J. Plasma Physics: page 1 of 10. c© Cambridge University Press 2012

doi:10.1017/S0022377812000189

1

CO2 Laser acceleration of forward directed MeV proton beamsin a gas target at critical plasma density

F. T S U N G1, S. Y A. T O C H I T S K Y2, D. J. H A B E R B E R G E R2, W. B. M O R I1,2

and C. J O S H I2

1Department of Physics, University of California at Los Angeles, Los Angeles, CA, USA2Department of Electrical Engineering, University of California at Los Angeles, Los Angeles, CA 90095, USA

(sergei12@ucla.edu)

(Received 20 September 2011; revised 20 September 2011; accepted 12 January 2012)

Abstract. The generation of 1–5 MeV protons from the interaction of a 3 ps TWCO2 laser pulse with a gas target with a peak density around the critical plasmadensity has been studied by 2D particle-in-cell simulations. The proton accelerationin the preformed plasma with a symmetric, linearly ramped density distributionoccurs via formation of sheath of the hot electrons on the back surface of the target.The maximum energy of the hot electrons and, hence, net acceleration of protons ismainly defined by Forward Raman scattering instability in the underdense part ofthe plasma. Forward directed ion beams from a debris free gaseous target can findan application as a high-brightness ion source-injector to a conventional acceleratoroperating up to kHz pulse repetition frequency.

1. IntroductionOver the last decade, forward directed beams of ener-getic protons have been observed in numerous experi-ments by interacting intense subpicosecond laser pulseswith the foil targets (Clark et al. 2000; Maksimchuk et al.2000; Snavely et al. 2000). These pulses are characterizedby the normalized amplitude of the laser vector potentialfield, a0 = eA/mc2, being �1. A handy formula for a0 isa0 ≈ 8.5 × 10−10I0.5[W/cm2] λ[µm], where I is intensity,and λ is wavelength of the laser. Forward directed MeVbeam of protons with a high-current is the most commonfeature of these experiments irrespective of the targetcomposition. These protons are thought to originatefrom either hydrogenated impurities (Clark et al. 2000;Maksimchuk et al. 2000; Snavely et al. 2000) or speciallydeposited hydrocarbon layer (Schwoerer et al. 2005;Betti et al. 2009) on the surface of the target. Suchbeams have attracted a lot of attention owing to theirvery high brightness resulting from a large number ofparticles (>1010) tightly confined in time (∼1 ps) andspace (source radius ∼10 µm) (Cowan et al. 2004). Theprotons are accelerated by the large space-charge fields,on the order of MV/µm, set up at the rear surface of thetarget, or by electrostatic shocks propagating throughthe target. At the rear surface, the accelerating field is setup by the expulsion of a hot electron cloud into vacuumproducing a negatively charged sheath irrespective of theangle of incidence of the laser beam. The electric fieldof this thin sheath ionizes and accelerates ions froma thin layer normal to the target. This so-called tar-get normal sheath acceleration (TNSA) mechanism hasbeen extensively studied numerically (Wilks et al. 2001;Fuchs et al. 2006) and its scalings are well established

experimentally for solid foils (Robson et al. 2007). Sucha solid foil-based proton source has drawbacks limitingits practical use, because of sensitivity to any prepulse(which leads to plasma formation at the target surfacebefore the arrival of the main pulse), produces debrisand its repetition rate is limited. If these problems canbe overcome and ions can be accelerated to 1–10 MeV/uat a high-repetition rate, such a laser-driven source ofions could find application as a picosecond injector fora conventional accelerator or a compact ion source forhigh-energy-density physics and material science.

