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Turbulent diffusion as a requirement for a f ( p )  p -5 spectrum

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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Turbulent diffusion as a requirement for a f ( p )  p -5 spectrum

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  1. SHINE 2006 Turbulent diffusion as a requirement for a f(p)  p-5spectrum J. A. le Roux& G. M. Webb IGPP, University of California, Riverside

  2. EQUATION FOR ENERGETIC PARTICLE TRANSPORT IN RELATIVELY LARGE-SCALE COMPRESSIVE PLASMA FLUID TURBULENCE Turbulent convection Non-linear diffusion expression whereT is turbulent diffusion Turbulent stochastic acceleration

  3. Solve transport equation assuming:(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:

  4. Solution using separation of variables is: 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

  5. Alternatively, 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 with4p2Ek - energy density form Diffusive energy flux through [p1,p2]

  6. Assume turbulent diffusion dominates- 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.

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