(a) An inertial-confinement laser-plasma experiment probes a plasma of length with a…

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

Problem

(a) An inertial-confinement laser-plasma experiment probes a plasma of length

L=500\,\mu\mathrm m

with a frequency-doubled probe beam of wavelength

\lambda=0.53\,\mu\mathrm m

. The measured phase shift across the plasma is

\Delta\phi=7.47\,\mathrm{rad}

. Using

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

with

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

, and a uniform density along the probe path, find the electron density. Compute the critical density

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

for this wavelength and check that

n_e\ll n_c

, so the probe is well below the density at which it would be reflected. (b) A pulsar has dispersion measure

\mathrm{DM}=12.4\,\mathrm{pc\,cm^{-3}}

. 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 delay between pulses observed at

f_1=150\,\mathrm{MHz}

and

f_2=800\,\mathrm{MHz}

. Then, assuming a mean interstellar electron density of

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

, estimate the pulsar's distance in parsecs. Imaging later shows an H II region

1.0\,\mathrm{pc}

thick with

n_e=10\,\mathrm{cm^{-3}}

on the same line of sight: re-estimate the distance, and explain why the measured delay could not have revealed this on its own.

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