An alternative method of obtaining laser-acceleratedions is by using a gaseous target. An ionized gas is aclean source of protons or ions from other gases. Asupersonic gas jet can provide neutral gas densities inthe range of 1018–1020 cm−3 with homogeneous densitydistribution in a 50–2000 µm plasma slab (Semushinand Malka 2001; Hao et al. 2005) and can be operatedup to 1 kHz. Recently, a He gas jet with a plasmadensity ne around 1019 cm−3 was successfully used forgenerating He ions using 1-µm laser (Krushelnick et al.1999; Sarkisov et al. 1999; Willingale et al. 2006). Inthis experiment, a forward directed beam of He2+ andHe1+ ions was observed at a highly relativistic laserintensity (a0 ∼ 15) in an underdense plasma (i.e. ne

∼ 0.1 nc, where nc is the critical plasma density nc =1.1 × 1021/λ2 [µm]cm−3) (Willingale et al. 2006). Atmodestly relativistic laser intensities (a0 � 1), radialtransport of electrons and ions dominates and the ionsare accelerated primarily at 90◦ to the axis of laserpropagation (Krushelnick et al. 1999; Sarkisov et al.1999). The situation would change dramatically if a longwavelength laser is used for laser-driven ion acceleration

2 F. Tsung et al.

(LDIA) in a gas jet. For a 10 µm, CO2 laser pulse forexample, the same gas jet target with a peak plasmadensity >1019 cm−3 can be opaque to radiation (sincethe critical plasma density for 10 µm CO2 laser light is1019 cm−3) but as the laser intensity is increased above a0

∼ 1 can become transparent to the incident laser beamdue to relativistic increase in the electron mass causinga decrease in the effective plasma density. Compared tosolid foils, using a gas jet is potentially very attractive asit produces no debris and can be run at a high-repetitionrate and the density of the plasma can be changed easilyin a well controllable manner.

Thus, 10 µm LDIA in a gas jet could represent apromising alternative to using solid foils to obtain ahigh-energy proton beam. In the previous nanosecondCO2 laser LDIA experiments with solid targets (I ∼1014–1015 W/cm2), a combination of a relatively largeinteraction volume (spot size ∼150 µm) and energypartitioning to fast ions (∼50%) resulted in high yieldson the order 109–1010 ions/keV (Joshi et al. 1979;Gitomer et al. 1986). To achieve relativistic laser fieldsbefore the deposited energy causes the gas target ex-pansion, a high-power picosecond CO2 laser is needed.CO2 lasers that can provide relativistic laser intensitieshave recently been developed and its use for LDIAhas been demonstrated (Pogorelsky et al. 2010). Atthe UCLA Neptune Laboratory a TW class (100 J,100 ps) CO2 laser system has been operational formany years (Tochitsky et al. 1999) and a 3 ps longpulse has recently been amplified to >10 TW with anormalized field strength of a0 > 1 in a focused beam(Haberberger et al. 2010). However, LDIA and the lasercoupling into gas plasma in the range of densities 0.5–5nc is practically unexplored at relativistic laser intensitieseither numerically or experimentally.

In this paper, we present full-scale particle-in-cell(PIC) simulations of ion acceleration in laser–plasmainteractions of a relativistic CO2 laser pulse with gastargets having critical plasma density. The main goalof the study is to determine whether a picosecond10 µm laser pulse incident on a symmetrically rampedpreformed plasma slab, that is tens of wavelength wide,is suitable for production of a forward directed multi-MeV proton beam and to study the physical mechanismsthat generate such a beam. We find that laser–plasmainteractions phenomena such as relativistic self-focusingand channeling (Sarkisov et al. 1999), electron accel-eration by plasma waves in the underdense region ofthe gas jet, and relativistic Stimulated Raman Scattering(SRS) occurring at ne ∼ nc (Adam et al. 1997) can allbe important in such a target.

2. Proton acceleration dynamics in thevicinity of critical plasma density

In this section, we consider proton acceleration in a H2

gas target irradiated by a focused CO2 laser beam witha vacuum intensity of I = 1016 W/cm2 (a0 ∼ 1) for two

