COSMIC RA ACCELERATION and TRANSPORT LECTURE I宇宙射线的加速和运输的演讲我.pptVIP

DIFFUSION COEFFICIENT THE RANDOM CHANGE OF THE PITCH ANGLE IS DESCRIBED BY A DIFFUSION COEFFICIENT FRACTIONAL POWER (δB/B0)2 =G(kres) THE DEFLECTION ANGLE CHANGES BY ORDER UNITY IN A TIME: PATHLENGTH FOR DIFFUSION ~ vτ SPATIAL DIFFUSION COEFF. PARTICLE SCATTERING EACH TIME THAT A RESONANCE OCCURS THE PARTICLE CHANGES PITCH ANGLE BY Δθ~δB/B WITH A RANDOM SIGN THE RESONANCE OCCURS ONLY FOR RIGHT HAND POLARIZED WAVES IF THE PARTICLES MOVES TO THE RIGHT (AND VICEVERSA) THE RESONANCE CONDITION TELLS US THAT 1) IF k1/rL PARTICLES SURF ADIABATICALLY AND 2) IF k1/rL PARTICLES HARDLY FEEL THE WAVES The Diffusion Equation In its simplest version, the diffusion of CR from a source can be described through an equation similar to that of Heat transfer The Green function of this partial differential equation is simple to calculate if D(E,r)=D(E): H 2h Rd disc Halo Particle escape In general: Rd H h ASSUMPTIONS: Instantaneous injection of particles in a point in the disc Infinitely thin disc, h ? 0 and infinitely extended disc, Rd?∞ 3. Free escape of the particles from above and below the halo In order to fulfill this boundary condition the correct Green function is Contribution of many sources Integral in tau is analytical In the limit H/Rd1 Diffusion time You can compare this result with the less fundamental leaky box model The Diffusion Model is not fully equivalent to the Leaky Box Model Diffusion Leaky Box CR primary CR electrons (with dominant Losses) Similar situation for nuclei when spallation dominates The Supernova remnant paradigm in numbers Let us assume that the rate of SN in the Galaxy is R and each produces a power law spectrum of protons N(E)=K (E/E0)-g and we take E0~m~1 GeV and energies are taken to be normalized to E0. The observed spectrum of protons at Earth is and taking D(E)~(r/3GV)d where r is the rigidity: and comparing with the observed spectrum Order 1051 erg Relatively large efficiencies require