Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-14T06:53:04.606Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical modeling of radiative recombination during ionization of atoms by means of particle-in-cell simulation

Published online by Cambridge University Press:  29 March 2016

E. Khalilzadeh ,
J. Yazdanpanah ,
J. Jahanpanah  and
A. Chakhmachi
E. Khalilzadeh*
Affiliation:
Department of Physics, Kharazmi University, 49 Mofateh Ave, P. O. Box 15614, Tehran, Iran The Plasma Physics and Fusion Research School, Tehran, Iran
J. Yazdanpanah
Affiliation:
The Plasma Physics and Fusion Research School, Tehran, Iran
J. Jahanpanah
Affiliation:
Department of Physics, Kharazmi University, 49 Mofateh Ave, P. O. Box 15614, Tehran, Iran
A. Chakhmachi
Affiliation:
The Plasma Physics and Fusion Research School, Tehran, Iran
*
Address correspondence and reprint requests to: Elnaz Khalilzadeh, Department of Physics, Kharazmi University, 49 Mofateh Ave, P. O. Box 15614, Tehran, Iran and The Plasma Physics and Fusion Research School, Tehran, Iran. E-mail: el_84111005@aut.ac.ir
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, a heuristic algorithm based on particle-in-cell (PIC) simulation is introduced to investigate the harmonic generation during the ionization and formation of plasma by a non-relativistic laser field when it propagates through hydrogen atoms. The harmonic generation is considered for the radiative recombination of an ionized electron with its nearest ion. The ionization algorithm is improved by considering the Stark effect and nonzero velocity for ionized electrons. Energy conservation is evaluated during the recombination process. In our code, for the first time, Maxwell's equations are integrated for harmonic fields in a separate mesh using the artificial recombination current as a source term. The simulation results are then used to illustrate the intensity spectrum of generated fields. It is shown that the initial momentum of ionized electrons affects the harmonic spectrum because the energy of radiated photons varies with the electron energy.

Keywords

Harmonic generationIonizationMonte CarloParticle-in-cell simulationRadiative recombination
Type
Research Article
Information
Laser and Particle Beams , Volume 34 , Issue 2 , June 2016 , pp. 284 - 293
Copyright
Copyright © Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Andreev, N.E., Veisman, M.E. & Chegotov, M.V. (2003). Third-harmonic generation in an ionized gas and its relation to the residual energy of electrons. J. Exp. Theor. Phys. 97, 554–565.Google Scholar
Bauer, D. (1997). Ejection energy of photoelectrons in strong-field ionization. Phys. Rev. A 55, 2180–2185.Google Scholar
Bauer, D. (2003). Plasma formation through field ionization in intense laser–matter interaction. Laser Part. Beams 21, 489–495.Google Scholar
Bauer, D. & Mulser, P. (1999). Exact field ionization rates in the barrier-suppression regime from numerical time-dependent Schrodinger-equation calculations. Phys. Rev. A 59, 569–577.Google Scholar
Becker, W., Grason, F., Kopold, R., Milosevic, D.B., Paulus, G.G. & Walther, H. (2002). Above-threshold ionization: From classical features to quantum effects. Adv. At. Mol. Opt. Phys. 48, 35–97.Google Scholar
