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Chapter#3: Plasma as Fluid

All Short Questions of Plasma as Fluid for the book Plasma Physics for BS/MSc Physics students.

Q.3.1 Why Lorentz force is called as collision drag force?

Answer: Because ions and electrons that present in a system and collide with each other. Electrons and ions attract each other due to their collision ion change their path. Due to change in path of ions momentum will also change and momentum losses is small then we cannot avoid the momentum loss. Therefore, Lorentz force is called as collision drag force.

    \[F_{total}=-eE-e\left(\vec{V}\times\vec{B}\right)-vm\vec{V}\]

Q.3.2 What are the macroscopic parameters of particles in plasma?

Answer: There are following macroscopic parameters of particles are such as density, mass of the particle (M), charge of particle (+e), drift velocity \left(\vec{V}\right) and temperature (T).

Q.3.3 What are the things which are measured by equation of motion and equation of continuity?

Answer: We must know the velocity and density of a particles of plasma. Velocity calculated by equation of motion and density calculated by equation of continuity. Particle flux changes which is fe+∆fe. This is due to changing of density and velocity of particles.

Q.3.4 Write down four Maxwell’s equation for VACUUM?

Answer: There are following Maxwell’s equation for Vacuum.

  • ∈°∇.E= σ →1
  • \overline{\nabla}.\overline{E}=-B\rightarrow\left(2\right)
  • \overline{\nabla}.\overline{B}=0\rightarrow(3)
  • \overline{\nabla}\times\overline{B}=μ°J+∈°E→(4)

Q.3.5 Why we consider plasma as a fluid?

Answer: We study plasma as a whole system. For example fluid, Basically we check the response of electric field and magnetic field by using the fluid model. Therefore, plasma is considered as a fluid (ions, electrons and neutral particles).

Q.3.6 Write down the equation of diamagnetic drift and explain it.

Answer: Diamagnetic drift, V_D=\frac{-\nabla p\times B}{qnB^2}. It means that diamagnetic drift is perpendicular to the direction of gradient.

Q.3.7 Differentiate between the applied and perturb magnetic field.

Answer:

Applied magnetic field: Basically electrostatic field may contain some magnetic field. When magnetic field is from external then it is called as applied magnetic field.

Perturb magnetic field: But when generate by itself without applying any field is called as perturb magnetic field.

Q.3.8 Write down the equation of motion according to dimension of fluid drift parallel to magnetic field.

Answer: When fluid drift is parallel to \vec{B} only one dimension is considered which is Z – component. Equation of motion is;

    \[mn\left[\frac{\partial V_z}{\partial t}+\left(V_z.\nabla\right)V_z\right]=qn\left(E_z+V_xB_z\right)-\frac{\partial P_z}{\partial z}\]

Here,

    \[V\times B_z=0\]

    \[\because V\times B=VBsin\theta\]

    \[\because\theta=0\]

    \[V\times B=VBsin\ 0^o\]

    \[V\times B=0\]

    \[\frac{\partial V_z}{\partial t}\ \gg\left(V_z.\nabla\right)V_z\]

Then,

    \[mn\left(\frac{\partial V_z}{\partial t}\right)=qn\vec{E_z}-\frac{\partial P_z}{\partial z}\]

Q.3.9 Write down the equation of motion of ions.

Answer: Equation of motion for ions is written as;

    \[m_i\left(\frac{\partial{\vec{V}}_i}{\partial t}+\ {\vec{V}}_i-\nabla{\vec{V}}_i\right)=e{\vec{E}} + e\left({\vec{V}}_i\times\vec{B}\right)-m_i{\vec{V}}_iV-\frac{1}{n_i}\nabla\left(n_iT_i\right)\]

Q.3.10 Why we focus only on fluid model in plasma?

Answer: Because 70% description is through fluid model, Approach of the fluid is macroscopic. Example: whole lake a stream. The generalized form of fluid model is consist or depends on the equation of continuity, equation of motion and equation of states of the particles in plasma.

Q.3.11 Write down the equation of diamagnetic drift and explain it.

Answer: Diamagnetic drift, Vd =∇p × B /qnB² It means that diamagnetic drift is perpendicular to the direction of gradient.

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