DDielectric Laser Acceleration
N. Schönenberger and P. Hommelhoff
Department of Physics, Friedrich-Alexander-University Erlangen-Nuremberg
Abstract
Dielectric Laser Accelerators (DLAs) use the nearfields created when a laserpulse impinges on a dielectric structure to accelerate charged particles. Weprovide an overview of the theory of operation of photon driven accelerators,from photons interacting with charged particles in a vacuum, to the advantagesgained by introducing dielectric structures, with a discussion of their advan-tages and limitations. Furthermore we show the state of the art of the currentdevelopment of dielectric laser accelerators, including acceleration, focusing,deflection, beam position monitoring, and advanced topics from the generationof microbunches to the adaptation of alternating phase focusing, allowing forthe next to lossless transport of the charged particles over long distances.
Keywords dielectric; laser; accelerator. Introduction
The idea of accelerators using dielectrics or stimulated emission to generate the necessary electromag-netic fields is not new. First proposals for such machines appeared in the 1970s. These consisted ofmaser pumped [1] accelerators — first demonstrated in 1987 using metallic gratings and mm wave ra-diation [2], laser pumped metallic gratings [3] and finally laser pumped dielectric [4, 5] accelerators.The first successful demonstrations of what we now call dielectric laser accelerators happened in 2013,independently at relativistic electron velocities [6] and subrelativistic speeds [7]. Several advancementswere necessary for a successful demonstration. Among others, the development of ultrashort laser pulsesand their amplification — honoured with the 2018 Nobel prize in physics for the invention of chirpedpulse amplification — to high peak intensities and the development of semiconductor technology thatpressed forward the ability of manufacturing tiny devices on a scale of the wavelength used to drivethese accelerators.Although the use of metal gratings was demonstrated early on, maser or laser driven acceleratorssuffer the same drawbacks of a rather low damage threshold when using metallic materials as conven-tional radio frequency (RF) accelerators. Although damage mechanisms can vary from thermal to peakfield driven effects metals, due to the availability of excitable electrons, the light can couple to the struc-ture and cause damage. In dielectrics the bandgap provides transparency allowing refractive media to beused instead of metallic ones with much greater peak fields before damage is observed. This facilitatesthe generation of higher acceleration gradients compared to RF accelerators.Due to the available laser sources that can provide short pulses and therefore sufficiently high peak fieldsand other considerations such as integrateability and wall plug power efficiency, the prefered wavelengthsare usually below nm. Therefore the structure features are roughly nm and below. This minia-turization opens the door for applications other accelerator concepts are not capable of supplying e.g.,medical irradiation in the body. This holds while DLAs currently require roughly an order of magnitudeless power per meter of accelerator compared to Laser Plasma Wakefield Accelerators (LPWA). Thishas still great potential for improvement since most of the laser power is unused and can be recycledimproving the DLAs efficiency in future devices. a r X i v : . [ phy s i c s . acc - ph ] A ug Theory