Birdsall, C.K., Langdon, A.B., Vehedi, V. & Verboncoeur, J.P. (1991). Plasma Physics via Computer Simulations. Bristol: Adam Hilger.Google Scholar
Bleda, E.A., Yavuz, I., Altun, Z. & Topcu, T. (2013). High-order-harmonic generation from Rydberg states at fixed Keldysh parameter. Phys. Rev. A 88, 043417.Google Scholar
Bruhwiler, D.L., Dimitrov, D.A., Cary, J.R., Esarey, E., Leemans, W. & Giacone, R.E. (2003). Particle-in-cell simulations of tunneling ionization effects in plasma based accelerators. Phys. Plasmas 10, 2022–2030.Google Scholar
Chen, M., Cormier-Michel, E., Geddes, C.G.R., Bruhwiler, D.L., Yu, L.L., Esarey, E., Schroeder, C.B. & Leemans, W.P. (2013). Numerical modeling of laser tunneling ionization in explicit particle-in-cell codes. J. Com. Phys. 236, 220–228.Google Scholar
Chessa, P., De Wispelaere, E., Dorchies, F., Malka, V., Marques, J. R., Hamoniaux, G., Mora, P. & Amiranoff, F. (1999). Temporal and angular resolution of the ionization-induced refraction of a short laser pulse in helium gas. Phys. Rev. Lett. 82. 552–555.Google Scholar
Ciappina, M.F., Chirilă, C.C. & Lein, M. (2007). Influence of Coulomb continuum wave functions in the description of high order harmonic generation with H2. Phys. Rev. A 75, 043405.Google Scholar
Colosimo, P., Doumy, G., Blaga, C.I., Wheeler, J., Hauri, C., Catoire, F., Tate, J., Chirla, R., Maech, A.M., Paulus, G.G., Muller, H.G., Agostin, P. & Dimauro, L.F. (2008). Scaling strong-field interactions towards the classical limit. Nat. phy. 4, 386–389.Google Scholar
Corkum, P.B. (1993). Plasma perspective on strong-field multiphoton ionization. Phys. Rev. Lett. 71, 1993–1997.Google Scholar
Delone, N.B. & Krainov, V.P. (1991). Energy and angular electron spectra for the tunnel ionization of atoms by strong low-frequency radiation. J. Opt. Soc. Am. B 8, 1207–1211.Google Scholar
Dionissopoulou, S., Mercouris, T. & Nicolaides, C.A. (1996). Ionization rates and harmonic generation for H interacting with laser pulses of λ=1064 nm and peak intensities in the range 2 × 1013–2 × 1014 W cm–2. J. Phys. B: At. Mol. Opt. Phys. 29, 4787–4794.Google Scholar
Ditmire, T. (1996). Simulations of heating and electron energy distributions in optical field ionized plasmas. Phys. Rev. E 54, 6735–6740.Google Scholar
Dollar, F., Cummings, P., Chvykov, V., Willingale, L., Vargas, M., Yanovsky, V., Zulick, C., Maksimchuk, A., Thomas, A.G.R. & Krushelnick, K. (2013). Scaling high-order harmonic generation from laser-solid interactions to ultrahigh intensity. Phys. Rev. Lett. 110, 175002.Google Scholar
Dromey, B., Bellei, C., Carroll, D.C., Clarke, R.J., Green, J.S., Kar, S., Kneip, S., Markey, K., Nagel, S.R., Willingale, L., Mckenna, P., Neely, D., Najmudin, Z., Krushelnick, K., Norreys, P.A. & Zepf, M. (2009). Third harmonic order imaging as a focal spot diagnostic for high intensity laser-solid interactions. Laser Part. Beams 27, 243–248.Google Scholar
Efimenko, E.S. & Kim, A.V. (2011). Strongly coupled regime of ionization-induced scattering in ultrashort laser-matter interactions. Phys. Rev. E 84, 036408.Google Scholar
Esarey, E., Sprangle, P., Krall, J. & Ting, A. (1997). Self-focusing and guiding of short laser pulses in ionizing gases and plasmas. IEEE J. Quant. Electron. 33, 1879–1914.Google Scholar
