Abstract
In this theoretical investigation, plasma wave aided heating scheme is analytically studied in collisional nanocluster plasma by two high power Hermite cosh-Gaussian laser beams. Due to the interaction of laser beams with plasma embedded nanocluster, the cluster gets ionize and become into plasma plume ball. Nonlinear interaction of two laser beams causes the beat wave with frequency \(\omega = \omega_{1} - \omega_{2}\) and beat wave number \(k = k_{1} - k_{2}\) in plasma embedded with clusters. The oscillatory velocities due to each laser beam produce the nonlinear ponderomotive force. This nonlinear force might have much potential to excite the plasma wave and lead the electron heating. Analytic expressions of anomalous heating rate and evolution of electron temperature are derived. The heating rate is found maximum at laser normalized transverse propagation distance from y-axis \(y/w_{0} \sim 0.4\). It is observed that anomalous heating rate is resonantly increased by the presence of surface plasmon oscillations. This extreme condition of heating rate is achieved when laser beat wave frequency is comparatively near the frequency of surface charge oscillations of nanoclustered plasma and is typically \(\omega \sim \omega_{pe} /\sqrt 3\). The graphical discussion of this theory promises that heating rate can be effectively enhanced by varying the beam decentred parameter, beam width, mode index, rippled clustered density, clustered radius, and collisional frequency. It is also analysed that laser beam decentred parameter plays a sensitive role on nanocluster heating. By generalizing this laser heating theory, soft X-ray emission can be achieved via Bremsstrahlung process.
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References
Bahcivan, H.: Plasma wave heating during extreme electric fields in the high-latitude E region. Geophys. Res. Lett. 34, L15106 (2007)
Beaudry, G., Martineau, J.: Plasma heating by beating of two laser beams. Phys. Lett. A 43, 331–332 (1973)
Bhasin, L., Tripathi, D., Uma, R., Tripathi, V.K.: Laser beat wave terahertz generation in a clustered plasma in an azimuthal magnetic field. Phys. Plasmas 18, 053109 (2011)
Boffard, J.B., Lin, C.C., DeJoseph, C.A., Jr.: Application of excitation cross sections to optical plasma diagnostics. J. Phys. D: Appl. Phys. 37, R143–R161 (2004)
Cai, H., Yu, W., Zhu, S., Zheng, C., Cao, L., Pei, W.: Vacuum heating in the interaction of ultrashort, relativistically strong laser pulses with solid targets. Phys. Plasmas 13, 063108 (2006)
Chen, L., Hasegawa, A.: Plasma heating by spatial resonance of Alfvén wave. Phys. Fluids 17, 1399 (1974)
Clayton, C.E., Joshi, C., Darrow, C., Umstadter, D.: Relativistic plasma-wave excitation by collinear optical mixing. Phys. Rev. Lett. 54, 2343–2346 (1985)
Cohen, B.I., Mostrom, M.A., Nicholson, D.R., Kaufman, A.N., Max, C.E., Langdon, A.: Simulation of laser beat heating of a plasma. Phys. Fluids 18, 474 (1975)
Ditmire, T., Smith, R.A., Tisch, J.W.G., Hutchinson, M.H.R.: High Intensity Laser Absorption by Gases of Atomic Clusters. Phys. Rev. Lett. 78, 3121–3124 (1997)
Fennel, T., Meiwes-Broer, K.H., Tiggesbäumker, J., Reinhard, P.G., Dinh, P.M., Suraud, E.: Laser-driven nonlinear cluster dynamics. Rev. Mod. Phys. 82, 1793–1842 (2010)
Gupta, M.K., Sharma, R.P., Gupta, V.L.: Cross focusing of two laser beams and plasma wave excitation. Phys. Plasmas 12, 123101 (2005)
Hasegawa, A., Chen, L.: Kinetic process of plasma heating due to Alfven wave excitation. Phys. Rev. Lett. 35, 370–373 (1974)
Jeet, R., Kumar, A., Kumar, A., Babu, S., Varma, A.: Acceleration of electrons by a lower hybrid wave in a magnetic mirror. J. Korean Phys. Soc. 78, 1179–1184 (2021)
Kaganovich, I.D., Startsev, E.A., Davidson, R.C.: Nonlinear plasma waves excitation by intense ion beams in background plasma. Phys. Plasmas 11, 3546–3552 (2004)
Kitagawa, Y., Matsumoto, T., Minamihata, T., Sawai, K., Matsuo, K., Mima, K., Nishihara, K., Azechi, H., Tanaka, K.A., Takabe, H., Nakai, S.: Beat-wave excitation of plasma wave and observation of accelerated electrons. Phys. Rev. Lett. 68, 48–51 (1992)
Kumar, M., Singh, R., Verma, U.: Bremsstrahlung soft X-ray emission from clusters heated by a Gaussian laser beam. Laser Part. Beams 32, 9–14 (2014)
Kumar, A., Kumar, A., Varma, A.: Excitation of electron Bernstein waves by beating of two cosh-Gaussian laser beams in a collisional plasma. Laser Phys. 31, 106001 (2021)
Liu, C.S., Tripathi, V.K.: Fast and slow plasma waves excitation by counterpropagating lasers in a hot plasma. Phys. Plasmas 9, 3995–3998 (2002)
