(38.7 + ln(Ek/Mc2)- 0.51nNe^2Mc2/Ek), if Ek <<Mc2, (74.1 + 21n(E/Mc2)- lnNe ) if (M/m)Mc2 >> E >> Mc2, (74.1 + InEMc2)-ln Ne) if E >>(M/m)Mc2. (1.5.2)
The Eq. 1.5.1 and Eq. 1.5.2 are valid only for the particles whose velocities v are much in excess of the mean velocities (ve) of electron motion in medium (in atomic hydrogen (ve} = e2/h ~ 2x108 cm/sec, in ionized hydrogen
(ve) = y[3kTjm = 6.8x105T12 cm/sec, where Te is the electron temperature in °K).
However, the region v < (ve} is of great interest to studying the mechanisms of CR
acceleration in magnetized completely or incompletely ionized plasma (especially for the problem of injection into an acceleration process under the conditions of chromospheric flares, in active solar regions, in shock waves, in supernova explosions, etc.). In this energy range the loss (in eV/sec) is
dt • ion in a gas with concentration of Natoms with atomic number Zg . In Eq. 1.5.3 Z* is the effective charge of particle, which is according to (Bohr, M1960) at 1 < v/iv^j < Z13 approximately
This relation reflects the simple fact that the loss of a subsequent electron takes place when the velocity of particle equalizes the orbital velocity of this electron. At v > (ve)Z and sufficiently frequent collisions, the ionization proves to be practically complete, Z * = Z . It should be borne in mind when studying the particle motion in rarified gas that the ionization cross section ai of shell i with ionization potential Ji is maximum at in energy Emi ~ 3(Mjm)Ji while the dependence of <7i on Ek is determined by the relation
Ji mEk where K is the coefficient of the order of unity (see in Post, M1959). According to Eq. 1.5.5, the characteristic cross section of the loss of the first electron is of the order of gas-kinetic cross section (~ 10-16cm2), whereas the cross section of the electron loss from inner shells is significantly smaller (for example, the cross section of the loss of the last electron from the K shell of Fe is only 10-21cm2).
In an ionized gas with concentration of Ne electrons and temperature Te the energy loss (in eV/sec) is dE dt
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