Relativistic laser–plasma interactions.pdf

INSTITUTE OF PHYSICS PUBLISHING

JOURNAL OF PHYSICS D: A PPLIED PHYSICS

J. Phys. D: Appl. Phys. 36 (2003) R151–R165

PII: S0022-3727(03)26928-X

TOPICAL REVIEW

Relativistic laser–plasma interactions Donald Umstadter Center for Ultrafast Optical Science, University of Michigan, Ann Arbor, MI 48109, USA E-mail: [email protected]

Received 19 November 2002 Published 2 April 2003 Online at stacks.iop.org/JPhysD/36/R151 Abstract

By focusing petawatt peak power laser light to intensities up to 10 21 W cm−2 , highly relativistic plasmas can now be studied. The force exerted by light pulses with this extreme intensity has been used to accelerate beams of electrons and protons to energies of a million volts in distances of only microns. This acceleration gradient is a thousand times greater than in radio-frequency-based accelerators. Such novel compact laser-based radiation sources have been demonstrated to have parameters that are useful for research in medicine, physics and engineering. They might also someday be used to ignite controlled thermonuclear fusion. Ultrashort pulse duration particles and x-rays that are produced can resolve chemical, biological or physical reactions on ultrafast (femtosecond) timescales and on atomic spatial scales. These energetic beams have produced an array of nuclear reactions, resulting in neutrons, positrons and radioactive isotopes. As laser intensities increase further and laser-accelerated protons become relativistic, exotic plasmas, such as dense electron–positron plasmas, which are of astrophysical interest, can be created in the laboratory. This paper reviews many of the recent advances in relativistic laser–plasma interactions.

1. Introduction Ever since lasers were invented, their peak power and focus ability ability have steadily steadily increased. increased. The most recent increases increases in power have been enabled by new techniques to produce shor shorte terr puls pulses es.. For For inst instan ance ce,, soli solidd-st stat atee lase lasers rs use use the the techni technique que of chirpe chirped-p d-puls ulsee amplifi amplificat cation ion (CPA) (CPA) [1, 2] to generate generate femtosecond femtosecond duration pulses. pulses. To accomplish this, a laser pulse is first stretched in time before it is amplified and then recompressed. Gas lasers using solid-state switches have have produced produced picosecond picosecond duration duration pulses [3]. Advanced Advanced laser laser system systemss now now have have multimulti-ter teraw awatt att peak peak power powerss and, and, when focused to micron spotsizes with adaptive optics, can produce produce electromagne electromagnetic tic intensities intensities I 1021 W cm−2 , as illustrated illustrated by figure 1. Such intensitie intensitiess create novel novel states of matter matter,, which which are just beginn beginning ing to be explored explored.. For For instance, electrons oscillate at relativistic velocities in laser fields that exceed 10 11 V cm−1 , which results in relativistic relativistic mass changes exceeding the electron rest mass. At this point, the magnetic field of the electromagnetic wave also becomes import important ant.. Electr Electrons ons behave behave in such such fields fields as if the light wave wave was rectified. rectified. The propagation propagation of light light also depends

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in this regime regime on the light intensity, intensity, resulting resulting in nonlinear nonlinear effects analogous to those studied with conventional conventional nonlinear optics—self-focusing, self-modulation, harmonic generation, and so on. Thus, Thus, a new new field of nonlin nonlinear ear optic optics, s, that of relativistic relativistic electrons, electrons, has begun, as illustrated illustrated by figure 2. Rapid Rapid advanc advanceme ement nt in our unders understan tandin ding g is underw underway ay and new new research tools, subfields and commercial products are on the horizo horizon, n, e.g. e.g. compac compactt and ultras ultrashor hortt pulse pulse durati duration on laser laser-ba -based sed electron accelerators and x-ray sources. At the next physical regime that will be encountered at even even higher higher intensities intensities ( I 1024 W cm−2 ), even even proton protonss will quiver relativistically. relativistically. In this strongly relativistic regime of laser–plasma interactions, even more copious fusion and fission fission reacti reactions ons and the genera generatio tion n of pions, pions, muons muons and neutrinos should occur as energetic nuclei collide. Discus Discussedin sedin this this revie review w aresome of thelatesthighligh thelatesthighlights ts in high-field high-field science, science, with greater greater emphasis emphasis given given to experiment experimental al results. results. See also past reviews reviews on relativisti relativisticc nonlinear nonlinear optics [4–6], high-intensity laser development [2], laser accelerators [7] and intens intensee laser– laser–pla plasma sma interact interaction ionss [8–13] [8–13].. Part Part of the discussion of the results obtained prior to the year 2000 first appeared appeared in [5]. The paper is organized organized as follows follows:: in

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Topical Review

freque frequenc ncy y as thelaser itself( itself( ω 2πc/λ ck ). At higherfield higherfield strengths, electrons become stripped from the atoms, i.e. the gas becomes ionized by tunnelling or multiphoton ionization. Linear perturbation theory can no longer be applied when the work done by the laser field on an electron ( eEr 0 ) over the distance of the Bohr radius ( r0 ) approaches the Coulomb binding energy ( e2 /r 0 ). At even higher intensities intensities,, electrons in the plasma that is formed will quiver at velocities close to the speed of light ( c ). Thus, the relativistic electron mass will increase and the v B force in the Lorentz equation of motion (equation (1)), will become important.

=

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F

= d(γp) = eE + e dt

v

×B c

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(1)

In the relati relativis vistic tic regim regime, e, the quive quiverr moment momentum um of the electrons, p0 , exceeds exceeds m0 c, where where m0 is the electron rest mass and c is the speed speed of light. light. The parame parameter ter that that sets the scale is a0 , the normalized vector potential, defined as a0 p0 /m 0 c eE/m0 ωc, where e is the electron charge and E and ω are the electric field amplitude and the frequency of the laser light, light, respectiv respectively ely.. In terms of other commonly commonly 9 − used units, a0 0.85 10 I λ, where I is the intensity of the laser light light in W cm−2 and λ is the wavelength of the laser light in in microns. microns. When a0 1, which is satisfied for 1 µm light at a laser intensity of 1018 W cm−2 , the electron mass me begins begins to change change signifi significan cantly tly compar compared ed to the electr electron on rest rest mass. (This relativisti relativisticc regime was first approached approached as early as the late 1970s with large CO 2 lasers operated at 10 µm wavelength and intensities of 10 15 W cm−2 , corresponding to a0 0.3 [14].) For low fields, the solution to equation (1), is an electron motion motion descri described bed by an oscill oscillati ation on at the laser laser freque frequency ncy along along a straight line parallel parallel to the polarization polarization vector vector.. For high fields, it is described by an average drift in the direction of laser propagation k and—in a frame that moves with the drift velocity—a figure-eight lying along the plane defined by the polarizatio polarization n vector vector and k . The drift drift motion motion origin originate atess from from the 2 fact that v B E k . As thefield streng strength th increa increases( ses( a02 1), 2 the longitudinal drift motion ( a0 ) begins to dominate the transverse motion ( a0 ), as shown in figure 3. Since Since the motion motion is period periodic, ic, electr electrons ons that that move move in these figure-eight figure-eight patterns should radiate radiate photons photons that are harmonics of each other, with each harmonic having its own unique angular angular distributi distribution on (see figure 4). This is referred referred to as nonlinear Thomson scattering or relativistic Thomson scattering, scattering, predicted predicted over 60 years ago [15]. If the electrons from which the light is scattered are initially in a directed beam, beam, then then the scatte scattered red light light will will be upshif upshifted ted by an additi additiona onall amount due to the relativistic Doppler shift, by a factor of 4 γ 2 (where γ is the relativistic Lorentz factor associated with the electr electron’ on’ss veloc velocity ity), ), which which for electr electrons ons accele accelerat rated ed to 30 MeV corresponds corresponds to a factor factor of 10 000. Thus a 1 eV photon can can be upshifted upshifted to 10 keV (illustrated (illustrated in figure 5). At even higher intensities, when the work done by the laser electric field over a distance of a Compton wavelength h/mc ) equals the rest mass of an electron, m0 c2 , (λ C

=

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Figure 1. Laser light has become concentrated to ever-smaller regions of space ( r ) and time (t ), ), dramatically increasing the peak electric field (E ) at the laser focus. Prior to the development of CPA, the energy of light was produced in long-duration pulses, as shown in the green pulse of the bottom figure. After CPA, the pulse duration decreased dramatically as shown in the red pulse in the middle. The latest improvement in laser technology has been the use of deformable mirrors, which has allowed lasers to be focused to a spatial dimension that is as small as the temporal dimension, a few laser wavelengths, as shown in the blue pulse on top.

section section 2, a brief basic theoretical theoretical overvie overview w of relativistic relativistic laser–plas laser–plasma ma interaction interactionss is presented; presented; detailed detailed theoretical theoretical and numerical results are given in section 3.1, experimental results in section 3.2 and prospects and applications are reviewed in section 4.

