A small antenna sits in the argon processing discharge, , ,

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · The plasma state and single-particle motion · The plasma state and single-particle motion

Plasma Physics, Ch What makes an ionised gas a plasma: shielding, the plasma parameter and the natural frequencies

Problem

A small antenna sits in the argon processing discharge,

n_e = n_i = 1.0\times10^{16}\,\mathrm{m^{-3}}

T_e = 2.0\,\mathrm{eV}

T_i = 0.030\,\mathrm{eV}

, with singly charged

\mathrm{Ar^+}

ions of mass

6.63\times10^{-26}\,\mathrm{kg}

. The charge on the antenna oscillates at

f = 50\,\mathrm{MHz}

. A quick estimate reasons that the colder species dominates the sum for

\lambda_D^{-2}

, computes a Debye length from the ion temperature,

7.43\times10^{3}(0.030/10^{16})^{1/2}\,\mathrm{m} = 13\,\mu\mathrm{m}

, and concludes that the antenna's field is screened within about thirteen micrometres. Treat the antenna's near field as electrostatic and the plasma as collisionless, and take a species to follow the antenna quasistatically if the antenna frequency is well below that species' plasma frequency, and not at all if it is well above. ((a)) Find

f_{pe}

and

f_{pi}

for this plasma, and use them to decide which species can rearrange itself within one period of the antenna's oscillation. ((b)) Identify the error and find the approximate shielding length in this model. ((c)) By what factor was the estimated shielding length too small? For what kind of test charge would that number have been about right?

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