Question

A Hall effect thruster generates a Te = 35 eV plasma within the annular discharge channel. The annular channel is 8 cm long/deep, 4 cm wide, and the mean diameter is 10 cm. The axial electric field is 4000 V/m, and radial magnetic field is 300 G. Assume a plasma density of 1017 m-3, a neutral gas density of 1019m-3, and ionization cross-section of 4.2 x 10-20 m2.

a. The E and B fields cause electrons to spin around the annulus via the ExB drift. How many trips around the annulus, on average, will an electron make before making an ionizing collision?

b. What is the average time it takes to make an ionizing-collisions while going around the annulus?

Answer 1

As per the given question,

A Hall effect thruster generates a Te = 35 eV plasma

The dimension of the annular channel(d) = 8cm long,

(w)= 4cm wide and

(d)diameter is= 10 cm

Axial electric field(E) = 4000 V/m

Radial magnetic field $= 300G=300\times10^{-4}T$

Plasma density$(\rho) = 1713 m^{-3}$

Density of natural gas $\rho_g=1719 m^{-3}$

ionization cross-section of= $4.2 \times 10^{-20} m^2.$

a) We know that $V=\dfrac{E}{B}=\dfrac{4000}{300\times 10^{-4}}=39.33\times 10^{4}m/sec$

t=$\dfrac{l}{v}=\dfrac{4}{39.33\times 10^{4}}=1\times10^{-5}$

b) Collision frequency = n c T

$c_e=\sqrt{\dfrac{8kT_e}{\pi m_e}}=9.9\times10^{-5}$

collision frequency = $9.9\times 10^{-5}\times 1\times 10^{-4}\times 35\times 1.6^{-19}=346.5\times10^{-28}$ /sec