## The Electrodynamics of Comet Dust

It was believed that the principle force acting on the dust in a comet’s trail was radiation pressure. In 1982, Professor M.K. Wallis and Professor M.H.A. Hassan (later Dean of the University of Khartoum and President of the Network of Academies of Science in Africa) showed that in a certain regime electromagnetic forces dominated those from radiation pressure. This had very practical consequences as certain spacecraft (such as Giotto and Vega) had shields that did not account for this fact.

1. A particle in a uniform magnetic field will naturally go in a circle with a characteristic radius and frequency (known equivalently as the cyclotron radius, Larmor radius, gyroradius, etc.). Given that $\omega=10^{-23}\frac{\omega_p}{a^2}$ where the initial factor is due to a plasma physics calculation, $.01 \mu m\leq a\leq .1 \mu m$ is the radius of our piece of comet dust, and $\omega_p$ is the cyclotron radius of the proton in a $10^{-4}$ Gauss magnetic field. Calculate the cyclotron radius of the proton and give the order of magnitude of the expected radius and period of circular motion using the fact that a typical speed of a grain caught in a solar wind is $\sim 10^5ms^{-1}$. Compare this to the 270m width of Hailey’s comet and the time it takes the comet to be in an entirely new place $\sim$.1s.
2. The long length and timescale of cyclotron motion compared to the comet means that linear motion is a good approximation in our case; show this by calculating the dominant contribution to  $m\dot{v}=q(E+v\times B)$, the acceleration tangential to the comet.
3. The smaller grains are also subject to radiation acceleration $a_r\sim g_1*(\frac{a}{.1\mu m})^s$. Calculate $v_{tot}$ assuming the grain undergoes cylotron motion with radius $8*10^7m$ (this radius is due to effects on the charge of the grain that we have elided for simplicity).
4. The stream of particles generated by these effects will be confined to a characteristic radius, calculate $L=\frac{v_{tot}^2}{|a_{tot}|}$ to see how far one must be from the comet to avoid this high-speed stream of charged particles.

References:

Electrodynamics of submicron dust in the cometary coma.
Wallis, M. K. ; Hassan, M. H. A.
Astronomy and Astrophysics (ISSN 0004-6361), vol. 121, no. 1, May 1983, p. 10-14.