2. Basic physical concepts The interaction physics can be divided into two categories, which are differentiated by the density of the target used. In an underdense plasma, a low-intensity laser pulse would be transmitted through the plasma, while in an overdense plasma, it would would be reflect reflected. ed. Atmosp Atmospher heric ic densit density y gas jet are typica typically lly used as targets in the former case, while solid-density films or slabs are used in the latter case.

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Figure 2. The various regimes of laser–matter interactions, represented by the ideal laser pulse. As the intensity of laser light increases, so

does the energy of electrons accelerated in the light field and the regime of conventional nonlinear optics with electrons bound to atoms is replaced by the regime of relativistic nonlinear optics with free electrons in relativistic plasmas. At the highest intensities, even protons become relativistic, giving rise to what might be called the regime of nuclear optics, in which various nuclear processes, such as fusion, can take place. (a)

(b)

Figure 4. Harmonics driven by relativistic Thomson scattering as the electrons in high-intensity laser fields (a02 1) undergo

∼

figure-eight motion display unique angular distributions.

Figure 3. Classical optics versus relativistic optics. (a) In classical

optics, the amplitude of the light wave is small, electrons oscillate in the direction of the electric field at the light’s frequency and there is

high laser laser intens intensity ity,, the 2.1.2. 2.1.2. Collec Collectiv tivee effec effects. ts. At high relati relativis vistic tic change change in the electr electron on mass mass alters alters the plasma plasma ωp0 /γ 1/2 (4π n e2 /γ m0 )1/2 where ωp0 frequency, ω

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Topical Review

P (n (ne I λ2 ), or the time-averaged quiver light pressure, P ne (γ energy density, P 1)m0 c 2 . A Gaussi Gaussianan-sha shaped ped laser intensity profile will tend to expel electrons radially from the axis, often referred to as ‘electron cavitation’. Eventually, thecharge thecharge displa displacem cementdue entdue to expell expelled ed electr electronswill onswill move move the ions, forming a channel with a density depression on axis, ne (0) < ne (r) (r ). Again gain,, γ (0) > γ ( r ) results, results, enhancing enhancing relativisticself-guid relativisticself-guiding ing or allowing allowing a second second trailing trailing laserpulse to be guided. Such density channels have also been created by a thermal gradient, which was produced by a long-duration laser pulse, or by means of a capillary discharge. It is obviou obviouss that that the interp interplay lay betwee between n modula modulatio tions ns of the light light intens intensity ity,, ponder ponderomo omoti tive ve modula modulatio tions ns of the plasma density, modulations of the index of refraction and eventually further modulations of the light intensity, can lead to instabilities, such as self-modulation and Raman scattering.

∇ ∝ ∇ = −

Figure 5. Harmonic generation and a relativistic Doppler shift can

up-shift the frequency of visible radiation from a laser that Compton scatters from an energetic electron beam to the x-ray region of the spectrum. Colliding a laser with 100 MeV energy electron electron beams from a tabletop laser accelerator can produce 50 keV x-rays, which are useful for atomic scale metrology with femtosecond temporal resolution and medical imaging. (a)

(b)

(c )

r

r

r

vφ

a2

kx

Figure 6. The mechanism of relativistic self-focusing. (a) An on-axis peak in laser intensity (a 2 ) for a Gaussian pulse produces greater electron quiver motion on axis than off axis. ( b) The phase velocity of light ( vφ ) depends inversely on the laser intensity via the

change in the index of refraction, which depends on the relativistic electron mass. (c) Variation of the phase velocity with radius causes the wavefronts to curve inward as the pulse propagates, focusing the light as with a positive lens.

of the light wave, given by η [1 (ωp /ω)2 ]1/2 . If there is an on-axis maximum of the radial profile of γ , such as is created by a laser beam with an intensity profile peaked on axis, as shown in figure 6, or γ (0) > γ ( r ), then the index of refraction, η(r), can have have a maximum maximum on axis. By causing the wavefront to curve inward and the laser beam to converge, converge, this will result in optical guiding of the laser light. light. Since Since the laser laser phase phase veloc velocity ity vφ depend dependss on the c/η , it will then depend on the index of refraction, vφ laser laser intens intensity ity.. Local Local varia variatio tion n in the phase velocit velocity y will will modify the shape of the laser pulse, and, consequently, the spatial and temporal profile of the laser intensity. Relativistic self-focusing occurs when the laser power exceeds a critical power, given by P c 17(ω0 /ωp )2 GW. On the other hand, photo-ionization can defocus the light and thus increase the self-focusing threshold, by increasing the on-axis density and refractiv refractivee index. When this focusing effect effect just balances balances the defocu defocusin sing g due to diffra diffracti ction, on, the laser laser pulse pulse can be selfselfguided, or propagate over a long distance with high intensity.

= −

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light-pressure ure driven driven 2.1.4. 2.1.4. Electr Electron on acceler accelerati ation. on. The light-press density modulations just discussed can drive large amplitude plasma waves. waves. The growth growth rates depend on the duration of the light pulse relative relative to the plasma period. period. For underdense underdense plasmas and the short pulse durations that are required to produc producee high high laser laser intens intensity ity,, there there is not enough enough time time for ions ions to move signific significant antly ly compared compared to electr electrons ons.. A local local charge displacement results when the electrons are pushed by the light pressure. pressure. The electrostat electrostatic ic restoring restoring force causes causes the plasma plasma electr electrons ons to oscill oscillate ate at the plasma plasma freque frequenc ncy y (ωp ), creating alternating regions of net positive and negative charge. An electrostatic wakefield plasma wave wave results, which propagatesataphasevelocitynearlyequaltothegroupvelocity of the light pulse, which can be close to the speed of light for low-den low-densit sity y plasma plasmas. s. A relati relativis vistic tic electron electron can then then be continuously continuously accelerated. accelerated. Remarkably Remarkably,, the acceleration acceleration 1 − gradie gradient nt (200 (200 GeVm ) can be four four ordersof ordersof magnit magnitudelarge udelargerr than in conventional rf linacs ( <20MeVm−1 ) [7]. A plethora plethora of methods have been proposed for driving such plasma waves [7], including the plasma beat-waves [17], laser wakefields (LWF (LWFA) A) [17], [17], tailor tailored ed pulse pulse trains[18], trains[18], andthe self-m self-modu odulat lated ed laser wakefields (SMLWFA) (SMLWFA) [19–21]. Of these these approa approache ches, s, laser laser beatwa beatwave vess were were first first to be demonstrate demonstrated d [22, 23] because because long-pulse long-pulse medium-po medium-power wer laserswere laserswere devel develope oped d 30 years years ago. ago. More More recent recently ly,, with with thedevolopment of short-pulse high-intensity lasers, the LWFA and the SMLWFA SMLWFA were demonstrated. In the LWFA, LWFA, an electron plasmawaveis plasmawaveis drive driven n resona resonantl ntly y by a short short laser laser pulse pulse ( τ τ p ) through through the laser ponderomotiv ponderomotivee force (see figure 7). In the resonant laser plasma accelerator, a train of Gaussian-shaped pulseswith variable variable durations durations and inter-puls inter-pulsee spacings spacings can stay in resonance with a wakefield as it grows nonlinearly [18]. In the SMLWFA, an electromagnetic wave ( ω0 , k0 ) decays into a plasma wave ( ωp , kp ) and another forward-propagating light wave (ω0 ωp , k0 kp ) via the stimulated Raman forward scattering scattering instability instability.. In this case, the laser pulse duration duration is τ p longer than an electron plasma period, τ 2π/ω p .