plasma densities slightly below and above the criticaldensity. Consequently, a target of a given thicknessis transparent at the plasma density of ne = 7.5 ×1018 cm−3 (0.75 nc) and opaque at 3 × 1019 cm−3 (3 nc).In the first case underdense laser–plasma interactionsdominate as the laser beam propagates through the ion-ized gas. The plasma dynamics is strongly nonlinear res-ulting in relativistic self-focusing (Sarkisov et al. 1999),which in turn leads to the production of a plasma chan-nel partially evacuated under the action of the enhancedponderomotive force of the self-focused laser pulse. Thesecond case represents overdense laser–plasma interac-tions where – similar to solid foils, in which a laserprepulse might create a plasma layer in front of thetarget – the laser beam interacts with the underdensepart of the gas target and then is stopped close to thecritical density layer inside the target. For laser pulseswith a0 > 1, the light pressure bores a hole in a plasma,process in which plasma electrons are pushed sidewaysand forward and the density profile is steepened (Younget al. 1995). In both cases, hot electrons produced bythe laser in the underdense region (which typically arehotter, albeit lower in density, than those created atthe critical density surface) are transported through thetarget and create a strong electrostatic field (sheath)that drives the surface proton acceleration. Both thesescenarios are realistic and important for understandingan interaction of the CO2 laser pulse with the gas jet.

We use a 2D, PIC code OSIRIS (Fonseca et al. 2008)for full-scale numerical studies of LDIA. In the twosimulations that we compare below, the incident ∼1TW laser pulse has a 3 ps (full width at half maximum)duration and a transverse spot size 2w0 = 100 µm. Thelaser beam interacts with the target at normal incidence,and its electric field is in the simulation plane. The gasjet is modeled as a triangular preformed plasma slabthat is symmetrically ramped from 0 to 0.75 (3) nc overa distance of 20λ resulting in a 400 µm thick target.It should be noted that both the plasma density andits profile in simulations represent parameters routinelyachieved in the experiments with a supersonic gas jetoperating in the 1018–1020 cm−3 plasma density range(Semushin and Malka 2001). In simulations, we considerthe laser pulse without any prepulse. This is equivalentto assuming that in the experiment contrast between anyprepulse and the 3 ps main pulse with an intensity of 1016

W/cm2 is >200, therefore, the prepulse can not ionizethe hydrogen gas and has no effect on the interactionphysics.

2.1. Interaction with underdense gas targets: Transparentregime

The linearly polarized longitudinal and transverse Gaus-sian laser pulse propagates from the left to the rightand interacts with the 0.75 nc plasma slab located atapproximately 200 µm from the left-hand side of thesimulation box. The simulation box is 485 µm wide and1750 µm long. The mesh size is 9000 and 2600 cells in the

CO2 Laser acceleration of forward directed MeV proton beams 3

Figure 1. Proton density distribution at t = 3.6 ps when thepeak of the 3 ps CO2 laser pulse reaches the center of the 0.75nc peak density target (a) and at t = 6.6 ps (b).

longitudinal and transverse direction, respectively, andthere are 16 particles per cell per species. The lateralboundary conditions are periodic. The front boundaryradiates the laser beam, while both front and backboundaries absorb outgoing radiation and particles.

In Fig. 1(a) we show the ion density at time, t =3.6 ps when the peak of the laser pulse reaches thecenter of the gas target. When the TW power laser pulsewith a power significantly larger than Pcr critical powerfor relativistic self-focusing interacts with an underdenseplasma, the plasma dynamics is strongly nonlinear andself-focusing results in laser filamentation (Sprangle et al.1987; Gibbon et al. 1996). Here Pcr = 17 (ω0/ωp)

2 [GW],where ω0 is the laser angular frequency and ωp = (4πnee

2

/m)1/2 is the plasma frequency. This filamentation causespartial evacuation of electrons in the filaments underthe action of the transverse ponderomotive force. Laterin time (t = 6.6 ps), as is apparent in Fig. 1(b), thehydrogen ions are pulled transversely by the electrostaticfields induced by expelled electrons and two channels canclearly be seen. The formation of such multiple filamentscan be attributed to an ‘inverted corona’ mechanism inwhich hot plasma particles from the channel walls heatedby the laser pulse are expanded toward the channel

(Sentoku et al. 2000). Later in time after the laser pulsehas passed (t > 12 ps), the ion filament dissipates andonly at this time hydrodynamic expansion of the entireplasma slab is noticeable. Therefore, during the timerequired for the laser pulse to cross the plasma slab,a sharp plasma-vacuum boundary important for theTNSA mechanism (Wilks et al. 2001) is in place. At theend of the computations at t = 21 ps the target’s widthhas expanded by a factor of 4.

