Optik 156 (2018) 191–196 Contents lists available at ScienceDirect Optik j ourna l ho me pa ge: www.elsevier.de/ijleo Original research article Early and strong relativistic self-Focusing of cosh-Gaussian laser beam in cold quantum plasma Vikas Nanda a , Harjit Singh Ghotra b , Niti Kant b,∗ a Department of Education, Govt. of Himachal Pradesh, 176023, India b Department of Physics, Lovely Professional University, Phagwara, 144411, Punjab, India a r t i c l e i n f o Article history: Received 14 August 2017 Accepted 25 October 2017 Keywords: Self-focusing Decentered parameter cosh-Gaussian beam Relative density parameter a b s t r a c t Relativistic self-focusing of cosh-Gaussian laser beam in the cold quantum plasma has been investigated theoretically. For a decentered parameter b = 0.9, we present a comparative analysis for self-focusing of cosh-Gaussian laser beam in relativistic cold quantum (RCQ) and classical relativistic (CR) case. It is observed that as the beam penetrates deeper inside the RCQ plasma, the self-focusing ability of the laser beam enhances and shifted towards lower value of normalized propagation distance due to quantum contribution. The beam width parameter as a function of normalized propagation distance for various values of relative density parameter of the medium and intensity parameter has also been studied. The self-focusing is observed to be stronger with the increase in relative density parameter. Observation of early and strong self-focusing for higher values of relative density parameter and intensity parameter are reported. The present study might be very useful in the applica- tions like the generation of inertial fusion energy driven by lasers, laser driven accelerators, scribing type of applications in electronics etc. © 2017 Elsevier GmbH. All rights reserved. 1. Introduction In the year 1962, Askar’yan [1] discovered the self-focusing effect of light. Hora [2], Siegrist [3] etc. have the remarkable contribution in the field of relativistic self-focusing of light. Thereafter, it attracts the attention of researcher and turn out to be most charming field of research. Researchers studied self-focusing of laser beam in plasma [2–4], cluster [5,6], liquid [7] etc. using various beam profiles like Gaussian beam [4], Hermite-Gaussian beam [8], cosh-Gaussian beam [9], Hermite-cosh- Gaussian beam [10–15] etc. Self-focusing of light has many socially useful applications like x-ray lasers and the laser driven charged particle accelerations [16], the generation of inertial fusion energy [17–19] etc. which makes the life of human being quite easier. Short pulse laser having high intensity of the order of 10 17 − 10 20 W/cm 2 enabled various high energy related experiments in the field of science and technology. Self-focusing phenomenon in plasma arises as the laser light passes through the plasma and modifies the dielectric con- stant related to plasma. It may be relativistic or ponderomotive or thermal self-focusing in nature. Now a day, propagation of laser beam through cold plasma is widely studied by researcher because the quantum plasma systems have many useful applications. Rathore & Kumar [20], Kumar et al. [21], Bergamin [22] and many other researchers has studied nonlinear interaction in quantum plasma. Quantum plasma has high density and low temperature. Moreover, quantum plasma sys- ∗ Corresponding author. E-mail address: nitikant@yahoo.com (N. Kant). https://doi.org/10.1016/j.ijleo.2017.10.147 0030-4026/© 2017 Elsevier GmbH. All rights reserved.