Journal of Nuclear Science, Engineering and Technology (JONSAT)
In cooperation with the Iranian Nuclear Society

The effect of rotation on the growth rate of magnetic Rayleigh-Taylor instability in stratified plasma with power-law density profile

Document Type : Research Paper

Authors

M.A. Masoumparast
S. Khoshbinfar

Department of Physics, Faculty of Basic Sciences, Gilan University, P, P.O.BOX: 41635-1914, Rasht – Iran

https://doi.org/10.24200/nst.2024.1586
Abstract
In this research, the effect of simultaneous application of plasma rotation and static external magnetic field in a plasma with a power law density function on the growth rate of Rayleigh-Taylor instability (RTI) has been studied analytically. Plasma is incompressible and enclosed between two planes z=0 and z=h. In a linear growth rate regime, the dispersion relation for the ideal MHD equations was first derived by applying the rotation effect and appropriate boundary conditions. The final dispersion relation represents the effect of the simultaneous combination of the axial magnetic field and the constant angular velocity of the plasma on the RTI growth rate. The results show that the growth rate of instability depends on the horizontal component of the magnetic field, the plasma rotation, and also on the dimensionless parameter λ*. The maximum instability occurs at *=-1.5 compared to the corresponding non-rotational case. Recent results show that the simultaneous combination of rotation and static external magnetic field improves the management of instability growth rate.

Highlights

  1. Sharma P.K, Tiwari A, Argal S, Chhajlani P.K. Rayleigh Taylor instability of two superposed compressible fluids in un-magnetized plasma. Journal of Physics. 2014;534(1):012054.

 

  1. Atzeni S, Meyer-ter-vehn J. The Physics of Inertial Fusion. Oxford: Clarendon Press. 2004;(4-6, 11-13, 33-36, 38-41, 76, 389, 399).

 

  1. Betti R, Umansky M, Lobatchev V, Goncharov V.N, McCrory R.L. Hot-spot dynamics and deceleration-phase Rayleigh-Taylor instability of imploding inertial confinement fusion capsules. Physics of Plasmas. 2001;8(12):5257.

 

  1. Basko M.M. New developments in the theory of ICF targets and fast ignition with heavy ions. Plasma physics and controlled fusion. 2003;45(12A),A125.

 

  1. Yang B.L, Wang L.F, Ye W.H, Xue C. Magnetic Field Gradient Effects on Rayleigh-Taylor Instability with Continuous Magnetic Field and Density Profiles. Physics of Plasmas. 2011;18:072111.

 

  1. Dolai B, Prajapati R.P. The rotating Rayleigh-Taylor instability in a strongly coupled dusty plasma. Physics of Plasmas. 2018;25(8):083708.

 

  1. Walsh C.A, O'Neill S, Chittenden J.P, Crilly A.J, Appelbe B, Strozzi D.J, Ho D, Sio H, Pollock B, Divol L, Hartouni E, Rosen M, Logan B.G, Moody J.D. Magnetized ICF implosions: Scaling of temperature and yield enhancement. Physics of Plasmas. 2022;29(4):042701.

 

  1. Walsh C.A, Florido R, Bailly-Grandvaux M, Suzuki-Vidal F, Chittenden J.P, Crilly A.J, Gigosos M.A, Mancini R.C, Pérez-Callejo G, Vlachos C, McGuffey C, Beg F.N, Santos J.J. Exploring extreme magnetization phenomena in directly driven imploding cylindrical targets. Plasma Physics and Controlled Fusion. 2022;64(2):025007.

 

  1. Velikovich A.L, Cochran F.L, Davis J. Suppression of Rayleigh-Taylor instability in Z-pinch loads with tailored density profiles. Physical Review Letters. 1996;77(5):853.

 

  1. Velikovich A.L, Cochran F.L, Davis J. Stabilized Z-pinch loads with tailored density profiles. AIP Conference Proceedings. 1997;409(1):549.

 

  1. Oreshkin V.I, Baksht R.B, Cherdizov R.K, Oreshkin E.V, Ratakhin N.A, Rousskikh A.G, Shishlov A.V, Vankevich V.A, Zhigalin A.S. Studies on the implosion of pinches with tailored density profiles. Plasma Physics and Controlled Fusion. 2021;63(4):045022.

 

  1. Khoshbinfar S. In: The 3rd Conference of plasma engineering and plasma Physics. (UT, Tabriz, Iran). 2015;316-319:[In Persian].

