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Effect of q Parameter and Critical Beam Radius on Propagation Dynamics of q Gaussian Beam in Cold Quantum Plasma

Part of the Springer Proceedings in Complexity book series (SPCOM)


The q Gaussian intensity distribution is very interesting as in the limit \( q \rightarrow \infty \), it reduces to the Gaussian intensity profile. Naturally, the freedom of exploring the q exponent enables us to study a wide range of propagation dynamics. The quantum plasma offers wide possibilities of its existence right from astrophysical situations to laboratory plasmas. Keeping in mind the wide applicability domain of cold quantum plasma, we have theoretically investigated the propagation behavior of q Gaussian laser beam in cold quantum plasma. The ordinary nonlinear differential equation is set up by following Akhmanov’s parabolic equation approach under WKB and paraxial approximations. The effect of the q parameter on the critical curve is explored graphically. The variation in the beam width parameter f over normalized distance \(\zeta \) due to variation in the q-parameter is graphically depicted and discussed at the end. It is observed that the supercritical region and self focusing length are affected by the q parameter significantly.


  • q-Gaussian
  • Cold quantum plasma
  • Critical beam radius
  • Self focusing

Supported by DST-SERB, New Delhi, the Special Assistance Program (SAP), Department of Physics, Shivaji University, Kolhapur.

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Correspondence to P. T. Takale .

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Takale, P.T. et al. (2022). Effect of q Parameter and Critical Beam Radius on Propagation Dynamics of q Gaussian Beam in Cold Quantum Plasma. In: Banerjee, S., Saha, A. (eds) Nonlinear Dynamics and Applications. Springer Proceedings in Complexity. Springer, Cham.

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