1
|
Jain A, Yoffe SR, Ersfeld B, Holt GK, Gupta DN, Jaroszynski DA. The effect of laser pulse evolution on down-ramp injection in laser wakefield accelerators. Sci Rep 2024; 14:19127. [PMID: 39155327 PMCID: PMC11330977 DOI: 10.1038/s41598-024-69049-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2023] [Accepted: 07/31/2024] [Indexed: 08/20/2024] Open
Abstract
Electron self-injection in laser wakefield accelerators (LWFAs) is an important determinator of electron beam parameters. Controllable and adjustable LWFA beams are essential for applications. Controlled injection by capturing sheath electrons can be achieved using plasma density down-ramps or bumps, which perturb the LWFA bubble phase velocity by varying the plasma frequency and by affecting relativistic self-focussing of the laser. We report on a comprehensive study, using particle-in-cell simulations, of the effect of laser pulse evolution on injection on density perturbations. We show how the LWFA can be optimised to make it suitable for use in a wide range of applications, in particular those requiring short duration, low slice-emittance and low energy spread, and high-charge electron bunches.
Collapse
Affiliation(s)
- Arohi Jain
- Department of Physics and Astrophysics, University of Delhi, Delhi, 110 007, India
| | - Samuel R Yoffe
- Department of Physics, SUPA and University of Strathclyde, Glasgow, G4 0NG, UK
| | - Bernhard Ersfeld
- Department of Physics, SUPA and University of Strathclyde, Glasgow, G4 0NG, UK
| | - George K Holt
- Department of Physics, SUPA and University of Strathclyde, Glasgow, G4 0NG, UK
| | - Devki Nandan Gupta
- Department of Physics and Astrophysics, University of Delhi, Delhi, 110 007, India.
| | - Dino A Jaroszynski
- Department of Physics, SUPA and University of Strathclyde, Glasgow, G4 0NG, UK.
| |
Collapse
|
2
|
Sun T, Zhao Q, Wan F, Salamin YI, Li JX. Generation of Ultrabrilliant Polarized Attosecond Electron Bunches via Dual-Wake Injection. PHYSICAL REVIEW LETTERS 2024; 132:045001. [PMID: 38335335 DOI: 10.1103/physrevlett.132.045001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/27/2022] [Revised: 08/20/2023] [Accepted: 12/11/2023] [Indexed: 02/12/2024]
Abstract
Laser wakefield acceleration is paving the way for the next generation of electron accelerators, for their own sake and as radiation sources. A controllable dual-wake injection scheme is put forward here to generate an ultrashort triplet electron bunch with high brightness and high polarization, employing a radially polarized laser as a driver. We find that the dual wakes can be driven by both transverse and longitudinal components of the laser field in the quasiblowout regime, sustaining the laser-modulated wakefield which facilitates the subcycle and transversely split injection of the triplet bunch. Polarization of the triplet bunch can be highly preserved due to the laser-assisted collective spin precession and the noncanceled transverse spins. In our three-dimensional particle-in-cell simulations, the triplet electron bunch, with duration about 500 as, six-dimensional brightness exceeding 10^{14} A/m^{2}/0.1% and polarization over 80%, can be generated using a few-terawatt laser. Such an electron bunch could play an essential role in many applications, such as ultrafast imaging, nuclear structure and high-energy physics studies, and the operation of coherent radiation sources.
Collapse
Affiliation(s)
- Ting Sun
- Ministry of Education Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Qian Zhao
- Ministry of Education Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Feng Wan
- Ministry of Education Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Yousef I Salamin
- Department of Physics, American University of Sharjah, Sharjah, POB 26666 Sharjah, United Arab Emirates
| | - Jian-Xing Li
- Ministry of Education Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
- Department of Nuclear Physics, China Institute of Atomic Energy, P.O. Box 275(7), Beijing 102413, China
| |
Collapse
|
3
|
Peng H, Huang TW, Jiang K, Li R, Wu CN, Yu MY, Riconda C, Weber S, Zhou CT, Ruan SC. Coherent Subcycle Optical Shock from a Superluminal Plasma Wake. PHYSICAL REVIEW LETTERS 2023; 131:145003. [PMID: 37862653 DOI: 10.1103/physrevlett.131.145003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2023] [Revised: 07/30/2023] [Accepted: 08/31/2023] [Indexed: 10/22/2023]
Abstract
We propose exploiting the superluminal plasma wake for coherent Cherenkov radiation by injecting a relativistic electron beam (REB) into a plasma with a slowly varying density up-ramp. Using three-dimensional particle-in-cell and far-field time-domain radiation simulations, we show that an isolated subcycle pulse is coherently emitted towards the Cherenkov angle by bubble-sheath electrons successively at the rear of the REB-induced superluminal plasma wake. A theoretical model based on a superluminal current dipole has been developed to interpret such coherent radiation, and agrees well with the simulation results. This radiation has ultrashort attosecond-scale duration and high intensity, and exhibits excellent directionality with ultralow angular divergence and stable carrier envelope phase. Its intensity increases with the square of the propagation length and its central frequency can be easily tuned over a wide range, from the far infrared to the ultraviolet.
