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-rw-r--r--Docs/source/conf.py7
-rw-r--r--Docs/source/refs.bib385
-rw-r--r--Docs/source/theory/intro.rst383
3 files changed, 399 insertions, 376 deletions
diff --git a/Docs/source/conf.py b/Docs/source/conf.py
index ba11eedae..f71cf8cc0 100644
--- a/Docs/source/conf.py
+++ b/Docs/source/conf.py
@@ -48,12 +48,17 @@ extensions = ['sphinx.ext.autodoc',
'sphinx.ext.napoleon',
'sphinx.ext.viewcode',
'sphinx_design',
- 'breathe'
+ 'breathe',
+ 'sphinxcontrib.bibtex'
]
# Add any paths that contain templates here, relative to this directory.
templates_path = ['_templates']
+# Relative path to bibliography file, bibliography style
+bibtex_bibfiles = ['./refs.bib']
+bibtex_default_style = 'unsrt'
+
# The suffix(es) of source filenames.
# You can specify multiple suffix as a list of string:
#
diff --git a/Docs/source/refs.bib b/Docs/source/refs.bib
new file mode 100644
index 000000000..58c0f7632
--- /dev/null
+++ b/Docs/source/refs.bib
@@ -0,0 +1,385 @@
+@article{Tsung2006,
+author = {Tsung,F. S. and Lu,W. and Tzoufras,M. and Mori,W. B. and Joshi,C. and Vieira,J. M. and Silva,L. O. and Fonseca,R. A. },
+title = {Simulation of monoenergetic electron generation via laser wakefield accelerators for 5–25TW lasers},
+journal = {Physics of Plasmas},
+volume = {13},
+number = {5},
+pages = {056708},
+year = {2006},
+doi = {10.1063/1.2198535}
+}
+
+@article{Geddes2008,
+doi = {10.1088/1742-6596/125/1/012002},
+year = {2008},
+volume = {125},
+number = {1},
+pages = {012002},
+author = {C G R Geddes and D L Bruhwiler and J R Cary and W B Mori and J-L Vay and S F Martins and T Katsouleas and E Cormier-Michel and W M Fawley and C Huang and X Wang and B Cowan and V K Decyk and E Esarey and R A Fonseca and W Lu and P Messmer and P Mullowney and K Nakamura and K Paul and G R Plateau and C B Schroeder and L O Silva and C Toth and F S Tsung and M Tzoufras and T Antonsen and J Vieira and W P Leemans},
+title = {Computational studies and optimization of wakefield accelerators},
+journal = {Journal of Physics: Conference Series}
+}
+
+@techreport{Geddes2009,
+title={Laser plasma particle accelerators: Large fields for smaller facility sources},
+author={Geddes, Cameron GR and Cormier-Michel, Estelle and Esarey, Eric H and Schroeder, Carl B and Vay, Jean-Luc and Leemans, Wim P and Bruhwiler, David L and Cary, John R and Cowan, Ben and Durant, Marc and others},
+year={2009},
+institution={Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)}
+}
+
+@article{Geddes2010,
+title={Scaled simulation design of high quality laser wakefield accelerator stages},
+author={Geddes, CGR},
+journal={},
+year={2010}
+}
+
+@article{Huang2009,
+doi = {10.1088/1742-6596/180/1/012005},
+year = {2009},
+volume = {180},
+number = {1},
+pages = {012005},
+author = {C Huang and W An and V K Decyk and W Lu and W B Mori and F S Tsung and M Tzoufras and S Morshed and T Antonsen and B Feng and T Katsouleas and R A Fonseca and S F Martins and J Vieira and L O Silva and E Esarey and C G R Geddes and W P Leemans and E Cormier-Michel and J-L Vay and D L Bruhwiler and B Cowan and J R Cary and K Paul},
+title = {Recent results and future challenges for large scale particle-in-cell simulations of plasma-based accelerator concepts},
+journal = {Journal of Physics: Conference Series}
+}
+
+@article{Leemans2014,
+title = {Multi-GeV Electron Beams from Capillary-Discharge-Guided Subpetawatt Laser Pulses in the Self-Trapping Regime},
+author = {Leemans, W. P. and Gonsalves, A. J. and Mao, H.-S. and Nakamura, K. and Benedetti, C. and Schroeder, C. B. and T\'oth, Cs. and Daniels, J. and Mittelberger, D. E. and Bulanov, S. S. and Vay, J.-L. and Geddes, C. G. R. and Esarey, E.},
+journal = {Phys. Rev. Lett.},
+volume = {113},
+issue = {24},
+pages = {245002},
+numpages = {5},
