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The synchrotron radiation spectrum is calculated for relativistic electrons in the case where no restriction is placed on the strength of the magnetic field. It is shown that in intense fields H⪞ H0 = m2c3/e0ħ =4.41 · 1013 G a major contribution to the total radiation intensity comes from transitions to the ground state and also to weakly excited levels. In particular, the contribution from transitions to the ground state (final electron energy E' =mc2) for electrons of initial energy E = 10 MeV in a field H = 2H0 is 14% of the contribution from transitions to highly excited states (E'≫mc2).

The article describes the spin self-polarization effects which occur when electrons move along spirals in a magnetic field, and discusses the various possibilities of describing the electron spin.

Classical-theory methods are applied to the emission from an electron moving in an ideal undulator of infinite length with piecewise-homogeneous magnetic field. The spectral and angular distributions of the radiation are deduced together with the polarization and total power.

The motion of a relativistic electron in a constant focusing magnetic field and a high-frequency rotational electromagnetic field, used to offset the radiative energy loss, is studied on the basis of the Klein-Gordon equation. The solutions found may be used to construct a theory for electron storage rings, in which quantum fluctuations are particularly important.

Using the methods of classical theory, the emission of radiation by electrons moving in an ideal magnetic ondulator of infinite length is investigated. The spectral angular distribution, the polarisation, and the full radiated power are obtained.

The probability of creation and annihilation of pairs in a superstrong magnetic field H ≳ H 0 = m 2 c 3 / e ⪆ 4.41 × 10 13 G is obtained. it is shown that in such a field the ground state of electrons (or positrons) provides considerable contribution to the total probability of the process.