Since electron acceleration is a prerequisite to the gen-eration of high-energy ions, we now discuss the electronheating mechanism in this underdense target case. Inaddition to transverse transport of electrons, electronsalso gain a longitudinal momentum in the direction oflaser propagation. There are several possible mechan-isms responsible for forward electron acceleration in theunderdense laser–plasma interaction. The longitudinalcomponent of the ponderomotive force pushes electronsleading to a snowplough effect. For laser pulses longerthan the plasma wavelength λp = 2πc/ωp and P >

Pcr (for 3 ps pulses these conditions are fulfilled forne > 1015 cm−3), the Forward Raman Scattering (FRS)instability below the quarter critical density can produceMeV electrons (Joshi et al. 1981; Krall et al. 1992;Modena et al. 1995).

Figure 2(a) presents the electron density at a time,when the front of the laser pulse reaches the backsideedge of the plasma. Electron filamentation caused by thelaser beam relativistic self-focusing is apparent in thedensity distribution. Since the laser power P reaches 58Pcr, at the peak density, the threshold of relativistic self-focusing is reached very early during the pulse (Sprangleet al. 1987). As seen in Fig. 2(b), as a result of strongrelativistic self-focusing, the peak laser field is enhancedsignificantly and the pulse steepens at the front. Thefinite rise time of the pulse creates a low-amplitudewakefield within the laser pulse and causes a low-amplitude modulation of the laser pulse at λp (Krall et al.1992). The modulated laser pulse can resonantly pumpthe wakefield and the process continues in an unstableway. This instability resembles a highly nonlinear two-dimensional form of usual FRS instability (Joshi et al.1981; Krall et al. 1992; Modena et al. 1995). Indeed,Fig. 2(c) depicts both the piling up of the electrons infront of the laser pulse and excitation of such a wakeright behind this front.

The phase space distribution of hot electrons on laserbeam axis, in Fig. 2(d), uncovers the dynamics of electronacceleration. In simulations, a group of electrons isaccelerated to a temperature of approximately 4 MeVin a front part of the plasma where the plasma densityis below 0.25 nc. However, some much hotter electronswith an energy reaching 15 MeV are observed in thepart of the plasma where the plasma density is above0.25 nc but the laser field is peaked. This may beattributed to an additional acceleration of electronscaused by the increasing ponderomotive force of thelaser, which is strongly enhanced due to the relativistic

4 F. Tsung et al.

Figure 2. Electron density distribution (a), laser field (b), electrical field of plasma (c), and phase space P1-X1 distribution ofelectrons (d) at t = 2.8 ps for the 0.75 nc gas target.

self-focusing effect in this part of the target. Indeed, a0

is enhanced up to ∼4, seen in Fig. 2(b), in the region ofthe target where this additional acceleration is observed.The highest energy electrons leave the plasma producinga target potential which in turn confines the rest of theheated electrons. The key point here is that even in anunderdense plasma, strong electron acceleration takesplace which in turn leads to a formation of sheathhaving a large electric field accelerating ions.

The ion phase space distribution P1 along the laseraxis direction X1 at t = 21 ps, long after the laser pulsehas traversed the plasma, is shown in Fig. 3(a). Thehighest proton velocity of ions reached in the underdenselaser–plasma interactions is 0.085c, which correspondsto the kinetic energy of 3.4 MeV. There are two distinctspatial features both giving rise to energetic protons.The first and the most important is located at the rearsurface of the target, where the most energetic ions arebeing produced. The second is apparently accelerationthroughout the target. The nature of these featurescan be understood based on the analysis of the phase

space distribution of ions in the P1–P2 plane shownin Fig. 3(b). Here, we see that there are two groupsof accelerated ions. The first is a highly directionalbeam of ions propagating forward (P1 > P2). But inaddition, there is a group of ions with a lower energythat are expelled in all directions (P1 ∼ P2). This lattergroup has a velocity <0.025c (low proton kinetic energy<0.2 MeV). The first group of particles, however, isfairly well collimated in a forward direction, propagatesexactly at normal to the target’s rear surface, and hasenergies in the range 0.4–3.4 MeV (velocity 0.01–0.085c).The maximum energy of the uncollimated group ofparticles can be estimated by balancing the electrostaticpotential between the protons and the expelled electronsand the laser ponderomotive potential, which expelsthe electrons in first place (Wilks et al. 2001). Therelativistic ponderomotive energy U can be estimatedas, U = mc2 (γ – 1), where γ = (1 + a0

