ln rlc sin (po
At acceleration of the collective of particles, the energy of the wave will be decrease and their amplitude will ^ 0 at r ~ rc, so the final energy will be some smaller. Now it is easy to check the supposition on the constant of the phase. The expected change of the phase will be ~ (rc/rc XQ/^L )43(sin(po )-^3, i.e. really very small (excluding the point (p0 _ 0). Therefore, charged particles are accelerated very fast and moved together with electromagnetic wave at constant phase. In the laboratory system of coordinates the test particle continuously gain energy in weekly inclined electric and magnetic fields which directions practically does not change in time. The mechanism of particle acceleration works effectively thanks very low frequency and very big amplitude of the field in the wave (the strength of magnetic field Hr at the basis of wave zone at present time is ~ 106 Gs, and at t _ 0 it was ~ 1010 Gs). Such non-linear interaction of charged particle with the very low frequency electromagnetic wave was discussed for another limit conditions in papers of Buchsbaum and Roberts (1964) and Jory and Trivelpiece (1968). In difference of these papers, in Gunn and c
Ostriker (1969) the parameter coLl O is so very big that it ensures the moving of charged test particle at the practically constant phase.
Let us consider now the suggestion used in Gunn and Ostriker (1969) that the charged particles moved as in vacuum. This approximation is valid if r0mLQ>m2e, (4.13.13)
where y0 = E0/macc2 at injection, and moe = (ne2Ne/me 1 is the plasma frequency. If the Eq. 4.13.13 does not satisfied, the considered above mechanism of charged particles acceleration will work with smaller efficiency.
4.13.3. On the maximal energy of accelerated particles from fast rotated magnetic star
Eq. 4.13.12 for accelerated particles with the mass mac = mpA and the charge Ze gives
Emax = 1.3 x 1014 A13Z23
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