Collapse
Affiliation(s)
- H Peng
- Shenzhen Key Laboratory of Ultraintense Laser and Advanced Material Technology, Center for Advanced Material Diagnostic Technology, and College of Engineering Physics, Shenzhen Technology University, Shenzhen 518118, China
| | - T W Huang
- Shenzhen Key Laboratory of Ultraintense Laser and Advanced Material Technology, Center for Advanced Material Diagnostic Technology, and College of Engineering Physics, Shenzhen Technology University, Shenzhen 518118, China
| | - K Jiang
- Shenzhen Key Laboratory of Ultraintense Laser and Advanced Material Technology, Center for Advanced Material Diagnostic Technology, and College of Engineering Physics, Shenzhen Technology University, Shenzhen 518118, China
| | - R Li
- Shenzhen Key Laboratory of Ultraintense Laser and Advanced Material Technology, Center for Advanced Material Diagnostic Technology, and College of Engineering Physics, Shenzhen Technology University, Shenzhen 518118, China
| | - C N Wu
- Shenzhen Key Laboratory of Ultraintense Laser and Advanced Material Technology, Center for Advanced Material Diagnostic Technology, and College of Engineering Physics, Shenzhen Technology University, Shenzhen 518118, China
| | - M Y Yu
- Shenzhen Key Laboratory of Ultraintense Laser and Advanced Material Technology, Center for Advanced Material Diagnostic Technology, and College of Engineering Physics, Shenzhen Technology University, Shenzhen 518118, China
| | - C Riconda
- LULI, Sorbonne Université, CNRS, École Polytechnique, CEA, F-75252 Paris, France
| | - S Weber
- Extreme Light Infrastructure ERIC, ELI Beamlines Facility, 25241 Dolní Břežany, Czech Republic
| | - C T Zhou
- Shenzhen Key Laboratory of Ultraintense Laser and Advanced Material Technology, Center for Advanced Material Diagnostic Technology, and College of Engineering Physics, Shenzhen Technology University, Shenzhen 518118, China
| | - S C Ruan
- Shenzhen Key Laboratory of Ultraintense Laser and Advanced Material Technology, Center for Advanced Material Diagnostic Technology, and College of Engineering Physics, Shenzhen Technology University, Shenzhen 518118, China
| |
Collapse
|
4
|
Dewhurst KA, Muratori BD, Brunetti E, van der Geer B, de Loos M, Owen HL, Wiggins SM, Jaroszynski DA. A beamline to control longitudinal phase space whilst transporting laser wakefield accelerated electrons to an undulator. Sci Rep 2023; 13:8831. [PMID: 37258601 DOI: 10.1038/s41598-023-35435-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 05/17/2023] [Indexed: 06/02/2023] Open
Abstract
Laser wakefield accelerators (LWFAs) can produce high-energy electron bunches in short distances. Successfully coupling these sources with undulators has the potential to form an LWFA-driven free-electron laser (FEL), providing high-intensity short-wavelength radiation. Electron bunches produced from LWFAs have a correlated distribution in longitudinal phase space: a chirp. However, both LWFAs and FELs have strict parameter requirements. The bunch chirp created using ideal LWFA parameters may not suit the FEL; for example, a chirp can reduce the high peak current required for free-electron lasing. We, therefore, design a flexible beamline that can accept either positively or negatively chirped LWFA bunches and adjust the chirp during transport to an undulator. We have used the accelerator design program MAD8 to design a beamline in stages, and to track particle bunches. The final beamline design can produce ambidirectional values of longitudinal dispersion ([Formula: see text]): we demonstrate values of + 0.20 mm, 0.00 mm and - 0.22 mm. Positive or negative values of [Formula: see text] apply a shear forward or backward in the longitudinal phase space of the electron bunch, which provides control of the bunch chirp. This chirp control during the bunch transport gives an additional free parameter and marks a new approach to matching future LWFA-driven FELs.
