The matter of problem

Giacalone and Jokipii (2005) discuss new results in the physics of charged-particle acceleration by shock waves propagating at an arbitrary angle to the magnetic field. For the usually discussed case of a parallel shock acceleration by a supernova blast wave up to the knee in the CR spectrum requires very special assumptions such as a strong increase in the magnetic field, perhaps due to excitation from the streaming CR. They show that no such special circumstances are required when one considers acceleration at nearly perpendicular shocks. The matter of problem is that the diffusive acceleration of charged particles at collisionless shocks, at which particles are accelerated by the converging flows and plasma compressions, naturally explains the observed universal power law of CR

up to the knee in the spectrum at about 1015 eV (see, e.g., the reviews by Drury, 1983; Blandford and Eichler, 1987; Jones and Ellison, 1991). The acute angle between the shock-normal direction and the incident magnetic fields, 0Bn , plays an important role in determining the resulting accelerated-particle spectrum. It was shown by Jokipii (1982, 1987) that the acceleration rate depends strongly on 0Bn and is the highest when the shock is perpendicular (0gn = 90°). Thus, given a particular time interval over which to accelerate particles, those with highest energy will originate from the perpendicular shock. An important issue in diffusive shock acceleration at nearly perpendicular shocks has been the well-known injection threshold problem. The problem arises because, until recently, it was assumed that particles move essentially along the lines of force which are convecting through the shock. Therefore, it was thought that there was no means by which low-energy particles could encounter the shock several times, which is required for efficient particle acceleration. Giacalone and Jokipii (2005) show that there is actually no such injection problem and, in fact, the injection does not depend strongly on the shock-normal angle. This can be understood in terms of the increased cross-field transport arising from so-called field-line random walk due to the large-scale (order of a parsec) turbulent interstellar magnetic field.

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