Starting from Maxwell’s equations, the feasibility of acceleration in vacuum, near dielectric boundariesand finally near microstructured dielectrics is explored, highlighting their respective advantages andlimitations. In the following section we derive the wave nature of electro magnetic waves. Maxwell’sequations ∇ · (cid:126)E = ρ(cid:15) (1) ∇ · (cid:126)B = 0 (2) ∇ × (cid:126)E = − ∂ (cid:126)B∂t (3) ∇ × (cid:126)B = µ (cid:15) ∂ (cid:126)E∂t + µ (cid:126)J (4)can be simplified with ρ = 0 and (cid:126)J = 0 since all considerations are done in vacuum and therefore thereare neither charges nor currents. Taking the curl of Faraday’s law of induction Eq. (3) changing the righthand side order of the differentiation yields ∇ × (cid:16) ∇ × (cid:126)E (cid:17) = − ∂∂t (cid:16) ∇ × (cid:126)B (cid:17) . (5)Substituting Ampere’s law Eq. (4) and assuming that the vacuum permittivity (cid:15) and vacuum permeabil-ity µ are not time varying we arrive at ∇ × (cid:16) ∇ × (cid:126)E (cid:17) = − µ (cid:15) ∂ (cid:126)E∂t . (6)Using the identity ∇ × (cid:16) ∇ × (cid:126)A (cid:17) = ∇ (cid:16) ∇ · (cid:126)A (cid:17) − ∇ (cid:126)A and Gauss’s law Eq. (1) yields the wave equationof the electric field ∇ (cid:126)E = µ (cid:15) ∂ (cid:126)E∂t . (7)Similar steps can be taken starting with Ampere’s law to arrive at the analogous wave equation for themagnetic field ∇ (cid:126)B = µ (cid:15) ∂ (cid:126)B∂t . (8)The easiest solution for these wave equations are the plane waves: (cid:126)E ( t, (cid:126)r ) = E · e i(cid:126)k(cid:126)r − iωt and (cid:126)B ( t, (cid:126)r ) = B · e i(cid:126)k(cid:126)r − iωt . (9) Interaction between a single plane wave and a charged particle only affects the particles momentumduring the interaction. After the interaction, averaging over the electromagnetic field, the particles mo-mentum is unchanged. This is due to the conservation of energy and momentum, sometimes referred toas the Lawson-Woodward theorem for the seven cases Lawson and Woodward postulated under which,if all are satisfied, no net acceleration can take place.One of the seven rules states that nonlinear forces must be neglected. By utilizing nonlinear forces,acceleration without any structures becomes possible. One such force is the ponderomotive force (cid:126)F p = − e mω ∇ E . (10)t is dependent on the square of the electric field and has the effect of pushing particles from high inten-sity regions to low intensity regions [8]. By utilizing two or more intersecting laser fields, a travellinginterference pattern can be created that is co-propagating with electrons. The properties of this travel-ling wave, e.g., its velocity, are set by the intersecting waves’ wavelengths and intersecting angles. Byadjusting the mode velocity to the electron velocity, synchronous interaction between the light wave andthe electrons can be achieved. One definite advantage of this approach is that due to the absence of anymedium, the peak intensity used can be easily increased without damaging structures, however scalabil-ity of the interaction distance is not trivial and due to the nonlinear nature of the interaction large pulseenergies are required to generate the large peak fields necessary. Fig. 1:
Setup to generate a travelling wave to change influence the electrons momenta (top) Ponderomotive wavewith group velocity v g synchronous to the electron velocity. Electrons experience a force according to the gradientfrom high intensity to low intensity. Electrons on the right hand side of a high intensity region get accelerated,where as electrons on the left side get decelerated. (bottom) Placing a dielectric close to the particle beam can alleviate some of the shortcomings of the ponderomo-tive method. By evaluating the electromagnetic fields in an infinitesimally small area or loop across aboundary, we can arrive at the continuity conditions n × (cid:16) (cid:126)E − (cid:126)E (cid:17) = 0 (11) (cid:16) (cid:126)D − (cid:126)D (cid:17) · n = σ s (12) (cid:16) (cid:126)B − (cid:126)B (cid:17) · n = 0 (13) × (cid:16) (cid:126)H − (cid:126)H (cid:17) = (cid:126)j s , (14)with n the normal vector of the interface, σ s the surface charge and (cid:126)j s thesurf acecurrent – whichboth are zero due to only considering dielectrics. From these equations we see that the tangential partof the electric field (cid:126)E and the magnetic field strength (cid:126)H have to be continuous across the interface.Furthermore, the normal components of the electric displacement field (cid:126)D and the magnetic field (cid:126)B haveto be continuous.Finally, when evaluating these boundary conditions together with the plane waves, we