Collapse
Affiliation(s)
- Kay A Dewhurst
- Department of Physics and Astronomy, The University of Manchester, Manchester, M13 9PL, UK.
- The Cockcroft Institute, Warrington, WA4 4AD, UK.
- Beams Department (BE), CERN, 1211, Geneva, Switzerland.
| | - Bruno D Muratori
- The Cockcroft Institute, Warrington, WA4 4AD, UK
- ASTeC, UKRI-STFC Daresbury Laboratory, Warrington, WA4 4FS, UK
| | - Enrico Brunetti
- SUPA, Department of Physics, University of Strathclyde, Glasgow, G4 0NG, UK
| | | | | | - Hywel L Owen
- The Cockcroft Institute, Warrington, WA4 4AD, UK
- ASTeC, UKRI-STFC Daresbury Laboratory, Warrington, WA4 4FS, UK
| | - S Mark Wiggins
- SUPA, Department of Physics, University of Strathclyde, Glasgow, G4 0NG, UK
| | - Dino A Jaroszynski
- SUPA, Department of Physics, University of Strathclyde, Glasgow, G4 0NG, UK.
| |
Collapse
|
5
|
Propagation of intense laser pulses in plasma with a prepared phase-space distribution. Sci Rep 2022; 12:20368. [DOI: 10.1038/s41598-022-24664-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2022] [Accepted: 11/18/2022] [Indexed: 11/28/2022] Open
Abstract
AbstractOptimizing the laser wakefield accelerator (LWFA) requires control of the intense driving laser pulse and its stable propagation. This is usually challenging because of mode mismatching arising from relativistic self-focusing, which invariably alters the velocity and shape of the laser pulse. Here we show how an intense pre-pulse can prepare the momentum/density phase-space distribution of plasma electrons encountered by a trailing laser pulse to control its propagation. This can also be used to minimize the evolution of the wakefield thus enhancing the stability of the LWFA, which is important for applications.
Collapse
|
6
|
Xu X, Li F, Tsung FS, Miller K, Yakimenko V, Hogan MJ, Joshi C, Mori WB. Generation of ultrahigh-brightness pre-bunched beams from a plasma cathode for X-ray free-electron lasers. Nat Commun 2022; 13:3364. [PMID: 35690617 PMCID: PMC9188572 DOI: 10.1038/s41467-022-30806-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2021] [Accepted: 05/18/2022] [Indexed: 11/23/2022] Open
Abstract
The longitudinal coherence of X-ray free-electron lasers (XFELs) in the self-amplified spontaneous emission regime could be substantially improved if the high brightness electron beam could be pre-bunched on the radiated wavelength-scale. Here, we show that it is indeed possible to realize such current modulated electron beam at angstrom scale by exciting a nonlinear wake across a periodically modulated plasma-density downramp/plasma cathode. The density modulation turns on and off the injection of electrons in the wake while downramp provides a unique longitudinal mapping between the electrons’ initial injection positions and their final trapped positions inside the wake. The combined use of a downramp and periodic modulation of micrometers is shown to be able to produces a train of high peak current (17 kA) electron bunches with a modulation wavelength of 10’s of angstroms - orders of magnitude shorter than the plasma density modulation. The peak brightness of the nano-bunched beam can be O(1021A/m2/rad2) orders of magnitude higher than current XFEL beams. Such prebunched, high brightness electron beams hold the promise for compact and lower cost XEFLs that can produce nanometer radiation with hundreds of GW power in a 10s of centimeter long undulator. Laser-produced plasma can be used for acceleration and tuning of particle beams. Here the authors discuss the generation of a bunched electron beam using simulations and its application to X-ray free-electron laser.
