Is magnetism important in particle interaction?

magphys
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If you fire energetic ionising particles, like electrons or protons, at a stationary target, the important interactions are ionisation, nuclear reactions and scattering.

But if the incoming particles are traveling at high speed, will they not generate a high magnetic field? Why is such a magnetic field not important in reactions other than ionisation?

If my assumptions are wrong, please feel free to point it out!
 
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In electron-electron scattering at high energy, the magnetic interaction is dominant.
 
Thanks that's helpful. Sometimes I can't see the wood for the trees!
 
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