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Chin. Phys. B, 2021, Vol. 30(1): 015201    DOI: 10.1088/1674-1056/abb224
PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES Prev   Next  

Propagation dynamics of relativistic electromagnetic solitary wave as well as modulational instability in plasmas

Rong-An Tang(唐荣安)†, Tiao-Fang Liu(刘调芳)‡, Xue-Ren Hong(洪学仁), Ji-Ming Gao(高吉明), Rui-Jin Cheng(程瑞锦), You-Lian Zheng(郑有莲), and Ju-Kui Xue(薛具奎)
Key Laboratory of Atomic and Molecular Physics and Functional Materials of Gansu Province, College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
Abstract  By one-dimensional particle-in-cell (PIC) simulations, the propagation and stability of relativistic electromagnetic (EM) solitary waves as well as modulational instability of plane EM waves are studied in uniform cold electron-ion plasmas. The investigation not only confirms the solitary wave motion characteristics and modulational instability theory, but more importantly, gives the following findings. For a simulation with the plasma density 1023 m-3 and the dimensionless vector potential amplitude 0.18, it is found that the EM solitary wave can stably propagate when the carrier wave frequency is smaller than 3.83 times of the plasma frequency. While for the carrier wave frequency larger than that, it can excite a very weak Langmuir oscillation, which is an order of magnitude smaller than the transverse electron momentum and may in turn modulate the EM solitary wave and cause the modulational instability, so that the solitary wave begins to deform after a long enough distance propagation. The stable propagation distance before an obvious observation of instability increases (decreases) with the increase of the carrier wave frequency (vector potential amplitude). The study on the plane EM wave shows that a modulational instability may occur and its wavenumber is approximately equal to the modulational wavenumber by Langmuir oscillation and is independent of the carrier wave frequency and the vector potential amplitude. This reveals the role of the Langmuir oscillation excitation in the inducement of modulational instability and also proves the modulational instability of EM solitary wave.
Keywords:  electromagnetic solitary wave      particle-in-cell (PIC) simulation      modulational instability      Langmuir oscillation  
Revised:  31 July 2020      Published:  17 December 2020
PACS:  52.35.Sb (Solitons; BGK modes)  
  52.35.-g (Waves, oscillations, and instabilities in plasmas and intense beams)  
  52.35.Mw (Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.))  
  52.38.-r (Laser-plasma interactions)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11765017, 11865014, 11847304, and 11764039), the Scientific Research Project of Gansu Higher Education, China (Grant No. 2019B-034), and the Science and Technology Project of Guizhou Province, China (Grant No. Qiankehe-LH-[2017]7008).
Corresponding Authors:  Corresponding author. E-mail: tangra79@163.com Corresponding author. E-mail: LTF25975@163.com   

Cite this article: 

Rong-An Tang(唐荣安), Tiao-Fang Liu(刘调芳), Xue-Ren Hong(洪学仁), Ji-Ming Gao(高吉明), Rui-Jin Cheng(程瑞锦), You-Lian Zheng(郑有莲), and Ju-Kui Xue(薛具奎) Propagation dynamics of relativistic electromagnetic solitary wave as well as modulational instability in plasmas 2021 Chin. Phys. B 30 015201