arrive at certainconditions the incident, transmitted and reflected waves have to satisfy. In Fig. 2 a) we see the incidentand transmitted wave at an interface. From (cid:16) (cid:126)k i − (cid:126)k r (cid:17) · (cid:126)r = 0 and (cid:16) (cid:126)k i − (cid:126)k t (cid:17) · (cid:126)r = 0 (15)we see that the x component of the wave vector, parallel to the materials interface, needs to have thesame value in all three waves k i,x = k r,x = k t,x . We use k i,x = | (cid:126)k i | sin φ = n i ωc sin φ, (16)with the dispersion relation k = nωc and the incident angle φ . Similarly we decompose the transmittedwave: | (cid:126)k t | = n t ωc = (cid:113) k t,x + k t,y (17)Finally we use that k t,x = k i,x to solve for k t,y k t,y = (cid:16) n t ωc (cid:17) − (cid:16) n i ωc (cid:17) sin φ. (18)In the special case that φ = sin − n t n i , we get a purely imaginary k t,y . k t,y = ± ik t (cid:115) n i n t sin φ − ± iβk t (19)One of the solutions is non physical and would lead to an exponentially growing field in the y direction.From the other we arrive at the transmitted evanescent wave (cid:126)E t = E e − βk t e ik t x − iωt . (20)To use these fields, it is necessary to phase match the electron velocity v e = cβ and the phase velocityof the excited evanescent mode v ph = cn sin φ . As can be seen this is adjustable via the angle of incidence φ . While possible [9], realizing an accelerator with this technique, starting from subrelativistic electrons,would be challenging. Furthermore there are no other tuning parameters other other than the angle ofincidence and the refractive index of the material making more complex field shapes to perform advancedmanipulations in phase space virtually impossible.Furthermore as can be seen in Fig. 2 b) the transmitted wave is evanescent, meaning that the ydirection decays exponentially. We can evaluate the characteristic decay length to Γ = cω (cid:112) n sin φ − π γβλ (21)with β the electron velocity, γ the Lorentz factor and λ the wavelength of the light. We see that thespatial extent of the evanescent wave is rather small and therefore the desired high field strengths areonly accessible very close to the surface of the dielectric. Therefore the electrons need to occupy a verynarrow region above the interface, requiring also a beam of very high quality.To overcome the issue of too few tuning parameters, the interface can be patterned in a periodic fashion. ig. 2: Left: refracted wave right: evanescent wave formed by total internal reflection
When considering the general case of a laser illuminating an infinite plane grating of periodicity λ p many parameters have to be considered, as seen in Fig. 3 a). By aligning all the coordinate systemsand choosing the laser incident angle to be perpendicular to the grating we can drastically simplify thearrangement. Here (cid:126)K is the incident wave vector, (cid:126)K the component parallel to the surface and (cid:126)k (cid:107) and (cid:126)k ⊥ the parallel and perpendicular diffracted components respectively. The most interesting part for thestudy of acceleration is the parallel diffracted component (cid:126)k (cid:107) . This can have multiple spatial harmonics (cid:126)k n (cid:107) = (cid:126)K + n (cid:126)k p . Fig. 3:
Left: general case of light illuminating a periodic grating Right: simplified case Taken from [10]
The grating fields can be described as a series of these spatial harmonics. (cid:126)A ( (cid:126)r, t ) = ∞ (cid:88) n = −∞ (cid:126)A n e i ( k n ⊥ z + k n (cid:107) r − ωt + φ ) (22)To achieve phase matching, the same condition must be satisfied as for the case of evanescentfields at a plane dielectric interface. The electron velocity and the mode velocity of the diffracted lightave must be the same. Here the mode velocity is given by v ph = ω/k p arallel cos φ resulting in k (cid:107) = ωβc cos φ = k β cos φ (23)Assuming that the particle trajectory is parallel to the grating vector, we arrive at the synchronicitycondition λ p = nβλ. (24)Using (cid:126)k (cid:107) and (cid:126)k ⊥ in Ampere’s and Faraday’s