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Topical Review (a)

(b)

Figure 7. The laser wakefield mechanism. (a) A laser pulse interacts with a plasma, an ionized gas, composed of electrons and ions. ( b) In

the relativistic regime, the electromagnetic force acting on the electron pushes the electrons forward in the laser direction. The charge separation between the light electrons and the massive ions in a plasma produces a large longitudinal static electric field comparable to the transverse field of the laser. Note that the plasma acts as an efficient optical rectifier.

plasma waves and sidescattering instabilities [24–26] or by wave-bre wave-breaking aking (longitudin (longitudinal al [7] or transverse transverse [27]). These electrons can become trapped in the fast wakefield plasma wave, but will produce a beam with a large energy spread. On the the othe otherr hand hand,, the the char charac acte teri rist stic icss of the the gene genera rate ted d electr electron on beam beam canbe contro controlle lled d by propos proposed ed inject injectionscheme ionschemess [28–33 [28–33,, 211], 211], in which which all of the plasma plasma electr electrons ons that that become become trapped (in the acceleration bucket of the fast plasma wave) have have the same same phase. phase. Beside Besidess compac compactt size, size, anothe anotherr advant advantage age of an all optica optically lly driven driven plasma plasma-ca -catho thode de electr electron on gun is absolute synchronization between the electrons and laser for pump and probe experiments in ultrafast science. The The larg largee 2.1. 2.1.5. 5. Self Self-g -gen ener erat ated ed magn magnet etic ic fields fields.. (kiloampere) currents that are produced by laser-accelerated electr electron on beams beams can induce induce large large poloid poloidal al magnet magnetic ic fields fields [34]. A circularly polarized polarized light beam can generate an axial magnetic field [35] by inducing current loops via the inverse Faraday Faraday effect. effect. If there is a temperature temperature gradient orthogonal orthogonal to a density gradient, then the thermoelectric effect can also induce a toroidal field. In all of these cases, megaGauss, even gigaGauss field strengths can be driven. 2.2. Solid-density targets

Low-i Low-inte ntensi nsity ty laser laser light light cannot cannot normal normally ly propag propagate ate into into overdense plasma, above the critical density, n defined by

can separate separate from plasma ions. ions. Such charge charge displacement displacement creates an electrostatic sheath, which eventually accelerates the ions. The ions are pulled pulled by the charge of the electron electronss and pushed by the other ions’ unshielded charges (similar to the ‘Coulomb explosion’ that can occur during the ionization of atoms) atoms).. Wh When en the char charge ge displa displace ceme ment nt is driv driven en by thermal expansion, as in long-pulse (low power) laser–plasma experi experimen ments, ts, the maximu maximum m ionenergies ionenergies are limite limited d to less less than than 100 keV. keV. However, However, when the charge displacement is driven by direct laser heating, heating, as in short-pulse short-pulse high-powe high-powerr laser–plasm laser–plasmaa experiment experiments, s, multi-mega multi-megaelectr electronv onvolt olt ion energies energies are possible. possible. This was first shown with gas jet targets [137, 136], in which case the ions were accelerated radially into 2 π , and then later with with thin thin solidsolid-den densit sity-fi y-films lms [138–1 [138–140] 40],, in which which case case the ions ions were accelerate accelerated d into collimated collimated beams. In the latter case, hydrocarbons and water on the surface of the film can become ionized and provide a source of protons to be accelerated. An intense laser can ponderomotiv ponderomotively ely heat electrons. electrons. If the laser contrast is high, vacuum heating can occur in the following following manner. manner. When light encounters encounters a sharp interface interface between vacuum and solid density, the electromagnetic field becomes evanescent in the region above the critical density. B ’ force can push electrons in the The instantaneous ‘ v direct direction ion of the light’ light’s propag propagati ation on vecto vector; r; it also also has a freque frequenc ncy y twice twice that that of the pump pump and a magnit magnitude ude propor proportio tional nal 2 to the square of the normalized vector potential, a0 . Thu Thus electr electrons ons can only only comple complete te half half of their their figurefigure-eig eight ht orbits orbits,, on

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Topical Review

the incoming incoming wave to create a standing standing wave. wave. The motion of electrons in such a wave can become chaotic, resulting in a large increase in electron temperature ( >100 keV). keV). As the heated electrons propagate through a solid, they can instantaneously field-ionize the neutral atoms of the solid. This will both modify the solid’s solid’s conductiv conductivity ity and provide provide a source source of protons protons on the rear-si rear-side de of the target target.. If the film is thin enough, the electrons can pass through, and create a sheath sheath on the rear-side rear-side of, the target. target. This latter mechanism mechanism has been been dubbed dubbed the target target normal normal sheath sheath accele accelerat ration ion (TNSA) (TNSA) mechanism. mechanism. The ions from thin foils have have been claimed claimed to originate from both the front and rear-side of the foil.

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B term of 2.2.2. 2.2.2. Critical Critical surface surface interaction interactions. s. The v equation (1) oscillates at 2 ω because it is a product of two sinusoidal terms oscillating at ω. Thus, Thus, the critical critical surfac surfacee (the (the locati location on of the critic critical al densit density) y) where where the light light is reflect reflected, ed, can also oscillate at 2 ω. Frequency Frequency mixing mixing can then produce harmonics harmonics in solid-targ solid-target et experiment experiments, s, as has been observed observed since the early days of intense laser interactions (with CO 2 lasers) [37]. As discus discussed sed above above,, relati relativis vistic tic mass mass shifts shifts can change change the plasma frequency. This will act to shift the critical-density to higher values for a fixed incident laser frequency, inducing transp transpare arenc ncy y of even solid target targetss by intense intense pulses. pulses. The pressu pressure re of intens intensee laser laser pulsescan pulsescan also also push push thecriticalsurfa thecriticalsurface ce towards the solid-density region [38,39], or also push plasma sideways in a process called ‘hole-boring’ [40].

3. Recent findings 3.1. Analytical and numerical

Most of all the phenomena discussed in section 2 have been extensively studied with analysis and numerical simulation. The nonlinear regime ( a02 1) of intense laser interactions with underdense plasma is very well understood theoretically assuming one dimension, or the laser spotsize is much greater than the plasma wavelength. wavelength. This includes includes nonlinear plasma waves, waves, wavebreak wavebreaking, ing, quasi-stati quasi-staticc laserpropagation, laserpropagation, nonlinear nonlinear growth growth rates rates for instab instabili ilitie tiess and harmon harmonic ic genera generatio tion. n. Numerous fluid, particle, and Vlasov codes are also valid in this approximati approximation. on. Many of the same phenomena phenomena are also understood in three dimensions, but only in the linear regime (a02 1).

