Linearization is a simplification to avoide complexities arise due to the presence of nonlinear terms. Most times linearization provides only leading order terms.

Dear Purvi Kikani,

I agree with Oleg Berngardt. I would like to add something else related to linearization. In overall, plasmas are unstable systems. As you know different types of instabilities occur. They can be discerned in its initial phase. At this stage it is easily to understand the parameters that govern that instability – e.g. plasma-beam densities and/or their ratio, plasma velocity, magnetic field strength, plasma and/or field gradients, etc. This is done by linearizing the governing equations, i.e. introducing infinitesimal perturbations. Note, linearization also helps in studying/understanding the pattern formation processes in non-linear systems.

Petko Nenovski

When we apply Fourier Transform on some expression, then its degree get reduced by the order of one. We linearize the expression of plasma waves, so that when we apply the Fourier Transform then its degree is reduced from one to zero (simple algebraic equation ) which are very easier to solve.

I agree to all of the above. Please note that in the case of instabilities OR in the cases where the dielectric function from the linear solution tends to infinity the non-linearities are introduced "selectively" so the extra complexity to become manageable !!!

Dear Dr. Purvi Kikani, in Landau & Lifshits Vol. 8 on the electrodynamics of continuous media, in the chapter on magnetohydrodynamics, the linearization of the set of MHD equations allows solving in detail the Alfvén mode, and the 2 magnetosonic (mw) slow and fast modes.

Otherwise, there will be a set of 9 roots for the general eigenvalue equation.

This linearization allows small reversible adiabatic perturbation to the equilibrium values for the density, pressure and magnetic field H.