law, we obtain (cid:126)E = icB y / ( ˜ β ˜ γ ) E y − cB y / ˜ β (25)and (cid:126)B = icE y / ( ˜ β ˜ γ ) B y E y / ( ˜ β ˜ γ ) . (26)With the commonly known equation for the Lorentz force (cid:126)F = q ( (cid:126)E + (cid:126)v × (cid:126)B ) we arrive at theresulting force from these electromagnetic fields (cid:126)F = icB y / ( βγ )0 − cB y / ( βγ ) . (27)The resulting forces are shown in Fig. 4. It is immediately apparent that there is an invariantdirection, where no forces are present. This direction is parallel to the grating teeth.Furthermore the mode still decays exponentially in the z direction. However the phase matching isnow accomplished via the periodicity λ p of the grating. This exponential decay has the side effect thatparticles that get pushed away from the grating surface due to the inherent transversal forces, can neverbe recaptured by the transversal forces, even if the phase is flipped and the force points towards thegrating, since the force at a greater distance is much weaker.Also like in the case of the evanescent wave at the interface, the peak field needed to accelerate electronsis much lower than when using nonlinear effects like the ponderomotive force. This is beneficial sinceany structure can be damaged.The other major drawback of this type of structure is that apart from the evanescent decay, nospeed of light mode is supported. That means that it is not possible to accelerate relativistic electronsat a single sided structure such as a dielectric interface or a single dielectric grating. Both these prob-lems can be solved when combining two gratings. The result can be seen in Fig. 5. There two gratingsare combined, opposing each other. The overlapping evanescent fields form a hyperbolic cosine or sineshape, depending on the phase of both incident lasers. While the usable spatial extent of the fields is notmuch increased, the gradient of the field decay is much less. Therefore electrons occupying the spacebetween the gratings experience a much more uniform energy modulation as in the same electron popu-lation would fly by a single grating.Furthermore the double sided grating supports a speed of light mode, enabling the acceleration of rela-tivistic electrons and also deflecting modes, when the incident lasers’ phases are adjusted. More infor-mation is available in [10]. ig. 4: Left: First spatial harmonic excited at a dielectric grating. Right: Third spatial harmonic excited at thesame grating. The x coordinate is stretched for easier visualization.
Fig. 5:
Combining two opposing gratings and their fields yields a configuration where the field is now also sym-metric in the y direction, removing the complications of the evanescent decay of the fields.
As briefly mentioned in the previous chapter, the transversal forces present in any DLA can deflect theparticles towards or away from the centre of the grating surfaces. Even in the case of the double sidedgrating, where the fields are symmetric, there is only one point in parameter space, where no transversalforce is present. This is perfectly on crest. Apart from it being virtually impossible to inject electronsonly perfectly on crest and keeping them there during the acceleration, manufacturing tolerances, laseramplitude fluctuations and other perturbations would destroy this balance.herefore another mechanism is required to make sure electrons are not deflected so much that they crashinto the structures and cause dramatic beam loss. There are different mechanism available to achieve thisgoal.One such technique is explored numerically by B. Naranjo [11] as part of the Galaxie proposal for aphotonic accelerator. Here multiple modes are excited, similar to the spatial modes mentioned previously.One mode, the synchronous one, is used for acceleration. However the modulation in the depth of thegrating teeth seen in Fig. 6 causes the emergence of a second mode. This mode is non synchronousto the electrons however when averaged over longer distances a net force appears that creates a movingpotential minimum and thus confines the electrons.
