• Mukesh Kumar

      Articles written in Pramana – Journal of Physics

    • X-ray diffraction analysis and occurrence of multiple phases in Bi-Sr-Ca-Cu-O superconductors

      N D Kataria Mukesh Kumar V S Tomar V N Ojha G S N Reddy K C Nagpal A K Gupta

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      Starting composition 1112 for Bi-Sr-Ca-Cu-oxide yields multiphase super-conductors with the proportion of constituent phases depending sensitively on the annealing temperature. The R-T curves show zero resistivity and the transition corresponding toTc = 80 K phase prominently. However, indexing of X-ray diffraction peaks reveals presence of 80 K (lowTc) as well as 108 K (highTc) phase. The lowTc phase thus corresponds to the orthorhombic structure with a unit cell ofa = 5.4Å,b = 27 Å andc = 30.56 Å. This is further understood to be composed of a pseudotetragonal cell ofa =b = 5.41 Å. The highTc phase similarly pertains to the orthorhombic structure withc = 36 Å.

    • Gauss law constraints on Debye–Hückel screening

      Ritesh Kumar Dubey V J Menon Madhukar Mishra Mukesh Kumar Pandey B K Patra

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      We demand that the Gauss law at the edge must be obeyed by the electric potential $\phi(r)$ generated within a neutral plasma/electrolyte of strictly finite size by the introduction of a test charge $q_{b}$. Our proposal has the nice features that total ionic numbers are conserved, the point-Coulomb behaviour of $\phi(r)$ is guaranteed at short-distance, and accumulation of induced charges near the centre and the surface can be demonstrated rigorously. In contrast, the standard Debye–Hückel potential $\phi_{D}(r)$ applicable to unbounded plasma has the strange features that the Gauss law cannot be obeyed at the plasma's edge, total ionic numbers themselves are altered, the short-distance Coulomb behaviour has to be imposed by hand, and induced charge appearance at the surface cannot be built-in.

    • Some invariant solutions for non-conformal perfect fluid plates in 5-flat form in general relativity

      Mukesh Kumar Y K Gupta

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      A set of six invariant solutions for non-conformal perfect fluid plates in 5-flat form is obtained using one-parametric Lie group of transformations. Out of the six solutions so obtained, three are in implicit form while the remaining three could be expressed explicitly. Each solution describes an accelerating fluid distribution and is new as far as authors are aware.

    • Hybrid recoil mass analyzer at IUAC – First results using gas-filled mode and future plans

      N Madhavan S Nath T Varughese J Gehlot A Jhingan P Sugathan A K Sinha R Singh K M Varier M C Radhakrishna E Prasad S Kalkal G Mohanto J J Das Rakesh Kumar R P Singh S Muralithar R K Bhowmik A Roy Rajesh Kumar S K Suman A Mandal T S Datta J Chacko A Choudhury U G Naik A J Malyadri M Archunan J Zacharias S Rao Mukesh Kumar P Barua E T Subramanian K Rani B P Ajith Kumar K S Golda

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      Hybrid recoil mass analyzer (HYRA) is a unique, dual-mode spectrometer designed to carry out nuclear reaction and structure studies in heavy and medium-mass nuclei using gas-filled and vacuum modes, respectively and has the potential to address newer domains in nuclear physics accessible using high energy, heavy-ion beams from superconducting LINAC accelerator (being commissioned) and ECR-based high current injector system (planned) at IUAC. The first stage of HYRA is operational and initial experiments have been carried out using gas-filled mode for the detection of heavy evaporation residues and heavy quasielastic recoils in the direction of primary beam. Excellent primary beam rejection and transmission efficiency (comparable with other gas-filled separators) have been achieved using a smaller focal plane detection system. There are plans to couple HYRA to other detector arrays such as Indian national gamma array (INGA) and $4\pi$ spin spectrometer for ER tagged spectroscopic/spin distribution studies and for focal plane decay measurements.

    • Measurement of nonlinear refractive index in open-aperture 𝑍-scan experiments

      Ritwick Das Mukesh Kumar Shukla

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      We present an experimental study on measurement of nonlinear refractive index ($n_2$) of organic liquids when the thermo-optic effects manifest into large nonlinear phase shifts ($\Delta\phi_0$) in an open-aperture 𝑍-scan configuration. Although we do not obtain the familiar peak–valley normalized transmittance curve as in the case of closed-aperture 𝑍-scan technique, we use a theoretical model using Gaussian beam decomposition (GD) technique to estimate the value of $n_2$. Using this recipe, we obtain the nonlinear refractive index $n_2 = −(4.90 \pm 1.20) \times 10^{−15}$ cm2/W for toluene (organic solvent) and $n_2 = −(10.60 \pm 2.10) \times 10^{−15}$ cm2/W for an organic polymer solution (10$^{−4}$ Min toluene). By carrying out absorption measurements directly with an unfocussed Gaussian beam, we found nonlinear absorptions $\beta_{\text{tol}} = (2.42 \pm 0.20) \times 10^{−13}$ m/W and $\beta_{\text{poly}} = (2.79 \pm 0.24) \times 10^{−13}$ m/W which are close to the expected results.

    • Lie symmetries and invariant solutions of (2 + 1)-dimensional breaking soliton equation


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      The present article deals with the symmetry reductions and invariant solutions of breaking soliton equation by virtue of similarity transformation method. The equation represents the collision of a Riemann wave propagating along the $y$-axis with a long wave along the $x$-axis. The infinitesimal transformations under one parameter for the governing system have been derived by exploiting the invariance property of Lie group theory. Consequently, the number of independent variables is reduced by one and the system remains invariant. A repeated application transforms the governing system into systems of ordinary differential equations. These systems degenerate well-known soliton solutions under some limiting conditions. The obtained solutions are extended with numerical simulation resulting in dark solitons, lumps, compactons, multisolitons, stationary and parabolic profiles and are shown graphically.

    • Computational soliton solutions to (2 + 1)-dimensional Pavlov equation using Lie symmetry approach


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      In this work, Lie symmetry analysis and one-dimensional optimal system for Pavlov equation are presented. All the possible vector fields, their commutative and adjoint relations are carried out under invariance property of Lie group theory. On the basis of optimal system, similarity reductions of Pavlov equation are obtained. A repeated process of similarity reductions transforms the Pavlov equation into ordinary differential equations, which generate invariant solutions. The obtained invariant solutions are supplemented by numerical simulation toanalyse the physical behaviour. Thus, their parabolic, multisoliton, nonlinear, kink and antikink wave profiles are traced in results and discussions sections.

    • Electromagnetic design of 325 MHz superconducting single-spoke resonators for Indian Facility for Spallation Research


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      We present an electromagnetic design of 325 MHz superconducting single-spoke resonators (SSRs) to accelerate the H$^−$ ions from 3 to ∼160 MeV for the proposed Indian Facility for Spallation Research project. The geometrical parameters of SSRs have been optimised to maximise the achievable acceleration gradient, and to minimise the multipacting growth rate, keeping a reasonably low value of heat dissipation on the cavity surface. For the geometrical optimisation of SSR cavities, we followed a one-dimensional procedure, where we vary and fix the geometrical parameters one by one in a sequential manner. We explain the behaviour of various RF parameters of the SSR with respect to its geometrical parameters, based on which the optimum value of each of the geometricalparameters has been chosen. For the optimised geometry of SSRs, we performed the higher-order mode (HOM) analysis and estimated the transverse and longitudinal kicks imparted to the beam by HOMs. The effect of azimuthala symmetry of the electromagnetic field is also analysed and presented for the adopted design. A holistic design approach is described in the paper that addresses the interlinked optimisation requirements.

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