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3.1.1. Propagation, plasma wave generation and acceleration in underdense plasma. There has been some progress in the three-dimensi three-dimensional onal nonlinear nonlinear regime. For instance, instance, there exists exists a unifiedcold-fluid-Maxw unifiedcold-fluid-Maxwell ell modeltreatmentof electron electron parametric parametric instabiliti instabilities, es, assuming assuming a one-dimens one-dimensional ional planeplanewave wave high-intensity high-intensity pump laser field [41, 42]. Novel Novel effects, effects, such as the coupling of forward Raman and self-modulation instabilities, including the effects of a radially bounded pump

considered [46]. It is found that when the pairs are sufficiently confined, they can start to exponentiate in number, achieving a pair density approaching 10 21 cm−3 . Several Several authors authors have have studied the acceleration of electrons directly from the laser field in vacuum [47,48]. Much progress has also been made in this regime through simulations simulations.. Although Although very very demanding demanding computati computationall onally y, three-dimensional full-scale particle-in-cell simulations solve Maxwell’s equations and the equation of motion, equation (1), without approximation for each particle simultaneously. simultaneously. The VLPL was an early example, which can run on a massively parallel computer CRAY CRAY-T3E with 784 processor elements. It 9 uses up to 10 particles and 10 8 grid cells and was used to study relativistic self-focusing and cavitation [49], and later hole-boring hole-boring [50]. Coalescence Coalescence of two laser-beam laser-beam filaments into a single filament was observed and thought to be due a self-generated magnetic field. Another three-dimensional PIC code, code, which which is fully fully expli explicit cit,, object object-or -orien iented ted and parall paralleli elizedis zedis OSIRIS. It was used to observe the formation of a braided pattern due to the mutual attraction of two co-propagating laser beams in a plasma [51]. [51]. The mechanism mechanism is similar similar to selffocusing, discussed in section 2.1.1, except the one filament modified the index of refraction seen by the other filament. The magnetic field of a plasma wake driven by laser pulse has also been studied [52]. A threethree-dim dimens ension ional al PIC code was used to study study the propag propagati ation on of an intens intensee pulse pulse throug through h an underd underdens ensee plasma plasma,, showing the formation of a ‘shock’ on the front of the pulse, ion filaments filaments and double layers layers [32]. The amplitude amplitude of the circularly polarized laser was a0 50, the mass ratio was mp /m e 1840, and ωp /ω 0.45. A three-dimensional versio version n of the VLPL VLPL code code has been been used used to inve investi stigat gatee electr electron on acceleratio acceleration n by the inverseinverse-freefree-electr electron-la on-laser ser mechanism mechanism [53]. Electrons Electrons propagating propagating in a plasma channel can execute betatron oscillations from the self-generated static electric and magnet magnetic ic fields. fields. If the power power of the laser laser greatl greatly y exceed exceedss the threshold threshold for relativis relativistic tic self-focusi self-focusing ng and the betatron betatron oscillations are in resonance with the light pulse’s electric field, field, then then the electr electrons ons can gain gain energ energy y direct directly ly from from the laser laser.. The results of a simulation of electron acceleration from an underdense target were used to support the argument that most of the energy acquired in a real experiment conducted under simila similarr condit condition ionss [54] [54] is due to direct direct laser laser accele accelerat ration ion,, while while laser wakefield acceleration (LWFA) (LWFA) drives only a minority of electrons. Anothe Anotherr code code that that has been used used to study study wakefie wakefield ld 2 genera generatio tion n and laser laser propag propagati ation on in the limit limit a 1 is named SIMLAC SIMLAC [55,197]. It follows follows the motion of the pulse in its group veloc velocity ity frame. frame. When When this code was used used to study wakefields, wakefields, the laser pulse and wake were observed observed to be maintained over long enough propagation distance to accelerate an electron to gigaelectronvolt energy. A three-dimensional envelope equation for the laser field was derived analytically, which includes nonparaxial effects,

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Topical Review

make the paraxial approximation, and thus allows for a wave with a finite group velocity, has been used to model selfmodula modulatio tion. n. It is found to reduce reduce the growth growth rate rate of the SMLWF SMLWFA A [43]. It was found that in the very-underdense very-underdense-plasma limit, a separation of the ω and ωp timescales need not be assumed in a Maxwell-fluid Maxwell-fluid model [56]. Rather than havin having g to grow grow from from noise, noise, theperturbat theperturbationfrom ionfrom which which Raman Raman forward scattering can grow can be seeded by either ionization fronts fronts or Raman backscatter backscatter [201]. [201]. Plasma wakes wakes can also be excited by colliding long and short pulse duration counterpropagating laser beams [210]. This is related to a method by which the wakefield of one ultrashort laser pulse is amplified by a second second co-propagating co-propagating laser pulse [207]. A mechanism that leads to efficient acceleration of electrons in plasma by two counterpropa counterpropagatin gating g laser pulses was proposed [209]. It is triggered by stochastic motion of electrons when the laser fields exceed some threshold amplitudes, as found in singleelectron electron dynamics. dynamics. It is further further confirmed confirmed in particle-inparticle-in-cell cell simulations. Tricks have been suggested to get around the Lawson– Woodward criteria, which limits the means by which electrons can be accele accelerat rated ed in vacuu vacuum. m. For For instan instance, ce, using using threethreedimensiona dimensionall test particle particle simulations simulations,, the characteris characteristics tics and essential conditions under which an electron in a vacuum laser beam can undergo a capture and acceleration [212] have been examined. examined. When a0  100, the electron can be captured and violently accelerated to energies 1 GeV with an acceleration acceleration gradient 10GeVcm−1 . Classical Classical fifth order calculations calculations in the diffracti diffraction on angleshow that electrons, electrons, injected injected sideways sideways into the tightly focused petawatt-power laser beam, get captured and gain energy in the gigaelectronvolt regime [205]. A multiple timescale expression for the ponderomotive force of an intense light pulse has also been proposed [57]. The generation of forward Raman radiation shifted by half the plasma plasma frequency frequency,, for laser intensities intensities of order or exceeding exceeding 18 2 − 10 W cm , has has recent recently ly been been predic predicte ted d [58]. [58]. It has been observed in PIC-code simulations that self-focusing and ponderomotive blow-out can be suppressed by the occurrence of Raman scatte scatterin ring g and plasma plasma heating heating [59]. It has been been shown shown theoreticall theoretically y that non-Gaussian non-Gaussian-shap -shaped ed pulses pulses can drive drive wakefields wakefields more effectiv effectively ely than Gaussian-s Gaussian-shaped haped pulses pulses [60]. Similar improvements might be obtained by the use of pulse shapes shapes that are more easily produced experimenta experimentally lly using a genetic genetic algorithm algorithm [61]. The behaviour behaviour of the electron beam

A simulation shows that stochastic heating of electrons in the beating of the incident and reflected wave heats the electrons to multi-megaelectronvolt energies and accelerates them into the dense plasma, plasma, where, where, at the rear rear surfac surfacee of the dense dense plasma (but the front of the target), they accelerate the ions into the target [ ?]. Another Another simulation shows shows the focusing focusing of fast protons created in the interaction of laser radiation with a spherical spherical target is possible possible with the focal spot of fast protons protons near the centre of the sphere. The conversi conversion on efficiency efficiency of laser energy energy into fast ion energy attains 5% [151]. Both front and backside backside ion acceleration acceleration and a 10 MG magnetic magnetic field are observed in simulations of an intense laser (10 19 W cm−2 and 150 fs) interacting interacting with a solid-densi solid-density ty thin film [152]. 3.1. 3.1.3. 3. Nonl Nonlin inea earr scat scatte teri ring ng and and harm harmon onic ic gene genera rati tion on.. Althou Although gh much much of the theore theoretic tical al analys analysis is of nonlin nonlinear ear Thomson scattering was originally done in the 1960s, several refinements have been published only recently. The The prod produc ucti tion on of harm harmon onic icss by nonl nonlin inea earr Rama Raman n backscatter backscattering ing mechanism mechanism has been reanalysed reanalysed [95] using the wave equation and fluid equations instead of relying on analysis of free electrons. The backscatter is found to occur at odd multiples of the Doppler-shifted pump frequency (for the case of an electron electron beam). The effects effects of stimulated Raman Raman scattering on radiation generation has also been explored [94]. It shows that for maximal growth rate a high level of spectral purity in the electron beam is required. Relati Relativis vistic tic harmon harmonic ic genera generatio tion n in a plasma plasma is consid considere ered d by determ determini ining ng a curren currentt densit density y based based on the relati relativis vistic tic Lorentz equations [87]. Maxwell’s equations equations are used to solve for harmonic generation, and this solution shows oscillation in the strength of the harmonic. Resonant density modulation of the plasma through an ion acoustic wave is shown to allow for linear growth of the harmonic. A comp comple lete te thre threee-di dime mens nsio iona nall theo theory ry of Comp Compto ton n scattering is described [96], which fully takes into account the effects of the electron beam emittance and energy spread upon the scattered x-ray spectral brightness. The radiation scattered by an electron subjected to an arbitrary electromagnetic field distribution in vacuum is first derived in the linear regime and and in the abse absenc ncee of radiat radiativ ivee corr correc ecti tion ons. s. It is foun found d that each vacuum eigenmode gives rise to a single Dopplershifted shifted classical classical dipole excitatio excitation. n. This formalism formalism is then