Fig. 6:
Galaxie structure: Not included in the picture are waveguides located at the top and bottom of the herevisible region to supply the optical power. The hole pattern is part of a photonic crystal used as the waveguide.Similar to the previously shown simple dual gratings, two opposing gratings generate a non evanescent field profilebetween them. In this case two periodicities are visible. The “tooth to tooth” periodicity exiting the mode thataccelerates the electrons and a macro periodicity responsible for exciting the mode that confines the electrons.The shown fields are the superposition of both the accelerating and the confining mode. More information andanimations of the fields and phase space can be found at [12]
Another method, currently being evaluated experimentally as of the writing of these proceedings,is an adaptation of alternating phase focusing. This method was previously used for RF accelerators.Compared to the previous method where two separate modes need to be excited, alternating phase focus-ing (APF) makes use of the inherent deflecting forces present in the accelerating mode. By choosing twooperating points that are slightly off rest in terms of acceleration, depicted in Fig. 7 by the red circles, andperiodically toggling between these points, the design electrons experience both transversally focusingand defocusing forces, which in total keep the electrons confined. For more information see [13]. ig. 7:
The shown graph illustrates the APF mechanism. The blue curve represents the longitudinal kick anelectron receives per unit cell of the periodic accelerator structure. The green curve shows the transverse kick.In theory if it were possible to hold the electrons exactly on crest of the accelerating field, no transverse forcesappear. However small manufacturing defects or perturbations will cause enough phase differences so this is notachievable. Choosing two design points i.e., the red points only slightly off crest, one looses only little accelerationforce but periodically varying between the two points gives on average a force that keeps the particles confined inthe channel. Electrons can also be just guided without experiencing acceleration by choosing the orange circles asdesign points. [13]
A Structure applying this principle can be seen in Fig. 8. Here periodic notches in the acceleratingstructure are used to introduce the required phase jumps. Preliminary tests show good agreement betweentheory and experiment proofing the viability of this method. With appropriate structures even the untilnow invariant direction can be controlled.
Fig. 8:
Implemented APF design. Visible are a Bragg reflector at the top of the structure. The 4 dielectric bladesact as a mirror and reflect the laser light, incident from the bottom, back. This mimics double sided illumination.Furthermore the periodicity of the accelerating structure and the periodic phase jumps are visible. This µ m longstructure is the longest structure tested at sub relativistic speeds to date. Lastly an important choice is the material of the structures. It must fulfil several criteria. First ofall it must be manufacturable at the sizes required for a DLA. Some processes are very well developedin terms of structure fabrication, mostly due to the semiconductor industry. However other materials likeAl O or Diamond can be very hard to manufacture.Secondly, the chosen material should have a damage threshold as high as possible. A selection of ma-terials can be seen in Fig. 9. For example while silicon is relatively easy to manufacture its damagethreshold for laser induced damage is fairly low. If suitable processes are available it could be beneficialto use different materials.However the damage threshold does not paint a complete picture. Especially at subrelativistic speeds,the mode excitation efficiency, so ho much of the incident laser light is diffracted into the usable accel-erating mode is dependent on the refractive index. The higher the refractive index the better the modexcitation efficiency. While it might be beneficial for damage threshold reasons to choose a differentmaterial than e.g., silicon, it might be that even though a higher incident laser peak field can be used, lessfield is coupled to the relevant mode, hurting the efficiency. Therefore a delicate balance must be struckbetween all material parameters. Fig. 9:
Overview of material parameters. Taken from [14] DLA Experiments and state of the art technology