+year = {2014},
+publisher = {American Physical Society},
+doi = {10.1103/PhysRevLett.113.245002}
+}
+
+@article{Blumenfeld2007,
+title={Energy doubling of 42 GeV electrons in a metre-scale plasma wakefield accelerator},
+author={Blumenfeld, Ian and Clayton, Christopher E and Decker, Franz-Josef and Hogan, Mark J and Huang, Chengkun and Ischebeck, Rasmus and Iverson, Richard and Joshi, Chandrashekhar and Katsouleas, Thomas and Kirby, Neil and others},
+journal={Nature},
+volume={445},
+number={7129},
+pages={741--744},
+year={2007},
+publisher={Nature Publishing Group UK London},
+doi={10.1038/nature05538}
+}
+
+@article{Bulanov2014,
+doi = {10.3367/UFNe.0184.201412a.1265},
+year = {2014},
+publisher = {Turpion Ltd and the Russian Academy of Sciences},
+volume = {57},
+number = {12},
+pages = {1149},
+author = {S V Bulanov and J J Wilkens and T Zh Esirkepov and G Korn and G Kraft and S D Kraft and M Molls and V S Khoroshkov},
+title = {Laser ion acceleration for hadron therapy},
+journal = {Physics-Uspekhi}
+}
+
+@article{Steinke2016,
+title={Multistage coupling of independent laser-plasma accelerators},
+author={Steinke, S and Van Tilborg, J and Benedetti, C and Geddes, CGR and Schroeder, CB and Daniels, J and Swanson, KK and Gonsalves, AJ and Nakamura, K and Matlis, NH and others},
+journal={Nature},
+volume={530},
+number={7589},
+pages={190--193},
+year={2016},
+publisher={Nature Publishing Group UK London},
+doi={10.1038/nature16525}
+}
+
+@article{Sprangle1990,
+title = {Nonlinear theory of intense laser-plasma interactions},
+author = {Sprangle, P. and Esarey, E. and Ting, A.},
+journal = {Phys. Rev. Lett.},
+volume = {64},
+issue = {17},
+pages = {2011--2014},
+year = {1990},
+publisher = {American Physical Society},
+doi = {10.1103/PhysRevLett.64.2011}
+}
+
+@article{Antonsen1992,
+title = {Self-focusing and Raman scattering of laser pulses in tenuous plasmas},
+author = {Antonsen, T. M. and Mora, P.},
+journal = {Phys. Rev. Lett.},
+volume = {69},
+issue = {15},
+pages = {2204--2207},
+year = {1992},
+publisher = {American Physical Society},
+doi = {10.1103/PhysRevLett.69.2204}
+}
+
+@article{Krall1993,
+title = {Enhanced acceleration in a self-modulated-laser wake-field accelerator},
+author = {Krall, J. and Ting, A. and Esarey, E. and Sprangle, P.},
+journal = {Phys. Rev. E},
+volume = {48},
+issue = {3},
+pages = {2157--2161},
+year = {1993},
+publisher = {American Physical Society},
+doi = {10.1103/PhysRevE.48.2157}
+}
+
+@article{Mora1997,
+author = {Mora,Patrick and Antonsen, Jr.,Thomas M. },
+title = {Kinetic modeling of intense, short laser pulses propagating in tenuous plasmas},
+journal = {Physics of Plasmas},
+volume = {4},
+number = {1},
+pages = {217-229},
+year = {1997},
+doi = {10.1063/1.872134}
+}
+
+@article{Huang2006,
+title = {QUICKPIC: A highly efficient particle-in-cell code for modeling wakefield acceleration in plasmas},
+journal = {Journal of Computational Physics},
+volume = {217},
+number = {2},
+pages = {658-679},
+year = {2006},
+issn = {0021-9991},
+doi = {10.1016/j.jcp.2006.01.039},
+author = {C. Huang and V.K. Decyk and C. Ren and M. Zhou and W. Lu and W.B. Mori and J.H. Cooley and T.M. Antonsen and T. Katsouleas}
+}
+
+@article{Benedetti2010,
+author = {Benedetti,C. and Schroeder,C. B. and Esarey,E. and Geddes,C. G. R. and Leemans,W. P. },
+title = {Efficient Modeling of Laser‐Plasma Accelerators with INF\&RNO},
+journal = {AIP Conference Proceedings},
+volume = {1299},
+number = {1},
+pages = {250-255},
+year = {2010},
+doi = {10.1063/1.3520323}
+}
+
+@article{Cowan2011,
+title = {Characteristics of an envelope model for laser–plasma accelerator simulation},
+journal = {Journal of Computational Physics},
+volume = {230},
+number = {1},
+pages = {61-86},
+year = {2011},
+issn = {0021-9991},
+doi = {10.1016/j.jcp.2010.09.009},