1 Mori W B, Decker C D and Leemans W P 1993 IEEE Trans. Plasma Sci. 21 110
2 Esarey E, Ting A, Sprangle P, Umstadter D and Liu X 1993 IEEE Trans. Plasma Sci. 21 95
3 Kuo C C, Pai C H, Lin M W, Lee K H, Lin J Y, Wang J and Chen S Y 2007 Phys. Rev. Lett. 98 033901
4 Niknam A R, Aliakbari A, Majedi S, Haji Mirzaei F and Hashemzadeh M 2011 Phys. Plasmas 18 112305
5 Bokaei B, Niknam A R and Milani M R J 2014 Plasma Sources Sci. Technol. 23 064011
6 Hashemzadeh M 2018 Phys. Plasmas 25 012309
7 Luo J, Chen M, Wu W Y, Weng S M, Sheng Z M, Schroeder C B, Jaroszynski D A, Esarey E, Leemans W P and Mori W B 2018 Phys. Rev. Lett. 120 154801
8 Razavinia S N and Ghorbanalilu M 2019 Phys. Rev. Accel. Beams 22 111305
9 Sprangle P, Joyce G, Esarey E and Ting A1988 AIP Conf. Proc. 175 231
10 Tian J M, Tang R A, Hong X R, Yang Y, Wang L, Zhou W J and Xue J K 2016 Phys. Plasmas 23 123117
11 Zhang L, Tang R A, Hong X R, Gao J M, Yin L R, Tian J M, Cheng R J and Xue J K 2019 Phys. Plasmas 26 043106
12 Luo J, Chen M, Zeng M, Vieira J, Yu L, Weng S M, Silva L O, Jaroszynski D A, Sheng Z M and Zhang J 2016 Sci. Rep. 6 29101
13 Sprangle P, Esarey E and Ting A 1990 Phys. Rev. A 41 4463
14 Sharma A and Kourakis I 2010 Plasma Phys. Controlled Fusion 52 065002
15 Farina D and Bulanov S V 2001 Phys. Rev. Lett. 86 5289
17 Hong X R, Xie B S, Zhang S, Wu H C and Zhao X Y 2011 Phys. Plasmas 18 103106
18 Zhang S, Xie B S, Hong X R, Wu H C and Zhao X Y 2011 Phys. Plasmas 18 033104
19 Xie B S and Hua C C 2005 Commun. Theor. Phys. 43 1119
20 Sen A and Kaw P K 1994 Phys. Scripta T50 47
21 Weber S, Riconda C and Tikhonchuk V T 2005 Phys. Rev. Lett. 94 055005
22 Xiao C Z, Liu Z J, Wu D, Zheng C Y and He X T 2015 Phys. Plasmas 22 052121
23 Kaw P K, Sen A and Katsouleas T 1992 Phys. Rev. Lett. 68 3172
24 Liu S Q and Li X Q 2000 Phys. Plasmas 7 3405
25 Cheng L H, Tang R A, Zhang A X and Xue J K 2013 Phys. Rev. E 87 025101
26 Lehmann G, Laedke E W and Spatschek K H 2008 Phys. Plasmas 15 072307
27 Liu S Q, Tang W and Li X Q 2012 Pramana-J. Phys. 78 439
28 Esirkepov T, Nishihara K, Bulanov S V and Pegoraro F 2002 Phys. Rev. Lett. 89 275002
29 Bulanov S V, Esirkepov T Zh, Naumova N M, Pegoraro F and Vshivkov V A 1999 Phys. Rev. Lett. 82 3440
30 Borghesi M, Campbell D H, Schiavi A, Haines M G, Willi O, MacKinnon A J, Patel P, Gizzi L A, Galimberti M and Clarke R J 2002 Phys. Plasmas 9 2214
31 Borghesi M, Bulanov S, Campbell D H, Clarke R J, Esirkepov T Zh, Galimberti M, Gizzi L A, MacKinnon A J, Naumova N M and Pegoraro F 2002 Phys. Rev. Lett. 88 135002
32 Kartal S, Tsintsadze L N and Berezhiani V I 1996 Phys. Rev. E 53 4225
33 Mikaberidze G and Berezhiani V I 2015 Phys. Lett. A 379 2730
34 Poornakala S, Das A, Kaw P K, Sen A, Sheng Z M, Sentoku Y, Mima K and Nishikawa K 2002 Phys. Plasmas 9 3802
35 Lontano M, Passoni M and Bulanov S V 2003 Phys. Plasmas 10 639
36 Sànchez-Arriaga G, Siminos E and Lefebvre E 2011 Phys. Plasmas 18 082304
37 Verma D, Bera R K, Kumar A, Patel B and Das A 2017 Phys. Plasmas 24 123111
38 Sentoku Y, Esirkepov T Zh, Mima K, Nishihara K, Califano F, Pegoraro F, Sakagami H, Kitagawa Y, Naumova N M and Bulanov S V 1999 Phys. Rev. Lett. 83 3434
39 Naumova N M, Bulanov S V, Esirkepov T Zh, Farina D, Nishihara K, Pegoraro F, Ruhl H and Sakharov A S 2001 Phys. Rev. Lett. 87 185004
40 Liu Y, Klimo O, Esirkepov T Zh, Bulanov S V, Gu Y J, Weber S and Korn G 2015 Phys. Plasmas 22 112302
