Apsimon, O.

Bonatto, Alexandre

Bontoiu, C

Kukstas, E.

Resta-lópez, J

Welsch, C.

Xia, Guoxing

Yadav, M.

English

With the advancement of high-power UV laser technology, the use of nanostructures for particle acceleration attracts renewed interest due to its possibility of achieving TV/m accelerating gradients in solid state plasmas. Electron acceleration in ionized materials such as carbon nanotubes and graphene is currently considered as a potential alternative to the usual laser wakefield acceleration (LWFA) schemes. An evaluation of the suitability of a graphene target for LWFA can be carried out using an effective density model, thus replacing the need to model each layer. We present a 2D evaluation of the longitudinal electric field driven by a short UV laser pulse in a multi-layer graphene structure, showing that longitudinal fields of ∼5 TV/m are achievable

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The University of Manchester ResearchAn Effective-Density Model for Accelerating Fields inLaser-Graphene InteractionsDOI:10.18429/JACoW-IPAC2022-WEPOST043Document VersionFinal published versionLink to publication record in Manchester Research ExplorerCitation for published version (APA):Bontoiu, C., Apsimon, O., Kukstas, E., Welsch, C., Yadav, M., Xia, G., Resta-lópez, J., & Bonatto, A. (2022). AnEffective-Density Model for Accelerating Fields in Laser-Graphene Interactions. In 13th International ParticleAccelerator Conference https://doi.org/10.18429/JACoW-IPAC2022-WEPOST043Published in:13th International Particle Accelerator ConferenceCiting this paperPlease note that where the full-text provided on Manchester Research Explorer is the Author Accepted Manuscriptor Proof version this may differ from the final Published version. If citing, it is advised that you check and use thepublisher's definitive version.General rightsCopyright and moral rights for the publications made accessible in the Research Explorer are retained by theauthors and/or other copyright owners and it is a condition of accessing publications that users recognise andabide by the legal requirements associated with these rights.Takedown policyIf you believe that this document breaches copyright please refer to the University of Manchester’s TakedownProcedures [http://man.ac.uk/04Y6Bo] or contact uml.scholarlycommunications@manchester.ac.uk providingrelevant details, so we can investigate your claim.Download date:21. Oct. 2022AN EFFECTIVE-DENSITY MODEL FOR ACCELERATING FIELDSIN LASER-GRAPHENE INTERACTIONSC. Bonţoiu∗, Ö. Apsimon1, E. Kukstas, C. Welsch1, M. YadavUniversity of Liverpool, Liverpool, UKG. Xia1, University of Manchester, MManchester, UKJ. Resta-López, University de Valencia, Valencia, SpainA. Bonatto, Federal University of Health Sciences of Porto Alegre, Brazil1also at Cockroft Institute, Daresbury, UKAbstractWith the advancement of high-power UV laser technology,the use of nanostructures for particle acceleration attractsrenewed interest due to its possibility of achieving TV/maccelerating gradients in solid state plasmas. Electron accel-eration in ionized materials such as carbon nanotubes andgraphene is currently considered as a potential alternative tothe usual laser wakefield acceleration (LWFA) schemes. Anevaluation of the suitability of a graphene target for LWFAcan be carried out using an effective density model, thusreplacing the need to model each layer. We present a 2Devaluation of the longitudinal electric field driven by a shortUV laser pulse in a multi-layer graphene structure, showingthat longitudinal fields of ∼5 TV/m are achievable.INTRODUCTIONUnlike LWFA in gases, which can be achieved with laserpulses in the IR range, at peak intensities of 1018-1019W/cm2 [1], the equivalent mechanism in solid-state plasmasrequires an UV laser pulse with peak intensity in the range1020-1021 W/cm2, because charge densities in solids are 4–5orders of magnitude higher than in gas targets. Graphene [2]can be grown in the form of 2D layers of Carbon atoms,stacked together with a controllable inter-layer gap of a fewnm. Due to its unique optical [3] and electronic [4] prop-erties graphene is used as a medium for applications suchas high-harmonic generation [5] or terahertz radiation [6].Moreover, when fully ionized by intense laser pulses, eachgraphene layer delivers plasma with an electron density of∼1023 cm−3 and the tunability of the inter-layer gap impliesthat variable effective plasma densities of ∼1022 cm−3 can beobtained. This enables resonant