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Lihua Cao

Publications and source records attributed to Lihua Cao.

6 recordsLinked to original sources
arXiv2022

Investigation of Langdon effect on the nonlinear evolution of SRS from the early-stage inflation to the late-stage development of secondary instabilities

In a laser-irradiated plasma, the Langdon effect can result in a super-Gaussian electron energy distribution function (EEDF), imposing significant influences on the stimulated backward Raman scattering (SRS). In this work, the influence of a super-Gaussian EEDF on the nonlinear evolution of SRS is investigated by three wave model simulation and Vlasov-Maxwell simulation for plasma parameters covering a wide range of kλDe from 0.19 to 0.48 at both high and low intensity laser drives. In the early-stage of SRS evolution, it is found that besides the kinetic effects due to electron trapping [Phys. Plasmas 25, 100702 (2018)], the Langdon effect can also significantly widen the parameter range for the absolute growth of SRS, and the time for the absolute SRS to reach saturation is greatly shorten by Langdon effect within certain parameter region. In the late-stage of SRS, when secondary instabilities such as decay of the electron plasma wave to beam acoustic modes, rescattering, and Langmuir decay instability become important, the Langdon effect can influence the reflectivity of SRS by affecting the secondary processes. The comprehension of Langdon effect on nonlinear evolution and saturation of SRS would contribute to a better understanding and prediction of SRS in inertial confinement fusion.

physics.plasm-ph↗
arXiv2021

Bivariate Lagrange interpolation at the checkerboard nodes

In this paper, we derive an explicit formula for the bivariate Lagrange basis polynomials of a general set of checkerboard nodes. This formula generalizes existing results of bivariate Lagrange basis polynomials at the Padua nodes, Chebyshev nodes, Morrow-Patterson nodes, and Geronimus nodes. We also construct a subspace spanned by linearly independent bivariate vanishing polynomials that vanish at the checkerboard nodes and prove the uniqueness of the set of bivariate Lagrange basis polynomials in the quotient space defined as the space of bivariate polynomials with a certain degree by the subspace of bivariate vanishing polynomials.

math.CA↗
arXiv2021

Collective stimulated Brillouin scattering modes of two crossing laser beams with shared ion acoustic wave

The overlapping of multiple beams is common in inertial confinement fusion (ICF), making the collective stimulated Brillouin scattering (SBS) with shared ion acoustic wave (IAW) potentially important because of the effectively larger laser intensities to drive the instability. In this work, based on a linear kinetic model, an exact analytic solution for the convective amplification of SBS with the shared IAW modes stimulated by two overlapped beams is presented. From this solution, effects of the wavelength difference, crossing angle, polarization states, and finite beam overlapping volume of the two laser beams on the shared IAW modes are studied. It is found that a wavelength difference of several nanometers between the laser beams has negligible effects, except for a very small crossing angle about one degree. However, the crossing angle, beam polarization states, and finite beam overlapping volume can have significant influences on the shared IAW modes. Furthermore, the out-of-plane modes, in which the wavevectors of daughter waves lie in the different planes from the two overlapped beams, are found to be important for certain polarization states and crossing angles of the laser beams with the finite beam overlapping volume. This work is helpful to comprehend and estimate the collective SBS with shared IAW in ICF experiments.

physics.plasm-ph↗
arXiv2015

Proton beams with controlled divergence and concentrated energy in TNSA regime by USUI laser pulse interaction with a tailored hole-target

An improved acceleration scheme to produce protons with controlled divergence and concentrated energy density is studied using ultrashort ultraintense (USUI) laser pulse interaction with a tailored hole-target in target normal sheath acceleration (TNSA) regime. Two-dimension-in-space and three-dimension-in-velocity (2D3V) particle-in-cell (PIC) simulations show that the tailored hole-target helps to reshape the sheath electric field and generate a transverse quasistatic electric field of $TV/m$ along the inner wall of the hole. The transverse electric field suppresses the transverse expansion of the proton beam effectively, as it tends to force the produced protons to focus inwards to the central axis, resulting in controlled divergence and concentrated energy density compared with that of a single plain target. The dependence of proton beam divergence and energy feature on depth of the hole is investigated in detail. A rough estimation of the hole depth ranges depending on $a_{0}$ of the incident laser is also given.

physics.plasm-ph↗
arXiv2014

Linear Difference Equations with a Transition Point at the Origin

A pair of linearly independent asymptotic solutions are constructed for the second-order linear difference equation {equation*} P_{n+1}(x)-(A_{n}x+B_{n})P_{n}(x)+P_{n-1}(x)=0, {equation*} where $A_n$ and $B_n$ have asymptotic expansions of the form {equation*} A_n\sim n^{-θ}\sum_{s=0}^\infty\frac{α_s}{n^s},\qquad B_n\sim\sum_{s=0}^\infty\frac{β_s}{n^s}, {equation*} with $θ\neq0$ and $α_0\neq0$ being real numbers, and $β_0=\pm2$. Our result hold uniformly for the scaled variable $t$ in an infinite interval containing the transition point $t_1=0$, where $t=(n+τ_0)^{-θ} x$ and $τ_0$ is a small shift. In particular, it is shown how the Bessel functions $J_ν$ and $Y_ν$ get involved in the uniform asymptotic expansions of the solutions to the above three-term recurrence relation. As an illustration of the main result, we derive a uniform asymptotic expansion for the orthogonal polynomials associated with the Laguerre-type weight $x^α\exp(-q_mx^m)$, $x>0$, where $m$ is a positive integer, $α>-1$ and $q_m>0$.

math.CA↗