By T. J. M. Boyd
A accomplished introductory graduate textbook illustrating specialized themes in present physics.
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11 47 where β = v/c. Note that for E = 0, the result of the previous exercise follows by inspection. 60), ignoring terms of order (da/dτ )/aω. Sketch the trajectory of the particle. The vector potential for a monochromatic, plane wave of arbitrary polarization propagating in the x-direction is A = a(τ )[0, α cos ωτ, (1 − α 2 )1/2 sin ωτ ] where τ = t − x/c, 0 ≤ α ≤ 1 and the amplitude a(τ ) is slowly varying. (a) Integrate the relativistic Lorentz equation to obtain the velocity of an electron interacting with this wave, assuming that the electron starts from rest at the origin.
6 towards the region of increasing B. 7 Magnetic mirrors B 27 B - field lines BM BM B0 Fig. 7. Magnetic mirror field. W⊥ must increase. Since energy is conserved this increase must be at the expense of W . Thus it may happen that for some value of B (B R say) W = 0, in which case the particle cannot penetrate further into the magnetic field and suffers reflection at this point (provided (v × B) · zˆ = 0). Such a field configuration has the properties of a magnetic mirror. 33) Then, from the invariance of µB = W⊥ /B, it follows that sin2 θ/B is constant.
The inner belt is characterized not only by its energy distribution but by the fact that it is more stable than the outer belts. Taken together these observations suggest distinct sources for inner and outer belt components. Cosmic rays colliding with atoms result in disintegrations into nuclear components. These include neutrons travelling outwards which decay to produce energetic protons and electrons. Observations have confirmed that cosmic rays are indeed a source for inner belt protons with energies of tens of MeV.