propagation of sufficientlyintense laser pulses with wavelengths of up to 300 nm, andalso allows electrons to move easier along the inter-layergaps. Realistic Particle-In-Cell (PIC) simulations rely thecapability of using mesh cells a few times smaller than thelayer thickness, 0.34 nm and this poses a significant numer-ical overhead. However, reasonably accurate estimates of theelectric fields can be obtained using an effective density equi-valent. However, one should note that this approximationprevents the possibility to realistically study transient plasmadynamics at a resolution smaller than the inter-layer gap. Tobuild it from a layered target model, the total amount of un-∗ Cristian.Bontoiu@liverpool.ac.ukperturbed charge is kept constant and uniformly distributedin the bulk volume of the target. The concept of effectivedensity was already applied for PIC simulations involvingelectron bunches colliding with carbon nanotubes [7]. Wehave used the PIConGPU code [8] to evaluate the dynamicsand magnitude of the longitudinal electric field in laser-graphene interactions.SIMULATION SETUPThe 2D model uses a 1.2 μm-wide and 1.5 μm-long tar-get, as the effective density equivalent of 60 graphene lay-ers, spaced by 20 nm-wide edge-to-edge gaps. The laserpulse is Gaussian, both transversely with an FWHM spotsize 400 nm, and longitudinally with 1 fs FWHM pulse dur-ation. It has a linear polarization within the 𝑦𝑥−plane.The carbon plasma effective density is initialized as 𝑛0 =1.94 × 1021 cm−3 but rises to 6 𝑛0 = 1.61 × 1022 cm−3 as thetarget is virtually instantaneously ionized completely. Themesh cell size is limited to 0.25 nm with 1 macroparticle permesh cell. Moving rightwards along the 𝑦−axis (longitud-inal), the laser pulse interacts with the target for 16 fs whichcorresponds to 48 cycles, and travels 4.8 μm. Table 1 listsall important laser parameters. The simulation ignores lat-Table 1: Laser ParametersQuantity Value Unitwavelength: _ 100 nmperiod: 𝑇𝑙𝑎𝑠𝑒𝑟 0.334 fspeak intensity: 𝐼0 1021 W/cm2spot size★: 𝑤0 0.4 μmfocal point: 𝑦0 0.25 μmpulse energy: Δ𝐸 8 mJpulse length§: Δ𝑡 3 fs★FWHM, §9 cyclestice effects since the carbon atoms are generated uniformlyacross the target volume and there is no ionization thresholdspecific to graphene. Three ionization mechanisms (barriersuppression, tunneling and collisional) are enabled but theyuse atom ionization levels. Recombination is not consideredbut it can be ignored, given the short interaction time stud-ied in this work (10 fs). For the same reason, the motion ofthe carbon ions, evaluated at a few nm, does not affect theoverall results.13th Int. Particle Acc. Conf. IPAC2022, Bangkok, Thailand JACoW PublishingISBN: 978-3-95450-227-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2022-WEPOST043MC3: Novel Particle Sources and Acceleration TechniquesA22: Plasma Wakefield AccelerationWEPOST0431795ContentfromthisworkmaybeusedunderthetermsoftheCCBY4.0licence(©2022).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOITHE ELECTRIC FIELDAs the carbon atoms are continuously ionized, electronsare expelled alternatively towards the upper/lower trans-verse edges of the target and drift backwards towards lower𝑦−coordinates. These electrons also tend to neutralize thecarbon ions behind the laser pulse, gathering towards thelongitudinal axis of the target, 𝑥 = 0.8 μm. A bubble regionis thus formed in the trail of the laser pulse. The first half ofthe bubble contains C6+ ions with a dense sheet of electronsto the right, yielding a positive longitudinal electric field,while for the second half of the bubble this is placed to theleft resulting in a negative electric field. This situation isshown in Fig. 1, where the local minimum and maximum ofthe longitudinal field are also marked within the first bubble.Figure 1: (a) Transverse and (b) longitudinal electric field,driven by the laser pulse at 𝑡/𝑇𝑙𝑎𝑠𝑒𝑟 ∼ 14. The unperturbedtarget boundaries are shown by the green rectangle and thetwo dots respectively indicate a local minimum and max-imum of 𝐸𝑦 , in the trail of the laser pulse, shown by thedashed black line.Electrons injected in the left half of the bubble by ex-ternal means (i.e. from a photocathode) or collected fromthe plasma can be accelerated by using the relatively stable4 − 6 TV/m longitudinal gradient. Stability here means thepersistence of only two compact regions of longitudinal elec-tric field: a positive one and a negative one. The curvatureof the 𝐸𝑦 = 0 contours increases gradually due to differentphase velocities across the target width (x, transverse direc-tion) which originates from the Gaussian transverse profileof the laser pulse. Thus, the bubbles deform and have atendency to split into halves. Such a situation is shown inFig. 