Conference Summary: Three-Dimensional Explosions

1.2 Dynamo Theory and Saturation Fields There has been a major breakthrough in the conceptual understanding of astrophysical dynamos in the last few years. In traditional mean field dynamo theory, the turbulent velocity field that drives the “alpha” portion of the α−Ω dynamo was specified and held fixed. A weakness of the original theory was that the turbulent velocity field cannot be constant. The buildup of small scale magnetic field tends to inhibit turbulence, cutting off the dynamo process for both small and large scale fields. Since the small scale field tended to grow faster than the large scale field, it appeared that the growth of the large scale field would be suppressed (Kulsrud & Anderson 1992; Gruzinov & Diamond 1994). In these theories, the magnetic field energy cascades to smaller length scales where it is ultimately dissipated at the resistive scale. Large scale fields tend to build up slowly, if at all. The solution to this problem has been the recognition (Blackman & Field 2000; Vishniac & Cho 2001; Field & Blackman 2002; Blackman & Brandenburg, 2002; Blackman & Field 2002; Kleeorin et al. 2002) that the magnetic helicity, H = A·B is conserved in ideal MHD and that this conservation had not been treated explicitly in mean field dynamo theory. Incorporation of this principle leads to an “inverse cascade” of helical field energy to large scales that is simultaneous with the cascade of helical field energy from the driving scale to the dissipation scale. Basically, the large scale helical field and inverse cascade must exist with opposite magnetic helicity to that of the field cascading to small scale. The result (Blackman & Brandenburg 2002) is the rapid growth of large scale field in a kinematic phase (prior to significant back-reaction) to a strength where the field on both large and small scales is nearly