Collapsing Traps

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Revision as of 18:48, 18 January 2009

Introduction

Particle acceleration is one of the more perplexing issues as we try to understand how solar flares work. The particles (electrons at 10s of keV, and ions at MeV energies) contain a large fraction of the total flare energy. Thus one cannot expect to find a self-consistent fluid ([MHD]) model. Nevertheless virtually all of the theoretical work on large-scale aspects of solar flares is presently within the MHD framework. In the topic described here there are features both of large-scale MHD concepts and also particle acceleration, so these ideas are somehow very attractive!

The coronal magnetic field can undergo large-scale restructurings during a flare or CME. If this restructuring happens [adiabatically], i.e. on scales large compared with the [Larmor motion] of the particles in question, they can gain or lose energy. A "collapsing trap" is exactly the sort of geometry expected from large-scale magnetic reconnection, and so this concept provides a basic mechanism for particle acceleration in a flare or CME. The sketches in Figure 1 show how this might work. There is a lot more detail than needed in the sketches; basically on the left one sees a reconnected magnetic field line "dipolarizing" rapidly, and on the left slowly. This process is the basic element of the standard reconnection models of solar flares, as explained copiously elsewhere among the Nuggets (for example, [here].

A collapsing magnetic trap following large-scale coronal reconnection. The longer arrow shows the field deforming, so rapidly as to induce a fast-mode shock wave ("SW").

Betatron vs First-order Fermi Acceleration

A collapsing trap actually may accelerate particles in two distinct ways: ["betatron"] and first-order [Fermi acceleration]. These result respectively from diminishing diameter of the collapsing flux tube, and from its decreasing length. The latter is easier to understand - as the trap shortens, the two reflective mirrors apparently approach one another. The motion of the mirror means that the reflected particle gains energy. To understand the betatron process one has to follow the basic physics of adiabatic particle motion; essentially the particle energy must increase as the magnitude of B increases during the collapse.

Simplification of the collapsing trap to show the two processes at work. Contraction of the trap in length causes Fermi acceleration, and contraction perpendicular to B causes betatron acceleration.

This rough description omits a great deal of complexity. Even though the basic physics is straightforward, and has been known for many decades, the application to an astrophysical situation requires that we know what particles are there, how the flows in the plasma proceed, and other somewhat intangible details involving wave-particle interactions. To assess these complicated issues in a satisfactory manner really requires model-building, using realistic parameters taken from the observations as a guide.

Some Data

Conclusion