Charged-particle acceleration in PW laser-plasma interaction X. T. He Institute of Applied Physics and Computational Mathematics, Beijing Present to International Conference on Frontier of Science

1.Introduction 2.Electron acceleration in intense-laser plasma interaction 3. Proton acceleration by normal incident intense-laser 4. Influence of laser large oblique incident angle on energetic proton beam 5. Plasma density effect on ion beam acceleration 6. Heavy ion acceleration and quark-gluon plasma research 7. Conclusions and discussions Outline

1. Introduction

With development of CPA technology, short-pulse and high-intense laser (PW w) system can provide intensities w/cm 2 for each beam. Interaction of the petawatt (PW) laser with matter may accelerate charged particles (electrons, protons and heavy ions) to kinetic energy over GeV. The acceleration of high-energy charged particle beam generated from interaction of an intense laser with solid target has been one of the most active fields of research in the last few years. It is of important potential applications in fast ignition and accelerator etc. So far, proton energy up to tens MeV for per nucleon is gained by experiments and simulations under conditions on existing petawatt (PW) laser ( w/cm 2 ) with normal incident to targets. 1.Introduction

So far only the PW lasers of x100J/0.5ps are used for experiments. New PW lasers are being constructed : 10kJ/4 beams/1-10ps in Japan, 2x2.6kJ/2 beams/1-10ps and NIF in US, 1.5kJ/1 beam/1-5ps (and future SG-IV) in China will be operating in 2-3 years. In this presentation, charged particle acceleration mechanisms and the dependence of acceleration on laser larger oblique angle and higher density target are discussed and application to QGP research is presented. It seems to be the traditional PIC code beyond its power, and a new developed 3D hybrid-Fluid+PIC (HF-PIC) code must be used to simulate the generation and transport of electrons, carbon ions, especially protons in solid target. 1.Introduction

2. Electron acceleration in intense- laser plasma interaction

2. Electron wake field acceleration in intense- laser plasma interaction (1) Wake-field acceleration: Laser beam propagates in plasma, a wake-field is generated by laser- drive plasma wave due to charge separation. Electrons are accelerated, like surf in plasma wave.

Laser intensity 3x10 20 w/cm 2, electron energy >300MeV is observed (Mangles et al., PRL94(05) 2. Electron wake-field acceleration in intense- laser plasma interaction Some electrons are trapped and accelerated with mono-energy and within an angular spread of a few degree in the bubble (Katsouleas et al., Nature, 515(04)).

(2) Resonant acceleration : Electrons are accelerated by spontaneous electric field E s and magnetic field B s, both generated in laser-plasma interaction. Resonance acceleration occurs when resonance condition ω b = ω- kv z is satisfied, where the betatron oscillation frequency ω b =[γe/mr 0 (E s + v z B s /c)] 1/2, and ω b / ω =1-v z /c as relativistic factor γ »1. Resonance acceleration gives γ=f(r,t,k B,k E,v g )/(v z -v g ), where v z axial velocity for electron and v g group velocity for laser. 2. Electron resonance acceleration in intense-laser plasma interaction

Test particle results of resonant acceleration : 2. Electron resonance acceleration in intense-laser plasma interaction Maximal kinetic energy ~ MeV for the Gaussian circularly polarized (CP) laser with intensity 3.1x10 19 w/cm 2 and plasma density n e /n c =0.1. Energy spread about 20% and divergent angle about 2 degrees.

3. Proton acceleration by normal incident intense-laser

Electrons driven out of the target front side by PW laser ponderomotive force set up electrostatic fields that accelerate protons backward against the PW laser direction. On the other hand, the electrons in the target front side can also be accelerated by ponderomotive force, a thin Debye sheath at the target rear is generated when electrons penetrate through the target. 3. Proton acceleration by normal incident intense-laser

When PW laser beam propagates along the target normal direction or a small angle, the proton emission cone is also aligned at same as direction or cone. Furthermore, the electron sheath has a Gaussian profile, and the central region as well as the edge of the sheath will expel proton normal to the surface. The Bragg peak proton energy is at the center the resulting Gaussian proton beam (Zhang and He, IAEA06). 3. Proton acceleration by normal incident intense-laser Electric field E=30GV/cm, laser intensity w/cm 2 Energetic proton in the rear CH target

Protons by PW laser acceleration was verified by experiments and simulations, see review papers: Plasma phys. Controlled Fusion 47, B841(05) by M. Roth et al and Fusion Science and Tech. 49, 412 (06) by M. Borghesi. Experimental results are shown in the following plots. Laser intensities of up to w/cm 2, But the pulse duration is < 100fs. 3. Proton acceleration by normal incident intense-laser

4. Influence of laser large oblique incident angle on energetic proton beam (simulation)

4. Influence of large oblique incident angle on energetic proton beam Model : C + H + 2 slab with thickness 5  m and linear ramps 1  m at both sides of slab, and initial density n e /n cr ~140 as shown in Figs. [n 0C, n 0H, n 0e ]=[6,1.2, 8.4]x10 22 cm -3. For laser normal incident ( θ =0 o ), laser I 0 =3x10 20 w/cm 2 with spot 6  m. For oblique incident (θ=60 o ), slab is rotated to target thickness 2  m. Zhou and He, APL 90,031503(07).

