Managing the Rayleigh–Taylor instability growth rate is one of the main challenges in inertial fusion. Among the proposed methods to tackle this issue, the application of a pre-embedded axial magnetic field and plasma density gradient of layers can be mentioned. Recent experimental evidence in Z-pinch devices shows that it is possible to suppress the growth rate of the Rayleigh-Taylor instability by applying a power law density gradient profile with exponent 2. In this work, in the framework of Cartesian coordinates, for a confined plasma between two fixed planes, the dispersion relation of a magnetized plasma has been obtained using linearization of the ideal MHD equations. Here, plasma with a power-law density profile of ∝r3 and magnetic field with the exponential profile is used. It is shown that for the relative strength of the magnetic field with a value of, ωf*=0.4 and more, the growth rate of instability appears only in a limited range of the range of reduced wave numbers, k*. By increasing this ratio, stability conditions are much improved. On the other hand, recent experimental studies show that self-generated plasma rotation is produced in an imploding Z-pinch device with an initial axial magnetic field. In the second part, the effect of plasma rotation on plasma stability conditions is investigated. Again, a new dispersion relation of the rotating magnetized plasma was derived. It is shown that in the non-magnetized case, a large relative angular velocity, Ω, is necessary to suppress the instability. However, for relative magnetic field strength, ωf*=0.4 and more, stable conditions can be achieved with a relatively lower angular velocity of about 5.
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