By V. N. Tsytovich

ISBN-10: 0080165877

ISBN-13: 9780080165875

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**Extra info for An Introduction to the Theory of Plasma Turbulence**

**Example text**

63) multiplied by Εκ. 22) with εκ + εκΛ· on the left-hand side instead of εκ and the term e° J · \Εκ\2 on the right-hand side. By definition, the last term must vanish to take into account all the terms diagonal in \Εκ\2 on the left-hand side. 22) is always a high-frequency field. Thus one needs to express the low-frequency field in terms of the high-frequency 5* 60 THE THEORY OF PLASMA TURBULENCE field Eu. 64). 25) one finds from them one of the terms diagonal in \Εκ\2; the other one comes from ρ(3).

1) depends on the turbulent energy which can, therefore, not be used as an expansion parameter. 1). Also, the transition to the turbulent state involves nonlinear interactions and thus a more precise description of the turbulent state is needed to include turbulent collisions. Maybe one can say that for the balance equations it is an academic question, because it is obvious that in a statistical description one can use a transition probability approach and that the increase in entropy needs a retarded potential.

43) ro = {*o, yo9 zo}, Xo and y0 are thus the coordinates of the centre of the Larmor orbit, z0 and φ are the initial z and phase φ of the particles at t - 0. 44) coH* £ The /„ are the Bessel functions of order v. 3)) [k2ôij — kikj—œ2Sij(œ, k)] (Ex)j = 4mœ(jx)i. 45). -„ . \ ^-x. 47) we get ^» /Λ Vi f ^3k g =-(2nf 4πί ni (2TtJ d0> d(û' ιί2_ω2εα +£ . * σ\ / σ* . 4*) V, v' — — oo J X— — δ(ω — kzvz — *>ω#α) <5(ω' — kzvz — ν'ωΗα) d3k dœ άω'. 43) for the current jK. 29) gives us general quasilinear equations valid, for example, for a relativistic plasma.

### An Introduction to the Theory of Plasma Turbulence by V. N. Tsytovich

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