+author = {Benjamin M. Cowan and David L. Bruhwiler and Estelle Cormier-Michel and Eric Esarey and Cameron G.R. Geddes and Peter Messmer and Kevin M. Paul}
+}
+
+@article{Vay2007,
+title = {Noninvariance of Space- and Time-Scale Ranges under a Lorentz Transformation and the Implications for the Study of Relativistic Interactions},
+author = {Vay, J.-L.},
+journal = {Phys. Rev. Lett.},
+volume = {98},
+issue = {13},
+pages = {130405},
+year = {2007},
+publisher = {American Physical Society},
+doi = {10.1103/PhysRevLett.98.130405}
+}
+
+@article{Vay2009a,
+doi = {10.1088/1742-6596/180/1/012006},
+year = {2009},
+volume = {180},
+number = {1},
+pages = {012006},
+author = {J-L Vay and D L Bruhwiler and C G R Geddes and W M Fawley and S F Martins and J R Cary and E Cormier-Michel and B Cowan and R A Fonseca and M A Furman and W Lu and W B Mori and L O Silva},
+title = {Simulating relativistic beam and plasma systems using an optimal boosted frame},
+journal = {Journal of Physics: Conference Series}
+}
+
+@article{Vay2009b,
+title = {Application of the reduction of scale range in a Lorentz boosted frame to the numerical simulation of particle acceleration devices.},
+author = {Vay, J and Fawley, W M and Geddes, C G and Cormier-Michel, E and Grote, D P},
+url = {https://www.osti.gov/biblio/952754},
+journal = {},
+place = {United States},
+year = {2009},
+}
+
+@article{Vay2010,
+author = {Vay,J.‐L. and Geddes,C. G. R. and Benedetti,C. and Bruhwiler,D. L. and Cormier‐Michel,E. and Cowan,B. M. and Cary,J. R. and Grote,D. P. },
+title = {Modeling Laser Wakefield Accelerators in a Lorentz Boosted Frame},
+journal = {AIP Conference Proceedings},
+volume = {1299},
+number = {1},
+pages = {244-249},
+year = {2010},
+doi = {10.1063/1.3520322}
+}
+
+@article{Vay2011a,
+title = {Numerical methods for instability mitigation in the modeling of laser wakefield accelerators in a Lorentz-boosted frame},
+journal = {Journal of Computational Physics},
+volume = {230},
+number = {15},
+pages = {5908-5929},
+year = {2011},
+issn = {0021-9991},
+doi = {10.1016/j.jcp.2011.04.003},
+author = {J.-L. Vay and C.G.R. Geddes and E. Cormier-Michel and D.P. Grote}
+}
+
+@article{Vay2011b,
+author = {Vay,J.-L. and Geddes,C. G. R. and Cormier-Michel,E. and Grote,D. P. },
+title = {Effects of hyperbolic rotation in Minkowski space on the modeling of plasma accelerators in a Lorentz boosted frame},
+journal = {Physics of Plasmas},
+volume = {18},
+number = {3},
+pages = {030701},
+year = {2011},
+doi = {10.1063/1.3559483}
+}
+
+@article{Vay2011c,
+author = {Vay,J.-L. and Geddes,C. G. R. and Esarey,E. and Schroeder,C. B. and Leemans,W. P. and Cormier-Michel,E. and Grote,D. P. },
+title = {Modeling of 10 GeV-1 TeV laser-plasma accelerators using Lorentz boosted simulations},
+journal = {Physics of Plasmas},
+volume = {18},
+number = {12},
+pages = {123103},
+year = {2011},
+doi = {10.1063/1.3663841}
+}
+
+@article{Martins2010a,
+title = {Numerical simulations of laser wakefield accelerators in optimal Lorentz frames},
+journal = {Computer Physics Communications},
+volume = {181},
+number = {5},
+pages = {869-875},
+year = {2010},
+issn = {0010-4655},
+doi = {10.1016/j.cpc.2009.12.023},
+author = {Samuel F. Martins and Ricardo A. Fonseca and Luís O. Silva and Wei Lu and Warren B. Mori}
+}
+
+@article{Martins2010b,
+title={Exploring laser-wakefield-accelerator regimes for near-term lasers using particle-in-cell simulation in Lorentz-boosted frames},
+author={Martins, Samuel F and Fonseca, RA and Lu, Wei and Mori, Warren B and Silva, LO},
+journal={Nature Physics},
+volume={6},
+number={4},
+pages={311--316},
+year={2010},
+publisher={Nature Publishing Group UK London},
+doi={10.1038/nphys1538}
+}
+
+@article{Martins2010c,
+author = {Martins,S. F. and Fonseca,R. A. and Vieira,J. and Silva,L. O. and Lu,W. and Mori,W. B. },
