Particle acceleration in twisted plasma waves with orbital angular momentum

Transcription

1 Particle acceleration in twisted plasma waves with orbital angular momentum J. Vieira 1 J. T. Mendonça 1, F. Quéré 2 1 GoLP / Instituto de Plasmas e Fusão Nuclear Instituto Superior Técnico, Lisbon Portugal 2 LIDYL, CEA, CNRS, Université Paris-Saclay, CEA Saclay, Gif-sur-Yvette France web.ist.utl.pt/jorge.vieira epp.tecnico.ulisboa.pt golp.tecnico.ulisboa.pt golp INSTITUTO DE PLASMAS E FUSÃO NUCLEAR Jorge Vieira E-AAC Isola d Elba, Italy September 26, 217

2 The topological freedom is an unique property of the plasma cannot be currently found in conventional devices Plasma waves can have any shape Plasma waves are sustained by free electrons Implications of wake topology Plasma waves are ubiquitous Fundamental plasma processes wave-particle interactions Nonlinear optics Accelerators and light sources Wakefields in conventional devices are sustained by metallic parts One-dimensional waves widely explored, require standard Gaussian drivers Plasma waves with non-trivial topologies unexplored, require non-gaussian drivers Changing the topology of the plasma can have deep ramifications and transform the outputs of plasma accelerators and radiation sources Jorge Vieira E-AAC Isola d Elba, Italy September 26, 217

3 PT_Padgett54.qxd 4/7/24 9:16 AM Page 36 The orbital angular momentum of light (OAM) Ultra-intense twisted lasers Orbital angular momentum = 1 PW twisted laser for ion acceleration Brabetz et al. CAL REVIEW LETTERS. C. Brabetz et al., PoP 22, 1312 (215). 2 = =1 ating helical beams has been the use of FIG. computed 4. Sketch of the holograms. used experiment Such numerically setup. holograms can generate beams with any desired value of orbital angular momentum from the same initial beam (see figure 3). The requisite hologram can be formed by recording, onto photographic film, the interference pattern between a plane wave IV. EXPERIMENTS and beam one seeks produce. has been used and thethe beam wavefront is also to recorded dur- Illuminating hologram ing the shot to ensure thatthe no resulting large distortion happenswith to theanother To cover a large parameter range, we studied foil thickwave produces a first-order beam (see Figureplane 3 for on-shot focus images). Changing diffracted the nesses from 3 lm to 2 lm in the experiments. Beside varybeam with the intensity focal spot geometry from a Gaussian shaped toand the phase smallestpattern ing the target thickness, the beam shape was also varied: of the ring focal spot with the desired SPE, the beam. focus radius doubled and from Gaussian for reference to the Laguerre-Gaussian-like take adtherefore the intensitythe dropsholographic to a quarter ifapproach the energy can of the laser mode LG1. For reproducible measurements, the target foil vantage of the2).high-quality laser beam is kept constant (Figure The variation inspatial inten- light was always aligned to the best focal position. The energy of (SLMs) delivered that have recently besity is induced modulators by different energies from the the shots was varied within the 12 cm round subaperture of come The available. These liquid-crystal devices take PHELIX laser system. maximum protonpixelated energy is measthe PHELIX beam, delivering 5 J 8 J of laser energy on placea oftypical the photographic film. ured with RCFthe stacks. energy detection gapfurthermore, numerithe target (for the Gaussian and the ring shaped beam). The calculated patterns between the last cally RCF films is about 2holographic MeV, and therefore, an can be displayed on laser pulse duration was always held constant at sl ¼ 65 fs. anmev SLM. These devices produce reconfigurable, computerenergy error of þ2 is assumed for all shots. We also had the opportunity to apply the new ultrafast opticontrolled holograms allow focal a simple laser beam to be It is observed that the data points withthat a Gaussian cal parametric amplifier of PHELIX to conduct some expericonverted into an exotic beam almost any desired spot (blue (a),(e) triangles) fit very well to a power scaling Ewith FIG. 1. Left panels: laser focal spots measured without p;max ments with ultra-high temporal contrast.18 With this method b phase and amplitude structure. And the beam pattern can ¼ a $ I with b ¼ :73 6 :4. The same power scaling "1 in the path of a ϕ laser and with (b),(f)contrast the spiral phase plate 25 mm be changed many times per second to meet experimental is reached beside a temporal level better than 1 "7 requirements. Figure 3 shows how a comparatively simple. This the normal contrast level of PHELIX of about 1 (up) and ϕ 45 mm (down) diameter laser beam. The bar scale forked holographic pattern can transform the planewas done to study the influence of the pre-plasma on the ion 5 indicates a length of 1 μm. Central panels: raw images Gaussian of the focal spot wave output of a conventional laser into a pair of LG beams acceleration. fit Gaussian 4 carrying orbital angular momentum.5 In recent years, Ring focal spot the comparison of ring and Gaussian focal spectrally First resolved high-order harmonic 1D spot angular profiles at fit ring SLMs have been used in applications as diverse as adapand their effect on the maximum proton 3 θx ¼ geometries mrad, produced by the UHI vortices in the CWE (paneltive c, optics, real-time holography, and optical tweezing. energy in the TNSA regime are studied. This is illustrated in 17 2 W=cm ), andat the ROM g,2 L λ=15 Unlike spin angular momentum, which has only two L λ=7 and I the 5.1 Figure 5, where maximum proton energy cut-off(panel is independent states corresponding to left- and right2 plotted19 against the calculated laser intensity. The laser intenand I 1 W=cm ) regimes. These values of L were deterhanded circular polarization, orbital angular momentum sity is inferred from the measured focal spot size and the has an unlimited number of possible states, corresponding mined on-shot usingmeasured the SDI interferometric technique described in [26. laser energy. The focal spot size is measto all integer values of. Although the link between spin =2 High intensity twisted light from plasma mirrors g a 8-mmate in the s designed azimuthal ure 1 comthis spiral Goal: to o diameters 5 mm. As doughnut- E Denoeud et al. PRL (217) / r w ` =3 L ` p ( r ) exp w 2 r w2 the angular momentum is associated with regions of high intensity, which for an LG mode is a bright annular ring. That association is well illustrated by a recent experiment by Lluis Torner and coworkers at the University of Catalonia in Barcelona, Spain.6 They showed that, after the beam passes through the focus of a cylindrical lens, the azimuthal component of the linear momentum near the vortex center is reversed, but the total orbital angular momentum of the beam remains unchanged. The reversal of the vortex is simply image inversion in geometrical optics; it has no implications for orbital angular momentum. Orbital angular momentum arises whenever a beam s phase fronts are not perpendicular to the propagation direction. In the approximation of geometric optics, one would say that the light rays that make up the beam are skewed with respect to its axis. Simplistic as it is, this skewed-ray model predicts the correct result in most experimental situations. cos ( t k z+` ) M. Padgett et al., Phys. Today 57(5), 35 (24) Maximum proton energy (MeV) 13 J=cm2 ) adjustable se [25. Its rferometry intensity I main beam he other of on (HHG) y coherent ting mirror inserted in ing by the am was p Figure 1. Orbital angular momentum of a light beam, unlike spin angular momentum, is independent of the beam s polarization. It arises from helical phase fronts (left column), at which the Poynting vector (green arrows) is no longer parallel to the beam axis. At any fixed radius within the beam, Phys.vector Plasmasfollows 22, 1315 the Poynting a (215) spiral trajectory around the axis. Rows are labeled by, the orbital angular-momentum quantum number. L = \ is the beam s orbital angular momentum per photon. For each, the left FIG. 3. of the on-shot of the column iscomparison a schematic snapshot focal spots measured afteran the instant mainbeam s instantaneous phase. later, normalized to the intensity the phaseamplifier, advance is indistinguishable from of the Gaussian spot (b). (a) The hola small rotation By focus. themselves, low focusof andthe (b) beam. the Gaussian beams with In (a),helical the effectwavefronts of the remaininghave laser simple is profiles seen and modulate annularaberrations intensity (centerthe column). intensity factor ofis 2 on the ring. But when suchbyaabeam made to interfere with a plane wave, it produces a telltale spiral intensity pattern (right column). week ending The number of spiral arms equals the JANUARY 217 number of intertwined helical phase fronts of the helical beam. propose new configuration that allows transfer the angular momentum of the laser to a relativistic plasma wakefield carrying OAM Jorge Vieira E-AAC Isola d Elba, Italy September 26, 217