2. Recording the evolution of the local minimum in theFigure 2: Longitudinal electric field, driven by the laser pulseat 𝑡/𝑇𝑙𝑎𝑠𝑒𝑟 ∼20. From this moment the first bubble cannotbe sustained by the laser pulse and gradually vanishes.first bubble is important as an estimate of the available field.As shown in Fig. 3 the local maximum and minimum are notequal in absolute value, but both grow linearly, as long asionization is ongoing, either by direct laser ionization or col-lisional ionization. The first bubble appears at 𝑡/𝑇𝑙𝑎𝑠𝑒𝑟 ∼14and propagates intact up to 𝑡/𝑇𝑙𝑎𝑠𝑒𝑟 ∼21. It is then graduallydestroyed due to laser depletion and, as a consequence, thereis a sharp decrease of the local maximum and minimum of𝐸𝑦 . While falling off, the time lag between the two extremepoints is ∼ 2.5𝑇𝑙𝑎𝑠𝑒𝑟 . The electric field configuration fa-vourable to acceleration lasts for 7 laser cycles due to thesignificant depletion of the laser pulse. This is shown inFig. 4 where 𝐸𝑦 and 𝐸𝑥 are shown at two distinct times. Theinsets show the on-axis electric fields inside the first bubblebehind the laser pulse.CONCLUSIONIn this study we have shown that TV/m electric fieldsare achievable in solid state plasmas based on multilayergraphene, in the form of stable longitudinal bubbles∼0.3 μm-long. The bubbles propagate for ∼1 μm and theirnegative phase may be used to accelerate electrons. This13th Int. Particle Acc. Conf. IPAC2022, Bangkok, Thailand JACoW PublishingISBN: 978-3-95450-227-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2022-WEPOST043WEPOST043ContentfromthisworkmaybeusedunderthetermsoftheCCBY4.0licence(©2022).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI1796MC3: Novel Particle Sources and Acceleration TechniquesA22: Plasma Wakefield AccelerationFigure 3: Maximum positive (red) and minimum negative(black, in absolute value) longitudinal electric field in thefirst bubble.work supports alternative routes to the design of high-gradient compact accelerators, using solid-state plasmas.ACKNOWLEDGEMENTSWe acknowledge the technical support received from thePIConGPU [8] software developers and the required compu-tational infrastructure provided by the University of Liver-pool LivDAT Framework [9]. J. Resta-López acknowledgessupport by the Generalitat Valencia under grant agreementCIDEGENT / 2019 / 058.REFERENCES[1] E. Esarey, C. Schroeder, W. Leemans, "Physics of laser-drivenplasma-based electron accelerators", Rev. Mod. Phys., vol.81, pp. 1229–1285, 2009.[2] M. Katsnelson, "The Physics of Graphene", Cambridge Uni-versity Press, 2020.[3] R. Binder, "Optical Properties of Graphene", World Scientific,2016.[4] A. Neto, F. Guinea, N. Peres, K. Novoselov, A. Geim, "Theelectronic properties of graphene", Rev. Mod. Phys., vol. 81,pp. 109–162, 2009.[5] M. Mrudul, G. Dixit, "High-harmonic generation from mono-layer and bilayer graphene", Phys. Rev. B., vol. 103, p. 094308,2021.[6] K. Batrakov, S. Maksimenko, "Graphene layered systems asa terahertz source with tuned frequency", Phys. Rev. B., vol.95, p. 205408, 2017.[7] A. Bonatto et al., "Exploring ultra-high-intensity wakefieldsin carbon nanotube arrays: an effective plasma-density ap-proach", in preparation.Figure 4: Transverse (dashed, red) and longitudinal (solid,green) on-axis electric fields shown: (a) at 𝑡/𝑇𝑙𝑎𝑠𝑒𝑟 ∼14when the first bubble appears and (b) at 𝑡/𝑇𝑙𝑎𝑠𝑒𝑟 ∼21 whenthe destruction of first bubble starts.[8] H. Burau et al., "PIConGPU: A Fully Relativistic Particle-in-Cell Code for a GPU Cluster", IEEE Trans. Plasma Sci., vol.38, pp. 2831–2839, 2010.[9] Liverpool Big Data Science Centre for Doctoral Training,www.liverpool.ac.uk/livdat13th Int. Particle Acc. Conf. IPAC2022, Bangkok, Thailand JACoW PublishingISBN: 978-3-95450-227-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2022-WEPOST043MC3: Novel Particle Sources and Acceleration TechniquesA22: Plasma Wakefield AccelerationWEPOST0431797ContentfromthisworkmaybeusedunderthetermsoftheCCBY4.0licence(©2022).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI

An Effective-Density Model for Accelerating Fields in Laser-Graphene Interactions

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An Effective-Density Model for Accelerating Fields in Laser-Graphene Interactions

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