We consider small perturbation in plasma to understand the concept of plasma oscillation.
We take perturbation in velocity, density and electric field.
que-1 how do we create this perturbation (with what frequency, voltage and how ?). want to understand with physical example.
que-2 we consider small perturbation, how can we quantify this ?
que -3 what will happen if we remove the given perturbation ?
Thank you in advance,
With kind regards,
Purvi
Q1.
For a simple physical example, you can think of this perturbation as slightly dipping your finger in a pool of perfectly still water. Before you touched it, the water had some constant pressure and density, and zero velocity. We call these values of the density, pressure and velocity the equilibrium (or background) values. When you dip your finger in, you introduce a small perturbation to the equilibrium values by changing the pressure, density and velocity around the surface your finger is in contact with the water.
Mathematically, we write this (for example, for the pressure) as P = P_0 + P_1, where P_0 is the equilibrium pressure, P_1 is the disturbance, and P_1
A small amplitude wave generally means that nonlinear terms can be neglected. It's a great advantage to have the plasma equations be linear, since then every plasma disturbance can be treated by Fourier-Laplace transformation, treating plasma quantities as sums of terms of with a single frequency and wavenumber (wavelength plus direction). This changes the plasma equations from differential equations to algebraic equations, which are much easier to handle.
A simple example is the divergence equation for plasma flow,
d/dt(n) + d/dz(nv) = 0
where d/dt mean partial derivatives. If the density n and velocity v
are the sum of an unperturbed and perturbed part,
n = n0 + n1
v = v0 + v1
with d/dt(n0) = 0, etc., the divergence equation turns into
d/dt(n1)+ + v0*d/dz(v1) + v1 * d/dz(n1) = 0
The last term in this equation is nonlinear, and has to be thrown away if Fourier methods are to be used. This is justified if n1
To study the basic characteristics of the plasma, we consider applying small perturbation to the system. This perturbation can be applied through mechanical means (say in dusty plasma) or by applying a small amplitude electrical signal. We consider this perturbation to be of small order in comparison to equilibrium value of the system parameters. If we remove the perturbation, then the system may come back to its equilibrium state.
The "small" perturbations mean only the lowest-order harmonics on the plasma parameters are excited. The squares, products, or higher-order contributions from the perturbations are negligibly small. It is immaterial of the fact whether "local" or "global" equilibria are considered for the next step of homology transformations.
Once the plasma is stable there will not be any perturbation in the values of plasma parameters. For the study of basic characteristics of plasma, small perturbation is applied in the plasma parameters that is very small in comparison to its equilibrium values. Such perturbations are generated in the plasma by applying a electrostatic force in plasma by a small electrical signal through a certain probe.
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