oblique incidence, a substantiallylarger portion of the electrons is blown off the target dueto the effect of ”vacuum heating.”In order to examine the dependence of the energyachieved by the protons on the incidence angle, θ , weperformed extensive 2D and 3D PIC simulations. Fig. 2shows the proton energy as a function of the laser pulseincidence angle, normalized by the maximum achievableenergy. We see that the maximum proton energy isreached at the incidence angle approximately equal to30 o , for which case we undertook 3D PIC simulationshown in Fig. 1(c,d). The proton energy value is ap-proximately doubled at θ =30 o compared to the case ofnormal incidence, θ =0 o . This also can be seen in the in-set in Fig. 2 showing the proton energy spectra at t=80.While the proton energy increased from ∼
20 MeV at nor-mal incidence to ∼
45 MeV at oblique incidence with anoptimal angle, the energy spread is also increased from10% to 23%.If we invoke the above mentioned ”vacuum heating”mechanism for the laser pulse energy transformation intothe electron component energy, and then, via acceleration
FIG. 2: Proton energy, normalized by the maximum, vs thelaser pulse incidence angle. In the inset: proton energy spec-tra at t=80, as obtained in 3D PIC simulation. in the electric field of the charge separation, into the en-ergy of fast protons, we find that the laser pulse energydeposited to the target and the efficiency of pushing theelectrons out from the target depend on the incidenceangle θ . The counterplay between these two effects leadsto the formation of the fast proton energy maximum at acertain incidence angle. Under the conditions of our sim-ulations this angle is approximately equal to 30 o . Theanalysis of the time evolution of the proton energy spec-trum shows that both the average energy and energyspread increase with time. The energy spread appearsto grow in the oblique incidence case, which can be ac-counted for by the asymmetry of the quasistatic electricfield along the target surface at oblique incidence. Wenote that, according to Ref. [12], the energy spread canbe decreased by reducing the thickness and transversesize of the low-Z ion (proton) layer.Since the proton acceleration occurs due to the elec-tric field generation through the electron ejection fromthe target, it is important to analyze the dependenceof the number of the electrons leaving the target underthe laser radiation action on the incidence angle. Fig-ure 3 shows the ratio of electrons pushed out from thetarget versus the incidence angle at time t=20. Thedependence at t=20 is chosen because at this time thenumber of ejected electrons saturates as seen in the in-set in Fig. 3. The ratio of ejected electrons as a func-tion of the incidence angle θ is defined by the expression η e = ( N e ( θ ) − N e,min ) / ( N e,max − N e,min ), where N e ( θ ) isthe number of ejected electrons, N e,max = max { N e ( θ ) } and N e,min = min { N e ( θ ) } are the maximum and mini-mum values, respectively. We see that this ratio reaches FIG. 3: Escaping electron ratio η e vs the laser pulse incidenceangle at t=20. In the inset: normalized number of electronsswept off the target vs time, as obtained in 3D PIC simulation. its maximum at the incidence angle about 30 o , which ev-idences a strong correlation between the dependences ofthe number of ejected electrons (Fig. 3) and the pro-ton energy (Fig. 2) on the laser pulse incidence an-gle. We see from Fig. 3 that the efficiency of theelectron ejection is substantially higher for θ =30 o thanin the case of normal incidence. As a consequence, astronger electric field is produced and the protons areaccelerated to higher energy. This is also illustratedin Fig. 4, by the correlation between the average pro-ton energy and the ejected electron number. Here theproton energy ratio at θ is defined by the expression η E = ( E p ( θ ) − E p,min ) / ( E p,max − E p,min ), where E p ( θ )is the average proton energy, E p,max = max {E p ( θ ) } and E p,min = min {E p ( θ ) } are the maximum and minimumvalues, respectively. We see that the fast proton energy isroughly proportional to the number of ejected electrons.As seen from Fig. 1, the accelerated proton bunch re-tains the form of the disk. In the case of the normalincidence, the proton disk moves in the direction normalto the target surface while its surface remains parallelto the first (high-Z ion) layer. In the case of oblique