SHINE 2006. Turbulent diffusion as a requirement for a f ( p ) p -5 spectrum. J. A. le Roux & G. M. Webb IGPP, University of California, Riverside. EQUATION FOR ENERGETIC PARTICLE TRANSPORT IN RELATIVELY LARGE-SCALE COMPRESSIVE PLASMA FLUID TURBULENCE. Turbulent convection.
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J. A. le Roux& G. M. Webb
IGPP, University of California, Riverside
EQUATION FOR ENERGETIC PARTICLE TRANSPORT IN RELATIVELY LARGE-SCALE COMPRESSIVE PLASMA FLUID TURBULENCE
Non-linear diffusion expression whereT is turbulent diffusion
Turbulent stochastic acceleration
Solve transport equation assuming: LARGE-SCALE (i) Equal compressive wave intensities in all directions (U* = 0)(ii) turbulent diffusion dominates spatial diffusion by Alfven waves (t >> )(iii) A steady state
Equation to solve is:
Solution using separation of variables is: LARGE-SCALE
S = 3 if 0S = 5 if 1/lc
Af(p) p-5spectrum is the natural outcome of turbulent diffusion and stochastic acceleration by relatively large-scale compressive plasma fluid turbulence
Alternatively, LARGE-SCALE assume: (i) Non-relativistic particles (ii) Equal compressive wave intensities in all directions (iii) A steady state (iv) integrate overpinterval [p1, p2] after multiplying transport equation with4p2Ek - energy density form
Diffusive energy flux through [p1,p2]
Assume turbulent diffusion dominates- LARGE-SCALE f(p) p-5 as shown before.Then one finds that:
Thus a constantdiffusive energy flux through interval [p1,p2] is a natural further consequence of turbulent diffusion and stochastic acceleration by relatively large-scale compressive plasma fluid turbulence.