Topical Review

the harmonics of Thomson scattering spectra, in general, do not occur at integer multiples of the laser frequency, and the maximum frequency is proportional to the first instead of the third power of the electric field field strength [82, 83]. A charge charged d partic particle le in circul circular ar orbit orbit at relati relativis vistic tic veloci velocitie tiess will create short pulse radiation for an observer in the plane of rotati rotation. on. Ifthis radiat radiationarise ionarisess outof a sourcesize sourcesize smalle smallerr than than a wavelength, we consider it coherent, because all secondary sources sources encounter encounter the same phasefrom the incident incident laser. laser. From scatte scatterin ring g theory theory,, cohere coherent nt radiat radiated ed powergoes powergoes as the square square of thesource thesource number number;; this this howe howeve verr motiv motivate atess a recons reconside iderat ration ion of radiat radiation ion reacti reaction on for the case case of cohere coherent nt scatte scatterin ring. g. Inclus Inclusion ion of this analysis is shown to result in an optimal number of electrons for maximum radiated energy [85]. Of course, even shorte shorterr pulses pulses would would be seen seen by partic particles les of relati relativis visticveloc ticvelocity ity directed directed along the plane of electron electron rotation. rotation. An additional additional benefit of the circular trajectory of the electrons is generation of an astronomically significant magnetic field at the centre of the rotation. A scheme scheme is propos proposed ed to create create a single single (as oppose opposed d to pulse pulse train train)) 500 as, as, VUV VUV pulse pulse [84]. [84]. Citi Citing ng the key key requ requir irem emen entt for for shor shortt puls pulsee radi radiat atio ion n as a sour source ce size size corresponding to a time spread less than the desired output, theauthors theauthors propos proposee using using a tightl tightly y focuse focused d electr electron on beam beam as the scattering scattering medium. medium. The proposed proposed method capitalizes capitalizes on the ponderomotive force originating from the spatial profile of the light to limit the electron scattering time to less than that of the original original pulse. A co-propagating co-propagating geometry geometry of two pulses shifted in phase by one-half wavelength helps to homogenize the field seen by electrons along the direction of propagation. The power, power, energy energy spectrum, spectrum, brilliance, brilliance, polarizatio polarization n and and time time stru struct ctur uree of x-ra x-rays ys prod produc uced ed by Larm Larmor or and and Bremsstrahlung radiation [93] were evaluated. Radiation Radiation emitted by an electron in arbitrary arbitrary,, extreme extreme relativistic motion has been described for the first time in terms of a standard spectrum of nonsynchrotron type [97]. Ultimately, such a nonsynchrotron spectrum is dependant not only only on instan instantan taneou eouss trajec trajector tory y curva curvatur turee butalso upon upon itsfirst two time derivatives and helicity to provide a basic correction to the synchrotron synchrotron approximat approximation. ion. A strong deviation deviation has been been predic predicted ted for above above gigael gigaelect ectron ronvol voltt electr electrons ons in orient oriented ed crystals. A scheme for bright sub-100 fs x-ray radiation generation

35% of the laser energy to radiation radiation [100]. This incoherent incoherent x-ray x-ray emissi emission on lasts lasts for only the pulse durati duration on and can be intense. intense. The radiati radiation on efficien efficiency cy is shown shown to increa increase se nonlinearly nonlinearly with laser intensity intensity.. Similar Similar to cyclotron cyclotron radiation, radiation, the radiation damping may restrain the maximal energy of relativistic electrons in ultraintense-laser-produced plasmas. 3.1.4. Solitons Solitons and electromag electromagnetic netic transpar transparency ency.. Two qualit qualitati ative vely ly differ different ent scenar scenarios ios for the penetr penetrati ation on of relativistic relativistically ally intense intense laserradiation into an overdenseplasma, overdenseplasma, accessible accessible by self-induce self-induced d transparenc transparency, y, were investiga investigated ted [75]. In the first one, penetration penetration of laser laser energy occurs occurs by soliton soliton like structures structures moving into the plasma. plasma. This scenario scenario occurs at plasma plasma densities densities less than approximately approximately 1.5 times critic critical al (dependi (depending ng on ion mass). mass). At higher higher backgrou background nd densities, laser light penetrates only over a finite length which increases increases with incident intensity intensity. In this regime regime the plasmaplasmafield structures represent alternating electron and, on longer timescales, ion layers separated by about half a wavelength of cavitation cavitation with concomitant concomitant strong charge separation. separation. With With particle-in-cell simulations, electromagnetic, relativistically strong solitons, formed in the wake of the laser pulse during the interaction of a high-intensity ultrashort laser pulse with a collisionless plasma, are shown to evolve asymptotically into post-solitons [76]. A post-soliton is a slowly expanding cavity in the ion and electron densities which traps electromagnetic energy energy and accelerates accelerates ions upon formation. formation. Post-solito Post-solitons ns are elementary components of the relativistic electromagnetic turbu turbulen lence ce in laser laser-ir -irrad radiat iated ed plasmas plasmas.. The ion motion motion influence on the relativistic soliton structure is investigated. In the case of moving multimode solitons, the effect of the ion dynami dynamics cs result resultss in the limiti limiting ng of the solito soliton’ n’ss amplit amplitude ude [77]. [77]. The constraint on the maximum amplitude corresponds corresponds to either the ion motion breaking breaking in the low-node-numbe low-node-numberr case, or to the electron trajectory self-intersection in the case of high-node-number solitons. The soliton breaking leads to the generation of fast ions and provides a novel mechanism for ion acceleration in a plasma irradiated by high-intensity laser pulses. 3.2. Experimental 3.2.1. Relativisti Relativisticc electron electron motion, motion, Thomson Thomson scattering and







Topical Review

The second-har second-harmonic monic emission generated generated by spatially spatially asymmetric quivering electrons caused by the ponderomotive force was studied [92]. The intensity of the second harmonic was proportional to the focused intensity of the pump pulse with with the power power of 1.8. This This intensity intensity depend dependenc encee can be explained by the relativistic effect of the quivering electrons. The genera generatio tion n of high high harmon harmonics ics create created d during during the inte intera ract ctio ion n of a 2.5 2.5 ps, ps, 1053nm 1053nm lase laserr puls pulsee with with a soli solid d target has been recorded for intensities up to 10 19 W cm−2 . Harmonic orders up to the 68th at 15.5 nm have been observed observed in first order diffraction with indications of up to the 75th at 14.0 nm using second-order second-order [98]. No differences differences in harmonic emission between s and p polarization of the laser beam were observed. observed. The power power of the 38th high harmonic at 27.7 nm is estimated to be 24 MW MW.. An experimentally measured increase in laser absorption was observed as the laser intensity is raised [99], which was attributed to vacuum heating, consistent with theoretical predictions [36]. The fact that the electric field in a frame moving with a relativistic electron beam is boosted by γ , where γ is the relativistic factor associated with electron beam, has allowed the observ observati ation on of pair pair produc productio tion n from from the vacuu vacuum m with with curren currentt laser laser techno technolog logy y [101,102 [101,102]. ]. Using Using the30 GeVelectron GeVelectron beam of the stanford linear accelerator, the field was increased by a factor of 5 104 , and therefore in this case, the threshold for observation of pair-production was exceeded with a laser operating at an intensity of only 10 19 W cm−2 .