2 /2)0.5 is therelativistic factor of the electron quiver motion in thelaser field. For a0 = 1 this energy is equal to 0.12 MeVand in a good agreement with the maximum energy

CO2 Laser acceleration of forward directed MeV proton beams 5

Figure 3. Proton phase space at time t = 21 ps after the peak of the interaction of 3 ps CO2 laser pulse with a 0.75 nc gas targetfor particles accelerated forward (a) and P1-P2 proton density map (b).

obtained in the simulations for transversely acceleratedprotons. Note that even an enhanced value of a0 = 4would result in proton energy of 1.02 MeV. However, acollimated proton beam propagating forward has muchhigher energy that indicates that other mechanisms areinvolved in electron and ion acceleration of this group.As is shown above, the self-modulated laser wakefieldacceleration of electrons is the main mechanism for theelectron heating in our case. The plasma density in aramped gas target where FRS can take place variesfrom 10−4 to 0.25 nc. Also, relativistic SRS in the plasmadensity range of 0.5–1 nc (Adam et al. 1997) may resultin an additional longitudinal heating of plasma electronsand higher energy electrons.

In order to distinguish between the FRS and re-lativistic SRS contributions, we modeled a gas jet tar-get where the 200 µm front up ramp of the targetwas replaced by a slab with a constant density of0.1 nc and 0.9 nc (the back side was the same asbefore) and compared the proton energies. The resultsclearly indicated that relativistic SRS occurring abovethe quarter critical density produces <0.2 MeV protonsand that for our conditions hot electron production,due to the regular FRS mechanism (Joshi et al. 1981;Krall et al. 1992; Modena et al. 1995) defines themaximum energy of electrons and, hence, the protons.Recently, a similar physical mechanism has been invokedto explain the generation of positrons in intense laser–solid target interactions (Chen et al. 2009). In thatexperiment enhanced electron acceleration was observedin an underdense plasma ramp produced on the frontsurface of the foil by the laser prepulse. Thus, in the caseof plasma densities slightly below nc (even at a vacuuma0 ∼ 1) a significant amount of ions are acceleratedforward and these plasmas prove to be useful source ofcollimated proton/ion beams.

Figure 4. Proton density distribution at t = 3.6 ps, when thepeak of the 3 ps CO2 laser pulse reaches the center of thetarget (a) and at t = 6.6 ps (b).

6 F. Tsung et al.

Figure 5. Electron density distribution (a), laser field (b), electrical field of plasma (c), and phase space P1-X1 distribution ofelectrons (d) at t = 3 ps for the 3 nc gas target.

2.2. Interaction with overdense gas targets: Opaqueregime

Simulation box for modeling overdense gas targets is270 µm wide and 900 µm long. The plasma is locatedat the same position as for the underdense target case.The plasma density profile is ramped from 0 to its peakvalue of 3 × 1019 cm−3, which is equal to 3 nc for a10-µm laser pulse.

At a plasma density of nc, the classical skin depthc/ωp is ∼1.7 µm and the CO2 laser beam is expectedbe completely stopped in the many wavelength thickoverdense plasma layer. In Fig. 4(a) for t = 3.6 ps (timewhen the peak of the laser pulse in vacuum shouldbe reaching the center of gas target), the laser pulse isseen to be stopped at the critical density layer ∼40 µm infront of the center of the density profile. In this overdensecase, the laser beam with a relatively small a0 ∼ 1 atfirst penetrates through the ∼150 µm thick underdensepart of the gas target causing laser self-focusing. As seenin Figs. 4(a) and (b), this results in the formation of aseries of almost circular cavities in the nc density surfacesimilar to ones reported earlier (Valeo and Estabrook

1975; Wilks et al. 1992). Some of the laser energy istrapped in these cavities and it is eventually absorbed.Remarkably, even at the end of the laser pulse att = 6.6 ps (see Fig. 4(b)), the depth of laser penetrationis unchanged. This is because the ponderomotive forceof the 3 ps laser pulse is not sufficient to bore a holethrough the critical density wall and the plasma worksas an opaque target for the CO2 laser beam.