Collapse
Affiliation(s)
- Xinlu Xu
- SLAC National Accelerator Laboratory, Menlo Park, CA, USA.
| | - Fei Li
- Department of Electrical Engineering, University of California Los Angeles, Los Angeles, CA, USA
| | - Frank S Tsung
- Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, CA, USA
| | - Kyle Miller
- Department of Electrical Engineering, University of California Los Angeles, Los Angeles, CA, USA
| | | | - Mark J Hogan
- SLAC National Accelerator Laboratory, Menlo Park, CA, USA
| | - Chan Joshi
- Department of Electrical Engineering, University of California Los Angeles, Los Angeles, CA, USA
| | - Warren B Mori
- Department of Electrical Engineering, University of California Los Angeles, Los Angeles, CA, USA.,Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, CA, USA
| |
Collapse
|
7
|
High-charge electron beams from a laser-wakefield accelerator driven by a CO 2 laser. Sci Rep 2022; 12:6703. [PMID: 35585094 PMCID: PMC9117239 DOI: 10.1038/s41598-022-10160-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2022] [Accepted: 04/04/2022] [Indexed: 11/08/2022] Open
Abstract
Laser-wakefield accelerators (LWFAs) driven by widely available 100s TW-class near-infrared laser systems have been shown to produce GeV-level electron beams with 10s-100s pC charge in centimetre-scale plasma. As the strength of the ponderomotive force is proportional to the square of the laser wavelength, more efficient LWFAs could be realised using longer wavelength lasers. Here we present a numerical study showing that [Formula: see text], sub-picosecond CO2 lasers with peak powers of 100-800 TW can produce high-charge electron beams, exceeding that possible from LWFAs driven by femtosecond near-infrared lasers by up to three orders of magnitude. Depending on the laser and plasma parameters, electron beams with 10s MeV to GeV energy and 1-100 nC charge can be generated in 10-200 mm long plasma or gas media without requiring external guiding. The laser-to-electron energy conversion efficiency can be up to 70% and currents of 100s kA are achievable. A CO2 laser driven LWFA could be useful for applications requiring compact and industrially robust accelerators and radiations sources.
Collapse
|
8
|
Brunetti E, van der Geer B, de Loos M, Dewhurst KA, Kornaszewski A, Maitrallain A, Muratori BD, Owen HL, Wiggins SM, Jaroszynski DA. Vacuum ultraviolet coherent undulator radiation from attosecond electron bunches. Sci Rep 2021; 11:14595. [PMID: 34272418 PMCID: PMC8285405 DOI: 10.1038/s41598-021-93640-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2021] [Accepted: 06/22/2021] [Indexed: 11/09/2022] Open
Abstract
Attosecond duration relativistic electron bunches travelling through an undulator can generate brilliant coherent radiation in the visible to vacuum ultraviolet spectral range. We present comprehensive numerical simulations to study the properties of coherent emission for a wide range of electron energies and bunch durations, including space-charge effects. These demonstrate that electron bunches with r.m.s. duration of 50 as, nominal charge of 0.1 pC and energy range of 100-250 MeV produce [Formula: see text] coherent photons per pulse in the 100-600 nm wavelength range. We show that this can be enhanced substantially by self-compressing negatively chirped 100 pC bunches in the undulator to produce [Formula: see text] coherent photons with pulse duration of 0.5-3 fs.
Collapse
Affiliation(s)
- Enrico Brunetti
- SUPA, Department of Physics, University of Strathclyde, Glasgow, UK. .,Cockcroft Institute, Warrington, UK.
| | | | | | - Kay A Dewhurst
- Cockcroft Institute, Warrington, UK.,The University of Manchester, Manchester, UK
| | | | | | - Bruno D Muratori
- Cockcroft Institute, Warrington, UK.,STFC Daresbury Laboratory, Daresbury, UK
| | - Hywel L Owen
- Cockcroft Institute, Warrington, UK.,The University of Manchester, Manchester, UK.,STFC Daresbury Laboratory, Daresbury, UK
| | - S Mark Wiggins
- SUPA, Department of Physics, University of Strathclyde, Glasgow, UK
| | | |
Collapse
|
9
|
Ferran Pousa A, Martinez de la Ossa A, Assmann RW. Intrinsic energy spread and bunch length growth in plasma-based accelerators due to betatron motion. Sci Rep 2019; 9:17690. [PMID: 31776391 PMCID: PMC6881450 DOI: 10.1038/s41598-019-53887-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2018] [Accepted: 10/28/2019] [Indexed: 11/19/2022] Open
Abstract
Plasma-based accelerators (PBAs), having demonstrated the production of GeV electron beams in only centimetre scales, offer a path towards a new generation of highly compact and cost-effective particle accelerators. However, achieving the required beam quality, particularly on the energy spread for applications such as free-electron lasers, remains a challenge. Here we investigate fundamental sources of energy spread and bunch length in PBAs which arise from the betatron motion of beam electrons. We present an analytical theory, validated against particle-in-cell simulations, which accurately describes these phenomena. Significant impact on the beam quality is predicted for certain configurations, explaining previously observed limitations on the achievable bunch length and energy spread. Guidelines for mitigating these contributions towards high-quality beams are deduced.