×

self-guiding g 3.2.2. 3.2.2. Guidin Guiding. g. As discussed in section 2, self-guidin is possib possible le when when laser laser power power exceed exceedss the thresh threshold old for relativistic self-guiding, P c . Various authors have reported the observati observation on of relativistic relativistic self-guiding self-guiding [103–108]. A second intense laser pulse has then been guided in such a preformed channe channell [109, [109, 79]. 79]. The critical critical power power for relativ relativist istic ic selfselffocusing P c has been shown experimentally [190] not the only relevant parameter, particularly when the laser pulse duration is comparable to plasma particle timescales: ωp−1 for electrons 1 and − p for ions. Using time-resolved shadowgraphy, pulses are observ observed ed to not relati relativis vistic ticall ally y self-f self-focu ocuss if the pulse pulse durati duration on is too short compar compared ed to ωp−1 , even even in the the case case where the power is greater than P c . For For pulses pulses longer longer than ωp−1 , self-focusing can occur even for powers lower than P c . When channel extension was characterized via the Thomson-

formed by using two transversely injected laser pulses, as in the igniter–heate igniter–heaterr scheme [112]. Capillary Capillary discharges discharges have been used to guide pulses, pulses, achieving achieving 70% transmission transmission of pulses with intensities reaching 10 17 W cm−2 over distances of up to 20 Rayleigh ranges ranges [113]. An innovativ innovativee technique technique for measuring the propagation of intense laser pulses through plasma channels is described [202]. At high laser intensities, temporally resolved stimulated Raman backscattering can be used used to diagno diagnose se both both the electron electron densit density y and the laser laser intensity intensity inside the plasma plasma channel. channel. Velocity elocity control and staging of laser wakefield accelerators in segmented capillary discharges has also been investigated [200]. The observation of laser self-focused channel formation into into overd overdens ensee plasma plasmass (hole(hole-bor boring ing)) has been been report reported ed in expe experi rime ment ntss maki making ng use use of a soft soft x-ra x-ray y lase laserr prob probee system system with a grid grid image image refrac refractom tometr etry y techni technique que.. Cross Cross sections of a 30- µm diamet diameter er channe channell were were obtain obtained ed that that the author authorss attrib attribute ute to hole-b hole-bori oring ng in overd overdens ensee plasma plasmass [114]. Hole-boring Hole-boring has also been investiga investigated ted by means of transmission measurements [115]. Sever Several al groups groups have have 3.2. 3.2.3. 3. Elec Electr tron on acce accele lera rati tion on.. observed the acceleration of megaelectronvolt electrons by the SMLWF SMLWFA A [25, 26, 108, 120, 116–118], 116–118], with a large energy energy spre spread ad.. Most Most of the the elec electr tron onss have have energi energies es less than than 5 MeV, MeV, with the number number decaying decaying exponentia exponentially lly and some electrons electrons at energies energies up to 200 MeV [118]. [118]. While in an early paper, the electron acceleration was attributed to catastrophic wavewave-bre breaki aking ng of a relati relativis vistic tic Raman Raman forwa forward rd scatte scattered red plasma wave wave [120], [120], this has more recently recently been attributed attributed to the wavebreaking of a slower velocity Raman backscattered wave wave [25, 26]. 26]. Recently Recently,, a two-temper two-temperature ature distribution distribution in the electron energy spectrum spectrum is reported reported [105], which was attrib attribute uted d to a combin combinati ation on of two differ different ent accele accelerat ration ion mechan mechanism isms: s: (1)directlyby (1)directlyby thelaserfield and(2) by theplasma theplasma wave. wave. A two-temperatur two-temperaturee distribution distribution was also observed in a different experiment [121], as well as a multi-component spatial profile of the electron beam, measured at a distance of 10 cm from the gas jet. Electrons Electrons in the low energy energy range were observed to undergo an abrupt change in temperature, coinciding with the onset of extension of the laser channel due to self-guiding of the laser pulse, when the laser power or plasma plasma densit density y was varie varied d [108]. [108]. In contra contradic dictio tion n to the theory theory







Topical Review

by a 35 fs laser pulse propagating propagating in explodingexploding-foil foil plasmas was was studi studied ed [196 [196]. ]. Up to 109 electr electrons ons per shot shot were were accelerate accelerated, d, most of which were in a beam of aperture below 10−3 sterad, with energies up to 40 MeV. MeV. Seve Several ral groups groups [123,124] [123,124] have have measur measured ed the plasma plasma wave wave amplit amplitude ude as a functi function on of time time by means means of collin collinear ear Thomso Thomson n scatte scatterin ring g and found that that it decays decays in 50τ p . By dire direcct measurement of ion waves, the modulational decay instability (in which electron plasma waves decay into ion waves) has been been show shown n to play play an impo import rtan antt role role in the the damp dampin ing g of plas plasma ma waves waves [125]. The longitudinal longitudinal spatial spatial profile of the plasma wave has been measured by means of coherent Thomson sidescattering. It appears that with the laser and plasma conditions of this particular experiment the plasma wave is localized to islands islands along the direction direction of laser propagatio propagation n [126]. [126]. TimeTimeresolved resolved measurements measurements of the growth growth of Raman instabilities instabilities were performed using a picosecond chirped laser pulse [195]. For a short laser pulse ( <10 ps), ps), forwar forward d and 30˚-Ra 30˚-Raman man scattering scattering occur occur at the back of the pulse. The growth growth of the instabilities was found to be independent of the sign of the chirp. chirp. In addition, addition, a simple simple temporal model model was developed developed and shows shows good good agreem agreement ent with with the experi experimen mental tal result results. s. This This model also indicates that the plasma wave driven by forward Raman scattering is severely damped in the case of pulses longer than a few picoseconds. Damping by the modulational instability instability is compatible compatible with the experimental experimental results. results. The effec effectt of asymme asymmetri tricc laser laser pulses pulses on electr electron on yield yield from from a laser laser wakefield accelerator has been experimentally studied [193]. Pulses (76 fs FWHM) with a steep rise and positive positive chirp were found to significantly enhance the electron yield compared to pulses with a gentle rise and negativ negativee chirp. Theory Theory and simulation show that fast-rising pulses can generate larger amplitude wakes that seed the growth of the self-modulation instability. Forward- and backward-Raman scattering and the emissi emission on of fast fast electr electrons ons indica indicate te that that intens intensee electr electron on heatin heating g is likelyto likelyto play play a major major role role in thetemporalgrow thetemporalgrowth th or inhibi inhibitio tion n of the instabilities [194]. The The reso resona nant nt wake wakefie field ld has has been been char charac acte teri rize zed d by temporal temporal interferomet interferometry ry [127, 128]. Howeve Howeverr this was done only for the tight-focus tight-focusing ing case in which the laser spotsize spotsize is λp ) much smaller than the plasma wave wavelength ( rl and thus the transverse wakefield was much greater than the longitudinal wakefield. The in fre lec las hanism hanism has bee