As mentioned in the introduction, the initial experiments at optical wavelengths were performed in 2013.One Experiment was executed at keV electron energy in a modified electron microscope [7]. Herea single sided fused silica grating was used in conjunction with a Ti:Sapphire laser. Due to the subrel-ativistic nature of the electrons and the laser wavelength using the synchronicity condition Eq. (24) therequired periodicity would have been around λ p = 260 nm which was not available at the time. There-fore, the third spatial harmonic was chosen to drive the interaction. Although possible, the excitationefficiency of the higher order spatial modes is very low. Also the relatively low refractive index of fusedsilica affects the mode excitation efficiency negatively. Therefore the achieved acceleration gradient waslimited to MeV/m. [7].The demonstration at relativistic energies — performed at SLAC’s NLCTA [6] — did not suffer theseshortcomings as the increased electron velocity at MeV was already relativistic, relaxing the structureparameters by a factor of three. However since β = 1 in this case, a double sided grating needed to beused, to generate a speed of light mode. With this, acceleration gradients of more than MeV/m wereachieved. Some results are shown in Fig. 10. ig. 10:
First results of dielectric laser acceleration both at subrelativistic electron velocities (left) and relativisticelectron speeds (right). The left results show the spectrum of the energy modulated electrons and dependence onthe polarization angle, grating-beam distance and initial beam energy. In the cases of the polarization angle theavailable x component of the field is diminished when the polarization is changed from the optimum and henceelectrons are accelerated less. The same holds when the beam-grating distance is increased. When decreasing thedistance, the beam is eventually clipped on the structure. Changing the initial electron energy changes the phasematching and hence the maximum acceleration gradient. The relativistic results show a full modulation of thecomplete electron population. Furthermore the modulates spectrum shows the onset of the characteristic doublehorn spectrum. This is an indicator that the fields are of good quality. Taken from [6, 7]
After these initial demonstrations it was concluded that for the subrelativistic side, structures madeof silicon in conjunction with near infrared (NIR) laser sources in the regime of λ =2000 nm are mostsuitable. With these, many important steps could be shown.Staging is arguably one of the most important properties of any accelerator. It needs to be possible toconcatenate accelerators without loosing performance. It was shown at a single sided dielectric gratingthat staging without performance loss is possible [15]. Here two identical laser illumination spots wereplaced on a grating. As seen in Fig. 11 in the blue and green curve, each interaction on their own causesthe same energy modulation. When both stages are illuminated simultaneous, it is dependent on the phaseof the two laser spots what final energy of the electrons is reached. When the two pulses are completelyout of phase, the energy gain contributed by the first interaction is almost completely negated by thesecond. Analogous when the two interactions happen in phase, the energy gain is almost doubled. Thesmall remaining energy and not quite energy doubling is attributed to the transversal forces. Electronsthat experience a transversal kick away from the grating surface in the second interaction will experiencea weaker force in the second, even if the phase is spot on. Due to the exponential decay of the fields thereis a big gradient even for small distance changes towards or away from the grating, as shown in Fig. 10.Another necessary requirement of an accelerator is steering of the particle beam. As we’ve alreadyseen, deflecting forces are easily available in the transverse direction perpendicular to the grating surface.Furthermore no forces are present in the other transverse direction parallel to the grating. This can simplybe remedied by not assuming the most simplified case as we did in the theory part but allow for an angle ig. 11: Proof of principle experiment for the staging of multiple DLAs. Left: Phase dependence of the finalenergy. Right: Measurement of each individual interaction (blue and green) at a phase difference of the twolaser pulses where destructive interference is reached (black) and similarly at a phase difference where there isconstructive interference, doubling the final energy of the electrons. Taken from citeMcNeur2018 between the particle propagation direction and the grating vector to be present, e.g., ψ (cid:54) = 0 in Fig. 3.This leads to a different force the particle feels in its reference frame: (cid:126)F = q icB y / ( ˜ β ˜ γ ) + tan φE y − icB y tan φ/ ( ˜ β ˜ γ ) − tan φ sin φE y − cB y (1 − ˜ β ) / ( ˜ β ) + i tan φE y / ˜ γ . (28)The force in y direction is now non zero. This can be used to deflect electrons [16]. A deflection of up to mrad was achieved over an interaction distance of roughly µ m. The same principle can be appliedto construct a lens. Using parabolic grating teeth a position dependent grating angle can be introducedacting as a deflector of different strength depending on the entrance offset of the beam with respect tothe symmetry axis of the parabolic grating [15]. Since