+title = {Modeling laser wakefield accelerator experiments with ultrafast particle-in-cell simulations in boosted frames},
+journal = {Physics of Plasmas},
+volume = {17},
+number = {5},
+pages = {056705},
+year = {2010},
+doi = {10.1063/1.3358139}
+}
+
+@article{Bruhwiler2009,
+author = {Bruhwiler,David L. and Cary,John R. and Cowan,Benjamin M. and Paul,Kevin and Geddes,Cameron G. R. and Mullowney,Paul J. and Messmer,Peter and Esarey,Eric and Cormier‐Michel,Estelle and Leemans,Wim and Vay,Jean‐Luc },
+title = {New Developments in the Simulation of Advanced Accelerator Concepts},
+journal = {AIP Conference Proceedings},
+volume = {1086},
+number = {1},
+pages = {29-37},
+year = {2009},
+doi = {10.1063/1.3080922}
+}
+
+@article{Yu2016,
+title = {Enabling Lorentz boosted frame particle-in-cell simulations of laser wakefield acceleration in quasi-3D geometry},
+journal = {Journal of Computational Physics},
+volume = {316},
+pages = {747-759},
+year = {2016},
+issn = {0021-9991},
+doi = {10.1016/j.jcp.2016.04.014},
+author = {Peicheng Yu and Xinlu Xu and Asher Davidson and Adam Tableman and Thamine Dalichaouch and Fei Li and Michael D. Meyers and Weiming An and Frank S. Tsung and Viktor K. Decyk and Frederico Fiuza and Jorge Vieira and Ricardo A. Fonseca and Wei Lu and Luis O. Silva and Warren B. Mori}
+}
+
+@inproceedings{Godfrey1985,
+title={The IPROP Three-Dimensional Beam Propagation Code},
+booktitle={},
+author={B. B. Godfrey},
+year={1985}
+}
+
+@article{Lifschitz2009,
+title = {Particle-in-Cell modelling of laser–plasma interaction using Fourier decomposition},
+journal = {Journal of Computational Physics},
+volume = {228},
+number = {5},
+pages = {1803-1814},
+year = {2009},
+issn = {0021-9991},
+doi = {10.1016/j.jcp.2008.11.017},
+author = {A.F. Lifschitz and X. Davoine and E. Lefebvre and J. Faure and C. Rechatin and V. Malka}
+}
+
+@article{Davidson2015,
+title = {Implementation of a hybrid particle code with a PIC description in r–z and a gridless description in ϕ into OSIRIS},
+journal = {Journal of Computational Physics},
+volume = {281},
+pages = {1063-1077},
+year = {2015},
+issn = {0021-9991},
+doi = {10.1016/j.jcp.2014.10.064},
+author = {A. Davidson and A. Tableman and W. An and F.S. Tsung and W. Lu and J. Vieira and R.A. Fonseca and L.O. Silva and W.B. Mori}
+}
+
+@article{Lehe2016,
+title = {A spectral, quasi-cylindrical and dispersion-free Particle-In-Cell algorithm},
+journal = {Computer Physics Communications},
+volume = {203},
+pages = {66-82},
+year = {2016},
+issn = {0010-4655},
+doi = {10.1016/j.cpc.2016.02.007},
+author = {Rémi Lehe and Manuel Kirchen and Igor A. Andriyash and Brendan B. Godfrey and Jean-Luc Vay}
+}
+
+@article{Andriyash2016,
+author = {Andriyash,Igor A. and Lehe,Remi and Lifschitz,Agustin },
+title = {Laser-plasma interactions with a Fourier-Bessel particle-in-cell method},
+journal = {Physics of Plasmas},
+volume = {23},
+number = {3},
+pages = {033110},
+year = {2016},
+doi = {10.1063/1.4943281}
+}
+
+@article{Shadwick2009,
+author = {Shadwick,B. A. and Schroeder,C. B. and Esarey,E. },
+title = {Nonlinear laser energy depletion in laser-plasma accelerators},
+journal = {Physics of Plasmas},
+volume = {16},
+number = {5},
+pages = {056704},
+year = {2009},
+doi = {10.1063/1.3124185}
+}
+
+@article{CormierMichel2009,
+author = {Cormier‐Michel,Estelle and Geddes,C. G. R. and Esarey,E. and Schroeder,C. B. and Bruhwiler,D. L. and Paul,K. and Cowan,B. and Leemans,W. P. },
+title = {Scaled simulations of a 10 GeV accelerator},
+journal = {AIP Conference Proceedings},
+volume = {1086},
+number = {1},
+pages = {297-302},
+year = {2009},
+doi = {10.1063/1.3080921}
+}
diff --git a/Docs/source/theory/intro.rst b/Docs/source/theory/intro.rst
index d81fdeab3..cbf56c919 100644
--- a/Docs/source/theory/intro.rst