Collapse
Affiliation(s)
- Angel Ferran Pousa
- Deutsches Elektronen-Synchrotron DESY, Hamburg, 22607, Germany.
- Institut für Experimentalphysik, Universität Hamburg, Hamburg, 22761, Germany.
| | | | - Ralph W Assmann
- Deutsches Elektronen-Synchrotron DESY, Hamburg, 22607, Germany
| |
Collapse
|
10
|
Kuschel S, Schwab MB, Yeung M, Hollatz D, Seidel A, Ziegler W, Sävert A, Kaluza MC, Zepf M. Controlling the Self-Injection Threshold in Laser Wakefield Accelerators. PHYSICAL REVIEW LETTERS 2018; 121:154801. [PMID: 30362794 DOI: 10.1103/physrevlett.121.154801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2018] [Indexed: 06/08/2023]
Abstract
Controlling the parameters of a laser plasma accelerated electron beam is a topic of intense research with a particular focus placed on controlling the injection phase of electrons into the accelerating structure from the background plasma. An essential prerequisite for high-quality beams is dark-current free acceleration (i.e., no electrons accelerated beyond those deliberately injected). We show that small-scale density ripples in the background plasma are sufficient to cause the uncontrolled (self-)injection of electrons. Such ripples can be as short as ∼50 μm and can therefore not be resolved by standard interferometry. Background free injection with substantially improved beam characteristics (divergence and pointing) is demonstrated in a gas cell designed for a controlled gas flow. The results are supported by an analytical theory as well as 3D particle in cell simulations.
Collapse
Affiliation(s)
- S Kuschel
- Helmholtz Insitute Jena, Fröbelstieg 3, 07743 Jena, Germany
- Institute of Optics and Quantumelectronics, University of Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - M B Schwab
- Helmholtz Insitute Jena, Fröbelstieg 3, 07743 Jena, Germany
- Institute of Optics and Quantumelectronics, University of Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - M Yeung
- Helmholtz Insitute Jena, Fröbelstieg 3, 07743 Jena, Germany
| | - D Hollatz
- Institute of Optics and Quantumelectronics, University of Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - A Seidel
- Institute of Optics and Quantumelectronics, University of Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - W Ziegler
- Helmholtz Insitute Jena, Fröbelstieg 3, 07743 Jena, Germany
- Institute of Optics and Quantumelectronics, University of Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - A Sävert
- Helmholtz Insitute Jena, Fröbelstieg 3, 07743 Jena, Germany
- Institute of Optics and Quantumelectronics, University of Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - M C Kaluza
- Helmholtz Insitute Jena, Fröbelstieg 3, 07743 Jena, Germany
- Institute of Optics and Quantumelectronics, University of Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - M Zepf
- Helmholtz Insitute Jena, Fröbelstieg 3, 07743 Jena, Germany
- Institute of Optics and Quantumelectronics, University of Jena, Max-Wien-Platz 1, 07743 Jena, Germany
- School of Mathematics and Physics, Queens University Belfast, BT7 1NN, United Kingdom
| |
Collapse
|
11
|
Reichwein L, Thomas J, Pukhov A. Two-dimensional structures of electron bunches in relativistic plasma cavities. Phys Rev E 2018; 98:013201. [PMID: 30110785 DOI: 10.1103/physreve.98.013201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2018] [Indexed: 11/07/2022]
Abstract
The spatial structure of an ultralow-emittance electron bunch in a plasma wakefield blowout regime is studied. The full Liénard-Wiechert potentials are considered for mutual interparticle interactions in the framework of the equilibrium slice model. This model uses the quasistatic theory which allows one to solve the Liénard-Wiechert potentials without knowledge of the electrons' history. The equilibrium structure we find is similar to already observed hexagonal lattices but shows topological defects. Scaling laws for interparticle distances are obtained from numerical simulations and analytical estimations.
Collapse
Affiliation(s)
- Lars Reichwein
- Institut für Theoretische Physik I, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Johannes Thomas
- Institut für Theoretische Physik I, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Alexander Pukhov
- Institut für Theoretische Physik I, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| |
Collapse
|