the input beam size was very small with respectto radius of curvature of the grating teeth, each interaction of one beam position with the grating couldbe viewed as a pure deflection. A knife edge is used behind the structure to determine the amount ofdeflection. This raytracing approach allowed for the measurement of the focal length of the structure.Obviously this lens only works for a certain energy range and is fairly chromatic.As alluded to in the theoretical description, the phase difference of two lasers driving a doublesided grating can also affect the mode that is present in the device. The modes can be switched betweenan accelerating and a deflecting mode [17]. Here a new type of structure was used, seen on the rightof Fig. 13. To ease the manufacturability of double sided gratings, the original approach of etchingtwo separate grating and aligning them afterwards, which is quite demanding and prone to inaccuracies,was exchanged for structures that can be produced in one etching step, with the accuracy limited bythe tolerances of the manufacturing machines. These structures consist of two rows of silicon pillars.If etched deep enough they approximate an infinitely wide double sided grating. In the shown data inFig. 13 one can observe the dependency of energy gain and maximum deflection angle on the relativephase of the electrons.In the case of Ψ = 0 the acceleration is maximised with minimal deflection. Opposite for
Ψ = π , thedeflection is maximised. Phase difference values in between lead to a mixed state of acceleration anddeflection.The current record gradients achieved by dielectric laser accelerators are MeV/m at β = 0 . [18], MeV/m at β = 0 . [19] and MeV/m with MeV electrons [20]. The current limitation ig. 12:
Lensing structure and corresponding data. Taken from [15]
Fig. 13:
Phase dependant deflection of electrons (left) and dual pillar structure geometry (right). Taken from [17] for nonrelativistic electrons are the poor damage threshold of silicon structures and the mode excitationefficiency. Different material and geometry choices can improve the gradient considerably.All experiments at subrelativistic electron speeds shown thus far were performed over short dis-tances of a few micron. As discussed in the theoretical section on beam guiding there are known mech-anisms of how to keep the electrons inside the accelerator channel. However for these mechanisms towork, the electrons need to inhabit a small region in phase space. This can be achieved in the structuresthemselves or externally through micro bunching.icro bunching happens in subrelativistic electrons when a sinusoidal energy modulation is imprintedon a set of particles. The electrons with higher energy have a higher velocity. Analogous electrons withreduces energy will be slower. This is depicted in Fig. 14. While drifting through vacuum, the fasterelectrons catch up with the slower ones, creating a higher electron density in real space. This mechanismis also often called ballistic microbunching, since no fields are applied after the initial modulation andthe electrons propagate ballistically.With this scheme, electron micro bunch durations of as [21] and as [22] have been shown. Thesebunches are short enough to be injected into another accelerator.
Fig. 14: (a) Setup for the generation and characterization of attosecond electron micro bunch trains. In the firstinteraction region, electrons are imprinted with a sinusoidal energy modulation that during a drift forms a densitymodulation in the longitudinal direction. The second interaction is used to characterize the micro bunch trains. (b)Longitudinal electron density over the whole length of the experiment. 100 fs long electron pulses are generatedvia photoemission at the electron emitter. During propagation various effects broaden the pulse to roughly 400 fs.After the first interaction a micro bunch train is formed. (c) Evolution in phase space from the initial sinusoidalenergy modulation to the ideally bunched beam. Fast electrons catch up with slow electrons to form the microbunches. (d) Electron spectrum after a single interaction vs relative delay between electron pulse and laser pulse.(e) Elektron spectrum after the analyzer vs relative phase of the two laser pulses. This spectrum can be comparedto simulations to reconstruct the micro bunch length. Taken from [22]