Eslami, E. & Basereh, K. (2013). Effects of plasma and ultrashort laser pulse on residual electron energy in optical-field-ionized oxygen plasma. Laser Part. Beams 31, 187–193.Google Scholar
Faisal, F.H.M. (1973). Multiple absorption of laser photons by atoms. J. Phys. B 6, L89–L92.Google Scholar
Falcao-Filho, E.L., Gkortsas, V.M., Gordon, A. & Kartner, F.X. (2009). Analytic scaling analysis of high harmonic generation conversion efficiency. Opt. Express 17, 11217.Google Scholar
Frolov, M.V., Knyazeva, D.V., Manakov, N.L., Geng, J.W., Peng, L.Y. & Starace, A.F. (2014). Analytic model for the description of above-threshold ionization by an intense short laser pulse. Phy. Rev. A 89, 063419.Google Scholar
Ghimire, S., Dichiara, A.D., Sistrunk, E., Agostini, P., Dimauro, L.F. & Reis, D.A. (2010). Observation of high-order harmonic generation in a bulk crystal. Nat. Phy. 1847, 138–141.Google Scholar
Gkortsas, V.M., Bhardwaj, S., L Falcão-Filho, E., Hong, K.H., Gordon, A. & X Kärtner, F. (2011). Scaling of high harmonic generation conversion efficiency. J. Phys. B: At. Mol. Opt. Phys. 44, 045601.Google Scholar
He, B. & Chang, T.Q. (2005). Residual energy in optical-field-ionized plasmas with the longitudinal motion of electrons included. Phys. Rev. E 71, 066411.Google Scholar
Hockney, R. & Eastwood, J. (1998). Computer Simulation using Particles. New York: Taylor & Francis Group.Google Scholar
Hosokai, T., Kinoshita, K., Ohkubo, T., Maekawa, A., Uesaka, M., Zhidkov, A., Yamazaki, A., Tomassini, P., Giulietti, A. & Giulietti, D. (2006). Observation of strong correlation between quasimonoenergetic electron beam generation by laser wakefield and laser guiding inside a preplasma cavity. Phy. Rev. E 73, 036407.Google Scholar
Janulewicz, K.A., Grout, M.J. & Pert, G.J. (1996). Electron residual energy of optical-field-ionized plasmas driven by subpicosecond laser pulses. J. Phys. B: At. Mol. Opt. Phys. 29, 901–914.Google Scholar
Keldysh, L.V. (1964). Ionization in the field of a strong electromagnetic wave. Eksp. Teor. Fiz. 47, 1945–1964.Google Scholar
Kemp, A.J., Pfund, R.E.W. & Meyer-ter-Vehn, J. (2004). Modeling ultrafast laser-driven ionization dynamics with Monte Carlo collisional particle in-cell simulations. Phys. Plasmas 11, 5648–5657.Google Scholar
Klaiber, M., Kohler, M.C., Hatsagortsyan, K.Z. & Keitel, C.H. (2012). Optimization of the recollision step in high-order harmonic generation. Phys. Rev. A 85, 063829.Google Scholar
Kohler, M.C., Ott, C., Raith, P., Heck, R., Schlegel, I., Keitel, C.H. & Pfeifer, T. (2010). High harmonic generation via continuum wave-packet interference. Phy. Rev. Lett. 105, 203902.Google Scholar
Krainov, V.P. & Shokri, B. (1995). Energy and angular distributions of electrons resulting from barrier-suppression ionization of atoms by strong low-frequency radiation. JETP 80, 657–661.Google Scholar
Landau, L. & Lifshitz, E. (1965). Quantum Mechanics. New York: Butterworth Heinemann.Google Scholar
Lewenstein, M., Balcou, Ph., Ivanov, Yu.M., L'Huillier, A. & Corkum, P.B. (1994). Theory of high-harmonic generation by low-frequency laser fields. Phys. Rev. A 49, 2117–2132.Google Scholar
Liu, J.S., Xia, C.Q., Wang, W.T., Lu, H.Y., Wang, C., Deng, A.H., Li, W.T., Zhang, H., Liang, X.Y., Leng, Y.X., Lu, X.M., Wang, C., Wang, J.Z., Nakajima, K., Li, R.X. & Xu, Z.Z. (2011). All-optical cascaded laser wakefield accelerator using ionization-induced injection. Phys. Rev. Lett. 107, 035001.Google Scholar
