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Additional info for Encyclopaedie der mathematischen Wissenschaften und Anwendungen. Mechanik

Sample text

Within the context of the requirement that the right-hand part has to vanish we obtain an equation that describes the free oscillations: e(G>,k)££2=0. 48) For this equation to have non-zero solutions, the frequencies and the wave vectors must satisfy the dispersion relation e(o>,k) = 0. 49) are associated with the plasma eigenmodes. 49) determines the frequency and the damping rate of the relevant mode ω£ and y£ ( a is introduced to label different eigenoscillations). 50) where E£0 and φ£ are the initial amplitude and phase of the oscillation.

46) be equal to zero we derive an equation which is responsible for the slow time-development of the linear amplitude Εζ and the phase φζ: ί^<~Κ Ot =Ί Ί ΰ ^ ΰ Σ ^\<^<^)Ki-(ki. 44) relevant expressions may be written also for the third iteration and so on. The intermedi- ELECTRODYNAMIC PROPERTIES OF A MAGNETO-ACTIVE PLASMA 53 ate algebra is simple but awkward, so we give here only the results: ^(COU^COM=Σψ^±-±-μΣ r""*\*K±iv).

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