+++ b/Docs/source/theory/intro.rst
@@ -4,387 +4,20 @@ Introduction
============
.. figure:: Plasma_acceleration_sim.png
- :alt: [fig:Plasma_acceleration_sim] Plasma laser-driven (top) and charged-particles-driven (bottom) acceleration (rendering from 3-D Particle-In-Cell simulations). A laser beam (red and blue disks in top picture) or a charged particle beam (red dots in bottom picture) propagating (from left to right) through an under-dense plasma (not represented) displaces electrons, creating a plasma wakefield that supports very high electric fields (pale blue and yellow). These electric fields, which can be orders of magnitude larger than with conventional techniques, can be used to accelerate a short charged particle beam (white) to high-energy over a very short distance.
+ :alt: Plasma laser-driven (top) and charged-particles-driven (bottom) acceleration (rendering from 3-D Particle-In-Cell simulations). A laser beam (red and blue disks in top picture) or a charged particle beam (red dots in bottom picture) propagating (from left to right) through an under-dense plasma (not represented) displaces electrons, creating a plasma wakefield that supports very high electric fields (pale blue and yellow). These electric fields, which can be orders of magnitude larger than with conventional techniques, can be used to accelerate a short charged particle beam (white) to high-energy over a very short distance.
- [fig:Plasma_acceleration_sim] Plasma laser-driven (top) and charged-particles-driven (bottom) acceleration (rendering from 3-D Particle-In-Cell simulations). A laser beam (red and blue disks in top picture) or a charged particle beam (red dots in bottom picture) propagating (from left to right) through an under-dense plasma (not represented) displaces electrons, creating a plasma wakefield that supports very high electric fields (pale blue and yellow). These electric fields, which can be orders of magnitude larger than with conventional techniques, can be used to accelerate a short charged particle beam (white) to high-energy over a very short distance.
+ Plasma laser-driven (top) and charged-particles-driven (bottom) acceleration (rendering from 3-D Particle-In-Cell simulations). A laser beam (red and blue disks in top picture) or a charged particle beam (red dots in bottom picture) propagating (from left to right) through an under-dense plasma (not represented) displaces electrons, creating a plasma wakefield that supports very high electric fields (pale blue and yellow). These electric fields, which can be orders of magnitude larger than with conventional techniques, can be used to accelerate a short charged particle beam (white) to high-energy over a very short distance.
-Computer simulations have had a profound impact on the design and understanding of past and present plasma acceleration experiments (Tsung et al. 2006; Geddes et al. 2008; C. Geddes et al. 2009; Huang et al. 2009), with
-accurate modeling of wake formation, electron self-trapping and acceleration requiring fully kinetic methods (usually Particle-In-Cell) using large computational resources due to the wide range of space and time scales involved. Numerical modeling complements and guides the design and analysis of advanced accelerators, and can reduce development costs significantly. Despite the major recent experimental successes(Leemans et al. 2014; Blumenfeld et al. 2007; Bulanov S V and Wilkens J J and Esirkepov T Zh and Korn G and Kraft G and Kraft S D and Molls M and Khoroshkov V S 2014; Steinke et al. 2016), the various advanced acceleration concepts need significant progress to fulfill their potential. To this end, large-scale simulations will continue to be a key component toward reaching a detailed understanding of the complex interrelated physics phenomena at play.
