where r is the distance from the Sun, t is the time after ejection, No(R) is the rigidity spectrum of total number of SEP at the source, and k(r) is the diffusion coefficient in the interplanetary space during SEP event. Let us suppose that at distance from the Sun r = r1 = 1AU and at several moments of time ti (i = 1, 2, 3,...) after SEP ejection into solar wind the observed rigidity spectrum out of the Earth's atmosphere N(R, r1, ti ) = Ni (R) are determined in high energy range on the basis of ground CR measurements by neutron monitors and muon telescopes (by using method of coupling functions, spectrographic and global spectrographic methods, see review in Dorman, M2004)) as well as determined directly in low energy range on the basis of satellite CR measurements. Let us suppose also that the UT time of ejection Te as well as the diffusion coefficient k(r) and the SEP rigidity spectrum in source No (R) are unknown. To solve the inverse problem, i.e. to determine these three unknown parameters, we need information on SEP rigidity spectrum Ni (R) at least at three different moments of time T1, T2 and T3 (in UT). In this case for these three moments of time after SEP ejection into solar wind we obtain:
t1 = T - Te = x, t2 = T2 - Te = T2 - T + x, t3 = T3 - Te = T3 - T1 + x , (2.42.3)
where T2- T1 and T3- T1 are known values and x = T1 - Te is unknown value to be determined (because Te is unknown). From three equations for t1 , t2 and t3 of the type of Eq. 2.42.2 by taking into account Eq. 2.42.3 and dividing one equation on other for excluding unknown parameter No (R), we obtain two equations for determining unknown two parameters x and k(r):
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