4. Influence of large oblique incident angle on energetic proton beam For laser normal incident on target, at t=500fs, (a) electrons accelerated by intense laser penetrate to target rear to form a collimated electron beam with energy ≤2MeV and an energetic electron jet with energy >2 MeV and a X-like angular distribution (divergent angle of 45 o ). Target normal sheath (TNS) of tens GV/cm is generated at both front and rear target surfaces. (b), (c) Proton beam and carbon ion beam at target rear are accelerated by TNS and both are of Gaussian profiles with maximal energy~17MeV (protons), ~2.5MeV(carbon ions).

For 60 o oblique incident, at t=500fs, energetic electrons are confined near target front surface and energetic electrons in X- like angular direction run to target (thickness 2μm) rear to form a TNS; at target rear, proton beam has a single peak energy distribution with maximal energy~20MeV and the number of protons seem to be less than that in normal incident, while at target front it has an asymmetry profile and double energy peaks due to target surface electromagnetic fields. Carbon ion beam is of maximal nergy~2.0MeV and better collimation. 4. Influence of large oblique incident angle on energetic proton beam

Conversion efficiency: for, about 35% from laser to energetic electrons with temperature >1.0 MeV. For, a fraction of laser energy is reflected, it leads to only 18% conversion. Energetic electrons (>2MeV) convert to proton energy about 14% and 25% for and, respectively. For θ= 60 o, angular distribution of proton energy, detailed the previous Fig.(e), is shown at four energy regions :(a), (b), (c) (d), protons emerge only in the backward direction and deviate the normal.

5. Density effect on proton acceleration from intense-laser interaction with CH target ( simulation)

Model: C + H + 2 slab (5eV) with thickness 5  m and ramps 1  m, for ρ =3gcm -3, [n 0e, n 0H, n 0c ]=[3.86, 2.57, 1.29]x10 23 cm -3 Laser intensity I=3.3x10 20 /cm 2, = 1  m, r 0 =3 micron, normal incident. Zhou and He, Opt. Lett. 32, 2444(07). 5. Density effect on proton acceleration from intense-laser interaction with CH target Results: at t=50-500fs, electrons are reflected many times due to mean free path much larger than foil thickness, TNSA electric filed tens GV/cm.

5. Density effect on proton acceleration from intense-laser interaction with CH target Proton acceleration for densities 1/3 gcm -3 (d-f) and 3 gcm -3 (a-c) at t=400fs. TNSA and shock acceleration for lower density target (d-f) are more effective than that for higher density target (a-c). However, for higher density target, TNSA of proton beam becomes more effective and the collimation is better, though the efficiency of both mechanisms decreases with density. At rear target surface, TNSA maximal electric fields |E ρ=1/3 | / |E ρ=3 |~4 lead to maximal forward energy ~28MeV with energy emission cone 5 MeV, red-e) for density 1/3 gcm -3 and ~6MeV (red-b) with emission cone 1.8 MeV) for density 3gcm -3. Black c and f are backward proton energy. 3 gcm -3 1/3 gcm -3

5. Density effect on proton acceleration from intense-laser interaction with CH target Proton acceleration for densities 1/3 gcm -3 (d-f) and 3 gcm -3 (a-c). Till t=500fs, conversion efficiency of laser energy to proton is about 5.6% for lower density and only 0.3% for higher density, as shown in plots. Experimental results for Al and CH targets have ranged between 2-7% (Fusion Sci. & Tech. 49, 412(06)). The proton number about 8.8x10 12 (1MeV) and the carbon ion number about 4.7x10 12 (1MeV) for lower density are roughly estimated.

Model: C + H + 2 slab (5eV)-left figure, =0.2(I), 1(II) and 3(III) gcm -3, Laser intensity I=2x10 20 /cm 2, λ=1µm r 0 =3 μm, normal incident. Zhou et al., JAP 101,103302(07) 5. Density effect on proton acceleration from intense-laser interaction with CH target ( thin target and acceleration within tens of femtosecond ) Results: for t=5-100fs, trajectories of several typical electrons for density (II) show that electrons experience multi- reflection, stochastic heat and collision. TNS fields of tens GV/cm at both front and rear of target are observed.