Patil, S.D., Takale, M.V., Fulari, V.J., Gupta, D.N., Suk, H.: Combined effect of ponderomotive and relativistic self-focusing on laser beam propagation in a plasma. Appl. Phys. B 111, 1–6 (2013)
Pushplata, Vijay, A.: Beat wave cyclotron heating of rippled density plasma, Laser Part. Beams 36, 465–469 (2018)
Rosenbluth, M.N., Liu, C.S.: Excitation of Plasma Waves by Two Laser Beams. Phys. Rev. Lett. 29, 701–705 (1972)
Saalmann, U.: Cluster nanoplasmas in strong FLASH pulses: formation, excitation and relaxation. J. Phys. B At. Mol. Opt. Phys. 43, 194012 (2010)
Safari, S., Niknam, A.R., Jahangiri, F., Jazi, B.: Terahertz radiation generation through the nonlinear interaction of Hermite and Laguerre Gaussian laser beams with collisional plasma: Field profile optimization. J. Appl. Phys. 123, 153101 (2018)
Sharma, R.P., Sharma, P., Chauhan, P.K.: Effect of laser beam filamentation on plasma wave localization and electron heating. Phys. Plasmas 14, 103112 (2007)
Sherlock, M., Hill, E.G., Evans, R.G., Rose, S.J.: In-depth plasma-wave heating of dense plasma irradiated by short laser pulses. Phys. Plasmas 12, 056703 (2005)
Shvets, G., Fisch, N.J.: Parametric excitations of fast plasma waves by counterpropagating laser beams. Phys. Rev. Lett. 86, 3328–3331 (2001)
Siahmazgi, R.N., Jafari, S.: Tunable terahertz radiation generation using the beating of two super-Gaussian laser beams in the collisional nanocluster plasma. J. Opt. Soc. Am. B 37, 3296–3302 (2020)
Siahmazgi, R.N., Jafari, S.: Soft X-ray emission from an anharmonic collisional nanoplasma by a laser–nanocluster interaction. J. Plasma Phys. 87, 905870312 (2021)
Taguchi, T., Antonsen, T.M., Jr., Milchberg, H.M.: Resonant heating of a cluster plasma by intense laser light. Phys. Rev. Lett. 92, 205003 (2004)
Tiwari, P.K., Tripathi, V.K.: Stimulated Raman scattering of a laser in a plasma with clusters. Phys. Plasmas 11, 1674–1679 (2004)
Tiwari, P.K., Tripathi, V.K.: Laser beat-wave excitation of plasma waves in a clustered gas. Phys. Scr. 73, 393–396 (2006)
Varma, A., Kumar, A.: Electron Bernstein wave excitation and heating by nonlinear interactions of Laguerre and Hermite Gaussian laser beams in a magnetized plasma. Optik 228, 166212 (2021a)
Varma, A., Kumar, A.: Electron Bernstein wave excitation by beating of two copropagating super-Gaussian laser beam in a collisional nanocluster plasma. Optik 240, 166872 (2021b)
Varma, A., Kumar, A.: Electron Bernstein wave aided beat wave of Hermite-cosh-Gaussian laser beam absorption in a collisional nanocluster plasma. Optik 245, 167702 (2021c)
Varma, A., Kumar, A.: Electron Bernstein wave aided heating of collisional nanocluster plasma by nonlinear interactions of two super-Gaussian laser beams. Laser Phys. 32, 016001 (2022)
Varma, A., Kumar, A., Kumar, A.: Nonlocal theory of excitation of electron Bernstein waves by a relativistic electron beam in plasma with loss-cone distribution of electron. Braz. J. Phys. 51, 661–666 (2021)
Vieira, J., Trines, R.M.G.M., Alves, E.P., Fonseca, R.A., Mendonc, J.T., Bingham, R., Norreys, P., Silva, L.O.: Amplification and generation of ultra-intense twisted laser pulses via stimulated Raman scattering. Nat. Commun. 7, 10371 (2016)
Vijay, A., Tripathi, V.K.: Laser beat frequency heating of a rippled density plasma. Phys. Plasmas 23, 093124 (2016)
White, R., Chen, L., Lin, Z.: Resonant plasma heating below the cyclotron frequency, Resonant plasma heating below the cyclotron frequency. Phys. Plasmas 9, 1890–1897 (2002)
Yadav, M., Kumar, A., Mandal, S.: Nonlinear laser absorption on metal surfaces embedded with metallic nanoparticles and nanotubes. Phys. Plasmas 27, 043302 (2020)
Acknowledgements
The authors would like grateful to Prof. V. K. Tripathi (IIT Delhi), Prof. M. S, Tiwari (Dr. H. S. Gour University, Sagar), and Prof. K. N. Uttam (Department of Physics, University of Allahabad, India) for valuable discussions and suggestion. We would like to thank Prof. P. N. Dongre (Principal) and Prof. A. K. Kushwaha (Head, Department of Physics) of K. N. Govt. P. G. College, Gyanpur-Bhadohi for providing the research facilities.
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AK and SPM have done the calculation part. MSY do the computational work. AV write the manuscript and AK supervised the whole problem.
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Kumar, A., Kumar, A., Mishra, S.P. et al. Plasma wave aided heating of collisional nanocluster plasma by nonlinear interaction of two high power laser beams. Opt Quant Electron 54, 753 (2022). https://doi.org/10.1007/s11082-022-04206-5
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DOI: https://doi.org/10.1007/s11082-022-04206-5