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macc , respectively) and

cp cos 9

In this case

V macc y d d where p// ~ Oi/kc. Here f is the particle distribution function; y(m) is the increment of the pulsations with frequency O and wave vector k; the upper and lower signs in Eq. 4.11.40 relate to the Alfvén and rapid magneto-sonic waves respectively. After averaging the Eq. 4.11.38 over the period T = 2njm of variation of the field (see Eq. 4.11.37) and over the angular variable 9, we obtain the equation f ' ± p2D(p)f

describing the particle acceleration process with diffusion coefficient n2 „t<ln

maccp

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