 

  1. Baldwin K.A, Scase M.M, Hill R.J. The inhibition of the Rayleigh-Taylor instability by rotation. Scientific Reports. 2015;5(1):1.

 

  1. Scase M.M, Baldwin K.A, Hill R.J. Rotating rayleigh-taylor instability. Physical Review Fluids. 2017;2(2):024801.

 

  1. Sharma P.K, Tiwari A, Argal S. Effect of magnetic field on the Rayleigh Taylor instability of rotating and stratified plasma. Journal of Physics: Conference Series. 2017;836(1):012009.

 

  1. Scase M.M, Hill R.J. Centrifugally forced Rayleigh–Taylor instability. Journal of Fluid Mechanics. 2018;852:543.

 

  1. Scase M.M, Baldwin K.A, Hill R.J. Magnetically induced Rayleigh-Taylor instability under rotation: Comparison of experimental and theoretical results. Physical Review E. 2020;102(4):043101.

 

  1. Samulski C, Srinivasan B, Manuel M.J.E, Masti R, Sauppe J.P, Kline J. Deceleration-stage Rayleigh–Taylor growth in a background magnetic field studied in cylindrical and Cartesian geometries. Matter and Radiation at Extremes. 2022;7(2):026902.

 

  1. Hoshoudy G.A. Rayleigh-Taylor Instability in Magnetized Plasma. World Journal of Mechanics. 2014;4:260.

 

  1. Slutz S.A, Herrmann M.C, Vesey R.A, AB Sefkow A.B, Sinars D.B, Rovang D.C, Peterson K.J, Cuneo M.E. Pulsed-power-driven cylindrical liner implosions of laser preheated fuel magnetized with an axial field. Physics of Plasmas. 2010;17(5): 056303.

 

  1. Cvejić M, Mikitchuk D, Kroupp E, Doron R, Sharma P, Maron Y, Velikovich A.L, Fruchtman A, Ochs I.E, Kolmes E.J, Fisch N. J. Self-generated plasma rotation in a Z-pinch implosion with preembedded axial magnetic field. Physical Review Letters. 2022;128(1):015001.

 

  1. Huneault J, Plant D, Higgins A.J. Rotational stabilisation of the Rayleigh–Taylor instability at the inner surface of an imploding liquid shell. Journal of Fluid Mechanics. 2019;873:531.

 

  1. Freidberg J.P. Plasma Physics and Fusion Energy. New York: Cambridge University Press. 2008;(3-30,139-222, 245-328).

 

  1. Masoumparast M.A, Khoshbinfar S. Stabilization of Magneto-Rayleigh-Taylor instability in a Plasma with Power density Gradient. Journal of Nuclear Science and Technology. Accepted (DOI: 10.24200/nst.2023.1285.1836) [In Persian].

Keywords

Plasma rotation
Axial magnetic field
Ideal MHD equations
Power law density gradient
Magnetic Rayleigh-Taylor instability
  1. Sharma P.K, Tiwari A, Argal S, Chhajlani P.K. Rayleigh Taylor instability of two superposed compressible fluids in un-magnetized plasma. Journal of Physics. 2014;534(1):012054.

 

  1. Atzeni S, Meyer-ter-vehn J. The Physics of Inertial Fusion. Oxford: Clarendon Press. 2004;(4-6, 11-13, 33-36, 38-41, 76, 389, 399).

 

  1. Betti R, Umansky M, Lobatchev V, Goncharov V.N, McCrory R.L. Hot-spot dynamics and deceleration-phase Rayleigh-Taylor instability of imploding inertial confinement fusion capsules. Physics of Plasmas. 2001;8(12):5257.

 

  1. Basko M.M. New developments in the theory of ICF targets and fast ignition with heavy ions. Plasma physics and controlled fusion. 2003;45(12A),A125.

 

  1. Yang B.L, Wang L.F, Ye W.H, Xue C. Magnetic Field Gradient Effects on Rayleigh-Taylor Instability with Continuous Magnetic Field and Density Profiles. Physics of Plasmas. 2011;18:072111.

 

  1. Dolai B, Prajapati R.P. The rotating Rayleigh-Taylor instability in a strongly coupled dusty plasma. Physics of Plasmas. 2018;25(8):083708.

