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u du where v and mac are respectively the velocity and mass of the accelerated particle. The Eq. 4.10.1 describes the influence of the radiation with chaotically phases.

4.10.2. On the injection in the particle acceleration by radiation

Detailed consideration is given in Tsytovich (1963b,d) to the problem of particle injection for the Fermi acceleration mechanism in the case of acceleration owed to radiation. With this purpose the curves of the energy gain are compared with the deceleration curves in the two mechanisms. For the same deceleration curves, the curves of acceleration gain prove to be significantly different, namely, the curves rise with increasing energy for the Fermi mechanism and fall for the mechanism of acceleration owed to radiation (in this case the decrease with increasing energy is always more rapid than that of the deceleration curve, so that the curves intersect at a certain value of energy). In connection with this the Fermi mechanism implies both injection and injection-less acceleration without visible limitation of the maximum energy of the accelerated particles (some limitation will be owed to only the inverse effect of the accelerated particles on the medium, the nuclear loss, and the escape from the acceleration region).

4.10.3. On the maximum energy and maximum density of accelerated particles in the case of particle acceleration by radiation

According to Tsytovich (1963b,d), in the case of the acceleration owed to radiation, there exists a maximum energy Ecr above which the deceleration is superior to the acceleration. If the radiation is characterized by the temperature Tf (in eV) it appears that Ecr ~ Teff. The total flux of the accelerated particles is determined by the condition that the density of their energy should not exceed the radiation energy density. This condition ensures an equilibrium energy distribution between the fast particles and the radiation, a fact which can be observed in the space. Tsytovich (1963b,d) notes that the state with E ~ Ecr is unstable because the energy decrease makes the acceleration force superior to the deceleration force and the particle energy increases; in its turn, the energy increase results in the inverse effect. Tsytovich (1963b,d) also pays attention to the fact of the examined mechanism of particle acceleration owed to radiation is especially effective when the mean density of the radiation energy is much in excess of the mean kinetic energy of matter (for example, in the objects of the supernova type).

4.10.4. Cyclotron acceleration of relativistic electrons by lateral waves

In the magnetic field the particle energy may prove to change owed to the energy gain or loss in case of cyclotron radiation and wave absorption. This is clearly exemplified by the possibility of acceleration by the high-frequency lateral waves. For relativistic particles, the absorption and radiation of the frequencies multiple to the gyro-frequency m~ ¡ua>i are of significance. According to Gailitis and Tsytovich (1963), we obtain in this case at m >> moe and v± >> Vf :

d- = 0 + n)Ks/3 (£)- nKipti)- no K/3 (^'K'MX ,(4.10.2

M = 1 - vll c2, n = 1 ClM), ç = ^(m + V). (4.10.3)

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