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Could a magnet shield astronauts?

Electricity and magnetism · level 8, lesson 6 of 6

A question to start

Earth's field turns aside most charged particles from space. On the way to Mars, astronauts have no such shield. Could a spacecraft carry its own magnet?

The idea

A magnet turns a particle only if the particle's circle is smaller than the region of field it crosses. The radius is \(r = p/(qB)\), and the fast particles from space move close to the speed of light, so we need the relativistic momentum. For a proton with kinetic energy \(K\), in MeV:

\[pc = \sqrt{K^2 + 2Kmc^2}, \qquad mc^2 = 938 \text{ MeV}.\]

A handy form of the radius, for a proton: \(r = \dfrac{p \text{ (in GeV/}c)}{0.3\,B \text{ (in T)}}\) metres.

Proton Momentum Radius in a 1 T field
100 MeV, from a solar storm 0.44 GeV/\(c\) about 1.5 m
1 GeV, a typical cosmic ray 1.70 GeV/\(c\) about 5.7 m
10 GeV, a fast cosmic ray 10.9 GeV/\(c\) about 36 m

So a 1 T field filling a few metres around a crew cabin could turn aside many solar storm protons, but not the faster cosmic rays. Making a 1 T field over metres needs huge superconducting coils, kept very cold, with a large mass of their own.

slower proton: turned awayfast cosmic ray: gets throughfield region

Worked examples

1. A solar storm proton. \(K = 100\) MeV: \(pc = \sqrt{100^2 + 2 \times 100 \times 938} = \sqrt{197{,}600} = 445\) MeV. \(r = 0.445/(0.3 \times 1) = 1.5\) m.

2. A cosmic ray. \(K = 1{,}000\) MeV: \(pc = \sqrt{10^6 + 1.876\times10^6} = 1{,}696\) MeV, so \(r = 1.696/0.3 = 5.7\) m.

3. Earth's shield. The same 1 GeV proton in a 30 µT field: \(r = 1.696/(0.3 \times 3\times10^{-5}) = 1.9\times10^5\) m, 190 km. Small next to Earth's field, which reaches tens of thousands of kilometres out.

Try it

  1. Why must we use relativistic momentum for cosmic rays?
  2. Find the radius of a 100 MeV proton in a 3 T field.
  3. What field would bend a 1 GeV proton in a 2 m circle?
  4. Why do most plans for protecting crews use thick material, like water, instead of magnets?
Answers
  1. They move close to the speed of light, where \(p = mv\) is far too small.
  2. \(0.445/(0.3 \times 3) = 0.49\) m.
  3. \(B = 1.696/(0.3 \times 2) = 2.8\) T.
  4. A field strong and wide enough is very hard to build and power; material shielding is simpler, and also stops neutral radiation that a magnet cannot turn.

Common mistake

"A magnet stops all radiation." It turns only charged particles. Gamma rays and neutrons pass straight through any magnetic field.

Where it leads