Misra, S., Mishra, S.K., Sodha, M.S. & Tripathi, V.K. (2014). Effect of electron-ion recombination on self-focusing/ defocusing of a laser pulse in tunnel ionized plasmas. Laser Part. Beams 32, 21–31.Google Scholar
Mocek, T., Sebban, S., Bettaibi, I., Zeitoun, Ph., Faivre, G., Cros, B., Maynard, G., Butler, A., Mckenna, C.M., Spence, D.J., Gonsavles, A.J., Hooker, S.M., Vorontsov, V., Hallou, S., Fajardo, M., Kazamias, S., Lepape, S., Mercere, P., Morlens, A.S., Valentin, C. & Balcou, Ph. (2005). Progress in optical-field-ionization soft X-ray lasers at LOA. Laser Part. Beams 23, 351–356.Google Scholar
Mulser, P., Cornolti, F. & Bauer, D. (1998). Modeling field ionization in an energy conserving form and resulting nonstandard fluid dynamics. Phys. Plasmas 5, 4466–4475.Google Scholar
Murakami, M., Korobkin, O. & Horbatsch, M. (2013). High-harmonic generation from hydrogen atoms driven by two-color mutually orthogonal laser fields. Phys. Rev. A 88, 063419.Google Scholar
Mur, V.D. & Popov, V.S. (1993). The Stark effect in strong fields: Perturbation theory, 1/n-expansion and scaling. Laser Physics 3, 462–474.Google Scholar
Ozaki, T., Elouga Bom, L.B., Ganeev, R., Kieffer, J.C., Suzuki, M. & Kuroda, H. (2007). Intense harmonic generation from silver ablation. Laser Part. Beams 25, 321–325.Google Scholar
Reiss, H.R. (1980). Effect of an intense electromagnetic field on a weakly bound system. Phys. Rev. A 22, 1786–1813.Google Scholar
Schafer, K.J., Yang, B., DiMauro, L.F. & Kulanderc, K.C. (1993). Above threshold ionization beyond the high harmonic cutoff’. Phys. Rev. Lett. 70, 1599–1602.Google Scholar
Seres, J., Seres, E., Verhoef, A.J., Tempea, G., Streli, C., Wobrauschek, P., Yakovlev, V., Scrinzi, A., Spielmann, C. & Krausz, F. (2005). Laser technology: Source of coherent kiloelectronvolt X-rays. Nature 433, 596–601.Google Scholar
Shiner, A.D., Trallero-Herrero, C., Kajumba, N., Bandulet, H.-C., Comtois, D., Legare, F., Giguere, M., Kieffer, J.-C., Corkum, P.B. & Villeneuve, D.M. (2009). Wavelength scaling of high harmonic generation efficiency. Phy. Rev. L 103, 073902.Google Scholar
Shoucri, M. & Afeyan, B. (2010). Studies of the interaction of an intense laser beam normally incident on an overdense plasma. Laser Part. Beams 28, 129–147.Google Scholar
Shuai, B., Shen, B., Li, R. & Xu, Z. (2002). High-order harmonic generation in ultra thin plasma foil. Physica Scripta 65, 438–443.Google Scholar
Strelkov, V.V. (2006). Theory of high-order harmonic generation and attosecond pulse emission by a low-frequency elliptically polarized laser field. Phys. Rev. A 74, 013405.Google Scholar
Svelto, O. (1998). Principles of Lasers. New York: Springer.Google Scholar
Tripathi, D., Bhasin, L., Uma, R. & Tripathi, V.K. (2010). Nonstationary ponderomotive self-focusing of a Gaussian laser pulse in a plasma. Phy. Plasmas 17, 113113.Google Scholar
Yazdanpanah, J. & Anvary, A. (2012). Time and space extended particle in cell model for electromagnetic particle algorithms. Phys. Plasmas 19, 033110.Google Scholar
Wang, W.M., Li, Y.T., Sheng, Z.M., Lu, X. & Zhang, J. (2013). Terahertz radiation by two-color lasers due to the field ionization of gases. Phys. Rev. E 87, 033108.Google Scholar