What is the impact of polarization drift on particle energy in plasma?

[sciboudy]

show that all of standred drifts only the polarization drift causes change in the particle energy
hint
consider what happen when following equation is dotted with velocity (v)
m(dv\dt)=f+(vxB)

where V and be cross product vector

 

[sciboudy]

i took it in plazma course i can't find answer tio this problem

 

[sciboudy]

i ca't understand the problem could anyone explain it to me and what this problem mean
what is dotted

 

[Clever-Name]

dot product. If you don't understand what a dot product is you probably shouldn't be taking a course on plasma physics.

 

[paranormal]

The polarization drift is a type of drift motion that occurs in plasma due to the presence of an external electric field. It is caused by the interaction between charged particles and the electric field, resulting in a force that causes the particles to drift. This drift motion can have a significant impact on the energy of the particles in the plasma.

When the equation m(dv/dt) = f + (v x B) is dotted with the velocity (v), we get:

m(dv/dt)•v = f•v + (v x B)•v

The first term on the right-hand side, f•v, represents the work done by the external force on the particle. This term does not contribute to any change in the particle's energy as it only affects its velocity. However, the second term, (v x B)•v, represents the work done by the magnetic field on the particle. This term can contribute to a change in the particle's energy as it is perpendicular to the particle's velocity and can thus do work on the particle to change its kinetic energy.

In the case of polarization drift, the electric field is perpendicular to both the velocity and magnetic field, resulting in a force that is also perpendicular to the velocity. This means that the work done by the electric field, (v x E)•v, is also perpendicular to the particle's velocity and can contribute to a change in its energy.

Therefore, the polarization drift can cause a change in the particle's energy by doing work on it through the electric field. This is in contrast to other drift motions, such as the E x B drift, which do not result in a change in the particle's energy.

In conclusion, the polarization drift is the only drift motion that can directly cause a change in the particle's energy in plasma. This is due to the perpendicular nature of the force from the electric field, which can do work on the particle and change its energy. This is an important consideration in understanding the dynamics of particles in plasma and their energy exchange processes.