4 Conditions to excite a twisted wakefield (Forward) Raman scattering Light spring with Δl = 1 OAM transfer requires different photons (with different frequencies) carrying different OAM levels Frequency and orbital angular momentum correlation l=l( ) Δl Δl gs. (a) Pulse spectrum (corresponding to a Light spring with Δl = 2 Δ = p Plasma absorbs OAM Δl Images adapted from G. Pariente, F. Quéré, Optics Letters (215) Jorge Vieira E-AAC Isola d Elba, Italy September 26, 217

5 Generation of an ultra-short light spring Experimental realisation* spiral phase plate Light spring forms when thickness laser duration a 2 / a 2 r,` + a 2 r,`+ `+ Mathematical model for simulations and theory Beating two Laguerre-Gaussian modes +2a r,`a r,`+ ` cos [ k(ct x)+ ` + '(x) angular dependent group velocity dispersion Δl is the OAM difference between the two modes Δk is the wavenumber difference Δφ is a phase difference *G. Pariente, F. Quéré, Optics Letters (215) Jorge Vieira E-AAC Isola d Elba, Italy September 26, 217

6 OSIRIS 3. s 3. O iris osiris framework Massivelly Parallel, Fully Relativistic Particle-in-Cell (PIC) Code Visualization and Data Analysis Infrastructure Developed by the osiris.consortium UCLA + IST code features Ricardo Fonseca ricardo.fonseca@tecnico.ulisboa.pt Frank Tsung tsung@physics.ucla.edu Scalability to ~ 1.6 M cores SIMD hardware optimized Parallel I/O Dynamic Load Balancing QED module Particle merging GPGPU support Xeon Phi support Jorge Vieira Imperial College, UK Monday 2 217

