Magnetic Helicity Associated with the Proton Temperature Anisotropy Instabilities in the Presence of an Imbalanced Solar Wind Turbulence

Some of the most common processes in the solar wind, such as turbulence and wave generation by instabilities, are associated with spectral magnetic helicity. Therefore, the helicity is a convenient tool to investigate these processes. We use three-dimensional nonlinear kinetic simulations with particle ions and fluid electrons to analyze the magnetic helicity produced by proton temperature anisotropy instabilities coexisting with an ambient turbulence. The symmetry of the unstable system is violated by alpha-particle streaming with respect to protons along the mean magnetic field. At the same time, the turbulent fluctuations are also imbalanced by a nonzero cross-helicity. We show that in the nonlinear phase of the instability the resulting helicity structure is different from the prediction of the linear theory. In particular, it contains sign reversals and multiple domains of nonzero helicity. The turbulence generates its own magnetic helicity signature, which extends over a wide range of angles around the direction perpendicular to the mean magnetic field, and can have a sign the same as or opposite to that of the instability. These findings are consistent with the observed helicity spectra in the solar wind.