375 ISSN 1063-7761, Journal of Experimental and Theoretical Physics, 2019, Vol. 129, No. 3, pp. 375–385. © Pleiades Publishing, Inc., 2019. Russian Text © The Author(s), 2019, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2019, Vol. 156, No. 3, pp. 449–460. Solar Cosmic Ray Acceleration by a Shock Wave in the Lower Solar Corona on November 22, 1977 S. N. Taneev a, *, S. A. Starodubtsev a, **, V. G. Grigor’ev a , and E. G. Berezhko a a Shafer Institute of Cosmophysical Research and Aeronomy, Siberian Branch, Russian Academy of Sciences, pr. Lenina 31, Yakutsk, 677980 Russia *e-mail: taneev@ikfia.ysn.ru **e-mail: starodub@ikfia.ysn.ru Received December 18, 2018; revised April 4, 2019; accepted April 23, 2019 Abstract—Based on the theory of diffusive shock acceleration of charged particles, we have investigated the spectra of protons recorded in the solar cosmic ray event near the Earth’s orbit on November 22, 1977 (ground level enhancement no. 30, GLE30). The proton flux data from the CPME instrument installed on the IMP-8 spacecraft and the worldwide network of neutron monitors have been used to analyze the event. Using GLE30 as an example, we have shown for the first time that solar cosmic rays of relativistic energies can be produced by a shock wave with a relatively low speed of 560 km s –1 in the lower solar corona at a dis- tance up to 1.6 ( is the solar radius) within 615 s. The calculated proton spectra satisfactorily reproduce the measurements in the Earth’s orbit. DOI: 10.1134/S1063776119080089 1. INTRODUCTION The development of a diffusive shock acceleration theory (see, e.g., the pioneering paper by Krymsky [1], the monograph by Berezhko et al. [2], the review by Berezhko and Krymsky [3], and references therein) as applied to phenomena in the inner heliosphere (the region bounded by the Earth’s orbit) is needed for a detailed understanding of the formation of energetic ion spectra at shock fronts. A detailed justification for the subject of studies is given in the Introduction of the paper by Berezhko and Taneev [4]; see also the review by Miroshnichenko [5], the article by Petukhov et al. [6], the paper by Lee [7], and references therein. This paper is a supplement (continuation) to our previous extended study of the solar cosmic ray (SCR) acceleration by shock waves in the solar corona [4]. Here we study the ground level enhancement (GLE) of SCRs on November 22, 1977. Ordinal numbers are assigned to such events. This is a universally accepted term and, therefore, below we will refer to this event as GLE30. It follows from the calculations presented below that SCRs of relativistic energies in this event were produced by a coronal shock with a relatively low speed of 560 km s –1 [8] at a close distance from the Sun (up to 1.6 ) in 615 s. Since the mean value of the maximum Alfvén speed ( ≈ 740 km s –1 ) in the solar corona at a distance of 3.8 [9] is considerably higher than the shock speed (560 km s –1 ) in GLE30, the particle acceleration to relativistic energies in this event ranks it among the unique events. Shock waves with a speed above 1000 km s –1 (higher than ≈ 740 km s –1 ) usually produce SCRs of relativistic ener- gies. The goal of this paper is to elucidate the conditions for applicability of the Berezhko–Taneev theory [4] to GLE30 in the lower solar corona, which is character- ized by the greatest shock speed. 2. MODEL First note that the linear theory of SCR accelera- tion to relativistic energies in the lower solar corona developed by Berezhko and Taneev [10] is the first example of applying the theory of diffusive shock acceleration of changed particles by taking into account the finiteness of the shock sizes (in the spher- ical approximation), the adiabatic deceleration of accelerated particles in an expanding solar wind stream, and the real coronal plasma parameters for an understanding and detailed explanation of the SCR generation by shock waves traveling from the lower solar corona into interplanetary space. Subsequently, allowance for the self-consistent generation of Alfvén waves by accelerated particles [4] led to the construc- tion of a quasi-linear theory of diffusive shock acceler- ation of SCRs at the front of a coronal shock. Since the statement of the problem is described in detail in [4], here we will dwell only on its basic ele- ⊙ R ⊙ R ⊙ R max A c ⊙ R max A c NUCLEI, PARTICLES, FIELDS, GRAVITATION, AND ASTROPHYSICS