41 Sànchez-Arriaga G and Lefebvre E 2011 Phys. Rev. E 84 036403
42 Esirkepov T, Bulanov S V, Nishihara K and Tajima T 2004 Phys. Rev. Lett. 92 255001
43 Li B, Ishiguro S, \vSkori\'c M M, Song M and Sato T 2005 Phys. Plasmas 12 103103
44 Li B, Ishiguro S, \vSkori\'c M M and Sato T 2007 Phys. Plasmas 14 032101
45 Xie J Y, Deng Z H, Chang X and Tang B 2019 Chin. Phys. B 28 77501
46 Ma Y R, Li L J and Duan W S 2019 Chin. Phys. B 28 25201
47 Bains A S, Misra A P, Saini N S and Gill T S 2010 Phys. Plasmas 17 012103
48 Marklund M, Eliasson B and Shukla P K 2006 Phys. Plasmas 13 083102
49 Shukla P K, Stenflo L and Fedele R 2003 Phys. Plasmas 10 310
50 Shatashvili N L, Javakhishvili J I and Kaya H 1997 Astrophys. Space Sci. 250 109
51 Zakharov V E and Ostrovsky L A 2009 Physica D 238 540
52 Meier J, Stegeman G I, Christodoulides D N, Silberberg Y, Morandotti R, Yang H, Salamo G, Sorel M and Aitchison J S 2004 Phys. Rev. Lett. 92 163902
53 Reece P J, Wright E M and Dholakia K 2007 Phys. Rev. Lett. 98 203902
54 Lontano M, Bulanov S V, Koga J, Passoni M and Tajima T 2002 Phys. Plasmas 9 2562
55 Eliasson B and Shukla P K 2006 Phys. Lett. A 354 453
56 Borhanian J 2012 Phys. Plasmas 19 082306
57 Cattaert T, Kourakis I and Shukla P K 2005 Phys. Plasmas 12 012319
58 Borhanian J, Kourakis I and Sobhanian S 2009 Phys. Lett. A 373 3667
59 Lee N C 2011 Phys. Plasmas 18 062310
60 Had\vzievski Lj, Jovanovi\'c M S, \vSkori\'c M M and Mima K 2002 Phys. Plasmas 9 2569
61 Lehmann G, Laedke E W and Spatschek K H 2006 Phys. Plasmas 13 092302
62 Saxena V, Das A, Sengupta S, Kaw P and Sen A 2007 Phys. Plasmas 14 072307
63 Saxena V, Das A, Sen A and Kaw P 2006 Phys. Plasmas 13 032309
64 Saxena V, Kourakis I, Sànchez-Arriaga G and Siminos E 2013 Phys. Lett. A 377 473
65 Rostampooran S and Aslaninejad M 2017 Phys. Plasmas 24 042302
66 Holkundkar A R and Brodin G 2018 Phys. Rev. E 97 043204
67 Sharma A, Malik H K, Kumar H and Goyal S2019 J. Appl. Phys. 13 31
68 Sharma A, Malik H K and Kumar H2018 J. Appl. Phys. 12 65
69 Hong X R, Zhou W J, Xie B S, Yang Y, Wang L, Tian J M, Tang R A and Duan W S 2017 Chin. Phys. B 26 065203
70 Wang H Y, Sun P, Jiang W, Zhou J and Xie B S 2014 Chin. Phys. B 24 065207
71 Weng S M, Murakami M, Mulser P and Sheng Z M 2012 New J. Phys. 14 063026
72 Dawson J M 1983 Rev. Mod. Phys 55 403
73 Pan K Q, Li S W, Guo L, Yang D, Li Z C, Zheng C Y, Jiang S E, Zhang B H and He X T 2018 Phys. Plasmas 25 052301
74 Wu D, Yu W, Fritzsche S, Zheng C Y and He X T 2019 Phys. Plasmas 26 063107
75 Hashemzadeh M and Niknam A R 2017 Phys. Plasmas 24 062102
76 Chen H Y, Liu S Q and Li X Q 2011 Opt. Int. J. Light Electron. Opt. 122 599
77 Borhanian J and Aghaei G H 2017 Phys. Plasmas 24 033116
78 Zheng X L, Weng S M, Zhang Z, Ma H H, Chen M, Mckenna P and Sheng Z M 2019 Opt. Express 28 15794
79 Zhao Y, Weng S M, Sheng Z M, Kang N, Liu H Y, Zhu J Q and Zhang J 2020 Opt. Express 27 19319
80 Farina D, Lontano M and Bulanov S 2000 Phys. Rev. E 62 4146
81 Tang R A, Hong X R, Gao J M and Xue J K 2016 Phys. Lett. A 380 1037
82 Tang R A, Cheng R J, Hong X R, Liu T F, Li X X, Gao J M, Guo P, Tian J M and Xue J K 2020 Phys. Lett. A 384 126267
83 Fedele R and Schamel H 2002 Eur. Phys. J. B 27 313
84 Shukla P K, Bharuthram R and Tsintsadze N L 1987 Phys. Rev. A 35 4889
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