Energy Loss of a Charged Particle Traversing Ionized Gas and Injection Energies of Cosmic Rays

Abstract

The energy loss of a charged particle traversing an electron gas is calculated by taking the direct collisions with free electrons and the plasma excitation into account. The contributions from ions and neutral atoms are added and the resultant energy loss is given as a function of the degree of ionization. The energy loss is found to increase with the degree of ionization, to which excess loss is approximately proportional. The critical injection energy of cosmic rays, based on the Fermi mechanism of acceleration, is given in Table 1. Its value is al:out fifty percent larger for the degree of ionization of ten percent than for a neutral medium and nearly four times larger for a half ionized medium. In the case of the solar production of cosmic rays the critical injection energy is below one MeV per nucleon; so that the secondary particles generated by nuclear reactions could be accelerated to cosmic ray energies. The mechanism of acceleration in a coronal region is proposed in the Appendix to explain the time delay of the cosmic ray increase compared with the solar eruption as well as the energy spectrum of solar cosmic rays. In some astrophysical problems, it is important to know the energy loss of a charged particle in a highly ionized gas. This fact has been emphasized in a number of occasions, for example, by Morrison, Olbert and Rossi1J in connection with the injection of cosmic rays and by Greenstein2J in discussing the role of electrons in the stellar atmosphere. These authors had to use the formula of the ionization loss for a neutral medium or its approximate modification, because no reliable knowledge of that for an ionized medium was available. Recently, however, Neufeld and Ritchie3> have worked out this problem by paying attention to the excitation of plasma waves. lndepently of them the present authors4> have also treated the same problem in a simple way. In this paper we present our method of derivation as well as its numerical results which may serve to astrophysical problems, and discuss the bearing of our formula in the injection of cosmic rays. 5J In deriving the formula of the energy loss in an electron gas, we use the method of impact parameter. For small impact parameters the energy loss is regarded as due to the direct collision with electrons, while for large impact parameters as due to the excita­ tion of plasma waves. The two regions are divided bv a critical impact parameter which is of the order of the Debye length. Adding the contributions from the respective regions, the critical impact parameter is eliminated from the final formula.