Even in the relatively well-studied case of ion scale turbulence, the role of electromagnetic perturbations remains unclear, particularly at beta greater than approximately 0.25. Gyrokinetic and multifluid turbulence simulations have shown that electromagnetic effects can dramatically influence the turbulence by altering the dynamics of zonal flows and primary/secondary instabilities, as well as by introducing small scale magnetic reconnection. Little is known, however, about the nature of reconnection in a turbulent plasma, or about the nature of transport in a plasma with significant magnetic and electrostatic perturbations. We can say little more than there is a critical role played by the dispersive kinetic Alfvén waves in reconnection and in gradient-driven electromagnetic turbulence.

With the focus and critical mass effort provided by the CMPD, it is expected that a clear theoretical picture of nonlinear kinetic Alfvén wave dynamics will emerge, with strong experimental support in the low beta regime accessible at the LAPD facility. Because it is of obvious interest to understand such phenomena at higher values of beta, CMPD also supports scientists working at DIII-D and NSTX to diagnose nonlinear kinetic Alfvén wave dynamics at values of beta approaching unity. In many ways, beta ~ 1 is most interesting, because sound waves and Alfvén waves interact strongly, producing significant wave damping and new instabilities. Of course, beta ~ 1 is also interesting because many plasmas found in nature lie in this range.

The nonlinear physics of shear Alfvén waves has direct relevance to magnetic turbulence in both astrophysical and fusion plasmas. Of particular interest is the turbulent cascade of Alfvén waves. This is truly a multiscale problem, considering the nonlinear transfer of energy from a large scale wave (the ``stirring'' scale) down to much smaller scales where dissipation becomes important. Alfvén wave cascades are believed to occur in many astrophysical situations, including the solar wind, the interstellar medium, and some accretion disks. In subluminous accretion disks, the observed radiation is inconsistent with a classical accretion process: angular momentum transport through classical collisions, resulting in energy transfer to the electrons which then efficiently radiate this energy away. Instead, anomalous angular momentum transport must be provided by an instability such as the magnetorotational instability (MRI). The MRI then acts as the large-scale stirring wave for an Alfvén wave cascade, sending energy many orders of magnitude in wavenumber space toward a dissipation scale. In high-beta accretion disks, this shear-Alfvén cascade first damps on the ions once it reaches the ion gyroradius scale, preferentially heating the ions, which are poor radiators. A portion of the cascade energy may continue on towards electron dissipation scales in the form of a kinetic Alfvén wave cascade (aka the "whistler" cascade). A cartoon depicting this cascade process is shown above.

In tokamaks, the large scale wave could be an MHD instability (e.g., tearing mode or fast-particle driven Alfvén eigenmode) and a nonlinear cascade driven by this instability could affect saturation of the instability and result in plasma heating as the cascade reaches dissipation scales. In addition, in high-beta plasmas drift wave turbulence is electromagnetic in nature through coupling to Alfvén waves. Hence studying the nonlinear physics of Alfvén waves will aid our understanding of electromagnetic drift wave turbulence -- understanding which is critical in order to succesfully predict turbulent transport in high-beta fusion reactors.