As mentioned above, all the shown experiments and even all experiments concluded, that the authors areaware of as of the time of writing, have been performed over distances of at most mm. This is stillpossible via a single elliptical laser spot. When building longer devices, using free space laser couplingto the structures is no longer feasible.Therefore another scheme to distribute power to the accelerator is needed. Similar to RF waveg-uides in RF accelerators, photonic waveguides can be used to distribute the power. Case studies of how ig. 15: Laser power delivery network. Laser light is coupled to a waveguide structure via input couplers. Theencoded length of the branch structure synchronizes the laser arrival to the electrons. Optical phase shifters can beused to fine adjust the optical phase. Taken from citeHughes2018 such a system might be designed, which tuning knobs are available and where the limitations lie havebeen done. The result of one such study is shown in Fig. 15. The accelerating structure is fed by a treebranch structure of dielectric waveguides. The necessary delay between the electrons and the incominglaser is encoded into the structure and can be finely controlled via included optical phase shifters to adjustfor fabrication inaccuracies or thermal expansion.These structures still require many inputs for the delivered power since the waveguides, con-structed form silicon or a derivative material such as silicon nitride, have a fairly low damage threshold.Adopting technologies such as photonic crystal waveguides and on chip pulse compression might allevi-ate the stress on the waveguides. Furthermore, the currently used wavelength of nm was not chosenat random. Fiber lasers are available at these wavelengths that can still produce short pulses. Hence anetwork of fiber lasers can be used to drive multiple inputs on these structures.Other research was focussed on the individual components such as the beam splitters at every treebranch. The shown example is a wavelength demultiplexer that takes an input of multiple wavelengthsand splits them into separate channels. This is easily adapted to splitting power instead of wavelengths.These devices are attractive for their small size. The very unintuitive design is generated by so calledinverse design. Here a design boundary and the inputs as well as the desired output are supplied. Theinverse design algorithm adjusts the geometry in the design region to achieve the desired goal.Finally a recycling of the laser power can be envisioned. Most of the laser pulse leaves the structurewithout giving energy to the electrons. Therefore the efficiency is quite poor. If it were possible to include ig. 16:
Photonic structure designed with the help of inverse design. Taken from [24]. the accelerator in a resonator cavity including a gain material, the optical power could be recirculated[25, 26].
Lastly we discuss the requirements the DLAs place upon the electron beams. From estimates conductedin [10] and [13], DLAs require normalized emittances of sub nm-rad. These emittances are usuallyonly approached by electron microscopes, where excellent beam quality is needed to achieve the bestresolutions. This however is achieved by filtering the electron beam until the quality is good enough.This means that such a source is not necessarily well suited for the application in DLAs. Since thesources are laser triggered, starting with a high emittance beam and filtering can cause pulse prolongationdue to space charge in the gun. An optimized emitter that emitts less electrons at a smaller emittancemight be advantageous. Research into many different types of emitters is being conducted. This includeslow emittance rf photoinjectors [27], diamond coated silicon pyramids [28], diamond coated tungstentips [29], LaB nano wires [30] and silicon tips and tip arrays. Conclusions
DLAs have come far since their proof of principle experiments in 2013. While they will likely notfind application as high energy particle physics machines due to the limited current available, they area unique tool in the world of novel accelerators because they don’t rely on huge infrastructure such asexisting accelerators or petawatt class lasers. Combined with the small size of the accelerator itself,various new opportunities are opening up that other accelerator technologies might not be suitable for.One example are medical devices. A miniaturized accelerator could be used endoscopically to irradiatetumours directly and reducing damage to surrounding tissues.Table top radiation sources using the principles of free electron lasers, Smith-Purcell radiation or inverseCompton scattering are feasible and could supply smaller research facilities with the means to not bedependent on the admittedly growing but still very limited number of FEL facilities. ig. 17:
Overview over some new electron emitter designs that show promising properties for DLA applications:low emittance rf photoinjectors [27], diamond coated silicon pyramids [28], diamond coated tungsten tips [29],LaB nano wires [30] and silicon tips and tip arrays Lastly the inherent time scales make DLAs well suited for the development of ultrafast machines forelectron microscopy and diffraction. As shown through simple methods very short electron bunches canbe created. In this form DLAs might also become useful for large scale facilities as a means to modulateelectron bunches on tiny time and length scales.
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