The Spring 1999 issue of SearchLites carried a guest editorial by Prof. Paul Davies, in which he wrote (based on a suggestion by Allen Tough) "that they could send a small smart space probe to eavesdrop on our activities...It might be no more than the size of a pea..." I argue that cosmic ray fluxes and energies mitigate against this suggestion.
The best reference I have found on cosmic ray fluxes and energies is "Cosmic-Ray Record in Solar System Matter" by Reedy, Arnold and Lal, Science Vol 219, pages 127-135, 14 January 1983 . There are probably many more recent reviews, perhaps in the Annual Review of Astronomy and Astrophysics and on the Web. However the Reedy et al paper is an excellent introduction and has a very useful Table 1 in which the energies (MeV/nucleon), mean flux (particles/second/square centimetre) and effective depth in solid matter (centimetres) are presented for solar and galactic cosmic rays (CRs). The data in the Reedy et al paper can be used to address the question of damage which CRs will do to interstellar probes.
Ignoring nearby stellar/solar cosmic rays (which will only exacerbate the damage) interstellar probes will be subject to galactic CR fluxes of about 3 particles/second/square centimetre with an effective penetration depth of between 0 to 100 cm. Taking microprobes of a few square cm area (say 10) and some mean travel time of say a few million years (10^14 seconds) to traverse a significant fraction of the galaxy at a few percent of the speed of light, the probe will encounter about 3 x 10^15 high energy (100 to 3000 MeV/nucleon) cosmic rays.
Although such microprobes will have about 10^24 atoms which is a billion times larger than the number of incident CR particles, the CR particles when colliding with the nuclei of the microprobe in their path will create cascade showers of many thousands high energy fragments thereby causing further damage to the probe. An analogy would be a very high powered dumdum bullet hitting a water melon and blasting a coneshaped trail of destruction through it. So my guess is that besides the problems of the large amount of energy required to get the probes up to some significant percentage of the speed of light and then slow them down, probes with less that a few metres shielding will not survive hostile CR environment for the times required for interstellar travel.
Regarding our satellites and probes (Voyager, Pioneer), some have survived for a couple of decades, but this is vastly shorter that the time scales required for interstellar travel and hence have experienced far less damage. Even the comparatively mild solar activity (particles with energies/nucleon of a million times smaller than galactic CRs) is enough to damage some communications satellites.
Peter Backus from the SETI Institute corresponded with me on this matter, and concluded that "whatever their technology, they can't avoid the physics. Small probes will require a thick shell to reduce damage from cosmic rays."
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