In Figs. 5(a)–(d), we show results on electron acceler-ation and transport through the target in the overdense(ne = 3 nc) case. Here, fast electrons accelerated dueto the plasma waves excited in the underdense part ofthis target propagate through the plasma and stronglyfilament behind the nc boundary. The plasma wake inFig. 5(c) is localized at the front ramp at approximately0.75 nc density layer. Due to the limited interactionlength for the underdense laser–plasma interactions, theelectrons are accelerated to an energy of ∼4 MeV, whichis smaller than that in the ne = 0.75 nc case. These elec-trons can be seen expanding next to the both surfaces,which are still intact at this time. Formation of a curvedelectron sheath along with filamentation of electrons is

CO2 Laser acceleration of forward directed MeV proton beams 7

Figure 6. Proton phase space at time t = 21 ps after the peak of the interaction of 3 ps CO2 laser pulse with the 3 nc gas targetfor particles accelerated forward (a) and backward (c) and P1–P2 proton density map for forward (b) and backward acceleratedparticles (d).

clearly seen in the electron density distribution (Fig. 5(a))at t ∼ 3 ps. Space charge separation formed as a result ofthese double electron-ion layer dynamics causes protonacceleration by the electrostatic field. Note that almostno significant target expansion due to the volumetricheating by the laser pulse is observed in the overdensecase up to the end of computations at t = 21 ps.

In Fig. 6(a), we show phase space (P1–X1) for protonsproduced at the rear surface due to the TNSA mechan-ism at t = 21 ps. The maximum kinetic energy of protonsis 2.8 MeV (velocity ∼0.077c), which is close to theenergy reached for the underdense plasma in Fig. 3(b).This result indicates that it is the underdense laser–plasma interactions at ne � 0.25 nc that determine themaximum kinetic energy of the hot electrons and, there-fore, the protons. However, as opposed to the underdensecase, the overdense target produces a single beam witha monotonically increasing velocity of particles. Thisis confirmed by analysis of proton density map inthe P1–P2 space presented in Fig. 6(b), where a well-

collimated forward ion beam is observed. A collimatedforward particle beam for overdense plasmas is charac-terized by a small divergence of approximately 5 degrees(FWHM), the longitudinal momentum of the ions beingapproximately ten times higher than their transversemomentum. This may be attributed to pinching ofthe MeV protons by quasistatic self-generated magneticfields at the plasma-vacuum boundary produced by thestrong directed current of electrons (Bulanov et al. 2000).An elementary mechanism for generation of a quasistatictransverse magnetic field in plasma is attributed to thedevelopment of an electromagnetic filamentation in-stability similar to the Weibel instability, which occurs inplasma with an anisotropic electron temperature (Weibel1959; Pukhov and Meyer-ter-Vehn 1996; Sentoku et al.2000). Although the dynamics of the electron transportfor the overdense and underdense cases is different, theyboth demonstrate strong laser and electron filamentationassisting production of the forward directed ion beams.As for the backward (toward the laser) accelerated ions,

8 F. Tsung et al.

Figure 7. Phase space distribution for protons accelerated in a CO2 laser-driven plasma with a peak density of 3 × 1019 cm−3

(ne = 3 nc) and a front ramp length of 20 µm (a) and 400 µm (b).

the overdense target with a ramped plasma densitydistribution works in a similar way as the underdensetarget. Particles are mainly accelerated radially in alldirections and only a small fraction of them propagatesat 0 degrees to the laser axis. Phase space ion distributionfor backward TNSA is shown in Figs. 6(c) and (d).

Below, we present results on gas plasma target profileoptimization in the plasma density range of 0.75–5 nc.