5. Density effect on proton acceleration from intense-laser interaction with CH target Plots show snapshots of density profiles of electrons, protons and carbon ions at 75fs. An ion hole driven by laser ponderomotive is formed on the front surface, the hole boring velocities [5.1, 2.3, 1.3]x10 -2 c are greater than the sound velocity~0.5x10 -4 c, the collisionless shock wave is formed. The ions are backward into left vacuum and forward into the target by the shock. At the rear target, ions are accelerated by TNSA and shock wave, the latter produces the mono-energy~1MeV. ρ=1.0gcm -3 ρ=3.0gcm -3 ρ=0.2gcm -3

5. Density effect on proton acceleration from intense-laser interaction with CH target Figs. show at t=75fs proton velocity and angular distributions. The proton energies reach ~15, 6 and 3 MeV from lower to higher density at rear target respectively, and the higher density is favorable to proton collimation as shown in Fig. (i). TNSA dominates at lower density, while shock wave acceleration may intensify TNSA at higher density > 3gcm -3. ρ=1.0gcm -3 ρ=3.0gcm -3 ρ=0.2gcm -3

At t=75fs, v z / c distribution. C + and P strongly respond to laser and space-charged fields at both sides of target, though C + has a longer response time due to its heavier mass. 5. Density effect on proton acceleration from intense-laser interaction with CH target The thermal energy (eV) of P accelerated by shock decreases with density increase, and is quite small at rear target. The divergent angle by TNSA also decreases. While C + by shock has a higher thermal energy than by TNSA at t=75fs. ρ=0.2gcm -3 ρ=1.0gcm -3 ρ=3.0gcm -3 PC+C+ P C+C+

Finding quark and gluon and understanding QGP in laboratory are an essential mission in high energy physics and high energy astrophysics Heavy ion beam colliding in the frame of center of mass has achieved QGP information. In the past 2-3 years, gold nuclei are accelerated by RHIC and collide in the frame of center of mass and the QGP like ideal fluid state was observed. The QGP state rapidly reaches thermo-equilibrium like equilibrium plasma and can be explained by the fluid equations. 6. Heavy ion acceleration and quark-gluon plasma

Motion equation for QGP ： 6. Heavy ion acceleration and quark-gluon plasma Equation for energy density : For ideal massless QG gas, The Solution: Pressure:

6. Heavy ion acceleration and quark-gluon plasma PW laser can be used to explore QGP instead of the traditional accelerators, such as RHIC and other new one. Relativistic momentum equation or relativistic Vlasov equation can be used to investigate such heavy ion beam Numerical simulation shows that when laser (intensity I≥10 23 W/cm 2 ) interacts with CH target foil (thickness l~λ), kinetic energy of protons can reach over 4GeV. The laser piston model shows that protons undergo two stages: longitudinal field acceleration, which is generated by charge separation; laser light reflection to transfer laser energy to target with reflectivity.

6. Heavy ion acceleration and quark-gluon plasma T. Esirkepov et al. PRL 92, (2004).

6. Heavy ion acceleration and quark-gluon plasma From numerical simulation and analytical estimation, as t, ion kinetic energy asymptotically where I is laser intensity, is foil thickness max ( ) For,, The acceleration time t ac and acceleration length X ac =ct ac =4.8mm

6. Heavy ion acceleration and quark-gluon plasma We may estimate kinetic energy of heavy ions from relativistic momentum equation for proton

6. Heavy ion acceleration and quark-gluon plasma Kinetic energy for heavy ion scaled from proton

During the collision of two beams, the number of reaction with cross section is Where s is the beam sectional area. If proton kinetic energy reaches 100GeV (laser intensity about w/cm 2 ), and z/A~1/2, then 6. Heavy ion acceleration and quark-gluon plasma It means that in the frame of center of mass, z- particle colliding with kinetic energy 100AGeV may generate QGP.

7. Conclusions and discussions

(1) Charged particle accelerations in PW laser interaction with matters have extensively investigated, to understand mechanism is challenging. Now only the PW lasers of x100J/0.5ps is used for experiments, numerical simulations are limited by computer capability. Today kinetic energy~ GeV is possibly gained. For the sub-picosecond intense-laser beam interacting with plasma: In present day electron acceleration can accelerated up to relativistic energy of hundreds MeV with approximate monoenergy and small divergent angle by wake-field and betatrron resonance acceleration.

7. Conclusions and discussions Proton beam accelerated from front and rear target surfaces are not completely aligned along the target normal due to electric sheath being not a Gaussian spatial profile if oblique incident angle large enough. The number of protons may be less than that in normal incident. Target density can significantly influence proton acceleration, for higher density TNSA is more effective than shock acceleration, while for lower density both acceleration processes are comparable. A lower density target is favorable to higher energy of TNSA. For tens femtosecond laser interaction with plasma, in higher density target protons accelerated by both TNS and shock have less energy at target rear, but more collimation.

7. Conclusions and discussions Conversion efficiency of laser energy to protons is about 5.6% for lower density and only 0.3% for higher density. The proton number about 8.8x1012 (1MeV) and the carbon ion number about 4.7x1012 (1MeV) for lower density are roughly estimated. (2) Due to advancing the study of fast ignition of inertial fusion driven by PW laser, based on present-day CPA technology, to obtain PW laser intensity over w/cm 2 is confident if tens beams are used and each beam has 2kJ/1 ps and the focused spot ~2. It means that there are possibility to design QGP experiment and to experimentally explore many important phenomena occurring in astrophysics in near future.

Thanks