7 Twisted wakefield structure Osir3.is Ex = -.35 E Ex =.35 E 12 N6-7 electrons Elaser [E 15 light spring 1 y [c twisted wakefield 6 / p -1 propagation direction Panofksy-Wenzel theorem x [c/ p z [c / p OAM wakefield Transverse force acting on relativistic particle Radial focusing (betatron r? @r Transverse wakefield Azimuthal force new W? = E? + (ex `p = r Jorge Vieira E-AAC Isola d Elba, Italy September 26, 217

8 Relativistic beams accelerated in OAM wakes Hamiltonian formulation Hamiltonian of a charged particle H = m e c 2 + e (r,, ) Energy Constants of motion 1 v v x /c 2 =1+ /m e c 2 Twisted wakefield structure Ratio of angular momentum flux to energy L x p x = `p k p ) L x E = `p p = (v t x + `p ) = (u) Angular momentum is quantised. Hamilton s equations dp x dt dp dt ' dp x dt = ' dl = = `p p c 2 1 Simulations confirm OAM quantisation l = 4 p /p x =.51 l = 2 p /p x =.23 l = 1 p /p x =.11 z [c/ p 1 8 time [1/ p 4 dh = v g l = p /p x =. 1 2 p x c y [c/ p Jorge Vieira E-AAC Isola d Elba, Italy September 26, 217

9 Beams have a vortex density structure Vortex particle beam with l = Similar to twisted light Ratio of angular momentum flux to energy flux for light prop. dir x [c/ p -1 y [c/ p -1 1 z [c/ p J cp = ` L. Allen et al., PRA (1992) Vortex particle beam with l = x [c/ p 1-1 y [c/ p -1 1 z [c/ p Ratio of angular momentum to energy for beam particle L x E = ` p Vortex beam electrons move as a twisted ray of light Jorge Vieira E-AAC Isola d Elba, Italy September 26, 217

10 Energy gain of the vortex beam Lower energy gain Reduced dephasing length / Energy gain 1 c 2 (1 + `2/r 2 ) v 2 apple 2 2 Transverse slide of longitudinal wakefield decreases with the plasma wave OAM Simulation confirmation 2 l=2 l=1 p c 1 l=4 l= 1 2 p x c Dephasing along the axial direction and also along the azimutal direction e θ Particles dragged along e θ due to the new azimuthal wakefield component E θ Jorge Vieira E-AAC Isola d Elba, Italy September 26, 217

11 Light springs spins in a plasma channel Twisted wavefronts can spiral in a plasma channel causing the rotation of the light spring t = p -1 t = 45 p -1 t = 9 p t = 45-1 z [c/ p -1-1 y [c/ p 1 prop. dir. 1 2 x-ct [c/ p E laser [E 2 Time Two key directions set wakefield response: rotation orientation: set by the OAM of light spring modes OAM orientation: set by the OAM difference between light spring modes Wakefield phase velocity depends the relative orientation between these two rotational directions Jorge Vieira E-AAC Isola d Elba, Italy September 26, 217

12 Tuneable phase velocities Wakefield phase velocity depends the relative sign between l and Δ l v,wake c = apple 1 k p () 2 2k 2 2(1+ ` + k 2 w2 ` ) + 2( ` + ` ` ) k w 2 k Phase velocity control Δl > and l> Δl < and and l> distance [ 1 c/ p 8 theory x-ct [c/ p.3 E x c p /e -.3 distance [ 1 c/ p 8 theory x-ct [c/ p.3 E x c p /e -.3 Jorge Vieira E-AAC Isola d Elba, Italy September 26, 217

13 Energy gain control beyond planar wakefields Wakefield phase velocity depends the relative sign between l and Δ l v,wake c = apple 1 k p () 2 2k 2 2(1+ ` + k 2 w2 ` ) + 2( ` + ` ` ) k w 2 k Energy gain control 4 2 l = 1 p / p x =.12 Ordering of energy gain with Δ for constant p c no spring ( l=) l = -1 p / p x =-.12 l= p / p x =. spring ( l=1) p x c 4 Δ Δ =1 Δ = Δ =-1 ΔE max ~4 ΔE max ~3 ΔE max ~1 Energy gain Jorge Vieira E-AAC Isola d Elba, Italy September 26, 217

14 Conclusions and future directions Plasma wave topology is a new degree of freedom that impacts accelerators and light sources Light spring laser pulses as drivers for twisted plasma waves Generation of relativistic vortex bunches with quantised OAM levels Rotation of light spring enable all optical control of the wake phase velocity Additional questions motivated by this work wakefield excitation by relativistic vortex bunches twisted THz generation using vortex beams vortex bunch magnetic moments and interaction with magnetic fields Jorge Vieira E-AAC Isola d Elba, Italy September 26, 217

15 Thank you golp INSTITUTO DE PLASMAS E FUSÃO NUCLEAR Jorge Vieira E-AAC Isola d Elba, Italy September 26, 217