(a) A fusion device measures the line-averaged electron density along a chord of…

PHYSICS · Subjective · Fermi University Physics · Plasma Physics · Laboratory, industrial and space plasmas · Laboratory, industrial and space plasmas

Plasma Physics, Ch Plasma oscillations and light in an unmagnetised plasma

Problem

(a) A fusion device measures the line-averaged electron density along a chord of length

L=3.0\,\mathrm m

using a

\lambda=119\,\mu\mathrm m

methanol-laser interferometer. The measured phase shift relative to vacuum is

\Delta\phi=50.3\,\mathrm{rad}

. Using

\Delta\phi=r_e\lambda\int n_e\,\mathrm dl

with the classical electron radius

r_e=2.82\times10^{-15}\,\mathrm m

, and taking the density uniform along the chord, find the line-averaged electron density

n_e

. Then compute the critical density

n_c=1.1\times10^{27}\lambda_{\mu\mathrm m}^{-2}\,\mathrm m^{-3}

for this wavelength and confirm

n_e\ll n_c

, so the small-parameter expansion behind the phase-shift formula is valid. (b) A pulsar is timed at two frequencies,

f_1=300\,\mathrm{MHz}

and

f_2=1.4\,\mathrm{GHz}

, and the pulse at

f_1

arrives

\Delta t=1.54\,\mathrm s

after the pulse at

f_2

. Using

\Delta t=4.15\,\mathrm{ms}\times\mathrm{DM[pc\,cm^{-3}]}\times\left[(f_1/\mathrm{GHz})^{-2}-(f_2/\mathrm{GHz})^{-2}\right]

, find the dispersion measure DM. Then, assuming a mean interstellar electron density of

0.03\,\mathrm{cm^{-3}}

along the line of sight, estimate the pulsar's distance in parsecs.

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