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Acceleration at Shocks Without Particle Scattering J. R. Jokipii and Joe Giacalone University of Arizona Shimada et al, 1999 • Observations of shockaccelerated electrons Mewaldt et al, 2005 Shock Acceleration of Electrons • In principle, there is no difference between electrons and ions in the basic picture of diffusive shock acceleration – What scatters the electrons? – We need a low-energy electron accelerator • Importance of large-scale fluctuations – Electrons move rapidly (nearly) along magnetic lines of force that can intersect the shock in multiple locations What is the Electron Accelerator? Surprisingly few mechanisms have been proposed: 1. Somehow, the relevant fluctuations are produced. 2. Stochastic acceleration (or injection). Acceleration by a Meandering Magnetic Field Line • Large-scale field line meandering leads to multiple connections at the shock (compression) – Electrons are fast enough to cross the shock several times by following along these meandering fields • This process will be most effective at a perpendicular shock. The Process of Adiabatic Acceleration • A particle moving nearly along the local magnetic field, with a pitch angle close to 0 degrees, conserving its first adiabatic invariant, will closely follow a magnetic field line. • As the x-component of the particle velocity changes, its energy increases or decreases in the observer's frame because of the motion of the magnetic field line with the local flow speed. Sample Electron Trajectory • This electron gains energy as it crosses and recrosses the shock – Similar to 1st-orderFermi acceleration, but does not involve resonant scattering • The particles move only along the local magnetic field, so we expect that the rate of energy change will go to zero as the field line meandering goes to zero and the particles can only move normal to the flow direction. • For finite field meandering, the acceleration rate should be • Where α = <(δBx/B)2>. Note that for an isotropic distribution of field-line directions, <(δBx/B)2>=1/3, and we recover the normal rate (Parker, 1965). • By analogy with the Parker transport equation, we can write for the distribution function of particles f(x,z,p,t). • Applying this to particles injected at some low momentum at a narrow compression yields a time-asymptotic spectrum of accelerated particles similar to that found in standard diffusive shock acceleration: • where the power law index becomes • where rsh is the shock ratio U1/U2 and 1 and 2 are the values evaluated upstream and downstream of the compression, respectively. Test-Particle Numerical Simulations • We follow the trajectories of an ensemble of electrons • The upstream random magnetic field is obtained by a discrete sum of individual waves • Satisfies Maxwell’s equations • The amplitudes A(kn) are determined from a power spectrum Computed Spectrum Shock-accelerated electrons: downstream distribution function • The simulated distribution of accelerated electrons is steeper than the prediction (diffusive shock acceleration) at low energies, but approaches it asymptotically at high energies Including shock microstructure • Generally, this mechanism will work at any compression. A shock-like discontinuity is not required • Including the microstructure is difficult because in addition to the cross-shock electric field, we must also include the rotation of the magnetic field out of the plane of coplanarity – This would vary along the shock since it depends on the local shock normal angle (as known from past studies) Results using ad-hoc scattering in the shock transition region • Fully kinetic particle simulations reveal that electrons can be efficiently accelerated/scattered by electromagnetic fluctuations inside the shock layer • This is modeled using ad-hoc scattering when the electron exists within the shock layer • The scattering time is taken to be 100 electron gyroperiods (independent of energy). Conclusions 1. New simulations and theory show that electrons can be efficiently accelerated by shocks They move along meandering magnetic field lines and interact with the shock (or compression) several times. They gain energy, even though resonant scattering is not required. 2. This process is most effective at nearlyperpendicular shocks. Diffusive shock acceleration has proved to be a very robust and attractive mechanism for ion acceleration. Acceleration and Transport of Energetic Particles at CIRs Joe Giacalone,University of Arizona (W ith thanks to Randy Jokipii and Jozsef K ota) 1. 2. Shocks are ubiquitous in space The spectrum is narrowly constrained and is what is needed SHINE 2006 Zermatt Resort, Utah