∼



electron energy reaches 70 MeV, MeV, increasing at lower electron densities densities and higher laser intensities intensities.. A total charge of 8 nC was measured. measured. Simulation Simulation of the experiment experiment [119] indicates that the electrons are accelerated mainly by relativistic plasma waves waves,, and, and, to some some extent extent,, by direct direct laser accele accelerat ration ion.. Electrons have been accelerated accelerated to an energy of 4 MeV during the ionization of a gas [199]. Free Free elec electr tron onss were were repo report rted ed to be acce accele lera rate ted d in vacuum vacuum to megaelectro megaelectronv nvolt olt energies energies by a high-intens high-intensity ity − 19 2 subpic subpicose osecon cond d laser laser pulse pulse (10 W cm , 300 300 fs) [116 [116]. ]. A subsequent discussion has helped to clarify the model used to explain the results results [131–133]. [131–133]. In numerical numerical simulations simulations [134] as well as experiments [135], megaelectronvolt energy electron beams have also been observed in the interactions of intense lasers with solid-targets and propagate in both the forward and backward directions (with respect to the direction of laser laser propag propagati ation on direct direction ion,, which which canalso be in thespecular thespecular direction). The The effe effect ctss of lase laserr pola polari riza zati tion on on fast fast elec electr tron on emission are studied from an aluminium target irradiated by ultrashort ultrashort laser pulses pulses [208]. Jet emission emission of outgoing fast fast electrons collimated in the polarization direction is observed for s-pola s-polariz rized ed laser laser irradi irradiati ation; on; wherea whereass for p-pola p-polariz rized ed irradi irradiati ation, on, highly highly direct direction ional al emissi emission on of outgoi outgoing ng fast fast electrons is found in the direction close to the normal of the target. 3.2.4. Ion acceleratio acceleration n and nuclear reactio reactions. ns. Energetic (megaelectronvolt) (megaelectronvolt) ions have been accelerated by electrostatic sheath sheathss create created d in underd underdens ensee plasma plasmass [136,137 [136,137]] when when intens intensee lasers are focused focused onto gaseous gaseous density targets. targets. The chargechargedisplacement was due to ponderomotive blow-out blow-out [136, 137]. When a helium-gas was used as the target, alpha particles were accelerated to several megaelectronvolts in the direction orthogonal to the direction of laser propagation, which is also along the direction of the maximum intensity gradient. Seve Several ral groups groups have have report reported ed the observ observati ation on of ions ions origin originati ating ng from thin-film thin-film solid-d solid-dens ensity ity targets targets.. Unlike Unlike previous previous long-pulse experiments, experiments, the ions were accelerate accelerated d alon along g the the dire direct ctio ion n norm normal al to the the side side of the the targ target et that that is oppo opposi site te to that that upon upon whic which h the the lase laserr was was inci incide dent nt.. The ions ions genera generally lly origin originate ate from from water water or hydroc hydrocarb arbons ons on the surface surface of the materi material. al. The accele accelerat ration ion results results







Topical Review

for a front-side origin, a recent experiment was conducted in which which deuter deuteriumwas iumwas coatedon coatedon a thin thin filmof mylar mylar,, anda boron boron target target was placed behind behind it [142]. [142]. Only when the deuterium deuterium was on the front side did the boron become activated by the reaction 10 B(d,n)11 C. The results of these experiments indicate that a large number of protons (10 13 p ) can be accelerated, corresponding to source current densities (10 8 A cm−2 ) that are nine ordersof-magnitude higher than produced by cyclotrons, but with comparable comparable transverse transverse emittances emittances ( ⊥  1.0π mm mrad). mrad). Proton Proton energies up to 60 MeV [140, 141] have have been observed in exper experime iments nts at intens intensiti ities es exceed exceeding ing 1020 W cm−2 (using (using the NOV NOVA petawatt laser). laser). The high end of the proton spectrum spectrum typically has a sharp cut-off, but, like the electrons discussed in section 3.2.3, 3.2.3, is a continuum. continuum. In one experiment, experiment, protons protons were were observ observed ed to be emitted emitted in ring ring patter patterns, ns, the radii of which depended on the proton energy, which was explained by self-generated magnetic fields [139]. When hen a 100 100 fs lase laserr puls pulsee at inte intens nsit itie iess abo above − 20 2 1 10 W cm was used in an exper experime iment nt to irradi irradiate ate 100 µm thick thick foils, a proton proton beam of 1.4 MeV tempera temperatur turee with a cut-off cut-off at 6.5 MeV was produced produced [160]. [160]. A 3 µm thick foil produced a beam temperature of 3.2 MeV with a cut-off at 24 MeV. MeV. Recirculati Recirculation on of the electrons during the laser pulse accoun accounts ts forthe sharp sharp drop drop off off in protonenerg protonenergy y when when thetarget thetarget thickness exceeds 10–15 µm ( 100 fs of recirculati recirculation on time). Thinner targets allow for the protons to experience a longer acceleration time because simulations show the sheath forms at the rear of the target target earlier in the interaction. interaction. In another exper experime iment nt [161], using a 1 ps laser pulse at 10 17 W cm−2 incide incident nt on a plasti plasticc target target,, it was shown shown that that in order order to maximize the energies of forward-emitted protons, the target thickness thickness must be selected selected such that it is smaller smaller than the hot electron range in the target but greater than the characteristic path path length length of the electr electron on heat heat wave wave genera generated ted by the prepul prepulse se and the leading edge of the laser pulse. If the target thickness is smaller than the heat wave path length, both the maximum and the mean proton energies can be a decreasing function of laser energy. Using liquid target technology, the generation of forwardaccelerate accelerated d sub-megae sub-megaelectro lectronv nvolt olt (up to 500 keV) protons from a 10 µm liquid water target at 1 kHz repetition rates was demonstrat demonstrated ed [143]. Up to 3 102 protons per shot in a 40˚ FWHM divergence beam were observed.

×

∼

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energies >5 MeV are observed observed [147]. [147]. In contradicti contradiction on to an earlier paper [146], the authors claim backside acceleration, based based on theobserva theobservatio tion n that that thenumber thenumber of accele accelerat rated ed proton protonss is greater than that available from the front surface irradiated area. A maximum carbon carbon energy energy of 7 MeV per nucleon nucleon is observed, as well as the production of the isotopes 34 Cl and 38 K. Isotopes are produced by fusion of 12 C and 27 Al, and the 63 Cu(p, n)63 Zn and 12 C(d, n)13 N reactions were used to determine proton energy spectrum and spatial extent. A 1 ps laser laser pulse at 10 17 W cm−2 is used to show that an increase in proton energy and current is possible when a double-layer foil target containing a high- Z layer and a low- Z hydrog hydrogenen-ric rich h layer layer on the back back is used used [149]. [149]. Proton Proton energi energies es and curren currentt increa increase se with with the Z of the the high high--Z layer layer and depend depend on the layer layer thick thicknes nesses ses.. More More than 109 forward-emitted protons of energy >100 keV have been been recorded within a cone angle <3˚. Collim Collimate ated d jets jets of carbonand carbonand fluorin fluorinee ions ions up to 5 MeVper nucleo nucleon n ( 100 MeV) MeV) areobserved areobserved from from therear surfac surfacee of thin thin 19 foils irradiated with laser intensities of up to 5 10 W cm−2 [153]. Proton acceleratio acceleration n was suppressed suppressed by resistiv resistivee heating heating of tar targe gets ts.. 1012 protons (Emax 25 MeV) MeV) per shot were observed without heating, and 10 10 (Emax 3 MeV) MeV) after after heating. heating. Using Al targets targets with a deposited deposited layer of C on the back at 600 K, the energy of the carbon carbon atoms increased by 2.5 with heating and the number to 2 1011 , corresponding to a laser-to-io laser-to-ion n energy conversion conversion of 0.5%. Using tungsten tungsten 7+ targets targets at 1200 K with a layer of CaF 2 they saw F ions with energies greater than 100 MeV. MeV. Targe argets ts of medi medium um and and high high atom atomic ic numb number erss were were irradiated by a 1 ps laser pulse of intensity up to 5 1016 W cm−2 . Up to 1 MeV highl highly y charged charged heav heavy y ions 38+ 33+ (Ta (Ta , Au ), as well as Ar-like Ag ions and fully striped Al ions were created [154]. The Trident laser facility facility (1.5 TW, TW, >1 J, 0.6 0.6 ps, ps, and 3 19 2 − 10 W cm ) wasused forhigh-res forhigh-resolu olutio tion n protonradio protonradiogra graphy phy of Au grids [155]. The effective proton source size affords an inherent inherent resolution resolution of 2–3 µm in the object plane: 100 times better than conventional conventional sources. 5 109 protons protons per shot in the 0.2–2 MeV energy energy range were generated. generated. 18 MeV protons protons were were observ observed ed from from 3 µm Al targ target etss and and 22 MeV MeV prot proton onss from from a 5 µm Au, but fewer total protons. TheVULCAN TheVULCAN laser laser operat operated ed at 1.054 1.054 µm, 1 psenergyand psenergyand up to 100 J was used to produce 10 12 s above 3