3. Optimization of plasma length-densityproduct

The maximum proton energy gained in LDIA is directlyrelated to the heated electron temperature which in thecase of TNSA defines the thickness of the sheath layerand the electrostatic force. In order to understand scal-ings for the maximum proton energy, we first extendedthe parametric study to other target densities for thesame gas target size as in Sec. 2 and a0 = 1. One-dimensional LDIA simulations demonstrated that thedensity in the range of 0.5–5 nc has little effect on themaximum proton energy. The proton energy is almostconstant for the ne < nc and monotonically falls by afactor of 1.5 at ne = 5 nc. This observation is consistentwith the 2D simulations shown above, confirming thatit is the underdense plasma or the underdense layer ofthe overdense gas target where the electrons gain themaximum energy due to plasma waves and enhanceTNSA.

Then, we fixed the peak plasma density at 3 nc andvaried only the length of the front ramp of the gastarget. The results of 2D simulations for 2λ and 40λare presented in the proton phase space plots in Fig. 7.For a target without underdense layer on the front (seeFig. 7(a)), protons reach velocity 0.025c (0.2 MeV). Thisenergy value is comparable with that defined by theponderomotive force. In the case shown in Fig. 7(b), the40λ long ramp allows for longer underdense interactionbetween the CO2 laser and plasma resulting in a v/c =

0.086 and a maximum proton energy of 4.6 MeV atthe end of computational run at t = 40 ps. Note thatthis energy value is 1.5 times higher than that for thesymmetric plasma described in Fig. 4. A surprising resultis that for the given laser parameters longer front rampsup to 60λ showed no further increase in the maximumproton energy reached in simulations. Thus, for gas jet-based LDIA at 10 µm a target profile optimization canresult in an increase of the maximum achievable protonenergy by a factor of two. It should be noted that byincreasing the length of the back ramp, it is possible tominimize the TNSA fields and accelerate the ions fromthe bulk of target via the shock wave mechanism. Theseresults are discussed elsewhere (Haberberger et al. 2012).

4. SummaryA 2D PIC code study of ion acceleration in CO2 laser–plasma interactions around the critical plasma density of1019 cm−3 has demonstrated production of a collimatedforward H+ beam. Modeling is carried out for realisticplasma profiles that are typical of supersonic gas jets.It is shown that for the 10 µm radiation at a relativelymodest laser intensity of 1016 W/cm2 (a0 = 1), themaximum achievable proton energy is ∼5 MeV. Thisenergy is more than an order of magnitude larger thanthat predicted by the ponderomotive scaling (Wilkset al. 2001). The main mechanism responsible for ionacceleration is production of a sheath field generatedby high-energy electrons on the rear surface of thetarget (TNSA mechanism). The maximum energy of thehot electrons and, therefore, net acceleration of protonsgained in the sheath is mainly related to self-modulatedlaser wakefield acceleration in the underdense plasma.

For underdense targets (0.5–0.75 nc), nonlinear laser–plasma interactions at a laser power P > Pcr causerelativistic self-focusing and plasma channel formationand strongly enhance laser wakefield electron accelera-tion. For targets with the peak density above nc (1–5 nc)

CO2 Laser acceleration of forward directed MeV proton beams 9

similar laser–plasma interactions and enhanced electronacceleration occur in a ∼20λ–300λ thick underdenseplasma layer on the front part of the gas jet. In bothcases the proton beams are pinched by self-generatedmagnetic fields in the plasma-vacuum boundary thatresults in small divergence angles for 1–5 MeV particles.Production of collimated forward ion beams with a highlaminarity allows for the capture and control of MeVions by using a compact magnetic solenoid and/or RFcavity devices (Noda et al. 2006; Schollmeier et al. 2008).This opens the possibility for development of plasmaaccelerators with a narrow energy spread. Future devel-opment of picosecond TW class CO2 lasers operatingat a low-pressure of 1–3 atm but a high repetition rate(Tochitsky et al. 2000) will enable a compact sourceof MeV ion beams suitable for a high-brightness pico-second injector for large RF-based accelerators or for alaboratory device for high-energy-density physics.

AcknowledgementsThis work is supported by DOE grant No. DE-FG03-92ER40727 and NSF grant PHY-0936266.

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