Question

A cylindrical column of hydrogen plasma (i.e. protons and electrons) has a uniform temperature Tₑ =Tᵢ =T₀ and a density profile nₑ =nᵢ =n(r), where r is the radial position in cylindrical coordinates. The plasma is immersed in a uniform external magnetic field along the z-axis of strength B₀. There is no electric field. The plasma density profile has the form n(r)=n₀ (1− (r/a)²) for r≤a, and is zero for r>a. Treat each species as an independent fluid for this problem (i.e. do not use MHD here). 1. Calculate the ion and electron diamagnetic fluid drift velocities v,ᵢ and v,ₑ.

Answer 1

To calculate the ion and electron diamagnetic fluid drift velocities v,ᵢ and v,ₑ, we need to use the equations for drift velocity in a magnetic field.

Step-by-step explanation:

To calculate the ion and electron diamagnetic fluid drift velocities v,ᵢ and v,ₑ, we need to use the equations for drift velocity in a magnetic field. The drift velocity of ions can be calculated using the equation: v,ᵢ = (e/mᵢ) * (n₀B₀)/(n₀e + n₀i), where e is the charge of an electron, mᵢ is the mass of an ion, n₀ is the peak density of the plasma, B₀ is the magnetic field strength, and n₀e and n₀i are the electron and ion densities, respectively.

The drift velocity of electrons can be calculated using the equation: v,ₑ = (e/mₑ) * (n₀B₀)/(n₀e + n₀i), where mₑ is the mass of an electron.