Incoherent Thoughts: Stochastic Acceleration

1. Incoherent Thoughts: Stochastic Acceleration Robert Sheldon June 27, 2005 National Space Science & Technology Center

2. Sychrocyclotrons • Resonant acceleration is like particle accelerators: to keep up the efficiency, the frequency must be adjusted for the accelerating particle. • But, to keep the power requirements down, the power must be strongly peaked around a narrow range of frequencies. • These two competing processes then require a very unusual arrangement of particles + waves: = low entropy. • Low entropy  improbable

3. Stochastic Acceleration • The other way to accelerate is high entropy:  heat • No specific frequency range, power distributed over many frequencies. • Therefore low power, and slow acceleration • Multisteps needed to get to high energy • Long time, so we need a trap. • High entropy  high probability

4. Dipole vs Quadrupole Trap • The nature of the trap determines the effectiveness of the stochastic acceleration. • Fermi-acceleration has a limited lifetime trap, therefore Emax is time-limited • Diffusion in dipole trap puts the highest-E at the atmosphere, so highest energies are precipitated and lost. • Quadrupole trap lasts a long time, and highest energies escape. A good place for stochastic diffusion. (Lots of good properties!)

5. Conclusions • Unless observations dictate otherwise, it is most probable to have high-entropy processes. • But high-entropy processes are inefficient, so the trap becomes most important. • Three (4?) traps have been found in near-Earth space: Fermi-trap, Dipole, and Quadrupole (Current Sheet?)

6. Incoherent Thoughts: Spatial Diffusion Coeeficients Rob Sheldon NSSTC

7. Transport • Quasi-Linear Diffusion is a resonant transport. • If first two invariants are good, then we can write a total energy hamiltonian: H = KE + PE = u Bm + q E Then particle trajectories mapped to the equatorial plane follow iso-energy contours where dH = 0. • So diffusion of this iso-energy contour, is spatial transport. This is really just the “radial” diffusion coefficient, but iso-contours may not be circular.

8. Calculation of this “radial” transport coefficient • Since dH/dt = 0, then <H> = 0 • Transport then, is <H2> <> 0 • So writing the full H = uB + qE we have: <H2> = <u d2B/dt2 + q d2E/dt2 + 2 uq dBdE/dt2> • So, stochastic power, without any particular resonance at the drift period (but of course, it contributes to the averaging integral more) • Note: the q/u ratio determines the effectiveness of <B2> versus <E2>. Hi u  Rad belt <B>, Lo uplasma <E>