The term "electrostatic ion cyclotron" refers to a type of plasma wave that arises due to the interaction between ions and an electrostatic field in a magnetized plasma. This wave is closely related to the ion cyclotron wave, but it differs in that it involves only the electrostatic component of the field, neglecting the magnetic field component.

ELI5: Imagine you have a bunch of tiny magnets floating around, and you have a really strong magnet nearby. When the tiny magnets move, they start spinning around because of the big magnet's pull. It's like they're dancing around the big magnet.

Now, imagine there's also an invisible force that pushes and pulls the tiny magnets. This force makes them move back and forth, but only in one direction, like they're jumping up and down. This jumping motion happens because of the invisible force interacting with the spinning motion caused by the big magnet.

In a similar way, in a special kind of gas called a plasma, there are small particles called ions that act like the tiny magnets. They can also spin around in circles because of a magnetic field. But here's the interesting part: if there's an electric field, which is like the invisible force, it can make the ions move back and forth, but only in one direction, like they're jumping up and down.

So, the electrostatic ion cyclotron is when the ions in the plasma spin around in circles because of the magnetic field, and they also move back and forth in one direction because of the electric field. It's like a dance where the ions spin and jump at the same time, and scientists study this dance to understand how the plasma works.

Electrostatic ion cyclotron wave nearly perpendicular to B

Let us consider infinite and Bo constant and uniform and vo = Eo = 0 and Ti =0. Also, we assume

We consider (π/2 - 𝜃 ) to be very small and

If 𝜃 is not exactly π/2, the electrons can move along the dashed line. Po carry charge from positive to negative regions in the wave and carry out Debye shield which the ions cannot do it effectively. Since their inertia prevent moving such a long disatance in a wave period, thus we can neglect kz for ions.

The equation of motion for ions is

The equation of continuity is

For linearization, we obtain

n_o = Eo = 0 and Ti =0

Also Vi = Vo + V1, E = Eo + E1

Equation 4 gives

M ( ∂Vi/∂t ) = e( Ei + Vi x Bo) .....6

x component

y component

z component

The oscillating quantities are assumed to behave sinusoidally as

If Electric field is along x axis such that E = - ∇𝜙

E1 = - ik𝜙x = - ik𝜙1 ......13

From 7,8,10,12,13

Combining equation 14 and 15 we get

Now, from equation 5

For electron, we assume Boltzmann distribution

By plasma approximation

which is ion acoustic velocity.

The ion acoustic velocity squared represents the speed at which small perturbations in the ion density propagate through the plasma, as discussed in the previous response.
The square of the ion cyclotron frequency Ω represents the characteristic frequency at which ions gyrate around magnetic field lines in a plasma.
The square of the wave vector k represents the spatial frequency or wavenumber squared associated with the propagating wave in the plasma.
Square of the Electron Thermal Velocity vs represents the average thermal velocity of the electrons in the plasma.

This relationship indicates that the square of the wave frequency is equal to the sum of the squares of the ion cyclotron frequency, the wave vector, and the electron thermal velocity.

This equation is known as the dispersion relation for ion acoustic waves in a magnetized plasma. It describes the relationship between the wave frequency, wave vector, and the plasma parameters such as ion charge, ion mass, ion density, magnetic field strength, and electron temperature. By analyzing this dispersion relation, one can determine the behaviour and properties of ion acoustic waves in the plasma, including their phase velocity, group velocity, and stability conditions.

This note is taken from Plasma, Msc physics, Nepal.

This note is a part of the Physics Repository.

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