in-cidence, the proton disk motion direction deflects fromthe target normal by a noticeable angle, φ , while thedisk surface is tilted with respect to the high-Z ion layer,Fig. 1(d). We note that a deflection of the acceleratedproton bunch has been observed in the experiments onthe laser - solid target interaction [19]. Under the con-ditions of our simulations, which correspond to the rela-tively higher laser intensity, the deflection and tilt can beexplained by relativistic effects. As is known, the Lorentztransformation to the frame of reference moving with the FIG. 4: Proton energy ratio vs escaping electron ratio att=20. velocity V = − c sin θ along the target surface, i.e. thegamma factor is given by γ = 1 / (cid:112) − V /c = 1 / cos θ ,changes the configuration of the wave–target interactionfrom oblique to normal incidence [20], so that the wavefrequency and wave vector of the incident electromag-netic wave become ω (cid:48) = ω cos θ and k (cid:48) = k cos θ e || , where e || is the unit vector along k (cid:48) . In this new boosted refer-ence frame, the protons have a transverse component ofmomentum equal to p (cid:48)⊥ = − m p c tan θ , where m p is theproton mass. As a result of the acceleration in the elec-tric charge separation field, the protons acquire the lon-gitudinal momentum p (cid:48)|| and their energy becomes equalto E (cid:48) p = (cid:113) m p c + p (cid:48) || c + p (cid:48) ⊥ c . Performing the Lorentztransformation back to the laboratory reference frame,we obtain that p || = p (cid:48)|| , p ⊥ = γ ( p (cid:48)|| − E (cid:48) p V /c ) and thedeflection angle φ = arctan( p ⊥ /p || ) is equal to φ = arctan m p c tan θp || cos θ (cid:115) (cid:18) p || cos θm p c (cid:19) − (1)In the limit p || /m p c (cid:28)
1, which corresponds to the pa-rameters of our simulations, this expression yields φ ≈ (cid:112) E p / m p c sin θ . For p || /m p c (cid:29)
1, the angle φ becomes φ ≈ θ , i.e. the protons are accelerated almost along thelaser pulse propagation direction.In order to account for the proton disk tilting, we notethat the obliquely incident laser pulse front propagatesalong the target surface with a superluminal velocity V F = c/ sin θ . The time delay between moments whendifferent disk elements separated by the distance ∆ l startto move is equal to ∆ t = ∆ l sin θ/c . The displacement ofthe proton layer elements in the direction of the targetnormal can be estimated as ∆ ξ || = p || ∆ t/m p . This givesthe angle of the proton disc tilt, χ = arctan(∆ ξ || / ∆ l ), i.e. χ ≈ (cid:112) E p /m p c sin θ . This effect is seen in the simula-tions at an early time of the proton acceleration. Later,higher dimensional effects come into play and the tilting FIG. 5: Deflection angle of the proton bunch vs the laserpulse incidence angle at t=80. The solid curve is given fromEq. (1). angle changes.The dependence of the angle of the deflection of theproton motion from the target normal, φ , on the laserpulse incidence angle, θ , is seen in Fig. 5. Here thedeflection angle, φ , is defined as the angle between thenormal to the target surface placed at the target centerand the average radius-vector from the target center tothe proton layer, which equals Σ N p i =1 x pi /N p , where x pi isthe radius-vector of the i -th proton out of N p protons inthe accelerated beam. As seen from Eq. (1), in the limitof a small incidence angle, θ , the proton bunch is accel-erated almost along the direction normal to the targetwith φ being a linear function of θ . When the incidenceangle, θ , increases, the growth of the deflection angle, φ ,saturates, in agreement with the results of simulations,shown in Fig. 2.In conclusion, we have found that the proton accel-eration during laser pulse interaction with double-layertargets is more efficient for oblique incidence than fornormal incidence. It is shown that the proton beam en-ergy reaches its maximum at a certain incidence angle ofthe laser pulse, where it can be much greater than the en-ergy at normal incidence. The proton beam propagatesat some angle with respect to the target surface normal,as determined by the proton energy and the incidenceangle. In the limit of nonrelativistic proton energy, thedeflection angle is relatively small. However, its value ≈ o (see Fig. 5) results in the proton beam deflection ofthe order of 10 cm after the protons have propagated over1 m distance. 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