+Computer simulations have had a profound impact on the design and understanding of past and present plasma acceleration experiments :cite:p:`Tsung2006,Geddes2008,Geddes2009,Geddes2010,Huang2009`, with
+accurate modeling of wake formation, electron self-trapping and acceleration requiring fully kinetic methods (usually Particle-In-Cell) using large computational resources due to the wide range of space and time scales involved. Numerical modeling complements and guides the design and analysis of advanced accelerators, and can reduce development costs significantly. Despite the major recent experimental successes :cite:p:`Leemans2014,Blumenfeld2007,Bulanov2014,Steinke2016`, the various advanced acceleration concepts need significant progress to fulfill their potential. To this end, large-scale simulations will continue to be a key component toward reaching a detailed understanding of the complex interrelated physics phenomena at play.
For such simulations,
the most popular algorithm is the Particle-In-Cell (or PIC) technique,
which represents electromagnetic fields on a grid and particles by
a sample of macroparticles.
However, these simulations are extremely computationally intensive, due to the need to resolve the evolution of a driver (laser or particle beam) and an accelerated beam into a structure that is orders of magnitude longer and wider than the accelerated beam.
-Various techniques or reduced models have been developed to allow multidimensional simulations at manageable computational costs: quasistatic approximation (Sprangle, Esarey, and Ting 1990; Antonsen and Mora 1992; Krall et al. 1993; Mora and Antonsen 1997; Huang et al. 2006),
-ponderomotive guiding center (PGC) models (Antonsen and Mora 1992; Krall et al. 1993; Huang et al. 2006; Benedetti et al. 2010; Cowan et al. 2011), simulation in an optimal Lorentz boosted frame (Vay 2007; Bruhwiler et al. 2009; Vay et al. 2009, 2010; Vay et al. 2009; Martins et al. 2009; Martins, Fonseca, Lu, et al. 2010; Martins, Fonseca, Vieira, et al. 2010; S. F. Martins et al. 2010; J L Vay et al. 2011; J. Vay et al. 2011; J -L. Vay et al. 2011; Yu et al. 2016),
-expanding the fields into a truncated series of azimuthal modes
-(Godfrey 1985; Lifschitz et al. 2009; Davidson et al. 2015; Lehe et al. 2016; Andriyash, Lehe, and Lifschitz 2016), fluid approximation (Krall et al. 1993; Shadwick, Schroeder, and Esarey 2009; Benedetti et al. 2010) and scaled parameters (Cormier-Michel et al. 2009; C. G. R. Geddes et al. 2009).
+Various techniques or reduced models have been developed to allow multidimensional simulations at manageable computational costs: quasistatic approximation :cite:p:`Sprangle1990,Antonsen1992,Krall1993,Mora1997,Huang2006`,
+ponderomotive guiding center (PGC) models :cite:p:`Antonsen1992,Krall1993,Huang2006,Benedetti2010,Cowan2011`, simulation in an optimal Lorentz boosted frame :cite:p:`Vay2007,Bruhwiler2009,Vay2009a,Vay2009b,Vay2010,Martins2010a,Martins2010b,Martins2010c,Vay2011a,Vay2011b,Vay2011c,Yu2016`,
+expanding the fields into a truncated series of azimuthal modes :cite:p:`Godfrey1985,Lifschitz2009,Davidson2015,Lehe2016,Andriyash2016`, fluid approximation :cite:p:`Krall1993,Shadwick2009,Benedetti2010` and scaled parameters :cite:p:`CormierMichel2009`.
-.. raw:: html
-
- <div id="refs" class="references">
-
-.. raw:: html
-
- <div id="ref-AndriyashPoP2016">
-
-Andriyash, Igor A., Remi Lehe, and Agustin Lifschitz. 2016. “Laser-Plasma Interactions with a Fourier-Bessel Particle-in-Cell Method.” *Physics of Plasmas* 23 (3). https://doi.org/http://dx.doi.org/10.1063/1.4943281.
-
-.. raw:: html
-
- </div>
-
-.. raw:: html
-
- <div id="ref-Antonsenprl1992">
-
-Antonsen, T M, and P Mora. 1992. “Self-Focusing and Raman-Scattering of Laser-Pulses in Tenuous Plasmas.” *Physical Review Letters* 69 (15): 2204–7. https://doi.org/10.1103/Physrevlett.69.2204.
-
-.. raw:: html
-
- </div>
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