∼

∼

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=

=

∼ ×

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Topical Review

reacti reaction on initia initiated ted by an intens intensee laser laser,, neutro neutrons ns have have been been 3 d d, n produced by the He fusion reaction ( ) He in the focus of 200 mJ, 160 fs Ti : sapphi sapphire re laser laser pulses pulses on a deuterat deuterated ed polyet polyethyl hylene ene target. target. Optimi Optimizin zing g the fast electron electron and ion genera generatio tion n by applyi applying ng a well-d well-defin efined ed prepul prepulse se led to an avera average ge rate of 140 neutro neutrons ns per shot [162]. [162]. Also, Also, bright bright x-rays from solid-target interactions have created isotopes of high-Z metals metals by means of photofission photofission [163–165]. [163–165]. LaserLaseraccelerated electron energies and angular distributions have been inferred from analysing ( γ , n) and ( γ , 2n) reactions in composite Pb/Cu targets [117] and in Ta/Cu targets [166]. Positrons Positrons were created created by colliding colliding laser-acce laser-accelerate lerated d electrons electrons with a tungsten target target [167, 192]. Measurementss of 3.2.5. 3.2.5. Self-gener Self-generated ated magnet magnetic ic fields. fields. Measurement magn magnet etic ic field fieldss gene genera rate ted d duri during ng ultr ultrah ahig igh h inte intens nsit ity y (1019 W cm−2 ), short pulse (0.71 ps) laser-solid laser-solid target interinteraction experiments have been reported using Faraday rotation of either the fundamental fundamental light at the critical critical density [184, 34] or the higher higher order order harmon harmonics ics above above critic critical al densit density y [185,186] [185,186].. Measur Measureme ements nts indica indicate te theexistenc theexistencee of peak peak fields fields greate greaterr than than 340 MG and below below 460 MG at such high intensit intensities. ies. Magnetic Magnetic fields in excess of 7 MG have been measured with high spatial and temporal temporal precision precision during during interaction interactionss of a circularlypolarcircularlypolarized ized laser laser pulse pulse with with an underd underdens ensee heliumplasm heliumplasmaa at intens intensiti ities es up to 10 19 W cm−2 [184 [184]. ]. The The fields, fields, while while of the form form expec expected ted from from the inve inverse rse Farada Faraday y effec effectt for a cold cold plasma plasma,, are much larger than expected, and have have a duration duration approaching approaching that of the high-intens high-intensity ity laser pulse ( <3 ps). These observaobservations can be explained by particle-in-cell simulations in three dimension. dimension. The simulations simulations show that the magnetic magnetic field is generated by fast electrons which spiral around the axis of the

Figure 8. Laser intensity versus time for two different laser-pulse

contrasts, ideal Gaussian and typical. Also shown are the various mechanisms that occur in solid–target interactions; those that occur at low intensities are initiated significantly in advance of the peak of the pulse, which corresponds to time zero. This illustrates the need for high laser contrast.

contra contrasts sts,, an ideal ideal Gaussi Gaussian an shape shape and a typica typicall pulse pulse (contr (contrast ast of 105 ). Also shown are the various mechanisms that occur in solid-targ solid-target et interactions interactions at various various intensities. intensities. The peak of a high-i high-inte ntensi nsity ty laser laser pulse pulse can be orders orders of magnit magnitude ude above above the thresholds of, and arrive significantly after, plasma creation and expansi expansion. on. Under Under such condit condition ions, s, the high intensit intensity y portion of the laser pulse will deposit its energy at the critical densit density y of a long long scalel scaleleng ength th plasmarathe plasmaratherr than than direct directly ly at solid solid density density. In order to mitigate mitigate this problem, the laser contrast is being improved by the use of frequency doubling, saturable absorbers [169] and frequency modulators to correct for highorder phase abberations abberations [170]. [170]. The latter technology technology is also permitting the generation of arbitrarily shaped pulses.







Topical Review

theoretica theoretically lly [91, 88, 83] and observed observed experimentally experimentally [81]. Several labs have already used short-pulse incoherent x-rays genera generated ted from from solidsolid-tar target get intera interacti ctions ons to study study timetimeresolved resolved ultrafast phenomena, phenomena, such as melting melting [174–176]. [174–176]. Sub-fe Sub-femto mtosec second ond high high harmon harmonic ic light light from from an atomic atomic medium medium has been used to study inner-shell atomic transitions with 8 fs time resolution [89]. Biomedical applications of this radiation have have been explored, including including differenti differential al absorption absorption and gated-viewing imaging [90]. A sufficient number of electrons have already been accelerated by laser–plasma accelerators to conduct time-resolved radio-chemistry experiments [177]. Time-resolved radio-biological studies with laser-accelerated protons are also feasible. 4.4. Relativistic ions

At the higher intensities that should be achievable in the near future( future( I λ2 1024 W cm−2 µm2 ), experi experimen ments ts will will move move to the regime in which even protons begin to quiver relativistically. Predictionsindicate Predictionsindicate that protons protons can be accelerated accelerated to relativisrelativistic velocities in plasma wakefields at much lower intensities (I λ2 1021 W cm−2 µm2 ) [32]. At intensitiesexceeding intensitiesexceeding I λ2 − 20 2 2 10 W cm µm , positrons will be produced more rapidly than they annihilate, making possible the creation of dense electron–positron plasmas [46]. Such exotic plasma exists at at the horizo horizons ns of black black holes holes and is thus thus relev relevant ant to astrop astrophys hysics ics..

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4.5. Fast ignitor fusion

Eviden Evidence ce sugges suggests ts that that a laserlaser-ind induce uced d burst burst of hot electr electrons ons or prot proton onss coul could d be used used as a spar spark k plug plug to igni ignite te a ther thermo monu nucl clea earr reaction reaction with inertial inertial confinement confinement fusion. fusion. A short but energetic energetic (1 kJ) laser pulse would drill through through the underdense underdense plasma

matterin a laser-dri laser-driven ven implosion implosion with picosecond-f picosecond-fast ast heating heating by a laser pulse timed to coincide with the peak compression. This approach therefore therefore permits efficient efficient compression compression and heating to be carried out simultaneously, providing a route to efficient fusion energy production. 4.6. Proton therapy

Proton therapy is now limited by the extraordinary expense of cyclotrons or synchrotrons and the large magnets required to transport the proton beams to the patient. Currently, there are only three hospital proton therapy centres, with an additional six planned planned or being being built. built. Beside Besidess reduce reduced d cost, cost, proton protonss are superior to other forms of ionizing radiation for cancer treatment because of less straggling and their ability to deposit their energy energy over a narrower narrower depth range. range. But in order for a proton beam to be useful for proton therapy, the intensity should be 1–5 1010 protons protons −1 with an energy energy of 200 MeV. MeV. Thus Thus the repeti repetitio tion n rate rate of laser laser-pr -produ oduced ced beams beams must must be increased. increased. Several Several ideas are being explored explored to improve improve the monochromaticity of proton beams [189].

×

4.7. Ion propulsion

Ions accelerated accelerated by short-pulse short-pulse high-intensity high-intensity lasers have have sever several al attrib attribute utess that that may make make them them advant advantage ageous ous for propul propulsio sion n [213, [213, 214]. 214]. Becaus Becausee of their their relati relativel vely y large large 6 −1 momentum, they deliver a high specific impulse (10 s ) but low thrust. thrust. As such, they are attractiv attractivee either for deep-space deep-space missio missions ns or for stationi stationing ng orbiti orbiting ng satell satellite ites. s. Becaus Becausee the accele accelerat rationof ionof ions ions with with short short durati duration on laser laser pulsesis pulsesis relati relative vely ly rapid, little energy energy is lost to thermal conduction conduction as compared compared with ions accelerated by long-duration laser pulses.







Topical Review

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Energy Propulsion (Huntsville, Alabama, USA, 5–7 November 2002) AIP Conf. Series to be published [214] [214] Horisawa Horisawa H et al Fundamental study of a relativistic Beamed laser-accelerated laser-accelerated plasma thruster 1st Int. Symp. on Beamed Energy Propulsion (Huntsville, Alabama, USA, 5–7 November 2002) AIP Conf. Series to be published

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