 

  1. Walsh C.A, O'Neill S, Chittenden J.P, Crilly A.J, Appelbe B, Strozzi D.J, Ho D, Sio H, Pollock B, Divol L, Hartouni E, Rosen M, Logan B.G, Moody J.D. Magnetized ICF implosions: Scaling of temperature and yield enhancement. Physics of Plasmas. 2022;29(4):042701.

 

  1. Walsh C.A, Florido R, Bailly-Grandvaux M, Suzuki-Vidal F, Chittenden J.P, Crilly A.J, Gigosos M.A, Mancini R.C, Pérez-Callejo G, Vlachos C, McGuffey C, Beg F.N, Santos J.J. Exploring extreme magnetization phenomena in directly driven imploding cylindrical targets. Plasma Physics and Controlled Fusion. 2022;64(2):025007.

 

  1. Velikovich A.L, Cochran F.L, Davis J. Suppression of Rayleigh-Taylor instability in Z-pinch loads with tailored density profiles. Physical Review Letters. 1996;77(5):853.

 

  1. Velikovich A.L, Cochran F.L, Davis J. Stabilized Z-pinch loads with tailored density profiles. AIP Conference Proceedings. 1997;409(1):549.

 

  1. Oreshkin V.I, Baksht R.B, Cherdizov R.K, Oreshkin E.V, Ratakhin N.A, Rousskikh A.G, Shishlov A.V, Vankevich V.A, Zhigalin A.S. Studies on the implosion of pinches with tailored density profiles. Plasma Physics and Controlled Fusion. 2021;63(4):045022.

 

  1. Khoshbinfar S. In: The 3rd Conference of plasma engineering and plasma Physics. (UT, Tabriz, Iran). 2015;316-319:[In Persian].

 

  1. Baldwin K.A, Scase M.M, Hill R.J. The inhibition of the Rayleigh-Taylor instability by rotation. Scientific Reports. 2015;5(1):1.

 

  1. Scase M.M, Baldwin K.A, Hill R.J. Rotating rayleigh-taylor instability. Physical Review Fluids. 2017;2(2):024801.

 

  1. Sharma P.K, Tiwari A, Argal S. Effect of magnetic field on the Rayleigh Taylor instability of rotating and stratified plasma. Journal of Physics: Conference Series. 2017;836(1):012009.

 

  1. Scase M.M, Hill R.J. Centrifugally forced Rayleigh–Taylor instability. Journal of Fluid Mechanics. 2018;852:543.

 

  1. Scase M.M, Baldwin K.A, Hill R.J. Magnetically induced Rayleigh-Taylor instability under rotation: Comparison of experimental and theoretical results. Physical Review E. 2020;102(4):043101.

 

  1. Samulski C, Srinivasan B, Manuel M.J.E, Masti R, Sauppe J.P, Kline J. Deceleration-stage Rayleigh–Taylor growth in a background magnetic field studied in cylindrical and Cartesian geometries. Matter and Radiation at Extremes. 2022;7(2):026902.

 

  1. Hoshoudy G.A. Rayleigh-Taylor Instability in Magnetized Plasma. World Journal of Mechanics. 2014;4:260.

 

  1. Slutz S.A, Herrmann M.C, Vesey R.A, AB Sefkow A.B, Sinars D.B, Rovang D.C, Peterson K.J, Cuneo M.E. Pulsed-power-driven cylindrical liner implosions of laser preheated fuel magnetized with an axial field. Physics of Plasmas. 2010;17(5): 056303.

 

  1. Cvejić M, Mikitchuk D, Kroupp E, Doron R, Sharma P, Maron Y, Velikovich A.L, Fruchtman A, Ochs I.E, Kolmes E.J, Fisch N. J. Self-generated plasma rotation in a Z-pinch implosion with preembedded axial magnetic field. Physical Review Letters. 2022;128(1):015001.

 

  1. Huneault J, Plant D, Higgins A.J. Rotational stabilisation of the Rayleigh–Taylor instability at the inner surface of an imploding liquid shell. Journal of Fluid Mechanics. 2019;873:531.

 

  1. Freidberg J.P. Plasma Physics and Fusion Energy. New York: Cambridge University Press. 2008;(3-30,139-222, 245-328).

 

  1. Masoumparast M.A, Khoshbinfar S. Stabilization of Magneto-Rayleigh-Taylor instability in a Plasma with Power density Gradient. Journal of Nuclear Science and Technology. Accepted (DOI: 10.24200/nst.2023.1285.1836) [In Persian].

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