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Incoherent Thoughts: Stochastic Acceleration

This work examines stochastic acceleration as a method to efficiently accelerate particles while managing power requirements. It discusses the critical balance between maintaining a narrow frequency range for efficiency and distributing power over a broader range to reduce heat, leading to high-entropy processes. The effectiveness of different traps, such as Fermi, dipole, and quadrupole, is analyzed in terms of their longevity and energy retention in the acceleration process. The research emphasizes the necessity of optimizing trap designs to harness high-energy particles effectively in near-Earth space.

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Incoherent Thoughts: Stochastic Acceleration

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  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>

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